{"id":68476,"date":"2026-01-30T06:33:07","date_gmt":"2026-01-29T22:33:07","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/68476.html"},"modified":"2026-01-30T06:33:07","modified_gmt":"2026-01-29T22:33:07","slug":"%e4%b8%87%e5%ad%97%e9%95%bf%e6%96%87%ef%bc%81%e6%90%9e%e6%87%82%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e4%b8%ad%e7%9a%84%e5%88%86%e7%b1%bb%e5%9b%9e%e5%bd%92%e8%81%9a%e7%b1%bb%e4%bb%bb%e5%8a%a1%e9%83%bd","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/68476.html","title":{"rendered":"\u4e07\u5b57\u957f\u6587\uff01\u641e\u61c2\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u5206\u7c7b|\u56de\u5f52|\u805a\u7c7b\u4efb\u52a1\u90fd\u6709\u54ea\u4e9b\u5e38\u7528\u7684\u8bc4\u4f30\u6307\u6807\uff01"},"content":{"rendered":"<p>\u63a8\u8350\u76f4\u63a5\u7f51\u7ad9\u5728\u7ebf\u9605\u8bfb&#xff1a;https:\/\/aicoting.cn<\/p>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u4e2d&#xff0c;\u8bc4\u4f30\u6307\u6807\u7528\u4e8e\u91cf\u5316\u6a21\u578b\u5728\u4e0d\u540c\u4efb\u52a1\u4e0a\u7684\u6027\u80fd&#xff0c;\u662f\u6a21\u578b\u9009\u62e9\u4e0e\u8c03\u4f18\u7684\u91cd\u8981\u4f9d\u636e\u3002\u4e0d\u540c\u7c7b\u578b\u7684\u4efb\u52a1\u5bf9\u5e94\u4e0d\u540c\u7684\u6307\u6807&#xff1a;\u5206\u7c7b\u4efb\u52a1\u5e38\u7528\u51c6\u786e\u7387\u3001\u7cbe\u786e\u7387\u3001\u53ec\u56de\u7387\u3001F1 \u503c\u4ee5\u53ca ROC-AUC \u7b49&#xff0c;\u7528\u4e8e\u8861\u91cf\u6a21\u578b\u5bf9\u4e0d\u540c\u7c7b\u522b\u7684\u8bc6\u522b\u80fd\u529b&#xff1b;\u56de\u5f52\u4efb\u52a1\u5e38\u7528\u5747\u65b9\u8bef\u5dee&#xff08;MSE&#xff09;\u3001\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee&#xff08;MAE&#xff09;\u548c\u51b3\u5b9a\u7cfb\u6570&#xff08;R\u00b2&#xff09;\u6765\u8bc4\u4ef7\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u7684\u504f\u5dee&#xff1b;\u805a\u7c7b\u4efb\u52a1\u5219\u53ef\u91c7\u7528\u8f6e\u5ed3\u7cfb\u6570\u3001\u5f52\u4e00\u5316\u4e92\u4fe1\u606f&#xff08;NMI&#xff09;\u548c\u8c03\u6574\u5170\u5fb7\u6307\u6570&#xff08;ARI&#xff09;\u6765\u8861\u91cf\u805a\u7c7b\u7ed3\u679c\u7684\u7d27\u5bc6\u6027\u548c\u4e00\u81f4\u6027\u3002\u901a\u8fc7\u5408\u7406\u9009\u62e9\u548c\u7efc\u5408\u4f7f\u7528\u8fd9\u4e9b\u8bc4\u4f30\u6307\u6807&#xff0c;\u53ef\u4ee5\u5168\u9762\u53cd\u6620\u6a21\u578b\u6027\u80fd&#xff0c;\u6307\u5bfc\u6a21\u578b\u4f18\u5316\u548c\u5e94\u7528\u3002<\/p>\n<h3>\u5206\u7c7b<\/h3>\n<p>\u5728\u5206\u7c7b\u4efb\u52a1\u4e2d&#xff0c;\u6a21\u578b\u7684\u76ee\u6807\u662f\u5c06\u6837\u672c\u6b63\u786e\u5730\u5212\u5206\u5230\u9884\u5b9a\u4e49\u7c7b\u522b\u3002\u4e3a\u4e86\u5168\u9762\u8bc4\u4f30\u6a21\u578b\u6027\u80fd&#xff0c;\u7814\u7a76\u8005\u901a\u5e38\u4f7f\u7528\u4e00\u7cfb\u5217\u5206\u7c7b\u8bc4\u4f30\u6307\u6807\u3002\u4e0d\u540c\u6307\u6807\u5173\u6ce8\u7684\u65b9\u9762\u4e0d\u540c&#xff0c;\u5408\u7406\u9009\u62e9\u6307\u6807\u53ef\u4ee5\u5e2e\u52a9\u53d1\u73b0\u6a21\u578b\u7684\u4f18\u52bf\u4e0e\u4e0d\u8db3&#xff0c;\u5e76\u6307\u5bfc\u6a21\u578b\u8c03\u4f18\u3002<\/p>\n<h4>\u6df7\u6dc6\u77e9\u9635&#xff08;Confusion Matrix&#xff09;<\/h4>\n<p>\u6df7\u6dc6\u77e9\u9635\u662f\u5206\u7c7b\u6a21\u578b\u8bc4\u4f30\u7684\u57fa\u7840\u5de5\u5177&#xff0c;\u5b83\u4ee5\u8868\u683c\u5f62\u5f0f\u5c55\u793a\u6a21\u578b\u9884\u6d4b\u7ed3\u679c\u4e0e\u771f\u5b9e\u6807\u7b7e\u7684\u5bf9\u5e94\u5173\u7cfb\u3002\u5bf9\u4e8e\u4e8c\u5206\u7c7b\u95ee\u9898&#xff0c;\u77e9\u9635\u901a\u5e38\u5305\u542b\u56db\u4e2a\u5143\u7d20&#xff1a;<\/p>\n<ul>\n<li>TP&#xff08;True Positive&#xff09;&#xff1a;\u771f\u5b9e\u4e3a\u6b63\u4f8b&#xff0c;\u9884\u6d4b\u4e3a\u6b63\u4f8b\u7684\u6837\u672c\u6570\u3002<\/li>\n<li>TN&#xff08;True Negative&#xff09;&#xff1a;\u771f\u5b9e\u4e3a\u8d1f\u4f8b&#xff0c;\u9884\u6d4b\u4e3a\u8d1f\u4f8b\u7684\u6837\u672c\u6570\u3002<\/li>\n<li>FP&#xff08;False Positive&#xff09;&#xff1a;\u771f\u5b9e\u4e3a\u8d1f\u4f8b&#xff0c;\u9884\u6d4b\u4e3a\u6b63\u4f8b\u7684\u6837\u672c\u6570\u3002<\/li>\n<li>FN&#xff08;False Negative&#xff09;&#xff1a;\u771f\u5b9e\u4e3a\u6b63\u4f8b&#xff0c;\u9884\u6d4b\u4e3a\u8d1f\u4f8b\u7684\u6837\u672c\u6570\u3002<\/li>\n<\/ul>\n<p>\u6df7\u6dc6\u77e9\u9635\u4e0d\u4ec5\u80fd\u591f\u76f4\u89c2\u5c55\u793a\u5206\u7c7b\u9519\u8bef\u7c7b\u578b&#xff0c;\u8fd8\u4e3a\u540e\u7eed\u6307\u6807\u8ba1\u7b97\u63d0\u4f9b\u57fa\u7840\u3002<\/p>\n<h4>\u51c6\u786e\u7387&#xff08;Accuracy&#xff09;<\/h4>\n<p>\u51c6\u786e\u7387\u662f\u6a21\u578b\u6b63\u786e\u9884\u6d4b\u6837\u672c\u7684\u6bd4\u4f8b\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         Accuracy <\/p>\n<p>         &#061; <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           T <\/p>\n<p>           N <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           T <\/p>\n<p>           N <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           N <\/p>\n<p>        \\\\text{Accuracy} &#061; \\\\frac{TP &#043; TN}{TP &#043; TN &#043; FP &#043; FN} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord text\"><span class=\"mord\">Accuracy<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">TN<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">FP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">FN<\/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: -3.394em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">TN<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u4e2a\u5f88\u76f4\u89c2&#xff0c;\u5c31\u662f\u522b\u7ba1\u6211\u9884\u6d4b\u8d1f\u6837\u672c\u5bf9\u4e86&#xff0c;\u8fd8\u662f\u9884\u6d4b\u6b63\u6837\u672c\u5bf9\u4e86&#xff0c;\u90fd\u7b97\u8fdb\u6765&#xff0c;\u7b97\u7684\u5c31\u662f\u9884\u6d4b\u5bf9\u7684\u6837\u672c\u5360\u603b\u6837\u672c\u7684\u6bd4\u4f8b&#xff0c;\u4f46\u662f\u5bf9\u4e8e\u7c7b\u522b\u4e0d\u5e73\u8861\u7684\u6570\u636e&#xff0c;\u51c6\u786e\u7387\u53ef\u80fd\u5177\u6709\u8bef\u5bfc\u6027\u3002\u4f8b\u5982\u5728\u6b63\u8d1f\u6837\u672c\u6bd4\u4f8b\u4e25\u91cd\u4e0d\u5e73\u8861\u65f6&#xff0c;\u6a21\u578b\u5373\u4f7f\u603b\u662f\u9884\u6d4b\u591a\u6570\u7c7b\u4e5f\u80fd\u83b7\u5f97\u9ad8\u51c6\u786e\u7387\u3002<\/p>\n<h4>\u7cbe\u786e\u7387&#xff08;Precision&#xff09;<\/h4>\n<p>\u7cbe\u786e\u7387\u7684\u5b9a\u4e49\u662f\u5728\u6240\u6709\u88ab\u6a21\u578b\u9884\u6d4b\u4e3a\u6b63\u4f8b\u7684\u6837\u672c\u4e2d&#xff0c;\u5b9e\u9645\u4e3a\u6b63\u4f8b\u7684\u6bd4\u4f8b\u3002 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         Precision <\/p>\n<p>         &#061; <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           P <\/p>\n<p>        \\\\text{Precision} &#061; \\\\frac{TP}{TP &#043; FP} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Precision<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">FP<\/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: -3.394em\"><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\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7cbe\u786e\u7387\u5173\u6ce8\u6a21\u578b\u9884\u6d4b\u4e3a\u6b63\u7c7b\u7684\u6837\u672c\u4e2d&#xff0c;\u5b9e\u9645\u4e3a\u6b63\u7c7b\u7684\u6bd4\u4f8b&#xff0c;\u662f\u5bf9\u6a21\u578b\u201c\u731c\u5bf9\u201d\u6b63\u7c7b\u7684\u80fd\u529b\u7684\u8861\u91cf\u3002<\/p>\n<h4>\u53ec\u56de\u7387&#xff08;Recall&#xff09;\u6216\u654f\u611f\u5ea6&#xff08;Sensitivity&#xff09;<\/h4>\n<p>\u53ec\u56de\u7387\u662f\u5728\u6240\u6709\u771f\u5b9e\u6b63\u4f8b\u4e2d&#xff0c;\u88ab\u6a21\u578b\u6b63\u786e\u9884\u6d4b\u4e3a\u6b63\u4f8b\u7684\u6bd4\u4f8b\u3002 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         Recall <\/p>\n<p>         &#061; <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           N <\/p>\n<p>        \\\\text{Recall} &#061; \\\\frac{TP}{TP &#043; FN} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">Recall<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">FN<\/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: -3.394em\"><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\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u53ec\u56de\u7387\u7528\u4e8e\u8861\u91cf\u6a21\u578b\u5bf9\u6b63\u7c7b\u6837\u672c\u7684\u8986\u76d6\u80fd\u529b&#xff0c;\u9ad8\u53ec\u56de\u7387\u610f\u5473\u7740\u6f0f\u62a5\u5c11&#xff0c;\u6bd4\u5982\u75be\u75c5\u7b5b\u67e5\u4e2d&#xff0c;\u5c3d\u91cf\u4fdd\u8bc1\u75c5\u4eba\u88ab\u6b63\u786e\u8bc6\u522b&#xff0c;\u5373\u4f7f\u53ef\u80fd\u51fa\u73b0\u5c11\u91cf\u8bef\u62a5\u3002<\/p>\n<h4>F1 \u503c&#xff08;F1 Score&#xff09;<\/h4>\n<p>F1 \u503c\u662f\u7cbe\u786e\u7387\u548c\u53ec\u56de\u7387\u7684\u8c03\u548c\u5e73\u5747\u6570&#xff0c;\u7528\u4e8e\u7efc\u5408\u8861\u91cf\u6a21\u578b\u5728\u7cbe\u786e\u6027\u548c\u53ec\u56de\u6027\u4e0a\u7684\u8868\u73b0\u3002 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         F1 <\/p>\n<p>         &#061; <\/p>\n<p>         2 <\/p>\n<p>         \u22c5 <\/p>\n<p>           Precision <\/p>\n<p>           \u22c5 <\/p>\n<p>           Recall <\/p>\n<p>           Precision <\/p>\n<p>           &#043; <\/p>\n<p>           Recall <\/p>\n<p>        \\\\text{F1} &#061; 2 \\\\cdot \\\\frac{\\\\text{Precision} \\\\cdot \\\\text{Recall}}{\\\\text{Precision} &#043; \\\\text{Recall}} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">F1<\/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: 0.6444em\"><\/span><span class=\"mord\">2<\/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><span class=\"base\"><span class=\"strut\" style=\"height: 1.2834em;vertical-align: -0.4033em\"><\/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: 0.8801em\"><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 text mtight\"><span class=\"mord mtight\">Precision<\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord text mtight\"><span class=\"mord mtight\">Recall<\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Precision<\/span><\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord text mtight\"><span class=\"mord mtight\">Recall<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5f53\u7cbe\u786e\u7387\u548c\u53ec\u56de\u7387\u4e0d\u5747\u8861\u65f6&#xff0c;F1 \u503c\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7efc\u5408\u6307\u6807&#xff0c;\u66f4\u9002\u5408\u7c7b\u522b\u4e0d\u5e73\u8861\u95ee\u9898\u3002<\/p>\n<p>\u5288\u91cc\u556a\u5566\u8bf4\u4e86\u4e00\u5927\u5806&#xff0c;\u662f\u4e0d\u662f\u4e0d\u592a\u597d\u7406\u89e3&#xff0c;\u73b0\u5728\u6211\u4eec\u8fd8\u662f\u7528\u9e22\u5c3e\u82b1\u5206\u7c7b\u4e3e\u4e00\u4e2a\u4f8b\u5b50&#xff1a; \u6211\u4eec\u5047\u8bbe\u505a\u4e00\u4e2a\u4e8c\u5206\u7c7b\u4efb\u52a1&#xff1a;\u5c06 Iris-versicolor \u89c6\u4e3a\u6b63\u7c7b&#xff08;1&#xff09;&#xff0c;\u5176\u5b83\u4e24\u7c7b\u89c6\u4e3a\u8d1f\u7c7b&#xff08;0&#xff09;\u3002<\/p>\n<table>\n<tr>\u6837\u672c\u771f\u5b9e\u7c7b\u522b\u6a21\u578b\u9884\u6d4b<\/tr>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6839\u636e\u4e0a\u8868&#xff0c;\u8ba1\u7b97 TP\u3001TN\u3001FP\u3001FN&#xff1a;<\/p>\n<ul>\n<li>TP&#xff08;True Positive&#xff09; &#061; 2 &#xff08;\u9884\u6d4b\u4e3a 1&#xff0c;\u771f\u5b9e\u4e3a 1&#xff09;<\/li>\n<li>TN&#xff08;True Negative&#xff09; &#061; 2 &#xff08;\u9884\u6d4b\u4e3a 0&#xff0c;\u771f\u5b9e\u4e3a 0&#xff09;<\/li>\n<li>FP&#xff08;False Positive&#xff09; &#061; 1 &#xff08;\u9884\u6d4b\u4e3a 1&#xff0c;\u771f\u5b9e\u4e3a 0&#xff09;<\/li>\n<li>FN&#xff08;False Negative&#xff09; &#061; 1 &#xff08;\u9884\u6d4b\u4e3a 0&#xff0c;\u771f\u5b9e\u4e3a 1&#xff09;<\/li>\n<\/ul>\n<p>\u8bf4\u4eba\u8bdd&#xff0c;\u4e5f\u5c31\u662f&#xff1a;<\/p>\n<ul>\n<li>TP&#xff1a;\u6a21\u578b\u6210\u529f\u6293\u5230\u6b63\u7c7b&#xff0c;\u6bd4\u5982\u6b63\u786e\u8bc6\u522b\u51fa\u4e00\u6735 Iris-versicolor\u3002<\/li>\n<li>FP&#xff1a;\u6a21\u578b\u201c\u8bef\u6293\u201d&#xff0c;\u628a\u5176\u4ed6\u79cd\u7c7b\u8bef\u8ba4\u4e3a Iris-versicolor\u3002<\/li>\n<li>FN&#xff1a;\u6a21\u578b\u201c\u6f0f\u6293\u201d&#xff0c;\u628a\u6b63\u7c7b\u5f53\u6210\u4e86\u8d1f\u7c7b\u3002<\/li>\n<li>TN&#xff1a;\u6a21\u578b\u6b63\u786e\u62d2\u7edd&#xff0c;\u8d1f\u7c7b\u9884\u6d4b\u4e3a\u8d1f\u7c7b\u3002<\/li>\n<\/ul>\n<p>\u6df7\u6dc6\u77e9\u9635\u5982\u4e0b&#xff1a;<\/p>\n<table>\n<tr>\u9884\u6d4b 0\u9884\u6d4b 1<\/tr>\n<tbody>\n<tr>\n<td>\u771f\u5b9e 0<\/td>\n<td>TN &#061; 2<\/td>\n<td>FP &#061; 1<\/td>\n<\/tr>\n<tr>\n<td>\u771f\u5b9e 1<\/td>\n<td>FN &#061; 1<\/td>\n<td>TP &#061; 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u51c6\u786e\u7387<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         Accuracy <\/p>\n<p>         &#061; <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           T <\/p>\n<p>           N <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           T <\/p>\n<p>           N <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           N <\/p>\n<p>         &#061; <\/p>\n<p>           2 <\/p>\n<p>           &#043; <\/p>\n<p>           2 <\/p>\n<p>           2 <\/p>\n<p>           &#043; <\/p>\n<p>           2 <\/p>\n<p>           &#043; <\/p>\n<p>           1 <\/p>\n<p>           &#043; <\/p>\n<p>           1 <\/p>\n<p>         &#061; <\/p>\n<p>         0.6667 <\/p>\n<p>        \\\\text{Accuracy} &#061; \\\\frac{TP &#043; TN}{TP &#043; TN &#043; FP &#043; FN} &#061; \\\\frac{2&#043;2}{2&#043;2&#043;1&#043;1} &#061; 0.6667 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord text\"><span class=\"mord\">Accuracy<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">TN<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">FP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">FN<\/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: -3.394em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">TN<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><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: 1.2484em;vertical-align: -0.4033em\"><\/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: 0.8451em\"><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\">2<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">2<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><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: 0.6444em\"><\/span><span class=\"mord\">0.6667<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6a21\u578b\u603b\u4f53\u6b63\u786e\u7387\u7ea6 66.7%\u3002<\/p>\n<p>\u7cbe\u786e\u7387<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         Precision <\/p>\n<p>         &#061; <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           P <\/p>\n<p>         &#061; <\/p>\n<p>          2 <\/p>\n<p>           2 <\/p>\n<p>           &#043; <\/p>\n<p>           1 <\/p>\n<p>         &#061; <\/p>\n<p>         0.6667 <\/p>\n<p>        \\\\text{Precision} &#061; \\\\frac{TP}{TP &#043; FP} &#061; \\\\frac{2}{2&#043;1} &#061; 0.6667 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Precision<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">FP<\/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: -3.394em\"><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\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><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: 1.2484em;vertical-align: -0.4033em\"><\/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: 0.8451em\"><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\">2<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><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: 0.6444em\"><\/span><span class=\"mord\">0.6667<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4e5f\u5c31\u662f\u5728\u6a21\u578b\u9884\u6d4b\u4e3a Iris-versicolor \u7684\u6837\u672c\u4e2d&#xff0c;\u6709 2\u20443 \u662f\u6b63\u786e\u7684\u3002<\/p>\n<p>\u53ec\u56de\u7387<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         Recall <\/p>\n<p>         &#061; <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           N <\/p>\n<p>         &#061; <\/p>\n<p>          2 <\/p>\n<p>           2 <\/p>\n<p>           &#043; <\/p>\n<p>           1 <\/p>\n<p>         &#061; <\/p>\n<p>         0.6667 <\/p>\n<p>        \\\\text{Recall} &#061; \\\\frac{TP}{TP &#043; FN} &#061; \\\\frac{2}{2&#043;1} &#061; 0.6667 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">Recall<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">FN<\/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: -3.394em\"><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\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><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: 1.2484em;vertical-align: -0.4033em\"><\/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: 0.8451em\"><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\">2<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><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: 0.6444em\"><\/span><span class=\"mord\">0.6667<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6a21\u578b\u627e\u51fa\u4e86 2\u20443 \u7684\u771f\u5b9e Iris-versicolor \u6837\u672c&#xff0c;\u8fd8\u6709 1 \u4e2a\u6f0f\u6389\u3002<\/p>\n<p>F1 \u503c<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         F1 <\/p>\n<p>         &#061; <\/p>\n<p>         2 <\/p>\n<p>         \u22c5 <\/p>\n<p>           Precision <\/p>\n<p>           \u22c5 <\/p>\n<p>           Recall <\/p>\n<p>           Precision <\/p>\n<p>           &#043; <\/p>\n<p>           Recall <\/p>\n<p>         &#061; <\/p>\n<p>         0.6667 <\/p>\n<p>        \\\\text{F1} &#061; 2 \\\\cdot \\\\frac{\\\\text{Precision} \\\\cdot \\\\text{Recall}}{\\\\text{Precision} &#043; \\\\text{Recall}} &#061; 0.6667 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">F1<\/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: 0.6444em\"><\/span><span class=\"mord\">2<\/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><span class=\"base\"><span class=\"strut\" style=\"height: 1.2834em;vertical-align: -0.4033em\"><\/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: 0.8801em\"><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 text mtight\"><span class=\"mord mtight\">Precision<\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord text mtight\"><span class=\"mord mtight\">Recall<\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Precision<\/span><\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord text mtight\"><span class=\"mord mtight\">Recall<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><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: 0.6444em\"><\/span><span class=\"mord\">0.6667<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>F1 \u503c\u7efc\u5408\u8003\u8651\u4e86\u7cbe\u786e\u7387\u548c\u53ec\u56de\u7387&#xff0c;\u7528\u4e00\u4e2a\u6570\u8861\u91cf\u6a21\u578b\u6574\u4f53\u6027\u80fd\u3002<\/p>\n<p>\u901a\u8fc7\u6df7\u6dc6\u77e9\u9635\u548c\u8fd9\u4e9b\u6307\u6807&#xff0c;\u4f60\u53ef\u4ee5\u76f4\u89c2\u5730\u770b\u5230\u6a21\u578b\u5728\u54ea\u4e9b\u6837\u672c\u4e0a\u8868\u73b0\u597d&#xff0c;\u54ea\u4e9b\u6837\u672c\u5bb9\u6613\u51fa\u9519&#xff0c;\u4ece\u800c\u51b3\u5b9a\u662f\u5426\u9700\u8981\u8c03\u53c2\u6216\u6539\u8fdb\u7279\u5f81\u3002<\/p>\n<h4>ROC \u66f2\u7ebf\u4e0e AUC<\/h4>\n<ul>\n<li>ROC \u66f2\u7ebf&#xff08;Receiver Operating Characteristic&#xff09;&#xff1a;\u6a2a\u8f74\u4e3a\u5047\u9633\u6027\u7387&#xff08;FPR&#xff09;&#xff0c;\u7eb5\u8f74\u4e3a\u771f\u6b63\u7387&#xff08;TPR&#xff09;&#xff0c;\u5c55\u793a\u5206\u7c7b\u5668\u5728\u4e0d\u540c\u9608\u503c\u4e0b\u7684\u6027\u80fd\u3002<\/li>\n<\/ul>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         FPR <\/p>\n<p>         &#061; <\/p>\n<p>           F <\/p>\n<p>           P <\/p>\n<p>           F <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           T <\/p>\n<p>           N <\/p>\n<p>         , <\/p>\n<p>         TPR <\/p>\n<p>         &#061; <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           &#043; <\/p>\n<p>           F <\/p>\n<p>           N <\/p>\n<p>        \\\\text{FPR} &#061; \\\\frac{FP}{FP &#043; TN}, \\\\quad \\\\text{TPR} &#061; \\\\frac{TP}{TP &#043; FN} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">FPR<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">FP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">TN<\/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: -3.394em\"><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\">FP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord text\"><span class=\"mord\">TPR<\/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: 1.2757em;vertical-align: -0.4033em\"><\/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: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">FN<\/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: -3.394em\"><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\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>AUC&#xff08;Area Under Curve&#xff09;&#xff1a;ROC \u66f2\u7ebf\u4e0b\u7684\u9762\u79ef&#xff0c;\u8303\u56f4\u5728 0.5&#xff08;\u968f\u673a\u731c\u6d4b&#xff09;\u5230 1&#xff08;\u5b8c\u7f8e\u5206\u7c7b&#xff09;\u4e4b\u95f4\u3002<\/li>\n<\/ul>\n<p>AUC \u53ef\u4ee5\u8861\u91cf\u5206\u7c7b\u5668\u5bf9\u6b63\u8d1f\u6837\u672c\u7684\u533a\u5206\u80fd\u529b&#xff0c;\u4e0d\u4f9d\u8d56\u7279\u5b9a\u9608\u503c&#xff0c;\u9002\u5408\u6a21\u578b\u6bd4\u8f83\u3002<\/p>\n<p>\u4e0b\u9762\u6211\u4eec\u4f7f\u7528 scikit-learn \u7ed8\u5236 ROC \u66f2\u7ebf\u5e76\u8ba1\u7b97 AUC&#xff0c;\u6211\u4eec\u4ee5 Iris \u6570\u636e\u96c6\u7684\u4e8c\u5206\u7c7b\u4efb\u52a1 \u4e3a\u4f8b&#xff0c;\u5c06 Iris-versicolor \u4f5c\u4e3a\u6b63\u7c7b\u3002<\/p>\n<p><span class=\"token comment\"># \u5bfc\u5165\u5fc5\u8981\u5e93<\/span><br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<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 \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>linear_model <span class=\"token keyword\">import<\/span> LogisticRegression<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> roc_curve<span class=\"token punctuation\">,<\/span> roc_auc_score<\/p>\n<p><span class=\"token comment\"># 1. \u52a0\u8f7d\u6570\u636e<\/span><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> <span class=\"token punctuation\">(<\/span>iris<span class=\"token punctuation\">.<\/span>target <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>astype<span class=\"token punctuation\">(<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># \u5c06 Iris-versicolor \u4f5c\u4e3a\u6b63\u7c7b<\/span><\/p>\n<p><span class=\"token comment\"># 2. \u5212\u5206\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6<\/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\">0.3<\/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><\/p>\n<p><span class=\"token comment\"># 3. \u8bad\u7ec3\u903b\u8f91\u56de\u5f52\u6a21\u578b<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> LogisticRegression<span class=\"token punctuation\">(<\/span>solver<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;liblinear&#039;<\/span><span class=\"token punctuation\">)<\/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\"># 4. \u83b7\u53d6\u9884\u6d4b\u6982\u7387&#xff08;\u6b63\u7c7b\u6982\u7387&#xff09;<\/span><br \/>\ny_prob <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>predict_proba<span class=\"token punctuation\">(<\/span>X_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><\/p>\n<p><span class=\"token comment\"># 5. \u8ba1\u7b97 ROC \u66f2\u7ebf<\/span><br \/>\nfpr<span class=\"token punctuation\">,<\/span> tpr<span class=\"token punctuation\">,<\/span> thresholds <span class=\"token operator\">&#061;<\/span> roc_curve<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_prob<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 6. \u8ba1\u7b97 AUC<\/span><br \/>\nauc_score <span class=\"token operator\">&#061;<\/span> roc_auc_score<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_prob<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;AUC &#061; <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>auc_score<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 7. \u53ef\u89c6\u5316 ROC \u66f2\u7ebf<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>figure<span class=\"token punctuation\">(<\/span>figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>fpr<span class=\"token punctuation\">,<\/span> tpr<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;blue&#039;<\/span><span class=\"token punctuation\">,<\/span> lw<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;ROC curve (AUC &#061; <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>auc_score<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">)&#039;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<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 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 punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;gray&#039;<\/span><span class=\"token punctuation\">,<\/span> linestyle<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;&#8211;&#039;<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;Random Guess&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlim<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylim<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.05<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;False Positive Rate&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;True Positive Rate&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;ROC Curve&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span>loc<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;lower right&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u5982\u4e0b\u56fe&#xff0c;ROC \u66f2\u7ebf\u5c55\u793a\u6a21\u578b\u5728\u4e0d\u540c\u9608\u503c\u4e0b\u7684\u5206\u7c7b\u80fd\u529b\u3002\u66f2\u7ebf\u8d8a\u9760\u8fd1\u5de6\u4e0a\u89d2&#xff0c;\u8bf4\u660e\u6a21\u578b\u8d8a\u597d\u3002AUC&#061;0.81 \u8868\u793a\u6a21\u578b\u533a\u5206\u6b63\u8d1f\u7c7b\u7684\u80fd\u529b\u8f83\u5f3a\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260129223305-697be0211977c.png\" alt=\"\u8bf7\u6dfb\u52a0\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>\u591a\u5206\u7c7b\u6307\u6807<\/h3>\n<p>\u5bf9\u4e8e\u591a\u5206\u7c7b\u4efb\u52a1&#xff0c;\u5e38\u7528\u65b9\u6cd5\u6709&#xff1a;<\/p>\n<ul>\n<li>\u5b8f\u5e73\u5747&#xff08;Macro Average&#xff09;&#xff1a;\u5bf9\u6bcf\u4e2a\u7c7b\u522b\u8ba1\u7b97\u6307\u6807&#xff0c;\u518d\u53d6\u5e73\u5747&#xff0c;\u5173\u6ce8\u6bcf\u4e2a\u7c7b\u522b\u7684\u91cd\u8981\u6027\u76f8\u540c\u3002<\/li>\n<li>\u5fae\u5e73\u5747&#xff08;Micro Average&#xff09;&#xff1a;\u5bf9\u6240\u6709\u6837\u672c\u7edf\u8ba1\u603b\u7684 TP\u3001FP\u3001FN&#xff0c;\u518d\u8ba1\u7b97\u6307\u6807&#xff0c;\u9002\u5408\u7c7b\u522b\u6837\u672c\u4e0d\u5747\u8861\u65f6\u4f7f\u7528\u3002<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u7c7b\u522b\u5747\u8861\u7684\u6570\u636e&#xff0c;\u51c6\u786e\u7387\u53ef\u4ee5\u4f5c\u4e3a\u4e3b\u8981\u6307\u6807\u3002\u5bf9\u4e8e\u7c7b\u522b\u4e0d\u5e73\u8861\u7684\u6570\u636e&#xff0c;\u5e94\u5173\u6ce8 \u7cbe\u786e\u7387\u3001\u53ec\u56de\u7387\u3001F1 \u503c&#xff0c;\u5fc5\u8981\u65f6\u4f7f\u7528 ROC-AUC\u3002<\/p>\n<p>\u5206\u7c7b\u8bc4\u4f30\u6307\u6807\u63d0\u4f9b\u4e86\u4ece\u4e0d\u540c\u89d2\u5ea6\u8861\u91cf\u6a21\u578b\u6027\u80fd\u7684\u5de5\u5177\u3002\u4ece\u6df7\u6dc6\u77e9\u9635\u5230\u7cbe\u786e\u7387\u3001\u53ec\u56de\u7387\u3001F1 \u503c&#xff0c;\u518d\u5230 ROC-AUC&#xff0c;\u591a\u7ef4\u5ea6\u8bc4\u4f30\u53ef\u4ee5\u5e2e\u52a9\u7814\u7a76\u8005\u7406\u89e3\u6a21\u578b\u4f18\u52bf\u4e0e\u4e0d\u8db3&#xff0c;\u4e3a\u6a21\u578b\u4f18\u5316\u3001\u8c03\u53c2\u548c\u9009\u62e9\u63d0\u4f9b\u4f9d\u636e\u3002\u5408\u7406\u7684\u6307\u6807\u9009\u62e9\u80fd\u591f\u786e\u4fdd\u6a21\u578b\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u65e2\u51c6\u786e\u53c8\u53ef\u9760\u3002<\/p>\n<h4>\u56de\u5f52<\/h4>\n<p>\u5728\u56de\u5f52\u4efb\u52a1\u4e2d&#xff0c;\u6a21\u578b\u7684\u76ee\u6807\u662f\u9884\u6d4b\u8fde\u7eed\u6570\u503c\u3002\u4e3a\u4e86\u8861\u91cf\u56de\u5f52\u6a21\u578b\u7684\u6027\u80fd&#xff0c;\u901a\u5e38\u91c7\u7528\u4e00\u7cfb\u5217\u91cf\u5316\u6307\u6807&#xff0c;\u8fd9\u4e9b\u6307\u6807\u53ef\u4ee5\u53cd\u6620\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u548c\u6a21\u578b\u7684\u62df\u5408\u80fd\u529b\u3002\u5408\u7406\u9009\u62e9\u548c\u7406\u89e3\u56de\u5f52\u8bc4\u4f30\u6307\u6807&#xff0c;\u6709\u52a9\u4e8e\u4f18\u5316\u6a21\u578b\u548c\u63d0\u5347\u9884\u6d4b\u7cbe\u5ea6\u3002<\/p>\n<h4>\u5747\u65b9\u8bef\u5dee&#xff08;Mean Squared Error, MSE&#xff09;<\/h4>\n<p>MSE \u662f\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u8bef\u5dee\u5e73\u65b9\u7684\u5e73\u5747\u503c&#xff0c;\u8ba1\u7b97\u516c\u5f0f\u4e3a<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         MSE <\/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>          y <\/p>\n<p>          i <\/p>\n<p>         \u2212 <\/p>\n<p>           y <\/p>\n<p>           ^ <\/p>\n<p>          i <\/p>\n<p>          ) <\/p>\n<p>          2 <\/p>\n<p>        \\\\text{MSE} &#061; \\\\frac{1}{n} \\\\sum_{i&#061;1}^{n} (y_i &#8211; \\\\hat{y}_i)^2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">MSE<\/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: 1.1901em;vertical-align: -0.345em\"><\/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: 0.8451em\"><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\">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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><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\"><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=\"mopen\">(<\/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=\"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: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/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=\"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=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;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><\/p>\n<p>\u5176\u4e2d\u4e3a\u771f\u5b9e\u503c&#xff0c;\u4e3a\u9884\u6d4b\u503c&#xff0c;\u4e3a\u6837\u672c\u6570\u3002<\/p>\n<p>\u975e\u5e38\u597d\u7406\u89e3&#xff0c;MSE\u5c31\u662f\u8ba1\u7b97\u771f\u5b9e\u503c\u4e0e\u9884\u6d4b\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u5927\u5c0f&#xff0c;\u8d8a\u5927\u80af\u5b9a\u9884\u6d4b\u7684\u8d8a\u4e0d\u51c6&#xff0c;MSE\u5bf9\u8f83\u5927\u8bef\u5dee\u66f4\u654f\u611f&#xff0c;\u9002\u5408\u5bf9\u5f02\u5e38\u503c\u654f\u611f\u7684\u573a\u666f&#xff0c;\u6bd4\u5982\u7ebf\u6027\u56de\u5f52\u3001\u795e\u7ecf\u7f51\u7edc\u7684\u635f\u5931\u51fd\u6570\u3002<\/p>\n<h4>\u5747\u65b9\u6839\u8bef\u5dee&#xff08;Root Mean Squared Error, RMSE&#xff09;<\/h4>\n<p>RMSE \u662f MSE \u7684\u5e73\u65b9\u6839&#xff0c;\u4f7f\u6307\u6807\u4e0e\u539f\u59cb\u6570\u636e\u5355\u4f4d\u4e00\u81f4&#xff0c;\u66f4\u6613\u89e3\u91ca\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         RMSE <\/p>\n<p>         &#061; <\/p>\n<p>          MSE <\/p>\n<p>        \\\\text{RMSE} &#061; \\\\sqrt{\\\\text{MSE}} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">RMSE<\/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: 1.04em;vertical-align: -0.1133em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9267em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord text\"><span class=\"mord\">MSE<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8867em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" 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: 0.1133em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>RMSE\u4fdd\u7559\u4e86 MSE \u5bf9\u5927\u8bef\u5dee\u654f\u611f\u7684\u7279\u6027&#xff0c;\u540c\u65f6\u91cf\u7eb2\u4e0e\u539f\u6570\u636e\u4e00\u81f4&#xff0c;\u76f4\u89c2\u53cd\u6620\u9884\u6d4b\u8bef\u5dee\u5927\u5c0f\u3002<\/p>\n<h4>\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee&#xff08;Mean Absolute Error, MAE&#xff09;<\/h4>\n<p>MAE \u662f\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u8bef\u5dee\u7edd\u5bf9\u503c\u7684\u5e73\u5747\u503c\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         MAE <\/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>         \u2223 <\/p>\n<p>          y <\/p>\n<p>          i <\/p>\n<p>         \u2212 <\/p>\n<p>           y <\/p>\n<p>           ^ <\/p>\n<p>          i <\/p>\n<p>         \u2223 <\/p>\n<p>        \\\\text{MAE} &#061; \\\\frac{1}{n} \\\\sum_{i&#061;1}^{n} |y_i &#8211; \\\\hat{y}_i| <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">MAE<\/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: 1.1901em;vertical-align: -0.345em\"><\/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: 0.8451em\"><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\">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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><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\"><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\">\u2223<\/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=\"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 accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/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=\"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><\/p>\n<p>\u5b83\u5bf9\u5f02\u5e38\u503c\u4e0d\u5982 MSE \u654f\u611f&#xff0c;\u66f4\u7a33\u5065&#xff0c;\u9002\u7528\u4e8e\u5f02\u5e38\u503c\u8f83\u591a\u6216\u5e0c\u671b\u5747\u8861\u8861\u91cf\u8bef\u5dee\u7684\u573a\u666f\u3002<\/p>\n<h4>\u51b3\u5b9a\u7cfb\u6570&#xff08;R\u00b2 Score, Coefficient of Determination&#xff09;<\/h4>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          R <\/p>\n<p>          2 <\/p>\n<p>        R^2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;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>\u8861\u91cf\u6a21\u578b\u5bf9\u6570\u636e\u65b9\u5dee\u7684\u89e3\u91ca\u80fd\u529b&#xff0c;\u53d6\u503c\u8303\u56f4\u901a\u5e38\u5728 0 \u5230 1 \u4e4b\u95f4&#xff0c;\u8d8a\u63a5\u8fd1 1 \u8868\u793a\u6a21\u578b\u62df\u5408\u8d8a\u597d\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          R <\/p>\n<p>          2 <\/p>\n<p>         &#061; <\/p>\n<p>         1 <\/p>\n<p>         \u2212 <\/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>            i <\/p>\n<p>           \u2212 <\/p>\n<p>             y <\/p>\n<p>             ^ <\/p>\n<p>            i <\/p>\n<p>            ) <\/p>\n<p>            2 <\/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>            i <\/p>\n<p>           \u2212 <\/p>\n<p>            y <\/p>\n<p>            \u02c9 <\/p>\n<p>            ) <\/p>\n<p>            2 <\/p>\n<p>        R^2 &#061; 1 &#8211; \\\\frac{\\\\sum_{i&#061;1}^{n}(y_i &#8211; \\\\hat{y}_i)^2}{\\\\sum_{i&#061;1}^{n}(y_i &#8211; \\\\bar{y})^2} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;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: 0.2778em\"><\/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: 1.7289em;vertical-align: -0.57em\"><\/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: 1.1589em\"><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=\"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 mtight\"><span class=\"mord mathnormal mtight\" 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: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/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\">2<\/span><\/span><\/span><\/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 mtight\"><span class=\"mord mathnormal mtight\" 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: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\"><span class=\"mord accent mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><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\">^<\/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=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/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: 0.8913em\"><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\">2<\/span><\/span><\/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: 0.57em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d\u4e3a\u771f\u5b9e\u503c\u5e73\u5747\u6570\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          R <\/p>\n<p>          2 <\/p>\n<p>         &#061; <\/p>\n<p>         0 <\/p>\n<p>        R^2 &#061; 0 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;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: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u6a21\u578b\u4ec5\u9884\u6d4b\u5747\u503c&#xff0c; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          R <\/p>\n<p>          2 <\/p>\n<p>         &#061; <\/p>\n<p>         1 <\/p>\n<p>        R^2 &#061; 1 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;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: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u9884\u6d4b\u5b8c\u5168\u6b63\u786e\u3002<\/p>\n<p>\u6ce8\u610f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          R <\/p>\n<p>          2 <\/p>\n<p>        R^2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;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>\u5bf9\u5f02\u5e38\u503c\u654f\u611f&#xff0c;\u8d1f\u503c\u53ef\u80fd\u51fa\u73b0&#xff0c;\u8868\u793a\u6a21\u578b\u8868\u73b0\u6bd4\u5747\u503c\u9884\u6d4b\u8fd8\u5dee\u3002<\/p>\n<h4>\u5e73\u5747\u7edd\u5bf9\u767e\u5206\u6bd4\u8bef\u5dee&#xff08;Mean Absolute Percentage Error, MAPE&#xff09;<\/h4>\n<p>MAPE \u8861\u91cf\u9884\u6d4b\u8bef\u5dee\u5360\u771f\u5b9e\u503c\u7684\u767e\u5206\u6bd4&#xff0c;\u9002\u5408\u5bf9\u76f8\u5bf9\u8bef\u5dee\u5173\u6ce8\u7684\u573a\u666f\u3002<\/p>\n<p>MAPE\u53ef\u4ee5\u76f4\u89c2\u663e\u793a\u9884\u6d4b\u504f\u79bb\u771f\u5b9e\u503c\u7684\u6bd4\u4f8b&#xff0c;\u4f46\u662f\u5f53\u771f\u5b9e\u503c\u63a5\u8fd1 0 \u65f6&#xff0c;MAPE \u4f1a\u975e\u5e38\u5927\u751a\u81f3\u65e0\u6cd5\u8ba1\u7b97\u3002<\/p>\n<p>\u5149\u8bf4\u4e0d\u7ec3\u778e\u628a\u5f0f&#xff0c;\u4e0b\u9762\u6211\u4eec\u4f7f\u7528 \u6ce2\u58eb\u987f\u623f\u4ef7\u6570\u636e\u96c6 \u7b97\u4e00\u4e0b\u4e0a\u9762\u7684\u5e38\u7528\u56de\u5f52\u8bc4\u4f30\u6307\u6807\u3002<\/p>\n<p><span class=\"token comment\"># \u5bfc\u5165\u5fc5\u8981\u5e93<\/span><br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_boston  <span class=\"token comment\"># \u65b0\u7248\u672c\u53ef\u7528 fetch_california_housing<\/span><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>linear_model <span class=\"token keyword\">import<\/span> LinearRegression<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> mean_squared_error<span class=\"token punctuation\">,<\/span> mean_absolute_error<span class=\"token punctuation\">,<\/span> r2_score<\/p>\n<p><span class=\"token comment\"># 1. \u52a0\u8f7d\u6570\u636e<\/span><br \/>\n<span class=\"token keyword\">try<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    boston <span class=\"token operator\">&#061;<\/span> load_boston<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    X<span class=\"token punctuation\">,<\/span> y <span class=\"token operator\">&#061;<\/span> boston<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">,<\/span> boston<span class=\"token punctuation\">.<\/span>target<br \/>\n<span class=\"token keyword\">except<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> fetch_california_housing<br \/>\n    cali <span class=\"token operator\">&#061;<\/span> fetch_california_housing<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    X<span class=\"token punctuation\">,<\/span> y <span class=\"token operator\">&#061;<\/span> cali<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">,<\/span> cali<span class=\"token punctuation\">.<\/span>target<\/p>\n<p><span class=\"token comment\"># 2. \u5212\u5206\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6<\/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\">0.3<\/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><\/p>\n<p><span class=\"token comment\"># 3. \u8bad\u7ec3\u7ebf\u6027\u56de\u5f52\u6a21\u578b<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> LinearRegression<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/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 \/>\ny_pred <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><\/p>\n<p><span class=\"token comment\"># 4. \u8ba1\u7b97\u56de\u5f52\u8bc4\u4f30\u6307\u6807<\/span><br \/>\nmse <span class=\"token operator\">&#061;<\/span> mean_squared_error<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\nrmse <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>sqrt<span class=\"token punctuation\">(<\/span>mse<span class=\"token punctuation\">)<\/span><br \/>\nmae <span class=\"token operator\">&#061;<\/span> mean_absolute_error<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\nr2 <span class=\"token operator\">&#061;<\/span> r2_score<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\nmape <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>y_test <span class=\"token operator\">&#8211;<\/span> y_pred<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">100<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;MSE: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>mse<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;RMSE: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>rmse<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;MAE: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>mae<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;R\u00b2: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>r2<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;MAPE: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>mape<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.2f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">%&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 5. \u53ef\u89c6\u5316\u9884\u6d4b\u8bef\u5dee<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>figure<span class=\"token punctuation\">(<\/span>figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;skyblue&#039;<\/span><span class=\"token punctuation\">,<\/span> edgecolor<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;k&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token builtin\">min<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">max<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token builtin\">min<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">max<\/span><span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;red&#039;<\/span><span class=\"token punctuation\">,<\/span> lw<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> linestyle<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;&#8211;&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;True Values&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Predicted Values&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;True vs Predicted Values&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 6. \u53ef\u89c6\u5316\u8bef\u5dee\u5206\u5e03<\/span><br \/>\nerrors <span class=\"token operator\">&#061;<\/span> y_test <span class=\"token operator\">&#8211;<\/span> y_pred<br \/>\nplt<span class=\"token punctuation\">.<\/span>figure<span class=\"token punctuation\">(<\/span>figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>hist<span class=\"token punctuation\">(<\/span>errors<span class=\"token punctuation\">,<\/span> bins<span class=\"token operator\">&#061;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span> color<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;lightcoral&#039;<\/span><span class=\"token punctuation\">,<\/span> edgecolor<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;k&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Prediction Error&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Frequency&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Distribution of Prediction Errors&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u5982\u4e0b&#xff0c;\u7b2c\u4e00\u4e2a\u56fe\u4e2d\u9884\u6d4b\u70b9\u843d\u5728\u7ea2\u8272\u865a\u7ebf<\/p>\n<p>\u9644\u8fd1\u8868\u793a\u9884\u6d4b\u7684\u51c6\u786e&#xff0c;\u504f\u79bb\u7ebf\u8d8a\u8fdc\u8868\u793a\u8bef\u5dee\u8d8a\u5927&#xff0c;\u7b2c\u4e8c\u4e2a\u8bef\u5dee\u5206\u5e03\u76f4\u65b9\u56fe\u5c55\u793a\u9884\u6d4b\u8bef\u5dee\u7684\u5206\u5e03&#xff0c;\u4e2d\u5fc3\u96c6\u4e2d\u8868\u793a\u6a21\u578b\u9884\u6d4b\u7a33\u5b9a&#xff0c;\u504f\u79bb\u5927\u8868\u793a\u5b58\u5728\u5f02\u5e38\u9884\u6d4b\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260129223305-697be0216b5bd.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260129223305-697be0217c02c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260129223305-697be021a2f3e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u603b\u7ed3\u4e00\u4e0b&#xff0c;\u56de\u5f52\u8bc4\u4f30\u6307\u6807\u63d0\u4f9b\u4e86\u4ece\u4e0d\u540c\u89d2\u5ea6\u8861\u91cf\u6a21\u578b\u9884\u6d4b\u6548\u679c\u7684\u5de5\u5177\u3002\u4ece\u7edd\u5bf9\u8bef\u5dee&#xff08;MAE&#xff09;\u3001\u5e73\u65b9\u8bef\u5dee&#xff08;MSE\u3001RMSE&#xff09;\u5230\u89e3\u91ca\u65b9\u5dee\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          R <\/p>\n<p>          2 <\/p>\n<p>        R^2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;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> &#xff0c;\u518d\u5230\u76f8\u5bf9\u8bef\u5dee MAPE&#xff0c;\u6bcf\u79cd\u6307\u6807\u90fd\u6709\u5176\u7279\u70b9\u548c\u9002\u7528\u573a\u666f\u3002<\/p>\n<h3>\u805a\u7c7b<\/h3>\n<p>\u805a\u7c7b\u662f\u4e00\u79cd\u65e0\u76d1\u7763\u5b66\u4e60\u65b9\u6cd5&#xff0c;\u5176\u76ee\u6807\u662f\u5c06\u6570\u636e\u6837\u672c\u5212\u5206\u4e3a\u82e5\u5e72\u7ec4&#xff0c;\u4f7f\u5f97\u540c\u4e00\u7ec4\u5185\u90e8\u7684\u6837\u672c\u76f8\u4f3c\u5ea6\u5c3d\u53ef\u80fd\u9ad8&#xff0c;\u800c\u4e0d\u540c\u7ec4\u4e4b\u95f4\u7684\u6837\u672c\u5dee\u5f02\u5c3d\u53ef\u80fd\u5927\u3002\u7531\u4e8e\u805a\u7c7b\u901a\u5e38\u6ca1\u6709\u771f\u5b9e\u6807\u7b7e&#xff0c;\u8bc4\u4f30\u805a\u7c7b\u8d28\u91cf\u9700\u8981\u4f7f\u7528\u4e13\u95e8\u7684\u6307\u6807\u3002\u6839\u636e\u662f\u5426\u4f9d\u8d56\u771f\u5b9e\u6807\u7b7e&#xff0c;\u805a\u7c7b\u8bc4\u4f30\u6307\u6807\u53ef\u4ee5\u5206\u4e3a \u5916\u90e8\u6307\u6807 \u548c \u5185\u90e8\u6307\u6807\u3002<\/p>\n<h4>\u5185\u90e8\u6307\u6807&#xff08;Internal Metrics&#xff09;<\/h4>\n<p>\u5185\u90e8\u6307\u6807\u53ea\u4f7f\u7528\u6570\u636e\u672c\u8eab\u548c\u805a\u7c7b\u7ed3\u679c\u8fdb\u884c\u8bc4\u4f30&#xff0c;\u4e0d\u4f9d\u8d56\u771f\u5b9e\u6807\u7b7e&#xff0c;\u4e3b\u8981\u5173\u6ce8\u7c07\u5185\u7d27\u5bc6\u5ea6\u548c\u7c07\u95f4\u5206\u79bb\u5ea6\u3002<\/p>\n<h5>\u8f6e\u5ed3\u7cfb\u6570&#xff08;Silhouette Coefficient&#xff09;<\/h5>\n<p>\u5b9a\u4e49&#xff1a;\u8861\u91cf\u6bcf\u4e2a\u6837\u672c\u4e0e\u81ea\u8eab\u7c07\u5185\u5176\u4ed6\u6837\u672c\u7684\u76f8\u4f3c\u5ea6&#xff0c;\u4e0e\u5176\u4e0e\u6700\u8fd1\u7c07\u6837\u672c\u7684\u76f8\u4f3c\u5ea6\u5dee\u5f02\u3002 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         s <\/p>\n<p>         ( <\/p>\n<p>         i <\/p>\n<p>         ) <\/p>\n<p>         &#061; <\/p>\n<p>           b <\/p>\n<p>           ( <\/p>\n<p>           i <\/p>\n<p>           ) <\/p>\n<p>           \u2212 <\/p>\n<p>           a <\/p>\n<p>           ( <\/p>\n<p>           i <\/p>\n<p>           ) <\/p>\n<p>           max <\/p>\n<p>           \u2061 <\/p>\n<p>           { <\/p>\n<p>           a <\/p>\n<p>           ( <\/p>\n<p>           i <\/p>\n<p>           ) <\/p>\n<p>           , <\/p>\n<p>           b <\/p>\n<p>           ( <\/p>\n<p>           i <\/p>\n<p>           ) <\/p>\n<p>           } <\/p>\n<p>        s(i) &#061; \\\\frac{b(i) &#8211; a(i)}{\\\\max\\\\{a(i), b(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\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/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=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><span class=\"mopen mtight\">{<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">b<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/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\">b<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/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<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          a <\/p>\n<p>          ( <\/p>\n<p>          i <\/p>\n<p>          ) <\/p>\n<p>         a(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\">a<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> &#xff1a;\u6837\u672c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          i <\/p>\n<p>         i <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u5230\u540c\u7c07\u5185\u5176\u4ed6\u6837\u672c\u7684\u5e73\u5747\u8ddd\u79bb\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          b <\/p>\n<p>          ( <\/p>\n<p>          i <\/p>\n<p>          ) <\/p>\n<p>         b(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\">b<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> &#xff1a;\u6837\u672c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          i <\/p>\n<p>         i <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u5230\u6700\u8fd1\u7c07\u7684\u5e73\u5747\u8ddd\u79bb\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          s <\/p>\n<p>          ( <\/p>\n<p>          i <\/p>\n<p>          ) <\/p>\n<p>         s(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\">s<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u8303\u56f4&#xff1a;[-1, 1]&#xff0c;\u8d8a\u63a5\u8fd1 1 \u8868\u793a\u805a\u7c7b\u6548\u679c\u8d8a\u597d\u3002 \u9ad8\u8f6e\u5ed3\u7cfb\u6570\u8868\u793a\u7c07\u5185\u6837\u672c\u7d27\u5bc6\u4e14\u7c07\u95f4\u5206\u79bb\u660e\u663e&#xff0c;\u8d1f\u503c\u8868\u793a\u6837\u672c\u53ef\u80fd\u88ab\u9519\u8bef\u5206\u914d\u3002<\/li>\n<\/ul>\n<h5>Calinski-Harabasz \u6307\u6570&#xff08;CH Index&#xff09;<\/h5>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         CH <\/p>\n<p>         &#061; <\/p>\n<p>           Tr <\/p>\n<p>           ( <\/p>\n<p>            B <\/p>\n<p>            k <\/p>\n<p>           ) <\/p>\n<p>           \/ <\/p>\n<p>           ( <\/p>\n<p>           k <\/p>\n<p>           \u2212 <\/p>\n<p>           1 <\/p>\n<p>           ) <\/p>\n<p>           Tr <\/p>\n<p>           ( <\/p>\n<p>            W <\/p>\n<p>            k <\/p>\n<p>           ) <\/p>\n<p>           \/ <\/p>\n<p>           ( <\/p>\n<p>           n <\/p>\n<p>           \u2212 <\/p>\n<p>           k <\/p>\n<p>           ) <\/p>\n<p>        \\\\text{CH} &#061; \\\\frac{\\\\text{Tr}(B_k) \/ (k-1)}{\\\\text{Tr}(W_k) \/ (n-k)} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">CH<\/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: 1.53em;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 text mtight\"><span class=\"mord mtight\">Tr<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">W<\/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: -2.3488em;margin-left: -0.1389em;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: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/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 mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/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 text mtight\"><span class=\"mord mtight\">Tr<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/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: -2.3488em;margin-left: -0.0502em;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: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/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\" style=\"margin-right: 0.0315em\">k<\/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: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5b9a\u4e49&#xff1a;\u8861\u91cf\u7c07\u95f4\u79bb\u6563\u5ea6\u4e0e\u7c07\u5185\u7d27\u5bc6\u5ea6\u4e4b\u6bd4\u3002<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           B <\/p>\n<p>           k <\/p>\n<p>         B_k <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0502em;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: 0.0315em\">k<\/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> &#xff1a;\u7c07\u95f4\u6563\u5e03\u77e9\u9635<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           W <\/p>\n<p>           k <\/p>\n<p>         W_k <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;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: 0.0315em\">k<\/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> &#xff1a;\u7c07\u5185\u6563\u5e03\u77e9\u9635<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          k <\/p>\n<p>         k <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> &#xff1a;\u7c07\u6570&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\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;\u6837\u672c\u603b\u6570 CH\u6307\u6570\u503c\u8d8a\u5927\u8868\u793a\u805a\u7c7b\u5206\u79bb\u5ea6\u9ad8\u3001\u7d27\u5bc6\u5ea6\u597d\u3002\u9002\u5408\u8bc4\u4f30\u4e0d\u540c\u7c07\u6570\u7684\u9009\u62e9\u3002<\/li>\n<\/ul>\n<h5>Davies-Bouldin \u6307\u6570&#xff08;DB Index&#xff09;<\/h5>\n<p>\u5b9a\u4e49&#xff1a;\u8861\u91cf\u7c07\u95f4\u76f8\u4f3c\u6027\u4e0e\u7c07\u5185\u6563\u5e03\u7684\u6bd4\u503c\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         D <\/p>\n<p>         B <\/p>\n<p>         &#061; <\/p>\n<p>          1 <\/p>\n<p>          k <\/p>\n<p>          \u2211 <\/p>\n<p>           i <\/p>\n<p>           &#061; <\/p>\n<p>           1 <\/p>\n<p>          k <\/p>\n<p>           max <\/p>\n<p>           \u2061 <\/p>\n<p>           j <\/p>\n<p>           \u2260 <\/p>\n<p>           i <\/p>\n<p>            \u03c3 <\/p>\n<p>            i <\/p>\n<p>           &#043; <\/p>\n<p>            \u03c3 <\/p>\n<p>            j <\/p>\n<p>           d <\/p>\n<p>           ( <\/p>\n<p>            c <\/p>\n<p>            i <\/p>\n<p>           , <\/p>\n<p>            c <\/p>\n<p>            j <\/p>\n<p>           ) <\/p>\n<p>        DB &#061; \\\\frac{1}{k} \\\\sum_{i&#061;1}^{k} \\\\max_{j \\\\neq i} \\\\frac{\\\\sigma_i &#043; \\\\sigma_j}{d(c_i, c_j)} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/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: 1.5313em;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: 0.8451em\"><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: 0.0315em\">k<\/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: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><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\"><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: 0.989em\"><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\" style=\"margin-right: 0.0315em\">k<\/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=\"mop\"><span class=\"mop\">max<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;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\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mrel mtight\"><span class=\"mrel mtight\"><span class=\"mord vbox mtight\"><span class=\"thinbox mtight\"><span class=\"rlap mtight\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord mtight\"><span class=\"mrel mtight\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel mtight\">&#061;<\/span><\/span><span class=\"mord mathnormal mtight\">i<\/span><\/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 class=\"mspace\" style=\"margin-right: 0.1667em\"><\/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: 0.9157em\"><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\">d<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><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\">i<\/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=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><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\" 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: 0.2819em\"><span class=\"\"><\/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: -3.5073em\"><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: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 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: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3281em\"><span class=\"\" style=\"top: -2.357em;margin-left: -0.0359em;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: 0.0572em\">j<\/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><\/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>           \u03c3 <\/p>\n<p>           i <\/p>\n<p>         \\\\sigma_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\" style=\"margin-right: 0.0359em\">\u03c3<\/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> &#xff1a;\u7c07$ i$\u5185\u6837\u672c\u7684\u5e73\u5747\u8ddd\u79bb<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          d <\/p>\n<p>          ( <\/p>\n<p>           c <\/p>\n<p>           i <\/p>\n<p>          , <\/p>\n<p>           c <\/p>\n<p>           j <\/p>\n<p>          ) <\/p>\n<p>         d(c_i, c_j) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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 class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> &#xff1a;\u7c07\u5fc3$i <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          \u4e0e\u7c07\u5fc3 <\/p>\n<p>         \u4e0e\u7c07\u5fc3 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord cjk_fallback\">\u4e0e\u7c07\u5fc3<\/span><\/span><\/span><\/span><\/span>j$ \u7684\u8ddd\u79bb<\/li>\n<\/ul>\n<p>DB\u6307\u6570\u7684\u503c\u8d8a\u5c0f\u8868\u793a\u7c07\u5206\u79bb\u826f\u597d&#xff0c;\u7d27\u5bc6\u5ea6\u9ad8\u3002<\/p>\n<h4>\u5916\u90e8\u6307\u6807&#xff08;External Metrics&#xff09;<\/h4>\n<p>\u5916\u90e8\u6307\u6807\u4f9d\u8d56\u771f\u5b9e\u6807\u7b7e&#xff08;\u5982\u679c\u5df2\u77e5&#xff09;&#xff0c;\u7528\u4e8e\u6bd4\u8f83\u805a\u7c7b\u7ed3\u679c\u4e0e\u771f\u5b9e\u7c7b\u522b\u7684\u4e00\u81f4\u6027\u3002<\/p>\n<h5>\u5f52\u4e00\u5316\u4e92\u4fe1\u606f&#xff08;Normalized Mutual Information, NMI&#xff09;<\/h5>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         NMI <\/p>\n<p>         ( <\/p>\n<p>         U <\/p>\n<p>         , <\/p>\n<p>         V <\/p>\n<p>         ) <\/p>\n<p>         &#061; <\/p>\n<p>           2 <\/p>\n<p>           I <\/p>\n<p>           ( <\/p>\n<p>           U <\/p>\n<p>           ; <\/p>\n<p>           V <\/p>\n<p>           ) <\/p>\n<p>           H <\/p>\n<p>           ( <\/p>\n<p>           U <\/p>\n<p>           ) <\/p>\n<p>           &#043; <\/p>\n<p>           H <\/p>\n<p>           ( <\/p>\n<p>           V <\/p>\n<p>           ) <\/p>\n<p>        \\\\text{NMI}(U,V) &#061; \\\\frac{2 I(U;V)}{H(U) &#043; H(V)} <\/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\">NMI<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/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: 0.0813em\">H<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0813em\">H<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.2222em\">V<\/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 mtight\">2<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mpunct mtight\">;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.2222em\">V<\/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<p>\u5b9a\u4e49&#xff1a;\u8861\u91cf\u805a\u7c7b\u7ed3\u679c\u4e0e\u771f\u5b9e\u6807\u7b7e\u4e4b\u95f4\u7684\u4fe1\u606f\u5171\u4eab\u7a0b\u5ea6&#xff0c;\u8303\u56f4 [0, 1]&#xff0c;1 \u8868\u793a\u5b8c\u5168\u4e00\u81f4\u3002<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          I <\/p>\n<p>          ( <\/p>\n<p>          U <\/p>\n<p>          ; <\/p>\n<p>          V <\/p>\n<p>          ) <\/p>\n<p>         I(U;V) <\/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: 0.0785em\">I<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mpunct\">;<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> &#xff1a;\u4e92\u4fe1\u606f<\/li>\n<li>$ H(U) , H(V)$&#xff1a;\u805a\u7c7b\u4e0e\u771f\u5b9e\u6807\u7b7e\u7684\u71b5<\/li>\n<\/ul>\n<p>\u7279\u70b9&#xff1a;\u5bf9\u7c07\u6570\u91cf\u654f\u611f&#xff0c;\u80fd\u591f\u6709\u6548\u8861\u91cf\u6807\u7b7e\u4e00\u81f4\u6027\u3002<\/p>\n<h5>\u8c03\u6574\u5170\u5fb7\u6307\u6570&#xff08;Adjusted Rand Index, ARI&#xff09;<\/h5>\n<p>\u5b9a\u4e49&#xff1a;\u57fa\u4e8e\u6837\u672c\u5bf9\u7684\u5339\u914d\u5173\u7cfb\u8861\u91cf\u805a\u7c7b\u8d28\u91cf&#xff0c;\u5e76\u5bf9\u968f\u673a\u7ed3\u679c\u8fdb\u884c\u4e86\u6821\u6b63\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         A <\/p>\n<p>         R <\/p>\n<p>         I <\/p>\n<p>         &#061; <\/p>\n<p>           R <\/p>\n<p>           I <\/p>\n<p>           \u2212 <\/p>\n<p>           E <\/p>\n<p>           [ <\/p>\n<p>           R <\/p>\n<p>           I <\/p>\n<p>           ] <\/p>\n<p>           max <\/p>\n<p>           \u2061 <\/p>\n<p>           ( <\/p>\n<p>           R <\/p>\n<p>           I <\/p>\n<p>           ) <\/p>\n<p>           \u2212 <\/p>\n<p>           E <\/p>\n<p>           [ <\/p>\n<p>           R <\/p>\n<p>           I <\/p>\n<p>           ] <\/p>\n<p>        ARI &#061; \\\\frac{RI &#8211; E[RI]}{\\\\max(RI) &#8211; E[RI]} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/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=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">I<\/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: 0.0077em\">R<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">I<\/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<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          R <\/p>\n<p>          I <\/p>\n<p>         RI <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><\/span><\/span><\/span><\/span> &#xff1a;Rand Index<\/li>\n<li>ARI \u8303\u56f4 [-1, 1]&#xff0c;1 \u8868\u793a\u5b8c\u5168\u4e00\u81f4&#xff0c;0 \u8868\u793a\u968f\u673a\u805a\u7c7b\u6548\u679c\u3002<\/li>\n<\/ul>\n<h5>Fowlkes-Mallows \u6307\u6570&#xff08;FMI&#xff09;<\/h5>\n<p>\u5b9a\u4e49&#xff1a;\u57fa\u4e8e TP\u3001FP\u3001FN \u8ba1\u7b97\u805a\u7c7b\u4e0e\u771f\u5b9e\u6807\u7b7e\u7684\u76f8\u4f3c\u5ea6\u3002<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         F <\/p>\n<p>         M <\/p>\n<p>         I <\/p>\n<p>         &#061; <\/p>\n<p>             T <\/p>\n<p>             P <\/p>\n<p>             T <\/p>\n<p>             P <\/p>\n<p>             &#043; <\/p>\n<p>             F <\/p>\n<p>             P <\/p>\n<p>           \u22c5 <\/p>\n<p>             T <\/p>\n<p>             P <\/p>\n<p>             T <\/p>\n<p>             P <\/p>\n<p>             &#043; <\/p>\n<p>             F <\/p>\n<p>             N <\/p>\n<p>        FMI &#061; \\\\sqrt{\\\\frac{TP}{TP&#043;FP} \\\\cdot \\\\frac{TP}{TP&#043;FN}} <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">FM<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/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: -0.6205em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2195em\"><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=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">FP<\/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: -3.394em\"><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\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/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\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8723em\"><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\">TP<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">FN<\/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: -3.394em\"><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\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4033em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.1795em\"><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: 0.6205em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>TP&#xff1a;\u540c\u7c07\u4e14\u540c\u7c7b\u7684\u6837\u672c\u5bf9<\/li>\n<li>FP&#xff1a;\u540c\u7c07\u4f46\u4e0d\u540c\u7c7b\u6837\u672c\u5bf9<\/li>\n<li>FN&#xff1a;\u4e0d\u540c\u7c07\u4f46\u540c\u7c7b\u6837\u672c\u5bf9<\/li>\n<\/ul>\n<p>FMI\u503c\u8d8a\u63a5\u8fd1 1 \u8868\u793a\u805a\u7c7b\u4e0e\u771f\u5b9e\u6807\u7b7e\u8d8a\u4e00\u81f4\u3002<\/p>\n<p>\u4e0b\u9762\u6211\u4eec\u4f7f\u7528 Iris \u6570\u636e\u96c6\u8fdb\u884c\u805a\u7c7b&#xff0c;\u8ba1\u7b97\u4ee5\u4e0a\u7684\u805a\u7c7b\u8bc4\u4f30\u6307\u6807<\/p>\n<p><span class=\"token comment\"># \u5bfc\u5165\u5fc5\u8981\u5e93<\/span><br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<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>preprocessing <span class=\"token keyword\">import<\/span> StandardScaler<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>cluster <span class=\"token keyword\">import<\/span> KMeans<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> silhouette_score<span class=\"token punctuation\">,<\/span> calinski_harabasz_score<span class=\"token punctuation\">,<\/span> davies_bouldin_score<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> normalized_mutual_info_score<span class=\"token punctuation\">,<\/span> adjusted_rand_score<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>decomposition <span class=\"token keyword\">import<\/span> PCA<\/p>\n<p><span class=\"token comment\"># 1. \u52a0\u8f7d Iris \u6570\u636e\u96c6<\/span><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_true <span class=\"token operator\">&#061;<\/span> iris<span class=\"token punctuation\">.<\/span>target  <span class=\"token comment\"># \u771f\u5b9e\u7c7b\u522b<\/span><\/p>\n<p><span class=\"token comment\"># 2. \u6570\u636e\u6807\u51c6\u5316<\/span><br \/>\nscaler <span class=\"token operator\">&#061;<\/span> StandardScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nX_scaled <span class=\"token operator\">&#061;<\/span> scaler<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\"># 3. \u4f7f\u7528 KMeans \u805a\u7c7b<\/span><br \/>\nk <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">3<\/span>  <span class=\"token comment\"># \u805a\u7c7b\u7c07\u6570<\/span><br \/>\nkmeans <span class=\"token operator\">&#061;<\/span> KMeans<span class=\"token punctuation\">(<\/span>n_clusters<span class=\"token operator\">&#061;<\/span>k<span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny_pred <span class=\"token operator\">&#061;<\/span> kmeans<span class=\"token punctuation\">.<\/span>fit_predict<span class=\"token punctuation\">(<\/span>X_scaled<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 4. \u8ba1\u7b97\u805a\u7c7b\u8bc4\u4f30\u6307\u6807<\/span><br \/>\nsil_score <span class=\"token operator\">&#061;<\/span> silhouette_score<span class=\"token punctuation\">(<\/span>X_scaled<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\nch_score <span class=\"token operator\">&#061;<\/span> calinski_harabasz_score<span class=\"token punctuation\">(<\/span>X_scaled<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\ndb_score <span class=\"token operator\">&#061;<\/span> davies_bouldin_score<span class=\"token punctuation\">(<\/span>X_scaled<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\nnmi_score <span class=\"token operator\">&#061;<\/span> normalized_mutual_info_score<span class=\"token punctuation\">(<\/span>y_true<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\nari_score <span class=\"token operator\">&#061;<\/span> adjusted_rand_score<span class=\"token punctuation\">(<\/span>y_true<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;Silhouette Score: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>sil_score<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;Calinski-Harabasz Index: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>ch_score<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;Davies-Bouldin Index: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>db_score<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;NMI (Normalized Mutual Information): <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>nmi_score<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;ARI (Adjusted Rand Index): <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>ari_score<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.4f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 5. \u53ef\u89c6\u5316\u805a\u7c7b\u7ed3\u679c&#xff08;\u4f7f\u7528 PCA \u964d\u5230 2D&#xff09;<\/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 \/>\nX_pca <span class=\"token operator\">&#061;<\/span> pca<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>X_scaled<span class=\"token punctuation\">)<\/span><\/p>\n<p>plt<span class=\"token punctuation\">.<\/span>figure<span class=\"token punctuation\">(<\/span>figsize<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\ncolors <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;red&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;green&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;blue&#039;<\/span><span class=\"token punctuation\">]<\/span><br \/>\n<span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>k<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    plt<span class=\"token punctuation\">.<\/span>scatter<span class=\"token punctuation\">(<\/span>X_pca<span class=\"token punctuation\">[<\/span>y_pred<span class=\"token operator\">&#061;&#061;<\/span>i<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> X_pca<span class=\"token punctuation\">[<\/span>y_pred<span class=\"token operator\">&#061;&#061;<\/span>i<span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                color<span class=\"token operator\">&#061;<\/span>colors<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;Cluster <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>i<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#039;<\/span><\/span><span class=\"token punctuation\">,<\/span> alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.6<\/span><span class=\"token punctuation\">,<\/span> edgecolor<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;k&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6807\u8bb0\u771f\u5b9e\u7c7b\u522b\u4e2d\u5fc3<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;PCA Component 1&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;PCA Component 2&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;KMeans Clustering of Iris Dataset (PCA 2D Visualization)&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>grid<span class=\"token punctuation\">(<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u7ed3\u679c\u5982\u4e0b\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260129223305-697be021c3545.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5728\u9009\u62e9\u6307\u6807\u7684\u65f6\u5019&#xff0c;\u65e0\u6807\u7b7e\u6570\u636e\u4f7f\u7528\u5185\u90e8\u6307\u6807\u5982\u8f6e\u5ed3\u7cfb\u6570\u3001Calinski-Harabasz\u3001Davies-Bouldin \u6765\u8bc4\u4f30\u805a\u7c7b\u8d28\u91cf\u3002\u6709\u6807\u7b7e\u6570\u636e\u53ef\u4ee5\u4f7f\u7528\u5916\u90e8\u6307\u6807 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