{"id":50367,"date":"2025-07-30T23:12:39","date_gmt":"2025-07-30T15:12:39","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/50367.html"},"modified":"2025-07-30T23:12:39","modified_gmt":"2025-07-30T15:12:39","slug":"02-%e5%9f%ba%e4%ba%8esklearn%e7%9a%84%e6%9c%ba%e6%a2%b0%e5%ad%a6%e4%b9%a0-%e7%89%b9%e5%be%81%e9%99%8d%e7%bb%b4%ef%bc%88%e7%89%b9%e5%be%81%e9%80%89%e6%8b%a9%e3%80%81pca%ef%bc%89%e3%80%81knn%e7%ae%97","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/50367.html","title":{"rendered":"02 \u57fa\u4e8esklearn\u7684\u673a\u68b0\u5b66\u4e60-\u7279\u5f81\u964d\u7ef4\uff08\u7279\u5f81\u9009\u62e9\u3001PCA\uff09\u3001KNN\u7b97\u6cd5\u3001\u6a21\u578b\u9009\u62e9\u4e0e\u8c03\u4f18\uff08\u4ea4\u53c9\u9a8c\u8bc1\u3001\u6734\u7d20\u8d1d\u53f6\u65af\u7b97\u6cd5\u3001\u62c9\u666e\u62c9\u65af\u5e73\u6ed1\uff09"},"content":{"rendered":"<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u7279\u5f81\u964d\u7ef4<\/li>\n<li>\n<ul>\n<li>\n<ul>\n<li>1 \u7279\u5f81\u9009\u62e9<\/li>\n<li>\n<ul>\n<li>\u4f4e\u65b9\u5dee\u8fc7\u6ee4\u7279\u5f81\u9009\u62e9<\/li>\n<li>\u57fa\u4e8e\u76f8\u5173\u7cfb\u6570\u7684\u7279\u5f81\u9009\u62e9<\/li>\n<\/ul>\n<\/li>\n<li>2 \u4e3b\u6210\u5206\u5206\u6790(PCA)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>KNN\u7b97\u6cd5<\/li>\n<li>\n<ul>\n<li>\u8ddd\u79bb<\/li>\n<li>\n<ul>\n<li>1. \u6b27\u6c0f\u8ddd\u79bb&#xff08;Euclidean Distance&#xff09;<\/li>\n<li>2. \u66fc\u54c8\u987f\u8ddd\u79bb&#xff08;Manhattan Distance&#xff09;<\/li>\n<li>3. \u5207\u6bd4\u96ea\u592b\u8ddd\u79bb&#xff08;Chebyshev Distance&#xff09;<\/li>\n<li>4. \u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb&#xff08;Minkowski Distance&#xff09;<\/li>\n<li>5. \u4f59\u5f26\u76f8\u4f3c\u5ea6&#xff08;Cosine Similarity&#xff09;<\/li>\n<li>6. \u6770\u5361\u5fb7\u76f8\u4f3c\u5ea6&#xff08;Jaccard Similarity&#xff09;<\/li>\n<li>7. \u9a6c\u6c0f\u8ddd\u79bb&#xff08;Mahalanobis Distance&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>KNN\u7b97\u6cd5<\/li>\n<li>\u6a21\u578b\u4fdd\u5b58\u4e0e\u52a0\u8f7d<\/li>\n<\/ul>\n<\/li>\n<li>\u6a21\u578b\u9009\u62e9\u4e0e\u8c03\u4f18<\/li>\n<li>\n<ul>\n<li>\u4ea4\u53c9\u9a8c\u8bc1<\/li>\n<li>\n<ul>\n<li>1 \u4fdd\u7559\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Train-Test Split&#xff09;<\/li>\n<li>2 K-\u6298\u4ea4\u53c9\u9a8c\u8bc1(K-fold)<\/li>\n<li>3 \u5206\u5c42K-\u6298\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Stratified k-fold&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>\u8d85\u53c2\u6570\u641c\u7d22 GridSearchCV<\/li>\n<\/ul>\n<\/li>\n<li>\u6734\u7d20\u8d1d\u53f6\u65af\u7b97\u6cd5<\/li>\n<li>\n<ul>\n<li>1.\u6761\u4ef6\u6982\u7387<\/li>\n<li>2. \u5168\u6982\u7387\u516c\u5f0f<\/li>\n<li>3. \u8d1d\u53f6\u65af\u5b9a\u7406<\/li>\n<li>4 \u6734\u7d20\u8d1d\u53f6\u65af\u63a8\u65ad<\/li>\n<li>5. \u62c9\u666e\u62c9\u65af\u5e73\u6ed1<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>\u7279\u5f81\u964d\u7ef4<\/h2>\n<p>\u7279\u5f81\u964d\u7ef4\u662f\u6307\u901a\u8fc7\u51cf\u5c11\u6570\u636e\u96c6\u7684\u7279\u5f81\u6570\u91cf\u540c\u65f6\u4fdd\u7559\u5173\u952e\u4fe1\u606f\u7684\u8fc7\u7a0b\u3002\u9ad8\u7ef4\u6570\u636e&#xff08;\u7279\u5f81\u8fc7\u591a&#xff09;\u4f1a\u5bfc\u81f4\u8ba1\u7b97\u590d\u6742\u5ea6\u589e\u52a0\u3001\u8fc7\u62df\u5408\u98ce\u9669\u63d0\u9ad8&#xff0c;\u4ee5\u53ca\u6240\u8c13\u7684 \u201c\u7ef4\u5ea6\u707e\u96be\u201d\u3002\u964d\u7ef4\u53ef\u4ee5\u51cf\u5c11\u6570\u636e\u96c6\u7ef4\u5ea6&#xff0c;\u540c\u65f6\u5c3d\u53ef\u80fd\u4fdd\u7559\u6570\u636e\u7684\u91cd\u8981\u6027\u3002<\/p>\n<p>\u964d\u7ef4\u53ef\u4ee5&#xff1a;<\/p>\n<li>\u51cf\u5c11\u8ba1\u7b97\u5f00\u9500<\/li>\n<li>\u964d\u4f4e\u8fc7\u62df\u5408\u98ce\u9669<\/li>\n<li>\u53ef\u89c6\u5316\u6570\u636e&#xff08;\u964d\u5230 2D \u6216 3D&#xff09;<\/li>\n<li>\u53bb\u9664\u566a\u58f0\u548c\u5197\u4f59\u4fe1\u606f<\/li>\n<p>\u7279\u5f81\u964d\u7ef4\u6280\u672f\u4e3b\u8981\u5206\u4e3a\u4e24\u7c7b&#xff1a;\u7279\u5f81\u9009\u62e9\u548c\u7279\u5f81\u63d0\u53d6\u3002<\/p>\n<h4>1 \u7279\u5f81\u9009\u62e9<\/h4>\n<p>\u7279\u5f81\u9009\u62e9\u662f\u6307\u76f4\u63a5\u4ece\u539f\u59cb\u7279\u5f81\u4e2d\u9009\u62e9\u6709\u7528\u7684\u7279\u5f81&#xff0c;\u800c\u4e0d\u8be5\u7279\u5f81\u672c\u8eab<\/p>\n<h5>\u4f4e\u65b9\u5dee\u8fc7\u6ee4\u7279\u5f81\u9009\u62e9<\/h5>\n<p>\u5982\u679c\u4e00\u4e2a\u7279\u5f81\u7684\u65b9\u5dee\u5f88\u5c0f&#xff0c;\u8bf4\u660e\u8be5\u7279\u5f81\u7684\u53d6\u503c\u51e0\u4e4e\u6ca1\u6709\u53d8\u5316&#xff0c;\u63d0\u4f9b\u7684\u4fe1\u606f\u91cf\u6709\u9650&#xff0c;\u53ef\u80fd\u5bf9\u6a21\u578b\u8d21\u732e\u4e0d\u5927&#xff0c;\u53ef\u8003\u8651\u5220\u9664\u3002<\/p>\n<p>\u65b9\u5dee\u8ba1\u7b97\u516c\u5f0f\u4e3a <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         Var<\/p>\n<p>         (<\/p>\n<p>         X<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          1<\/p>\n<p>          n<\/p>\n<p>          \u2211<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          n<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          i<\/p>\n<p>         \u2212<\/p>\n<p>          x<\/p>\n<p>          \u02c9<\/p>\n<p>          )<\/p>\n<p>          2<\/p>\n<p>         \\\\text{Var}(X) &#061; \\\\frac{1}{n} \\\\sum_{i&#061;1}^{n} (x_i &#8211; \\\\bar{x})^2 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">Var<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.9291em;vertical-align: -1.2777em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5982\u679c\u4e00\u4e2a\u7279\u5f81\u7684\u65b9\u5dee\u5f88\u5c0f&#xff0c;\u8bf4\u660e\u8fd9\u4e2a\u7279\u5f81\u7684\u503c\u5728\u6837\u672c\u4e2d\u51e0\u4e4e\u76f8\u540c\u6216\u8005\u53d8\u5316\u4e0d\u5927&#xff0c;\u5305\u542b\u7684\u4fe1\u606f\u5f88\u5c11&#xff0c;\u90a3\u8fd9\u4e2a\u7279\u5f81\u5c31\u53ef\u4ee5\u53bb\u9664<\/p>\n<p>sklearn.feature_selection.VarianceThreshold(threshold&#061;2.0)<\/p>\n<ul>\n<li>\u8bbe\u5b9a\u9608\u503cthreshold&#xff1a;\u4efb\u4f55\u4f4e\u4e8e\u9608\u503c\u7684\u7279\u5f81\u90fd\u5c06\u88ab\u89c6\u4e3a\u4f4e\u65b9\u5dee\u7279\u5f81<\/li>\n<li>\u8fc7\u6ee4&#xff1a;\u79fb\u9664\u6240\u6709\u4f4e\u65b9\u5dee\u7279\u5f81<\/li>\n<\/ul>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>feature_selection <span class=\"token keyword\">import<\/span> VarianceThreshold<br \/>\ndata <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><br \/>\n<span class=\"token comment\"># \u521b\u5efa\u65b9\u5dee\u9608\u503c\u9009\u62e9\u5668<\/span><br \/>\ntransfer <span class=\"token operator\">&#061;<\/span> VarianceThreshold<span class=\"token punctuation\">(<\/span>threshold<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\ndata <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><\/p>\n<p>[[0]<br \/>\n [4]<br \/>\n [1]]<\/p>\n<p>\u3010\u5904\u7406\u9e22\u5c3e\u82b1\u6570\u636e\u96c6\u3011<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>feature_selection <span class=\"token keyword\">import<\/span> VarianceThreshold<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<\/p>\n<p>x<span class=\"token punctuation\">,<\/span>y <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx_train<span class=\"token punctuation\">,<\/span>x_test<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">,<\/span>test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u521b\u5efa\u8f6c\u6362\u5668<\/span><br \/>\ntransfer <span class=\"token operator\">&#061;<\/span> VarianceThreshold<span class=\"token punctuation\">(<\/span>threshold<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.8<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx_train <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">)<\/span><br \/>\nx_test <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">)<\/span><\/p>\n<p>[[1.6]<br \/>\n [1.5]<br \/>\n [4. ]<br \/>\n [4.4]<br \/>\n &#8230;<br \/>\n [4.5]<br \/>\n [5.9]<br \/>\n [6. ]<br \/>\n [1.9]<br \/>\n [5.6]<br \/>\n [6.7]]<\/p>\n<h5>\u57fa\u4e8e\u76f8\u5173\u7cfb\u6570\u7684\u7279\u5f81\u9009\u62e9<\/h5>\n<p>\u76f8\u5173\u6027&#xff1a;\u6307\u4e24\u4e2a\u6216\u591a\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u7684\u5173\u8054\u5173\u7cfb\u2014\u2014 \u5f53\u4e00\u4e2a\u53d8\u91cf\u7684\u53d6\u503c\u53d1\u751f\u53d8\u5316\u65f6&#xff0c;\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u53d6\u503c\u4e5f\u503e\u5411\u4e8e\u4ee5\u67d0\u79cd\u89c4\u5f8b\u53d8\u5316\u3002\u3002\u8fd9\u79cd\u53d8\u5316\u4e0d\u4e00\u5b9a\u662f\u76f4\u63a5\u5f15\u8d77\u7684&#xff0c;\u53ef\u4ee5\u95f4\u63a5\u6216\u8005\u5076\u7136\u3002<\/p>\n<ul>\n<li>\u76f8\u5173\u6027\u4e0d\u610f\u5473\u7740\u56e0\u679c\u5173\u7cfb&#xff08;\u201c\u76f8\u5173\u975e\u56e0\u679c\u201d&#xff09;&#xff1a;\u4f8b\u5982 \u201c\u51b0\u6dc7\u6dcb\u9500\u91cf\u201d \u548c \u201c\u6eba\u6c34\u4e8b\u6545\u201d \u6b63\u76f8\u5173&#xff0c;\u4f46\u5e76\u975e\u56e0\u679c&#xff0c;\u800c\u662f\u5171\u540c\u53d7 \u201c\u6c14\u6e29\u201d \u5f71\u54cd\u3002<\/li>\n<li>\u76f8\u5173\u6027\u6709\u65b9\u5411\u548c\u5f3a\u5ea6&#xff1a;\n<ul>\n<li>\u65b9\u5411&#xff1a;\u6b63\u76f8\u5173&#xff08;\u4e00\u4e2a\u53d8\u91cf\u589e\u5927&#xff0c;\u53e6\u4e00\u4e2a\u4e5f\u589e\u5927&#xff0c;\u5982 \u201c\u8eab\u9ad8\u201d \u4e0e \u201c\u4f53\u91cd\u201d&#xff09;\u3001\u8d1f\u76f8\u5173&#xff08;\u4e00\u4e2a\u53d8\u91cf\u589e\u5927&#xff0c;\u53e6\u4e00\u4e2a\u51cf\u5c0f&#xff0c;\u5982 \u201c\u5546\u54c1\u4ef7\u683c\u201d \u4e0e \u201c\u9500\u91cf\u201d&#xff09;\u3002<\/li>\n<li>\u5f3a\u5ea6&#xff1a;\u4ece \u201c\u5f31\u76f8\u5173\u201d \u5230 \u201c\u5f3a\u76f8\u5173\u201d&#xff08;\u53ef\u7528\u6570\u503c\u91cf\u5316&#xff0c;\u5982\u76f8\u5173\u7cfb\u6570&#xff09;\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570&#xff08;Pearson Correlation Coefficient&#xff09;<\/p>\n<p>\u8861\u91cf\u7ebf\u6027\u76f8\u5173\u6027\u7684\u6307\u6807&#xff0c;\u53d6\u503c\u8303\u56f4\u4e3a[-1, 1]<\/p>\n<ul>\n<li>\u03c1 &#061; 1&#xff1a;\u5b8c\u5168\u6b63\u7ebf\u6027\u76f8\u5173&#xff1b;<\/li>\n<li>\u03c1 &#061; -1&#xff1a;\u5b8c\u5168\u8d1f\u7ebf\u6027\u76f8\u5173&#xff1b;<\/li>\n<li>\u03c1 &#061; 0&#xff1a;\u65e0\u7ebf\u6027\u76f8\u5173&#xff08;\u4f46\u53ef\u80fd\u5b58\u5728\u975e\u7ebf\u6027\u76f8\u5173&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u4e24\u7ec4\u6570\u636e &#x1d44b;&#061;{&#x1d465;1,&#x1d465;2,\u2026,&#x1d465;&#x1d45b;} \u548c &#x1d44c;&#061;{&#x1d466;1,&#x1d466;2,\u2026,&#x1d466;&#x1d45b;}&#xff0c;\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u53ef\u4ee5\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u03c1<\/p>\n<p>        &#061;<\/p>\n<p>          Cos<\/p>\n<p>          \u2061<\/p>\n<p>          (<\/p>\n<p>          x<\/p>\n<p>          ,<\/p>\n<p>          y<\/p>\n<p>          )<\/p>\n<p>            D<\/p>\n<p>            x<\/p>\n<p>          \u22c5<\/p>\n<p>            D<\/p>\n<p>            y<\/p>\n<p>        &#061;<\/p>\n<p>          E<\/p>\n<p>          [<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           \u2212<\/p>\n<p>          E<\/p>\n<p>          x<\/p>\n<p>          )<\/p>\n<p>          (<\/p>\n<p>          y<\/p>\n<p>          \u2212<\/p>\n<p>          E<\/p>\n<p>          y<\/p>\n<p>          )<\/p>\n<p>          ]<\/p>\n<p>            D<\/p>\n<p>            x<\/p>\n<p>          \u22c5<\/p>\n<p>            D<\/p>\n<p>            y<\/p>\n<p>        &#061;<\/p>\n<p>           \u2211<\/p>\n<p>            i<\/p>\n<p>            &#061;<\/p>\n<p>            1<\/p>\n<p>           n<\/p>\n<p>          (<\/p>\n<p>          x<\/p>\n<p>          \u2212<\/p>\n<p>           x<\/p>\n<p>           ~<\/p>\n<p>          )<\/p>\n<p>          (<\/p>\n<p>          y<\/p>\n<p>          \u2212<\/p>\n<p>           y<\/p>\n<p>           \u02c9<\/p>\n<p>          )<\/p>\n<p>          \/<\/p>\n<p>          (<\/p>\n<p>          n<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>          )<\/p>\n<p>             \u2211<\/p>\n<p>              i<\/p>\n<p>              &#061;<\/p>\n<p>              1<\/p>\n<p>             n<\/p>\n<p>            (<\/p>\n<p>            x<\/p>\n<p>            \u2212<\/p>\n<p>             x<\/p>\n<p>             \u02c9<\/p>\n<p>             )<\/p>\n<p>             2<\/p>\n<p>            \/<\/p>\n<p>            (<\/p>\n<p>            n<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>            )<\/p>\n<p>          \u22c5<\/p>\n<p>             \u2211<\/p>\n<p>              i<\/p>\n<p>              &#061;<\/p>\n<p>              1<\/p>\n<p>             n<\/p>\n<p>            (<\/p>\n<p>            y<\/p>\n<p>            \u2212<\/p>\n<p>             y<\/p>\n<p>             \u02c9<\/p>\n<p>             )<\/p>\n<p>             2<\/p>\n<p>            \/<\/p>\n<p>            (<\/p>\n<p>            n<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>            )<\/p>\n<p>       \\\\rho&#061;\\\\frac{\\\\operatorname{Cos}(x, y)}{\\\\sqrt{D x} \\\\cdot \\\\sqrt{D y}}&#061;\\\\frac{E[(x_-E x)(y-E y)]}{\\\\sqrt{D x} \\\\cdot \\\\sqrt{D y}}&#061;\\\\frac{\\\\sum_{i&#061;1}^{n}(x-\\\\tilde{x})(y-\\\\bar{y}) \/(n-1)}{\\\\sqrt{\\\\sum_{i&#061;1}^{n}(x-\\\\bar{x})^{2} \/(n-1)} \\\\cdot \\\\sqrt{\\\\sum_{i&#061;1}^{n}(y-\\\\bar{y})^{2} \/(n-1)}}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.6161em;vertical-align: -0.6061em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.5374em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9323em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8923em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1077em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8351em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">Dy<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7951em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2049em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mord mathrm mtight\">Cos<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6061em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.6161em;vertical-align: -0.6061em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.5374em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9323em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8923em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1077em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8351em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">Dy<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7951em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2049em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen mtight\">[(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2737em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mbin mtight\">\u2212<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2025em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose mtight\">)]<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6061em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.8896em;vertical-align: -0.8296em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.06em\"><span class=\"\" style=\"top: -2.4892em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0012em\"><span class=\"svg-align\" style=\"top: -3.4286em\"><span class=\"pstrut\" style=\"height: 3.4286em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 1.19em\"><span class=\"mop mtight\"><span class=\"mop op-symbol small-op mtight\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7047em\"><span class=\"\" style=\"top: -2.1786em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8971em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3214em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord mtight\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7463em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\/<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9732em\"><span class=\"pstrut\" style=\"height: 3.4286em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.5429em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4554em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0012em\"><span class=\"svg-align\" style=\"top: -3.4286em\"><span class=\"pstrut\" style=\"height: 3.4286em\"><\/span><span class=\"mord mtight\" style=\"padding-left: 1.19em\"><span class=\"mop mtight\"><span class=\"mop op-symbol small-op mtight\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7047em\"><span class=\"\" style=\"top: -2.1786em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8971em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3214em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord mtight\">\u02c9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7463em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\/<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9732em\"><span class=\"pstrut\" style=\"height: 3.4286em\"><\/span><span class=\"hide-tail mtight\" style=\"min-width: 0.853em;height: 1.5429em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4554em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.535em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mop op-symbol small-op mtight\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7385em\"><span class=\"\" style=\"top: -2.1786em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.931em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3214em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord mtight\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord mtight\">\u02c9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mtight\">\/<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8296em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>|\u03c1|&lt;0.4\u4e3a\u4f4e\u5ea6\u76f8\u5173; 0.4&lt;&#061;|\u03c1|&lt;0.7\u4e3a\u663e\u8457\u76f8\u5173&#xff1b; 0.7&lt;&#061;|\u03c1|&lt;1\u4e3a\u9ad8\u5ea6\u76f8\u5173<\/p>\n<p><span class=\"token keyword\">from<\/span> scipy<span class=\"token punctuation\">.<\/span>stats <span class=\"token keyword\">import<\/span> pearsonr<br \/>\nr1 <span class=\"token operator\">&#061;<\/span> pearsonr<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">from<\/span> scipy<span class=\"token punctuation\">.<\/span>stats <span class=\"token keyword\">import<\/span> pearsonr<br \/>\nx<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">12<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">]<\/span><br \/>\ny<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><br \/>\np <span class=\"token operator\">&#061;<\/span> pearsonr<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">)<\/span><\/p>\n<p>PearsonRResult(statistic&#061;np.float64(0.3504442861308587), pvalue&#061;np.float64(0.32081529829352373))<\/p>\n<h4>2 \u4e3b\u6210\u5206\u5206\u6790(PCA)<\/h4>\n<p>PCA\u7684\u6838\u5fc3\u76ee\u6807\u662f\u4ece\u539f\u59cb\u7279\u5f81\u7a7a\u95f4\u4e2d\u627e\u5230\u4e00\u4e2a\u65b0\u7684\u5750\u6807\u7cfb\u7edf&#xff0c;\u4f7f\u5f97\u6570\u636e\u5728\u65b0\u5750\u6807\u8f74\u4e0a\u7684\u6295\u5f71\u80fd\u591f\u6700\u5927\u7a0b\u5ea6\u5730\u4fdd\u7559\u6570\u636e\u7684\u65b9\u5dee&#xff0c;\u540c\u65f6\u51cf\u5c11\u6570\u636e\u7684\u7ef4\u5ea6\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151234-688a36620afee.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<li>\u4e2d\u5fc3\u5316\u6570\u636e&#xff1a;\u6bcf\u4e2a\u7279\u5f81\u51cf\u53bb\u5176\u5747\u503c<\/li>\n<li>\u8ba1\u7b97\u534f\u65b9\u5dee\u77e9\u9635&#xff1a;\u8861\u91cf\u7279\u5f81\u95f4\u7684\u76f8\u5173\u6027<\/li>\n<li>\u7279\u5f81\u503c\u5206\u89e3&#xff1a;\u8ba1\u7b97\u534f\u65b9\u5dee\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf<\/li>\n<li>\u9009\u62e9\u4e3b\u6210\u5206&#xff1a;\u6839\u636e\u4e3b\u6210\u5206\u7684\u65b9\u5dee\u7b49&#xff0c;\u786e\u5b9a\u6700\u7ec8\u4fdd\u7559\u7684\u4e3b\u6210\u5206\u4e2a\u6570&#xff0c; \u65b9\u5dee\u5927\u7684\u8981\u7559\u4e0b&#xff1b;\u82e5\u4e00\u4e2a\u7279\u5f81\u7684\u591a\u4e2a\u6837\u672c\u7684\u503c\u90fd\u76f8\u540c&#xff0c;\u5219\u65b9\u5dee\u4e3a0&#xff0c;\u8bf4\u660e\u8be5\u7279\u5f81\u503c\u4e0d\u80fd\u533a\u5206\u6837\u672c<\/li>\n<li>\u6295\u5f71\u6570\u636e&#xff1a;\u5c06\u539f\u59cb\u6570\u636e\u6295\u5f71\u5230\u9009\u5b9a\u7684\u7279\u5f81\u5411\u91cf\u4e0a<\/li>\n<p>from sklearn.decomposition import PCA<\/p>\n<ul>\n<li>PCA(n_components&#061;None)\n<ul>\n<li>\u4e3b\u6210\u5206\u5206\u6790<\/li>\n<li>n_components:\n<ul>\n<li>\u5b9e\u53c2\u4e3a\u5c0f\u6570\u65f6&#xff1a;\u8868\u793a\u964d\u7ef4\u540e\u4fdd\u7559\u767e\u5206\u4e4b\u591a\u5c11\u7684\u4fe1\u606f<\/li>\n<li>\u5b9e\u53c2\u4e3a\u6574\u6570\u65f6&#xff1a;\u8868\u793a\u51cf\u5c11\u5230\u591a\u5c11\u7279\u5f81<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>decomposition <span class=\"token keyword\">import<\/span> PCA<br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\ndata <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>array<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                 <span class=\"token punctuation\">[<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                 <span class=\"token punctuation\">[<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\npca <span class=\"token operator\">&#061;<\/span> PCA<span class=\"token punctuation\">(<\/span>n_components<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\ndata_new <span class=\"token operator\">&#061;<\/span> pca<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data_new<span class=\"token punctuation\">)<\/span><\/p>\n<p>[[-1.28620952e-15  3.82970843e&#043;00]<br \/>\n [-5.74456265e&#043;00 -1.91485422e&#043;00]<br \/>\n [ 5.74456265e&#043;00 -1.91485422e&#043;00]]<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>decomposition <span class=\"token keyword\">import<\/span> PCA<br \/>\niris <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx<span class=\"token operator\">&#061;<\/span>iris<span class=\"token punctuation\">.<\/span>data<br \/>\ny<span class=\"token operator\">&#061;<\/span>iris<span class=\"token punctuation\">.<\/span>target<br \/>\nx_train<span class=\"token punctuation\">,<\/span>x_test<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">,<\/span>test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><br \/>\ntransfer <span class=\"token operator\">&#061;<\/span> PCA<span class=\"token punctuation\">(<\/span>n_components<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx_train <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\">#\u8bad\u7ec3\u6a21\u578b<\/span><br \/>\n<span class=\"token comment\">#\u7528\u6a21\u578b\u9884\u6d4b<\/span><br \/>\nx_test <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">)<\/span><\/p>\n<p>[[-2.36170948  0.64237919]<br \/>\n [ 2.05485818  0.16275091]<br \/>\n [ 1.23887735  0.10868042]<br \/>\n&#8230;<br \/>\n [ 0.3864534  -0.37888638]<br \/>\n [ 1.57303541 -0.53629936]<br \/>\n [-2.73553694 -0.15148737]<br \/>\n [ 2.53493848  0.51260491]<br \/>\n [ 1.91514709  0.1205521 ]<br \/>\n [ 2.42377809  0.38254852]<br \/>\n [ 1.41198549 -0.14338675]]<\/p>\n<h2>KNN\u7b97\u6cd5<\/h2>\n<h3>\u8ddd\u79bb<\/h3>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u4e2d&#xff0c;\u6837\u672c\u8ddd\u79bb\u662f\u8861\u91cf\u6570\u636e\u70b9\u4e4b\u95f4\u76f8\u4f3c\u6027\u6216\u5dee\u5f02\u6027\u7684\u6838\u5fc3\u6982\u5ff5&#xff0c;\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5206\u7c7b\u3001\u805a\u7c7b\u3001\u964d\u7ef4\u7b49\u7b97\u6cd5\u4e2d\u3002<\/p>\n<h4>1. \u6b27\u6c0f\u8ddd\u79bb&#xff08;Euclidean Distance&#xff09;<\/h4>\n<p>\u6700\u5e38\u89c1\u7684\u4e24\u70b9\u6216\u591a\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u8868\u793a\u65b9\u6cd5&#xff0c;\u6307\u5728m\u7ef4\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u771f\u5b9e\u8ddd\u79bb&#xff0c;\u6216\u8005\u5411\u91cf\u7684\u81ea\u7136\u957f\u5ea6&#xff08;\u5373\u8be5\u70b9\u5230\u539f\u70b9\u7684\u8ddd\u79bb&#xff09;\u3002\u5728\u4e8c\u7ef4\u548c\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6b27\u6c0f\u8ddd\u79bb\u5c31\u662f\u4e24\u70b9\u4e4b\u95f4\u7684\u5b9e\u9645\u8ddd\u79bb\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151234-688a36624b77c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5728 n \u7ef4\u7a7a\u95f4\u4e2d&#xff0c;\u4e24\u4e2a\u70b9\u6b27\u6c0f\u8ddd\u79bb\u4e3a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         ,<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            1<\/p>\n<p>           \u2212<\/p>\n<p>            y<\/p>\n<p>            1<\/p>\n<p>            )<\/p>\n<p>            2<\/p>\n<p>           &#043;<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            2<\/p>\n<p>           \u2212<\/p>\n<p>            y<\/p>\n<p>            2<\/p>\n<p>            )<\/p>\n<p>            2<\/p>\n<p>           &#043;<\/p>\n<p>           \u22ef<\/p>\n<p>           &#043;<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            n<\/p>\n<p>           \u2212<\/p>\n<p>            y<\/p>\n<p>            n<\/p>\n<p>            )<\/p>\n<p>            2<\/p>\n<p>         \u00a0<\/p>\n<p>         d(A,B) &#061; \\\\sqrt{(x_1 &#8211; y_1)^2 &#043; (x_2 &#8211; y_2)^2 &#043; \\\\dots &#043; (x_n &#8211; y_n)^2}\\\\ <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.2561em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9839em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.9439em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2561em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\">\u00a0<\/span><\/span><\/span><\/span><\/span><\/span> \u516c\u5f0f\u53ef\u7b80\u5316\u4e3a\u5411\u91cf\u5f62\u5f0f&#xff08;\u82e5 A \u548c B \u8868\u793a\u4e3a\u5411\u91cf&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         ,<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         \u2225<\/p>\n<p>         A<\/p>\n<p>         \u2212<\/p>\n<p>         B<\/p>\n<p>          \u2225<\/p>\n<p>          2<\/p>\n<p>         \u00a0<\/p>\n<p>         d(A,B) &#061; \\\\| A &#8211; B \\\\|_2\\\\ <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\">\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>2. \u66fc\u54c8\u987f\u8ddd\u79bb&#xff08;Manhattan Distance&#xff09;<\/h4>\n<p>\u4e24\u70b9\u5728\u7f51\u683c\u72b6\u5750\u6807\u7cfb\u4e2d\u8d70\u8fc7\u7684\u6700\u77ed\u8def\u5f84&#xff08;\u53ea\u80fd\u6cbf\u5750\u6807\u8f74\u65b9\u5411\u79fb\u52a8&#xff09;&#xff0c;\u53c8\u79f0 \u201c\u57ce\u5e02\u8857\u533a\u8ddd\u79bb\u201d\u3002<\/p>\n<p>\u5728 n \u7ef4\u7a7a\u95f4\u4e2d&#xff0c;A \u4e0e B \u4e4b\u95f4\u7684\u66fc\u54c8\u987f\u8ddd\u79bb\u516c\u5f0f\u4e3a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         ,<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          1<\/p>\n<p>         \u2212<\/p>\n<p>          y<\/p>\n<p>          1<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          2<\/p>\n<p>         \u2212<\/p>\n<p>          y<\/p>\n<p>          2<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u22ef<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          n<\/p>\n<p>         \u2212<\/p>\n<p>          y<\/p>\n<p>          n<\/p>\n<p>         \u2223<\/p>\n<p>         d(A,B) &#061; |x_1 &#8211; y_1| &#043; |x_2 &#8211; y_2| &#043; \\\\dots &#043; |x_n &#8211; y_n| <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/span> \u516c\u5f0f\u53ef\u7b80\u5316\u4e3a\u5411\u91cf\u5f62\u5f0f&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         ,<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         \u2225<\/p>\n<p>         A<\/p>\n<p>         \u2212<\/p>\n<p>         B<\/p>\n<p>          \u2225<\/p>\n<p>          1<\/p>\n<p>         d(A,B) &#061; \\\\| A &#8211; B \\\\|_1 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151234-688a366269e45.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>3. \u5207\u6bd4\u96ea\u592b\u8ddd\u79bb&#xff08;Chebyshev Distance&#xff09;<\/h4>\n<p>\u4e24\u70b9\u5728\u5404\u7ef4\u5ea6\u4e0a\u5dee\u503c\u7684\u6700\u5927\u503c&#xff0c;\u76f8\u5f53\u4e8e \u201c\u56fd\u9645\u8c61\u68cb\u4e2d\u56fd\u738b\u7684\u79fb\u52a8\u8ddd\u79bb\u201d\u3002 <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           max<\/p>\n<p>           \u2061<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          n<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          i<\/p>\n<p>         \u2212<\/p>\n<p>          y<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>         d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\max_{i&#061;1}^{n} |x_i &#8211; y_i| <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.7596em;vertical-align: -0.7277em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.032em\"><span class=\"\" style=\"top: -2.3723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">max<\/span><\/span><\/span><span class=\"\" style=\"top: -3.6306em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7277em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/span> \u516c\u5f0f\u53ef\u901a\u8fc7\u6570\u5b66\u53d8\u6362\u4e0e\u66fc\u54c8\u987f\u8ddd\u79bb\u5173\u8054&#xff08;\u9700\u501f\u52a9\u5750\u6807\u8f6c\u6362&#xff09;&#xff0c;\u4f46\u6838\u5fc3\u662f\u5bf9 \u201c\u6700\u5927\u7ef4\u5ea6\u5dee\u5f02\u201d \u7684\u76f4\u63a5\u5ea6\u91cf\u3002<\/p>\n<h4>4. \u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb&#xff08;Minkowski Distance&#xff09;<\/h4>\n<p>\u6b27\u6c0f\u8ddd\u79bb\u548c\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u5e7f\u4e49\u5f62\u5f0f&#xff0c;\u901a\u8fc7\u53c2\u6570 p \u63a7\u5236\u8ddd\u79bb\u5ea6\u91cf\u7684\u9636\u6570\u3002 <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           (<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>           \u2223<\/p>\n<p>            x<\/p>\n<p>            i<\/p>\n<p>           \u2212<\/p>\n<p>            y<\/p>\n<p>            i<\/p>\n<p>            \u2223<\/p>\n<p>            p<\/p>\n<p>           )<\/p>\n<p>           1<\/p>\n<p>           \/<\/p>\n<p>           p<\/p>\n<p>         d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\left( \\\\sum_{i&#061;1}^{n} |x_i &#8211; y_i|^p \\\\right)^{1\/p} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.3056em;vertical-align: -1.2777em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">(<\/span><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7144em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.0279em\"><span class=\"\" style=\"top: -4.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1\/<\/span><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u5f53 (p&#061;1) \u65f6&#xff0c;\u9000\u5316\u4e3a\u66fc\u54c8\u987f\u8ddd\u79bb&#xff1b;<\/li>\n<li>\u5f53 (p&#061;2) \u65f6&#xff0c;\u5373\u4e3a\u6b27\u6c0f\u8ddd\u79bb&#xff1b;<\/li>\n<li>\u5f53 (p \\\\to \\\\infty) \u65f6&#xff0c;\u6536\u655b\u4e8e\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb\u3002<\/li>\n<\/ul>\n<h4>5. \u4f59\u5f26\u76f8\u4f3c\u5ea6&#xff08;Cosine Similarity&#xff09;<\/h4>\n<p>\u8ba1\u7b97\u4e24\u5411\u91cf\u5939\u89d2\u7684\u4f59\u5f26\u503c&#xff0c;\u8861\u91cf\u65b9\u5411\u7684\u76f8\u4f3c\u6027&#xff08;\u800c\u975e\u5927\u5c0f&#xff09;\u3002 <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         cosine<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           x<\/p>\n<p>           \u22c5<\/p>\n<p>           y<\/p>\n<p>           \u2223<\/p>\n<p>           \u2223<\/p>\n<p>           x<\/p>\n<p>           \u2223<\/p>\n<p>           \u2223<\/p>\n<p>           \u22c5<\/p>\n<p>           \u2223<\/p>\n<p>           \u2223<\/p>\n<p>           y<\/p>\n<p>           \u2223<\/p>\n<p>           \u2223<\/p>\n<p>         &#061;<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>            x<\/p>\n<p>            i<\/p>\n<p>            y<\/p>\n<p>            i<\/p>\n<p>              \u2211<\/p>\n<p>               i<\/p>\n<p>               &#061;<\/p>\n<p>               1<\/p>\n<p>              n<\/p>\n<p>              x<\/p>\n<p>              i<\/p>\n<p>              2<\/p>\n<p>           \u22c5<\/p>\n<p>              \u2211<\/p>\n<p>               i<\/p>\n<p>               &#061;<\/p>\n<p>               1<\/p>\n<p>              n<\/p>\n<p>              y<\/p>\n<p>              i<\/p>\n<p>              2<\/p>\n<p>         \\\\text{cosine}(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\frac{\\\\mathbf{x} \\\\cdot \\\\mathbf{y}}{||\\\\mathbf{x}|| \\\\cdot ||\\\\mathbf{y}||} &#061; \\\\frac{\\\\sum_{i&#061;1}^{n} x_i y_i}{\\\\sqrt{\\\\sum_{i&#061;1}^{n} x_i^2} \\\\cdot \\\\sqrt{\\\\sum_{i&#061;1}^{n} y_i^2}} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">cosine<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223\u2223<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mord\">\u2223\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">\u2223\u2223<\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mord\">\u2223\u2223<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.624em;vertical-align: -1.13em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.494em\"><span class=\"\" style=\"top: -2.1727em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9373em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7959em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.0448em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8973em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3027em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9373em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7959em\"><span class=\"\" style=\"top: -2.4231em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.0448em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8973em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3027em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.6897em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.13em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4f59\u5f26\u76f8\u4f3c\u5ea6\u7684\u7ed3\u679c\u8303\u56f4\u662f [-1, 1]&#xff0c;\u5177\u4f53\u542b\u4e49\u5982\u4e0b&#xff1a;<\/p>\n<ul>\n<li>\u03b8 &#061; 0\u00b0&#xff1a;(\\\\cos(\\\\theta) &#061; 1) \u2192 \u4e24\u5411\u91cf\u65b9\u5411\u5b8c\u5168\u76f8\u540c&#xff08;\u76f8\u4f3c\u5ea6\u6700\u9ad8&#xff09;&#xff1b;<\/li>\n<li>\u03b8 &#061; 90\u00b0&#xff1a;(\\\\cos(\\\\theta) &#061; 0) \u2192 \u4e24\u5411\u91cf\u5782\u76f4&#xff0c;\u65b9\u5411\u65e0\u5173&#xff1b;<\/li>\n<li>\u03b8 &#061; 180\u00b0&#xff1a;(\\\\cos(\\\\theta) &#061; -1) \u2192 \u4e24\u5411\u91cf\u65b9\u5411\u5b8c\u5168\u76f8\u53cd&#xff08;\u76f8\u4f3c\u5ea6\u6700\u4f4e&#xff09;\u3002<\/li>\n<\/ul>\n<h4>6. \u6770\u5361\u5fb7\u76f8\u4f3c\u5ea6&#xff08;Jaccard Similarity&#xff09;<\/h4>\n<p>\u7528\u4e8e\u6bd4\u8f83\u4e24\u4e2a\u96c6\u5408\u7684\u76f8\u4f3c\u6027&#xff0c;\u5b9a\u4e49\u4e3a\u4ea4\u96c6\u4e0e\u5e76\u96c6\u7684\u6bd4\u503c\u3002<\/p>\n<p>\u5bf9\u4e8e\u4e24\u4e2a\u96c6\u5408 A \u548c B&#xff0c;\u6770\u5361\u5fb7\u76f8\u4f3c\u5ea6\u4e3a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         J<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         ,<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           \u2223<\/p>\n<p>           A<\/p>\n<p>           \u2229<\/p>\n<p>           B<\/p>\n<p>           \u2223<\/p>\n<p>           \u2223<\/p>\n<p>           A<\/p>\n<p>           \u222a<\/p>\n<p>           B<\/p>\n<p>           \u2223<\/p>\n<p>         \u00a0<\/p>\n<p>         J(A, B) &#061; \\\\frac{|A \\\\cap B|}{|A \\\\cup B|}\\\\ <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0962em\">J<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u222a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2229<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\">\u00a0<\/span><\/span><\/span><\/span><\/span><\/span> \u6770\u5361\u5fb7\u8ddd\u79bb\u4e3a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         ,<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         1<\/p>\n<p>         \u2212<\/p>\n<p>         J<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         ,<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         d(A, B) &#061; 1 &#8211; J(A, B) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0962em\">J<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u6770\u5361\u5fb7\u76f8\u4f3c\u5ea6\u7684\u7ed3\u679c\u8303\u56f4\u662f [0, 1]&#xff0c;\u5177\u4f53\u542b\u4e49\u5982\u4e0b&#xff1a;<\/p>\n<ul>\n<li>J &#061; 1&#xff1a;\u4e24\u4e2a\u96c6\u5408\u5b8c\u5168\u76f8\u540c&#xff08;\u4ea4\u96c6 &#061; \u5e76\u96c6&#xff09;&#xff1b;<\/li>\n<li>J &#061; 0&#xff1a;\u4e24\u4e2a\u96c6\u5408\u6ca1\u6709\u4efb\u4f55\u5171\u540c\u5143\u7d20&#xff08;\u4ea4\u96c6\u4e3a\u7a7a&#xff09;&#xff1b;<\/li>\n<li>\u6570\u503c\u8d8a\u63a5\u8fd1 1&#xff0c;\u8bf4\u660e\u4e24\u4e2a\u96c6\u5408\u7684\u91cd\u53e0\u5ea6\u8d8a\u9ad8&#xff0c;\u76f8\u4f3c\u6027\u8d8a\u5f3a\u3002<\/li>\n<\/ul>\n<h4>7. \u9a6c\u6c0f\u8ddd\u79bb&#xff08;Mahalanobis Distance&#xff09;<\/h4>\n<p>\u8003\u8651\u6570\u636e\u5206\u5e03\u534f\u65b9\u5dee\u7684\u8ddd\u79bb\u5ea6\u91cf&#xff0c;\u53ef\u6d88\u9664\u7279\u5f81\u95f4\u76f8\u5173\u6027\u7684\u5f71\u54cd&#xff0c;\u4e14\u5bf9\u5c3a\u5ea6\u4e0d\u654f\u611f\u3002<\/p>\n<p>\u5bf9\u4e8e\u4e24\u4e2a\u6570\u636e\u70b9 x \u548c y&#xff0c;\u82e5\u5b83\u4eec\u6765\u81ea\u540c\u4e00\u5206\u5e03&#xff08;\u534f\u65b9\u5dee\u77e9\u9635\u4e3a S&#xff0c;\u5219\u4e24\u8005\u4e4b\u95f4\u7684\u9a6c\u6c0f\u8ddd\u79bb\u4e3a&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           \u2212<\/p>\n<p>           y<\/p>\n<p>            )<\/p>\n<p>            T<\/p>\n<p>            S<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           \u2212<\/p>\n<p>           y<\/p>\n<p>           )<\/p>\n<p>         d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\sqrt{(\\\\mathbf{x} &#8211; \\\\mathbf{y})^T S^{-1} (\\\\mathbf{x} &#8211; \\\\mathbf{y})} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.84em;vertical-align: -0.5475em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2925em\"><span class=\"svg-align\" style=\"top: -3.8em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7673em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2525em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.88em\"><\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5475em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>KNN\u7b97\u6cd5<\/h3>\n<p>K \u8fd1\u90bb&#xff08;K-Nearest Neighbors, KNN&#xff09;\u662f\u4e00\u79cd\u57fa\u672c\u4e14\u5e38\u7528\u7684\u76d1\u7763\u5b66\u4e60\u7b97\u6cd5&#xff0c;\u53ef\u7528\u4e8e\u5206\u7c7b\u548c\u56de\u5f52\u4efb\u52a1\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f&#xff1a;\u7ed9\u5b9a\u4e00\u4e2a\u8bad\u7ec3\u6570\u636e\u96c6&#xff0c;\u5bf9\u4e8e\u65b0\u7684\u8f93\u5165\u5b9e\u4f8b&#xff0c;\u5728\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u627e\u5230\u4e0e\u8be5\u5b9e\u4f8b\u6700\u90bb\u8fd1\u7684 k \u4e2a\u5b9e\u4f8b&#xff0c;\u7136\u540e\u57fa\u4e8e\u8fd9 k \u4e2a\u5b9e\u4f8b\u7684\u4fe1\u606f\u6765\u8fdb\u884c\u9884\u6d4b\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151234-688a3662851e3.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<li>\u8ba1\u7b97\u5f85\u9884\u6d4b\u6837\u672c\u4e0e\u8bad\u7ec3\u96c6\u4e2d\u6240\u6709\u6837\u672c\u7684\u8ddd\u79bb\u3002<\/li>\n<li>\u9009\u62e9\u8ddd\u79bb\u6700\u5c0f\u7684 k \u4e2a\u6837\u672c\u3002<\/li>\n<li>\u6839\u636e\u8fd9 k \u4e2a\u6837\u672c\u8fdb\u884c\u5206\u7c7b,\u5219\u9884\u6d4b\u6837\u672c\u5c5e\u4e8ek\u4e2a\u6837\u672c\u4e2d\u6837\u672c\u6570\u6700\u591a\u7684\u90a3\u4e00\u7c7b\u3002<\/li>\n<p>\u7f3a\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u5927\u89c4\u6a21\u7684\u6570\u636e\u96c6&#xff0c;\u8ba1\u7b97\u91cf\u8fc7\u5927<\/li>\n<li>\u7ef4\u5ea6\u707e\u96be\u2013\u5bf9\u4e8e\u9ad8\u7ef4\u6570\u636e&#xff0c;\u6700\u8fd1\u90bb\u4e0e\u6700\u8fdc\u90bb\u7684\u8ddd\u79bb\u5dee\u5f02\u7f29\u5c0f&#xff0c;\u5bfc\u81f4\u6a21\u578b\u6027\u80fd\u4e0b\u964d\u3002<\/li>\n<li>K \u503c\u9009\u62e9\u56f0\u96be\n<ul>\n<li>K \u503c\u8fc7\u5c0f&#xff1a;\u6a21\u578b\u8fc7\u62df\u5408&#xff0c;\u5bf9\u566a\u58f0\u654f\u611f&#xff08;\u5982 K&#061;1 \u65f6\u6613\u53d7\u79bb\u7fa4\u70b9\u5f71\u54cd&#xff09;\u3002<\/li>\n<li>K \u503c\u8fc7\u5927&#xff1a;\u6a21\u578b\u6b20\u62df\u5408&#xff0c;\u5ffd\u7565\u5c40\u90e8\u7279\u5f81&#xff08;\u5982 K&#061;n \u65f6\u9000\u5316\u4e3a\u5168\u5c40\u591a\u6570\u8868\u51b3&#xff09;\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u6a21\u578b\u4fdd\u5b58\u4e0e\u52a0\u8f7d<\/h3>\n<p><span class=\"token keyword\">import<\/span> joblib<br \/>\n<span class=\"token comment\"># \u4fdd\u5b58\u6a21\u578b<\/span><br \/>\njoblib<span class=\"token punctuation\">.<\/span>dump<span class=\"token punctuation\">(<\/span>estimator<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;my_ridge.pkl&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u52a0\u8f7d\u6a21\u578b<\/span><br \/>\nestimator <span class=\"token operator\">&#061;<\/span> joblib<span class=\"token punctuation\">.<\/span>load<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;my_ridge.pkl&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\">#\u4f7f\u7528\u6a21\u578b\u9884\u6d4b<\/span><br \/>\ny_test<span class=\"token operator\">&#061;<\/span>estimator<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.7<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><\/p>\n<h2>\u6a21\u578b\u9009\u62e9\u4e0e\u8c03\u4f18<\/h2>\n<h3>\u4ea4\u53c9\u9a8c\u8bc1<\/h3>\n<p>\u4ea4\u53c9\u9a8c\u8bc1\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u539f\u59cb\u6570\u636e\u96c6\u5212\u5206\u4e3a\u591a\u4e2a\u5b50\u96c6&#xff0c;\u8f6e\u6d41\u5c06\u5176\u4e2d\u4e00\u4e2a\u5b50\u96c6\u4f5c\u4e3a\u6d4b\u8bd5\u96c6&#xff0c;\u5176\u4f59\u4f5c\u4e3a\u8bad\u7ec3\u96c6&#xff0c;\u591a\u6b21\u8bad\u7ec3\u548c\u8bc4\u4f30\u6a21\u578b\u540e\u53d6\u5e73\u5747\u503c\u4f5c\u4e3a\u6700\u7ec8\u6027\u80fd\u6307\u6807\u3002<\/p>\n<p>\u4ea4\u53c9\u9a8c\u8bc1\u4e3b\u8981\u89e3\u51b3\u4ee5\u4e0b\u95ee\u9898&#xff1a;<\/p>\n<ul>\n<li>\u4f20\u7edf\u7684\u5355\u6b21\u8bad\u7ec3\u6d4b\u8bd5\u5206\u5272\u53ef\u80fd\u5bfc\u81f4\u7ed3\u679c\u4e0d\u7a33\u5b9a<\/li>\n<li>\u6a21\u578b\u5728\u7279\u5b9a\u6d4b\u8bd5\u96c6\u4e0a\u53ef\u80fd\u8fc7\u62df\u5408<\/li>\n<li>\u5145\u5206\u5229\u7528\u6709\u9650\u7684\u6570\u636e\u8fdb\u884c\u6a21\u578b\u8bc4\u4f30<\/li>\n<\/ul>\n<h4>1 \u4fdd\u7559\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Train-Test Split&#xff09;<\/h4>\n<p>\u4fdd\u7559\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Hold-Out Cross Validation&#xff0c;\u53c8\u79f0 Train-Test Split&#xff09;\u662f\u6700\u76f4\u89c2\u3001\u6700\u7b80\u5355\u7684\u6a21\u578b\u9a8c\u8bc1\u65b9\u6cd5&#xff0c;\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u539f\u59cb\u6570\u636e\u96c6\u4e00\u6b21\u6027\u5206\u5272\u4e3a\u4e24\u4e2a\u4e92\u65a5\u7684\u5b50\u96c6&#xff1a;\u8bad\u7ec3\u96c6&#xff08;Train Set&#xff09;\u548c\u6d4b\u8bd5\u96c6&#xff08;Test Set&#xff09;&#xff0c;\u7528\u8bad\u7ec3\u96c6\u8bad\u7ec3\u6a21\u578b&#xff0c;\u7528\u6d4b\u8bd5\u96c6\u8bc4\u4f30\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<p>\u5e38\u89c1\u6bd4\u4f8b\u4e3a\u8bad\u7ec3\u96c6 70%-80%&#xff0c;\u6d4b\u8bd5\u96c6 20%-30%\u3002<\/p>\n<p>sklearn.model_selection.train_test_split<\/p>\n<ul>\n<li>test_size&#xff1a;\u6d4b\u8bd5\u96c6\u5360\u6bd4&#xff08;\u5982 0.2 \u8868\u793a 20% \u6570\u636e\u4f5c\u4e3a\u6d4b\u8bd5\u96c6&#xff09;\u3002<\/li>\n<li>random_state&#xff1a;\u968f\u673a\u79cd\u5b50&#xff0c;\u56fa\u5b9a\u540e\u5206\u5272\u65b9\u5f0f\u4e0d\u53d8&#xff0c;\u4fdd\u8bc1\u5b9e\u9a8c\u53ef\u590d\u73b0\u3002<\/li>\n<li>stratify&#xff1a;\u7528\u4e8e\u7c7b\u522b\u4e0d\u5e73\u8861\u6570\u636e&#xff08;\u5982\u4e8c\u5206\u7c7b\u4e2d\u6b63\u8d1f\u6837\u672c\u6bd4\u4f8b\u60ac\u6b8a&#xff09;&#xff0c;\u8bbe\u7f6e\u4e3ay\u65f6&#xff0c;\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u4f1a\u4fdd\u6301\u4e0e\u539f\u59cb\u6570\u636e\u76f8\u540c\u7684\u7c7b\u522b\u6bd4\u4f8b&#xff08;\u907f\u514d\u6d4b\u8bd5\u96c6\u67d0\u7c7b\u6837\u672c\u8fc7\u5c11\u5bfc\u81f4\u8bc4\u4f30\u5931\u771f&#xff09;\u3002<\/li>\n<\/ul>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\nx<span class=\"token punctuation\">,<\/span>y <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx_train<span class=\"token punctuation\">,<\/span>x_test<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span>  train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">,<\/span>test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">,<\/span>shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span>stratify<span class=\"token operator\">&#061;<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\">#stratify&#061;y &#xff1a;\u6309\u7167y\u7684\u5206\u5e03\u8fdb\u884c\u5206\u5c42<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><\/p>\n<p>[1 2 0 0 0 0 0 2 1 0 1 2 1 1 2 1 0 2 0 1 1 1 1 0 2 2 2 0 2 2]<\/p>\n<p>\u4f18\u70b9<\/p>\n<li>\u7b80\u5355\u9ad8\u6548&#xff1a;\u4ec5\u5206\u5272\u4e00\u6b21&#xff0c;\u8ba1\u7b97\u6210\u672c\u4f4e&#xff08;\u5c24\u5176\u9002\u5408\u5927\u6570\u636e\u96c6&#xff09;\u3002<\/li>\n<li>\u76f4\u89c2\u6613\u61c2&#xff1a;\u76f4\u63a5\u6a21\u62df \u201c\u8bad\u7ec3\u2192\u6d4b\u8bd5\u201d \u7684\u771f\u5b9e\u573a\u666f&#xff0c;\u7ed3\u679c\u6613\u89e3\u91ca\u3002<\/li>\n<p>\u7f3a\u70b9<\/p>\n<li>\u7ed3\u679c\u7a33\u5b9a\u6027\u5dee&#xff1a;\u8bc4\u4f30\u7ed3\u679c\u53d7\u5206\u5272\u65b9\u5f0f\u5f71\u54cd\u5927&#xff08;\u4e0d\u540c\u968f\u673a\u79cd\u5b50\u53ef\u80fd\u5bfc\u81f4\u6d4b\u8bd5\u96c6\u5206\u5e03\u5dee\u5f02&#xff0c;\u8fdb\u800c\u5f71\u54cd\u6307\u6807&#xff09;\u3002<\/li>\n<li>\u6570\u636e\u5229\u7528\u7387\u4f4e&#xff1a;\u6d4b\u8bd5\u96c6\u672a\u53c2\u4e0e\u8bad\u7ec3&#xff0c;\u5bf9\u4e8e\u5c0f\u6570\u636e\u96c6&#xff0c;\u53ef\u80fd\u6d6a\u8d39\u6709\u6548\u4fe1\u606f&#xff08;\u8bad\u7ec3\u6570\u636e\u4e0d\u8db3\u5bfc\u81f4\u6a21\u578b\u6b20\u62df\u5408&#xff09;\u3002<\/li>\n<li>\u5bf9\u5c0f\u6570\u636e\u96c6\u4e0d\u53cb\u597d&#xff1a;\u82e5\u6570\u636e\u91cf\u5c0f&#xff0c;\u6d4b\u8bd5\u96c6\u53ef\u80fd\u65e0\u6cd5\u4ee3\u8868\u6574\u4f53\u6570\u636e\u5206\u5e03&#xff08;\u5982\u6781\u7aef\u503c\u96c6\u4e2d\u5728\u6d4b\u8bd5\u96c6&#xff09;&#xff0c;\u5bfc\u81f4\u8bc4\u4f30\u5931\u771f\u3002<\/li>\n<h4>2 K-\u6298\u4ea4\u53c9\u9a8c\u8bc1(K-fold)<\/h4>\n<p>\u5c06\u6570\u636e\u96c6\u5212\u5206\u4e3aK \u4e2a\u4e92\u4e0d\u91cd\u53e0\u7684\u5b50\u96c6&#xff08;\u6298&#xff09;&#xff0c;\u6bcf\u4e2a\u5206\u533a\u88ab\u79f0\u4e3a \u4e00\u4e2a\u201dFold\u201d\u3002\u4e00\u4e2aFold\u88ab\u7528\u4f5c\u9a8c\u8bc1\u96c6&#xff0c;\u5176\u4f59\u7684K-1\u4e2aFold\u88ab\u7528\u4f5c\u8bad\u7ec3\u96c6&#xff0c;\u91cd\u590d K \u6b21\u3002\u6700\u7ec8\u6a21\u578b\u6027\u80fd\u662f K \u6b21\u8bc4\u4f30\u7ed3\u679c\u7684\u5e73\u5747\u503c\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151237-688a36658087a.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>from sklearn.model_selection import KFold<\/p>\n<ul>\n<li>n_splits&#xff1a;\u6298\u6570&#xff0c;\u901a\u5e38\u53d6 5 \u6216 10<\/li>\n<li>shuffle&#xff1a;\u662f\u5426\u5728\u5212\u5206\u524d\u6253\u4e71\u6570\u636e<\/li>\n<li>random_state&#xff1a;\u968f\u673a\u79cd\u5b50&#xff0c;\u786e\u4fdd\u7ed3\u679c\u53ef\u91cd\u73b0<\/li>\n<\/ul>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> KFold<span class=\"token punctuation\">,<\/span>StratifiedKFold<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<br \/>\nx<span class=\"token punctuation\">,<\/span>y <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nk <span class=\"token operator\">&#061;<\/span> KFold<span class=\"token punctuation\">(<\/span>n_splits<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span>shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><br \/>\nre <span class=\"token operator\">&#061;<\/span> k<span class=\"token punctuation\">.<\/span>split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># print(re)# \u8fed\u4ee3\u5668<\/span><br \/>\n<span class=\"token comment\"># print(next(re))<\/span><\/p>\n<p><span class=\"token keyword\">for<\/span> train_index<span class=\"token punctuation\">,<\/span>test_index <span class=\"token keyword\">in<\/span> re<span class=\"token punctuation\">:<\/span><br \/>\n    x_train<span class=\"token punctuation\">,<\/span>x_test <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">[<\/span>train_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>x<span class=\"token punctuation\">[<\/span>test_index<span class=\"token punctuation\">]<\/span><br \/>\n    y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span> y<span class=\"token punctuation\">[<\/span>train_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">[<\/span>test_index<span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><\/p>\n<p>[0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2]<\/p>\n<p>\u7f3a\u70b9&#xff1a;\u5bf9\u4e0d\u5e73\u8861\u6570\u636e\u96c6\u4e0d\u53cb\u597d&#xff08;\u53ef\u80fd\u5bfc\u81f4\u67d0\u7c7b\u6837\u672c\u5728\u6d4b\u8bd5\u96c6\u4e2d\u7f3a\u5931&#xff09;<\/p>\n<p>\u968f\u673a\u5212\u5206\u53ef\u80fd\u5bfc\u81f4\u67d0\u4e9b\u6298\u4e2d\u67d0\u7c7b\u522b\u6837\u672c\u6781\u5c11\u751a\u81f3\u7f3a\u5931&#xff0c;\u5c24\u5176\u662f\u5f53\u67d0\u7c7b\u522b\u6837\u672c\u5360\u6bd4\u8f83\u4f4e\u65f6&#xff08;\u5982\u6b3a\u8bc8\u68c0\u6d4b\u4e2d\u6b3a\u8bc8\u6837\u672c\u901a\u5e38\u4e0d\u8db3 1%&#xff09;\u3002\u8fd9\u79cd\u4e0d\u5e73\u8861\u4f1a\u5bfc\u81f4&#xff1a;<\/p>\n<ul>\n<li>\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u5206\u5e03\u4e0d\u4e00\u81f4<\/li>\n<li>\u6a21\u578b\u8bc4\u4f30\u6307\u6807\u4e0d\u53ef\u9760&#xff08;\u5982\u51c6\u786e\u7387\u865a\u9ad8&#xff09;<\/li>\n<li>\u5bf9\u5c11\u6570\u7c7b\u522b\u7684\u9884\u6d4b\u80fd\u529b\u65e0\u6cd5\u5f97\u5230\u6709\u6548\u9a8c\u8bc1<\/li>\n<\/ul>\n<h4>3 \u5206\u5c42K-\u6298\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Stratified k-fold&#xff09;<\/h4>\n<p>\u5206\u5c42 K &#8211; \u6298\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Stratified K-Fold Cross-Validation&#xff09;\u662f K &#8211; \u6298\u4ea4\u53c9\u9a8c\u8bc1\u7684\u6539\u8fdb\u7248\u672c&#xff0c;\u7279\u522b\u9002\u7528\u4e8e\u5206\u7c7b\u95ee\u9898&#xff0c;\u5c24\u5176\u662f\u7c7b\u522b\u4e0d\u5e73\u8861\u7684\u6570\u636e\u96c6\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f\u5728\u6bcf\u6b21\u5212\u5206\u65f6\u4fdd\u6301\u6bcf\u4e2a\u6298\u4e2d\u5404\u7c7b\u522b\u6837\u672c\u7684\u6bd4\u4f8b\u4e0e\u539f\u59cb\u6570\u636e\u96c6\u4e00\u81f4&#xff0c;\u4ece\u800c\u786e\u4fdd\u8bc4\u4f30\u7ed3\u679c\u7684\u53ef\u9760\u6027\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151237-688a3665bc76d.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>from sklearn.model_selection import StratifiedKFold<\/p>\n<p>strat_k_fold&#061;sklearn.model_selection.StratifiedKFold(n_splits&#061;5, shuffle&#061;True, random_state&#061;42)<\/p>\n<ul>\n<li>n_splits\u5212\u5206\u4e3a\u51e0\u4e2a\u6298\u53e0<\/li>\n<li>shuffle\u662f\u5426\u5728\u62c6\u5206\u4e4b\u524d\u88ab\u6253\u4e71(\u968f\u673a\u5316),False\u5219\u6309\u7167\u987a\u5e8f\u62c6<\/li>\n<li>random_state\u968f\u673a\u56e0\u5b50<\/li>\n<\/ul>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> StratifiedKFold<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<br \/>\nx<span class=\"token punctuation\">,<\/span>y <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nk <span class=\"token operator\">&#061;<\/span> StratifiedKFold<span class=\"token punctuation\">(<\/span>n_splits<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span>shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><br \/>\nre <span class=\"token operator\">&#061;<\/span> k<span class=\"token punctuation\">.<\/span>split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># print(re)# \u8fed\u4ee3\u5668<\/span><br \/>\n<span class=\"token comment\"># print(next(re))<\/span><\/p>\n<p><span class=\"token keyword\">for<\/span> train_index<span class=\"token punctuation\">,<\/span>test_index <span class=\"token keyword\">in<\/span> re<span class=\"token punctuation\">:<\/span><br \/>\n    x_train<span class=\"token punctuation\">,<\/span>x_test <span class=\"token operator\">&#061;<\/span> x<span class=\"token punctuation\">[<\/span>train_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>x<span class=\"token punctuation\">[<\/span>test_index<span class=\"token punctuation\">]<\/span><br \/>\n    y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span> y<span class=\"token punctuation\">[<\/span>train_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">[<\/span>test_index<span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><\/p>\n<p>[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]<br \/>\n[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2]<\/p>\n<h3>\u8d85\u53c2\u6570\u641c\u7d22 GridSearchCV<\/h3>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u4e2d&#xff0c;\u8d85\u53c2\u6570\u662f\u6a21\u578b\u8bad\u7ec3\u524d\u9700\u8981\u4eba\u4e3a\u8bbe\u5b9a\u7684\u53c2\u6570&#xff08;\u5982 KNN \u4e2d\u7684k\u503c\u3001\u51b3\u7b56\u6811\u7684max_depth\u7b49&#xff09;\u3002\u8d85\u53c2\u6570\u641c\u7d22\u662f\u5bfb\u627e\u6700\u4f18\u8d85\u53c2\u6570\u7ec4\u5408\u7684\u8fc7\u7a0b&#xff0c;\u800c **\u7f51\u683c\u641c\u7d22&#xff08;Grid Search&#xff09;**\u662f\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002<\/p>\n<p>GridSearchCV API<\/p>\n<p>class sklearn.model_selection.GridSearchCV(estimator, param_grid)<\/p>\n<p>GridSearchCV<span class=\"token punctuation\">(<\/span><br \/>\n    estimator<span class=\"token punctuation\">,<\/span>                  <span class=\"token comment\"># \u6a21\u578b&#xff08;\u5982KNN\u3001RandomForest\u7b49&#xff09;<\/span><br \/>\n    param_grid<span class=\"token punctuation\">,<\/span>                 <span class=\"token comment\"># \u8d85\u53c2\u6570\u7f51\u683c&#xff08;\u5b57\u5178\u5f62\u5f0f&#xff09;<\/span><br \/>\n    score<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span>               <span class=\"token comment\"># \u8bc4\u4f30\u6307\u6807<\/span><br \/>\n    cv<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">None<\/span><span class=\"token punctuation\">,<\/span>                    <span class=\"token comment\"># \u4ea4\u53c9\u9a8c\u8bc1\u6298\u6570\u6216\u7b56\u7565<\/span><br \/>\n    <span class=\"token punctuation\">.<\/span><span class=\"token punctuation\">.<\/span><span class=\"token punctuation\">.<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<li>estimator<\/li>\n<ul>\n<li>\n<p>\u542b\u4e49&#xff1a;\u9700\u8981\u4f18\u5316\u7684\u6a21\u578b\u5bf9\u8c61\u3002<\/p>\n<p> <span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>neighbors <span class=\"token keyword\">import<\/span> KNeighborsClassifier<br \/>\nestimator <span class=\"token operator\">&#061;<\/span> KNeighborsClassifier<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u521b\u5efaKNN\u6a21\u578b<\/span>\n <\/li>\n<\/ul>\n<li>param_grid<\/li>\n<ul>\n<li>\n<p>\u542b\u4e49&#xff1a;\u5f85\u641c\u7d22\u7684\u8d85\u53c2\u6570\u7ec4\u5408&#xff0c;\u683c\u5f0f\u4e3a\u5b57\u5178\u7684\u5217\u8868\u3002<\/p>\n<p> param_grid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token string\">&#039;n_neighbors&#039;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">7<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">9<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>      <span class=\"token comment\"># K\u503c<\/span><br \/>\n    <span class=\"token string\">&#039;weights&#039;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;uniform&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;distance&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u6743\u91cd\u8ba1\u7b97\u65b9\u5f0f<\/span><br \/>\n    <span class=\"token string\">&#039;p&#039;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span>                     <span class=\"token comment\"># \u8ddd\u79bb\u5ea6\u91cf&#xff08;1&#061;\u66fc\u54c8\u987f&#xff0c;2&#061;\u6b27\u6c0f&#xff09;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span>\n <\/li>\n<\/ul>\n<li>cv<\/li>\n<ul>\n<li>\n<p>\u542b\u4e49&#xff1a;\u4ea4\u53c9\u9a8c\u8bc1\u7684\u6298\u6570\u6216\u81ea\u5b9a\u4e49\u7b56\u7565\u3002<\/p>\n<\/li>\n<li>\n<p>\u5e38\u7528\u503c<\/p>\n<ul>\n<li>\u6574\u6570&#xff1a;\u6307\u5b9a K \u6298&#xff08;\u5982cv&#061;5&#xff09;<\/li>\n<li>\u4ea4\u53c9\u9a8c\u8bc1\u751f\u6210\u5668&#xff1a;\u5982StratifiedKFold&#xff08;\u5904\u7406\u7c7b\u522b\u4e0d\u5e73\u8861&#xff09;<\/li>\n<\/ul>\n<p> <span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> StratifiedKFold<br \/>\ncv <span class=\"token operator\">&#061;<\/span> StratifiedKFold<span class=\"token punctuation\">(<\/span>n_splits<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span>\n <\/li>\n<\/ul>\n<p>\u7f51\u683c\u641c\u7d22\u7ed3\u675f\u540e&#xff0c;\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u5c5e\u6027\u83b7\u53d6\u7ed3\u679c&#xff1a;<\/p>\n<li>\u6700\u4f73\u53c2\u6570\u7ec4\u5408&#xff1a;grid_search.best_params_<\/li>\n<li>\u6700\u4f73\u6a21\u578b&#xff1a;grid_search.best_estimator_<\/li>\n<li>\u6700\u4f73\u4ea4\u53c9\u9a8c\u8bc1\u5206\u6570&#xff1a;grid_search.best_score_<\/li>\n<li>\u6240\u6709\u53c2\u6570\u7ec4\u5408\u7684\u7ed3\u679c&#xff1a;grid_search.cv_results_<\/li>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> GridSearchCV<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>neighbors <span class=\"token keyword\">import<\/span> KNeighborsClassifier<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<\/p>\n<p>iris <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx<span class=\"token punctuation\">,<\/span>y <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>knn <span class=\"token operator\">&#061;<\/span> KNeighborsClassifier<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> GridSearchCV<span class=\"token punctuation\">(<\/span>knn<span class=\"token punctuation\">,<\/span>param_grid<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">{<\/span><span class=\"token string\">&#039;n_neighbors&#039;<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span>cv <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u67e5\u770b\u7ed3\u679c<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6700\u4f73\u53c2\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span>model<span class=\"token punctuation\">.<\/span>best_params_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6700\u4f73\u7ed3\u679c:&#034;<\/span><span class=\"token punctuation\">,<\/span>model<span class=\"token punctuation\">.<\/span>best_score_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6700\u4f73\u6a21\u578b:&#034;<\/span><span class=\"token punctuation\">,<\/span>model<span class=\"token punctuation\">.<\/span>best_estimator_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># print(&#034;\u4ea4\u53c9\u9a8c\u8bc1\u7ed3\u679c:&#034;,model.cv_results_)<\/span><\/p>\n<p><span class=\"token comment\">#model\u672c\u8eab\u662f\u4e2a\u6a21\u578b<\/span><br \/>\n<span class=\"token comment\"># \u4f7f\u7528\u6a21\u578b<\/span><br \/>\ny_predict <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">5.1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3.5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1.4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u9884\u6d4b\u7ed3\u679c\u4e3a:&#034;<\/span><span class=\"token punctuation\">,<\/span>y_predict<span class=\"token punctuation\">,<\/span>iris<span class=\"token punctuation\">.<\/span>target_names<span class=\"token punctuation\">[<\/span>y_predict<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u6700\u4f73\u53c2\u6570: {&#039;n_neighbors&#039;: 6}<br \/>\n\u6700\u4f73\u7ed3\u679c: 0.9800000000000001<br \/>\n\u6700\u4f73\u6a21\u578b: KNeighborsClassifier(n_neighbors&#061;6)<br \/>\n\u9884\u6d4b\u7ed3\u679c\u4e3a: [0] [&#039;setosa&#039;]<\/p>\n<h2>\u6734\u7d20\u8d1d\u53f6\u65af\u7b97\u6cd5<\/h2>\n<h3>1.\u6761\u4ef6\u6982\u7387<\/h3>\n<p>\u6761\u4ef6\u6982\u7387\u662f\u6982\u7387\u8bba\u4e2d\u7684\u6838\u5fc3\u6982\u5ff5&#xff0c;\u7528\u4e8e\u63cf\u8ff0\u5728\u5df2\u77e5\u67d0\u4e00\u4e8b\u4ef6\u53d1\u751f\u7684\u60c5\u51b5\u4e0b&#xff0c;\u53e6\u4e00\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151237-688a3665f1e2c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8bbe A \u548c B \u662f\u6837\u672c\u7a7a\u95f4\u03a9\u4e2d\u7684\u4e24\u4e2a\u4e8b\u4ef6&#xff0c;\u4e14 (P(B) &gt; 0)&#xff0c;\u5219\u5728\u4e8b\u4ef6 B \u53d1\u751f\u7684\u6761\u4ef6\u4e0b&#xff0c;\u4e8b\u4ef6 A \u53d1\u751f\u7684\u6761\u4ef6\u6982\u7387\u8bb0\u4e3a (P(A|B))&#xff0c;\u5b9a\u4e49\u4e3a&#xff1a;&#x1d443;(&#x1d434;|&#x1d435;)&#061;&#x1d443;(&#x1d434;\u2229&#x1d435;)\/&#x1d443;(&#x1d435;)<\/p>\n<p>&#x1d443;(&#x1d434;\u2229&#x1d435;)&#061;&#x1d443;(&#x1d434;|&#x1d435;)&#x1d443;(&#x1d435;)<\/p>\n<p>&#x1d443;(&#x1d434;\u2229&#x1d435;)&#061;&#x1d443;(&#x1d435;|&#x1d434;)&#x1d443;(&#x1d434;)<\/p>\n<p>&#x1d443;(&#x1d434;|&#x1d435;)&#061;&#x1d443;(B|A)&#x1d443;(&#x1d434;)\/&#x1d443;(&#x1d435;)<\/p>\n<h3>2. \u5168\u6982\u7387\u516c\u5f0f<\/h3>\n<p>\u5047\u5b9a\u6837\u672c\u7a7a\u95f4S&#xff0c;\u662f\u4e24\u4e2a\u4e8b\u4ef6A\u4e0eA\u2019\u7684\u548c\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151238-688a36668cc78.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4e8b\u4ef6B\u53ef\u4ee5\u5212\u5206\u6210\u4e24\u4e2a\u90e8\u5206&#xff1a;&#x1d443;(&#x1d435;)&#061;&#x1d443;(&#x1d435;\u2229&#x1d434;)&#043;&#x1d443;(&#x1d435;\u2229&#x1d434;\u2032)<\/p>\n<p>\u56e0\u4e3a&#x1d443;(&#x1d435;\u2229&#x1d434;)&#061;&#x1d443;(&#x1d435;|&#x1d434;)&#x1d443;(&#x1d434;)<\/p>\n<p>\u6240\u4ee5&#x1d443;(&#x1d435;)&#061;&#x1d443;(&#x1d435;|&#x1d434;)&#x1d443;(&#x1d434;)&#043;&#x1d443;(&#x1d435;|&#x1d434;\u2032)&#x1d443;(&#x1d434;\u2032)<\/p>\n<p>\u5c06\u8fd9\u4e2a\u516c\u5f0f\u4ee3\u5165\u4e0a\u4e00\u8282\u7684\u6761\u4ef6\u6982\u7387\u516c\u5f0f&#xff0c;\u5c31\u5f97\u5230\u4e86\u6761\u4ef6\u6982\u7387\u7684\u53e6\u4e00\u79cd\u5199\u6cd5&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        \u2223<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          B<\/p>\n<p>          \u2223<\/p>\n<p>          A<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          A<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          B<\/p>\n<p>          \u2223<\/p>\n<p>          A<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          A<\/p>\n<p>          )<\/p>\n<p>          &#043;<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          B<\/p>\n<p>          \u2223<\/p>\n<p>           A<\/p>\n<p>           ,<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>           A<\/p>\n<p>           ,<\/p>\n<p>          )<\/p>\n<p>       P(A|B)&#061;\\\\frac{P(B|A)P(A)}{P(B|A)P(A)&#043;P(B|A^,)P(A^,)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.53em;vertical-align: -0.52em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3614em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mpunct mtight\">,<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3614em\"><span class=\"\" style=\"top: -2.786em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mpunct mtight\">,<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>3. \u8d1d\u53f6\u65af\u5b9a\u7406<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730151238-688a3666d3aa7.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u63cf\u8ff0\u4e86\u6761\u4ef6\u6982\u7387\u4e4b\u95f4\u7684\u5173\u7cfb \u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li>P(A)&#xff1a;\u201c\u5148\u9a8c\u6982\u7387\u201d&#xff0c;\u5373\u5728B\u4e8b\u4ef6\u53d1\u751f\u4e4b\u524d&#xff0c;\u6211\u4eec\u5bf9A\u4e8b\u4ef6\u6982\u7387\u7684\u4e00\u4e2a\u5224\u65ad\u3002<\/li>\n<li>P(A|B)&#xff1a;\u201c\u540e\u9a8c\u6982\u7387\u201d&#xff08;Posterior probability&#xff09;&#xff0c;\u5373\u5728B\u4e8b\u4ef6\u53d1\u751f\u4e4b\u540e&#xff0c;\u6211\u4eec\u5bf9A\u4e8b\u4ef6\u6982\u7387\u7684\u91cd\u65b0\u8bc4\u4f30\u3002<\/li>\n<li>P(B|A)\/P(B)&#xff1a;\u201c\u53ef\u80fd\u6027\u51fd\u6570\u201d&#xff0c;\u8fd9\u662f\u4e00\u4e2a\u8c03\u6574\u56e0\u5b50&#xff0c;\u4f7f\u5f97\u9884\u4f30\u6982\u7387\u66f4\u63a5\u8fd1\u771f\u5b9e\u6982\u7387\u3002<\/li>\n<li>\u540e\u9a8c\u6982\u7387\u3000&#xff1d;\u3000\u5148\u9a8c\u6982\u7387&#xff58;\u8c03\u6574\u56e0\u5b50<\/li>\n<\/ul>\n<h3>4 \u6734\u7d20\u8d1d\u53f6\u65af\u63a8\u65ad<\/h3>\n<p>\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u7684\u5173\u952e\u5047\u8bbe\u662f\u7279\u5f81\u4e4b\u95f4\u7684\u6761\u4ef6\u72ec\u7acb\u6027&#xff0c;\u5373\u7ed9\u5b9a\u7c7b\u522b a &#xff0c;\u7279\u5f81 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         i<\/p>\n<p>       x_i<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         j<\/p>\n<p>       x_j<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        i<\/p>\n<p>        \u2260<\/p>\n<p>        j<\/p>\n<p>       i \\\\neq j<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span> \u76f8\u4e92\u72ec\u7acb\u3002)<\/p>\n<p>\u56e0\u6b64&#xff0c;\u6211\u4eec\u53ef\u4ee5\u5c06\u8054\u5408\u6982\u7387 P(X|a) \u5206\u89e3\u4e3a\u5404\u4e2a\u7279\u5f81\u7684\u6982\u7387\u4e58\u79ef&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        X<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         1<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>         2<\/p>\n<p>        ,<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>         n<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         1<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         2<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         n<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       P(X|a) &#061; P(x_1, x_2, &#8230;, x_n|a) &#061; P(x_1|a)P(x_2|a)&#8230;P(x_n|a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">&#8230;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">&#8230;<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5c06\u8fd9\u4e2a\u6761\u4ef6\u72ec\u7acb\u6027\u5047\u8bbe\u5e94\u7528\u4e8e\u8d1d\u53f6\u65af\u516c\u5f0f&#xff0c;\u6211\u4eec\u5f97\u5230&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        a<\/p>\n<p>        \u2223<\/p>\n<p>        X<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           1<\/p>\n<p>          \u2223<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           2<\/p>\n<p>          \u2223<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          .<\/p>\n<p>          .<\/p>\n<p>          .<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           n<\/p>\n<p>          \u2223<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          X<\/p>\n<p>          )<\/p>\n<p>       P(a|X) &#061; \\\\frac{P(x_1|a)P(x_2|a)&#8230;P(x_n|a)P(a)}{P(X)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.53em;vertical-align: -0.52em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mtight\">&#8230;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>5. \u62c9\u666e\u62c9\u65af\u5e73\u6ed1<\/h3>\n<p>\u67d0\u4e9b\u4e8b\u4ef6\u6216\u7279\u5f81\u53ef\u80fd\u4ece\u672a\u51fa\u73b0\u8fc7&#xff0c;\u8fd9\u4f1a\u5bfc\u81f4\u5b83\u4eec\u7684\u6982\u7387\u88ab\u4f30\u8ba1\u4e3a\u96f6\u3002<\/p>\n<p>\u89e3\u51b3&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         i<\/p>\n<p>        \u2223<\/p>\n<p>        y<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>           N<\/p>\n<p>            y<\/p>\n<p>            ,<\/p>\n<p>             x<\/p>\n<p>             i<\/p>\n<p>          &#043;<\/p>\n<p>          \u03b1<\/p>\n<p>           N<\/p>\n<p>           y<\/p>\n<p>          &#043;<\/p>\n<p>          \u03b1<\/p>\n<p>          n<\/p>\n<p>       P(x_i|y) &#061; \\\\frac{N_{y,x_i} &#043; \\\\alpha}{N_y &#043; \\\\alpha n}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.5881em;vertical-align: -0.5423em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0458em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.109em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2819em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.5675em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.109em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3448em;margin-left: 0em;margin-right: 0.1em\"><span class=\"pstrut\" style=\"height: 2.6595em\"><\/span><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3147em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3678em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5423em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u03b1<\/p>\n<p>        \\\\alpha<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u5e73\u6ed1\u7cfb\u6570&#xff08;\u901a\u5e38\u4e3a1&#xff09;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         n<\/p>\n<p>        n<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u7279\u5f81\u53d6\u503c\u6570<\/li>\n<\/ul>\n<p>sklearn.naive_bayes.MultinomialNB() estimator.fit(x_train, y_train) y_predict &#061; estimator.predict(x_test)<\/p>\n<p>\u3010\u8d1d\u53f6\u65af\u5bf9\u9e22\u5c3e\u82b1\u7684\u5206\u7c7b\u3011<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>naive_bayes <span class=\"token keyword\">import<\/span> MultinomialNB<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\niris <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx<span class=\"token punctuation\">,<\/span>y <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>x_train<span class=\"token punctuation\">,<\/span>x_test<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">,<\/span>test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> MultinomialNB<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\">#\u8bad\u7ec3&#xff1a;\u7edf\u8ba1\u5148\u9a8c\u6982\u7387<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">)<\/span><br \/>\nscore <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>score<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">,<\/span>y_test<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u51c6\u786e\u7387:&#034;<\/span><span class=\"token punctuation\">,<\/span>score<span class=\"token punctuation\">)<\/span><\/p>\n<p>x_new <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">5.1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3.5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1.4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n         <span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><br \/>\ny_new <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>x_new<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u9884\u6d4b\u7ed3\u679c\u4e3a:&#034;<\/span><span class=\"token punctuation\">,<\/span>y_new<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u9884\u6d4b\u7ed3\u679c\u4e3a:&#034;<\/span><span class=\"token punctuation\">,<\/span>model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>x_new<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>iris<span class=\"token punctuation\">.<\/span>target_names<span class=\"token punctuation\">[<\/span>y_new<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u51c6\u786e\u7387: 0.6666666666666666<br \/>\n\u9884\u6d4b\u7ed3\u679c\u4e3a: [0 2]<br \/>\n\u9884\u6d4b\u7ed3\u679c\u4e3a: [0 2]<br \/>\n[&#039;setosa&#039; &#039;virginica&#039;]<\/p>\n<p>\u3010\u8d1d\u53f6\u65af\u5bf9\u8461\u8404\u9152\u7684\u5206\u7c7b\u3011<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_wine<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>preprocessing <span class=\"token keyword\">import<\/span> MinMaxScaler<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>naive_bayes <span class=\"token keyword\">import<\/span> MultinomialNB<\/p>\n<p><span class=\"token comment\"># \u52a0\u8f7d\u6570\u636e\u96c6<\/span><br \/>\nwine <span class=\"token operator\">&#061;<\/span> load_wine<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx<span class=\"token punctuation\">,<\/span>y <span class=\"token operator\">&#061;<\/span> load_wine<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u65e0\u91cf\u7eb2\u5316\u5904\u7406&#8211;\u591a\u9879\u5f0f\u6734\u7d20\u8d1d\u53f6\u65af\u8981\u6c42\u8f93\u5165\u7279\u5f81\u975e\u8d1f<\/span><br \/>\ntransfer <span class=\"token operator\">&#061;<\/span> MinMaxScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx<span class=\"token operator\">&#061;<\/span>transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6570\u636e\u96c6\u7684\u5212\u5206<\/span><br \/>\nx_train<span class=\"token punctuation\">,<\/span>x_test<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span>  train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">,<\/span>test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u6a21\u578b<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> MultinomialNB<span class=\"token punctuation\">(<\/span>alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6a21\u578b\u8bad\u7ec3<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6a21\u578b\u8bc4\u4f30<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u51c6\u786e\u7387:&#034;<\/span><span class=\"token punctuation\">,<\/span>model<span class=\"token punctuation\">.<\/span>score<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">,<\/span>y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny_predict <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>y_predict<span class=\"token punctuation\">)<\/span><\/p>\n<p>\u51c6\u786e\u7387: 0.8888888888888888<br \/>\n[1 2 2 2 0 1 0 1 1 1 1 1 0 0 1 0 0 0 2 2 1 1 2 1 1 2 1 1 2 2 0 0 0 1 0 2]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb389\u6b21\uff0c\u70b9\u8d5e6\u6b21\uff0c\u6536\u85cf10\u6b21\u3002\u7279\u5f81\u964d\u7ef4\u4e0eKNN\u7b97\u6cd5\u6982\u8ff0 \u7279\u5f81\u964d\u7ef4\u662f\u901a\u8fc7\u51cf\u5c11\u7279\u5f81\u6570\u91cf\u6765\u4f18\u5316\u6570\u636e\u7684\u6280\u672f\uff0c\u4e3b\u8981\u5305\u62ec\u7279\u5f81\u9009\u62e9\uff08\u5982\u4f4e\u65b9\u5dee\u8fc7\u6ee4\u3001\u76f8\u5173\u7cfb\u6570\u5206\u6790\uff09\u548c\u7279\u5f81\u63d0\u53d6\uff08\u5982PCA\uff09\u3002\u5b83\u80fd\u964d\u4f4e\u8ba1\u7b97\u590d\u6742\u5ea6\u3001\u51cf\u5c11\u8fc7\u62df\u5408\u98ce\u9669\u3001\u4fbf\u4e8e\u6570\u636e\u53ef\u89c6\u5316\u3002KNN\u7b97\u6cd5\u5219\u4f9d\u8d56\u8ddd\u79bb\u5ea6\u91cf\uff08\u5982\u6b27\u6c0f\u8ddd\u79bb\u3001\u66fc\u54c8\u987f\u8ddd\u79bb\uff09\u8fdb\u884c\u5206\u7c7b\uff0c\u5176\u6027\u80fd\u53d7\u7279\u5f81\u7ef4\u5ea6\u5f71\u54cd\u663e\u8457\u3002\u4e24\u8005\u7ed3\u5408\u53ef\u63d0\u5347KNN\u5728\u9ad8\u7ef4\u6570\u636e\u4e2d\u7684\u6548\u7387\u548c\u51c6\u786e\u6027\u3002 \uff08\u5b57\u6570\uff1a148\uff09<\/p>\n","protected":false},"author":2,"featured_media":50358,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[81,3676,50,207,4909,427],"topic":[],"class_list":["post-50367","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-python","tag-sklearn","tag-50","tag-207","tag-4909","tag-427"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>02 \u57fa\u4e8esklearn\u7684\u673a\u68b0\u5b66\u4e60-\u7279\u5f81\u964d\u7ef4\uff08\u7279\u5f81\u9009\u62e9\u3001PCA\uff09\u3001KNN\u7b97\u6cd5\u3001\u6a21\u578b\u9009\u62e9\u4e0e\u8c03\u4f18\uff08\u4ea4\u53c9\u9a8c\u8bc1\u3001\u6734\u7d20\u8d1d\u53f6\u65af\u7b97\u6cd5\u3001\u62c9\u666e\u62c9\u65af\u5e73\u6ed1\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta 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