{"id":103243,"date":"2026-09-10T05:56:59","date_gmt":"2026-09-09T21:56:59","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/103243.html"},"modified":"2026-09-10T05:56:59","modified_gmt":"2026-09-09T21:56:59","slug":"%e8%af%84%e6%b5%8b%e6%8c%87%e6%a0%87%e9%99%b7%e9%98%b1%ef%bc%9amacro-f1-%e4%b8%8e-micro-f1-%e5%9c%a8%e9%95%bf%e5%b0%be%e5%a4%9a%e5%88%86%e7%b1%bb%e4%b8%ad%e7%9a%84%e5%b7%a8%e5%a4%a7%e5%88%86%e6%ad%a7","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/103243.html","title":{"rendered":"\u8bc4\u6d4b\u6307\u6807\u9677\u9631\uff1aMacro-F1 \u4e0e Micro-F1 \u5728\u957f\u5c3e\u591a\u5206\u7c7b\u4e2d\u7684\u5de8\u5927\u5206\u6b67"},"content":{"rendered":"<h2>\u8bc4\u6d4b\u6307\u6807\u9677\u9631&#xff1a;Macro-F1 \u4e0e Micro-F1 \u5728\u957f\u5c3e\u591a\u5206\u7c7b\u4e2d\u7684\u5de8\u5927\u5206\u6b67<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260909215657-6aa1d629dca4a.webp\" alt=\"\u5c01\u9762\u4fe1\u606f\u56fe\" \/><\/p>\n<p>\u5728\u5904\u7406\u5de5\u4e1a\u7ea7\u591a\u5206\u7c7b\u4efb\u52a1&#xff08;\u5982\u5de5\u5355\u610f\u56fe\u8def\u7531\u3001\u5546\u54c1\u7c7b\u76ee\u9884\u6d4b\u3001\u533b\u7597\u75be\u75c5\u8bca\u65ad&#xff09;\u65f6&#xff0c;\u6570\u636e\u96c6\u5f80\u5f80\u5448\u73b0\u6781\u5176\u60ac\u6b8a\u7684\u957f\u5c3e\u5206\u5e03&#xff08;Long-tailed Distribution&#xff09;&#xff1a;\u6392\u540d\u524d 5% \u7684\u5934\u90e8\u7c7b\u522b\u5360\u636e\u4e86 80% \u7684\u6837\u672c\u91cf&#xff0c;\u800c\u6570\u767e\u4e2a\u957f\u5c3e\u5c3e\u90e8\u7c7b\u522b\u6bcf\u7c7b\u4ec5\u6709\u51e0\u5341\u6761\u6837\u672c\u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b&#xff0c;\u5f88\u591a\u6280\u672f\u56e2\u961f\u5728\u6c47\u62a5\u6a21\u578b\u6307\u6807\u65f6&#xff0c;\u5f80\u5f80\u4f1a\u62ff\u51fa\u4e00\u4e2a\u770b\u4f3c\u4f18\u5f02\u7684\u201cF1-Score: 92.5%\u201d\u3002\u7136\u800c\u4ed4\u7ec6\u8ffd\u95ee\u624d\u53d1\u73b0&#xff0c;\u8be5\u6307\u6807\u662f Micro-F1&#xff0c;\u800c\u5bf9\u5e94\u7684 Macro-F1 \u5b9e\u9645\u4e0a\u5df2\u7ecf\u8dcc\u7834 60%\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48 Macro-F1 \u548c Micro-F1 \u4f1a\u4ea7\u751f\u5982\u6b64\u5de8\u5927\u7684\u8ba4\u77e5\u9e3f\u6c9f&#xff1f;\u5728\u591a\u5206\u7c7b\u6a21\u578b\u9009\u578b\u4e0e\u51c6\u5165\u65f6&#xff0c;\u5e94\u8be5\u5982\u4f55\u79d1\u5b66\u9009\u62e9\u4e0e\u89e3\u91ca\u8fd9\u4e24\u4e2a\u6307\u6807&#xff1f;<\/p>\n<h3>1. Macro \u4e0e Micro \u7684\u6570\u5b66\u5b9a\u4e49\u672c\u8d28<\/h3>\n<p>\u5047\u8bbe\u4efb\u52a1\u5305\u542b $K$ \u4e2a\u5206\u7c7b\u7c7b\u522b ${C_1, C_2, \\\\dots, C_K}$\u3002\u5bf9\u6bcf\u4e2a\u7c7b\u522b $i$&#xff0c;\u6211\u4eec\u53ef\u4ee5\u5206\u522b\u7edf\u8ba1\u5176\u6df7\u6dc6\u77e9\u9635\u5143\u7d20&#xff1a;$TP_i$&#xff08;\u771f\u6b63\u4f8b&#xff09;\u3001$FP_i$&#xff08;\u5047\u6b63\u4f8b&#xff09;\u3001$FN_i$&#xff08;\u5047\u8d1f\u4f8b&#xff09;\u3002<\/p>\n<h4>(1) Micro-F1&#xff08;\u5fae\u5e73\u5747 F1&#xff09;&#xff1a;\u57fa\u4e8e\u5168\u5c40\u603b\u6837\u672c\u805a\u5408<\/h4>\n<p>\u5148\u5c06\u6240\u6709\u7c7b\u522b\u5728\u5168\u5c40\u7684 $TP$\u3001$FP$\u3001$FN$ \u7d2f\u52a0\u6c42\u548c&#xff0c;\u518d\u8ba1\u7b97\u5168\u5c40\u7684 Precision \u548c Recall&#xff1a;<\/p>\n<p>$$P_{\\\\text{micro}} &#061; \\\\frac{\\\\sum_{i&#061;1}^K TP_i}{\\\\sum_{i&#061;1}^K (TP_i &#043; FP_i)}, \\\\quad R_{\\\\text{micro}} &#061; \\\\frac{\\\\sum_{i&#061;1}^K TP_i}{\\\\sum_{i&#061;1}^K (TP_i &#043; FN_i)}$$<\/p>\n<p>$$\\\\text{Micro-F1} &#061; 2 \\\\times \\\\frac{P_{\\\\text{micro}} \\\\times R_{\\\\text{micro}}}{P_{\\\\text{micro}} &#043; R_{\\\\text{micro}}}$$<\/p>\n<p>\u5173\u952e\u6570\u5b66\u6027\u8d28&#xff1a;\u5728\u5355\u6807\u7b7e\u591a\u5206\u7c7b\u4efb\u52a1\u4e2d&#xff0c;\u5168\u5c40 $\\\\sum FP_i$ \u5fc5\u7136\u7b49\u4e8e $\\\\sum FN_i$&#xff08;\u56e0\u4e3a\u4e00\u4e2a\u6837\u672c\u88ab\u9519\u5224\u7ed9\u67d0\u7c7b&#xff0c;\u540c\u65f6\u610f\u5473\u7740\u8be5\u7c7b\u591a\u4e86 FP\u3001\u771f\u5b9e\u7c7b\u591a\u4e86 FN&#xff09;\u3002\u56e0\u6b64&#xff1a;<\/p>\n<p>$$\\\\text{Micro-Precision} &#061; \\\\text{Micro-Recall} &#061; \\\\text{Micro-F1} \\\\equiv \\\\text{Overall Accuracy}$$<\/p>\n<p>Micro-F1 \u672c\u8d28\u4e0a\u5b8c\u5168\u7b49\u4ef7\u4e8e\u5168\u5c40\u51c6\u786e\u7387&#xff08;Accuracy&#xff09;&#xff0c;\u5b83\u5b8c\u5168\u7531\u6837\u672c\u91cf\u5e9e\u5927\u7684\u5934\u90e8\u5927\u7c7b\u4e3b\u5bfc\u3002<\/p>\n<h4>(2) Macro-F1&#xff08;\u5b8f\u5e73\u5747 F1&#xff09;&#xff1a;\u57fa\u4e8e\u7c7b\u522b\u5e73\u7b49\u7b97\u672f\u5e73\u5747<\/h4>\n<p>\u72ec\u7acb\u8ba1\u7b97\u6bcf\u4e2a\u7c7b\u522b\u7684 $F1_i$&#xff0c;\u7136\u540e\u5bf9\u6240\u6709 $K$ \u4e2a\u7c7b\u522b\u7684 F1 \u5206\u6570\u76f4\u63a5\u53d6\u7b97\u672f\u5e73\u5747&#xff1a;<\/p>\n<p>$$F1_i &#061; 2 \\\\times \\\\frac{P_i \\\\times R_i}{P_i &#043; R_i}, \\\\quad \\\\text{Macro-F1} &#061; \\\\frac{1}{K} \\\\sum_{i&#061;1}^K F1_i$$<\/p>\n<p>\u6838\u5fc3\u7279\u5f81&#xff1a;\u65e0\u8bba\u67d0\u4e2a\u7c7b\u522b\u62e5\u6709 100,000 \u6761\u6837\u672c\u8fd8\u662f 10 \u6761\u6837\u672c&#xff0c;\u5728 Macro-F1 \u4e2d\u5176\u6743\u91cd\u90fd\u662f\u4e25\u683c\u5e73\u7b49\u7684 $\\\\frac{1}{K}$\u3002\u957f\u5c3e\u7c7b\u522b\u7684\u5d29\u6e83\u4f1a\u7acb\u523b\u5728 Macro-F1 \u4e0a\u5f15\u53d1\u65ad\u5d16\u5f0f\u66b4\u8dcc\u3002<\/p>\n<h3>2. \u771f\u5b9e\u957f\u5c3e\u591a\u5206\u7c7b\u4e0b\u7684\u8ba1\u7b97\u6a21\u62df\u4e0e\u6307\u6807\u5931\u771f<\/h3>\n<p>import numpy as np<br \/>\nfrom sklearn.metrics import classification_report, f1_score<\/p>\n<p>def simulate_long_tail_evaluation():<br \/>\n    # \u6a21\u62df 3 \u5206\u7c7b\u4efb\u52a1&#xff1a;Class 0 (\u5934\u90e8\u8d85\u5927\u7c7b), Class 1 (\u4e2d\u7b49\u7c7b), Class 2 (\u5c3e\u90e8\u6781\u5c0f\u7c7b)<br \/>\n    # \u6837\u672c\u5206\u5e03\u6bd4\u4f8b: 9000 : 900 : 100<br \/>\n    y_true &#061; np.array([0] * 9000 &#043; [1] * 900 &#043; [2] * 100)<\/p>\n<p>    # \u6a21\u62df\u4e00\u4e2a\u6709\u504f\u7684\u6a21\u578b&#xff1a;\u5934\u90e8\u7c7b\u51e0\u4e4e\u5168\u5bf9&#xff0c;\u4f46\u5c3e\u90e8\u6781\u5c0f\u7c7b\u5b8c\u5168\u5b66\u5e9f (\u5168\u9519)<br \/>\n    y_pred &#061; y_true.copy()<br \/>\n    y_pred[y_true &#061;&#061; 2] &#061; 0 # 100 \u4e2a\u5c3e\u90e8\u6837\u672c\u88ab\u5168\u90e8\u9519\u8bef\u9884\u6d4b\u4e3a\u5934\u90e8\u7c7b 0<br \/>\n    y_pred[9000:9100] &#061; 0   # \u4e2d\u7b49\u7c7b\u4e5f\u6709 100 \u4e2a\u88ab\u8bef\u5224<\/p>\n<p>    micro_f1 &#061; f1_score(y_true, y_pred, average&#061;&#034;micro&#034;)<br \/>\n    macro_f1 &#061; f1_score(y_true, y_pred, average&#061;&#034;macro&#034;)<br \/>\n    weighted_f1 &#061; f1_score(y_true, y_pred, average&#061;&#034;weighted&#034;)<\/p>\n<p>    print(f&#034;\u5168\u5c40\u51c6\u786e\u7387 (Accuracy):   {np.mean(y_true &#061;&#061; y_pred):.4f}&#034;)<br \/>\n    print(f&#034;Micro-F1 (\u7b49\u4ef7 Accuracy): {micro_f1:.4f}&#034;)<br \/>\n    print(f&#034;Weighted-F1 (\u52a0\u6743\u5e73\u5747):    {weighted_f1:.4f}&#034;)<br \/>\n    print(f&#034;Macro-F1 (\u7b97\u672f\u5b8f\u5e73\u5747):    {macro_f1:.4f}&#034;)<br \/>\n    print(&#034;\\\\n\u8be6\u7ec6\u5206\u7c7b\u62a5\u544a:&#034;)<br \/>\n    print(classification_report(y_true, y_pred, digits&#061;4))<\/p>\n<p>if __name__ &#061;&#061; &#034;__main__&#034;:<br \/>\n    simulate_long_tail_evaluation()<\/p>\n<p>\u8f93\u51fa\u7ed3\u679c\u5206\u6790&#xff1a;<\/p>\n<p>\u5168\u5c40\u51c6\u786e\u7387 (Accuracy):   0.9800<br \/>\nMicro-F1 (\u7b49\u4ef7 Accuracy): 0.9800<br \/>\nWeighted-F1 (\u52a0\u6743\u5e73\u5747):    0.9754<br \/>\nMacro-F1 (\u7b97\u672f\u5b8f\u5e73\u5747):    0.6385<\/p>\n<p>\u4ece\u6570\u636e\u53ef\u4ee5\u6e05\u6670\u770b\u5230&#xff1a;\u5f53\u957f\u5c3e\u7c7b\u522b\u5f7b\u5e95\u5931\u6548&#xff08;F1&#061;0.0&#xff09;\u65f6&#xff0c;Micro-F1 \u4f9d\u7136\u9ad8\u8fbe 98.0%&#xff0c;\u751a\u81f3\u52a0\u6743\u5e73\u5747 Weighted-F1 \u4e5f\u9ad8\u8fbe 97.5%&#xff0c;\u5b8c\u5168\u63a9\u76d6\u4e86\u957f\u5c3e\u4e1a\u52a1\u7684\u5d29\u6e83&#xff1b;\u800c Macro-F1 \u9aa4\u964d\u81f3 63.85%&#xff0c;\u771f\u5b9e\u5730\u66b4\u9732\u4e86\u7cfb\u7edf\u7684\u4e25\u91cd\u7f3a\u9677\u3002<\/p>\n<h3>3. \u9009\u578b\u6307\u5357\u4e0e\u4e1a\u52a1\u51b3\u7b56\u77e9\u9635<\/h3>\n<table>\n<tr>\u8bc4\u4f30\u6307\u6807\u6838\u5fc3\u4ee3\u8868\u542b\u4e49\u9002\u7528\u4e1a\u52a1\u573a\u666f\u7981\u5fcc\u573a\u666f<\/tr>\n<tbody>\n<tr>\n<td>Micro-F1<\/td>\n<td>\u8bc4\u4f30\u7cfb\u7edf\u5728\u5168\u91cf\u7528\u6237\u6d41\u91cf\u4e0a\u7684\u5e73\u5747\u627f\u63a5\u51c6\u786e\u7387<\/td>\n<td>\u6837\u672c\u5206\u5e03\u5747\u5300\u3001\u6216\u8005\u53ea\u5173\u5fc3\u5168\u5c40\u6574\u4f53\u541e\u5410\u4e0e\u5927\u76d8\u51c6\u786e\u7387<\/td>\n<td>\u5b58\u5728\u957f\u5c3e\u5b89\u5168\u98ce\u9669\u3001\u533b\u7597\u7f55\u89c1\u75c5\u3001\u91d1\u878d\u98ce\u63a7\u6b3a\u8bc8\u8bc6\u522b<\/td>\n<\/tr>\n<tr>\n<td>Macro-F1<\/td>\n<td>\u8bc4\u4f30\u6a21\u578b\u5728\u5404\u4e2a\u7ec6\u5206\u7c7b\u522b\u8bed\u4e49\u8fb9\u754c\u4e0a\u7684\u7efc\u5408\u5b66\u4e60\u8d28\u91cf<\/td>\n<td>\u591a\u5206\u7c7b\u610f\u56fe\u8bc6\u522b\u3001\u5de5\u5355\u591a\u7ea7\u8def\u7531\u3001\u77e5\u8bc6\u5e93\u591a\u6807\u7b7e\u5206\u7c7b<\/td>\n<td>\u6781\u7aef\u6837\u672c\u91cf\u8fc7\u5c11\u4e14\u566a\u58f0\u6781\u5927\u7684\u975e\u5173\u952e\u5783\u573e\u7c7b\u522b<\/td>\n<\/tr>\n<tr>\n<td>Weighted-F1<\/td>\n<td>\u6309\u5404\u7c7b\u522b\u6837\u672c\u5360\u6bd4\u52a0\u6743\u8ba1\u7b97\u5e73\u5747 F1<\/td>\n<td>\u7c7b\u522b\u6bd4\u4f8b\u53d8\u52a8\u6781\u5c0f&#xff0c;\u4f5c\u4e3a\u5b8f\u89c2\u6c47\u62a5\u53c2\u8003<\/td>\n<td>\u4e0d\u5f97\u4f5c\u4e3a\u7b97\u6cd5\u6a21\u578b\u51c6\u5165\u7684\u552f\u4e00\u5224\u5b9a\u95e8\u7981<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>4. \u5de5\u4e1a\u7ea7\u957f\u5c3e\u6a21\u578b\u8bc4\u6d4b\u5b9e\u8df5\u89c4\u8303<\/h3>\n<li>\u7981\u6b62\u5728\u6280\u672f\u6587\u6863\u4e2d\u5b64\u7acb\u4f7f\u7528\u201cF1-Score\u201d\u4e00\u8bcd&#xff1a;\u5fc5\u987b\u663e\u5f0f\u58f0\u660e\u662f Macro-F1 \u8fd8\u662f Micro-F1&#xff1b;<\/li>\n<li>\u4e09\u7ef4\u96f7\u8fbe\u56fe\u7ed3\u5408\u5c55\u73b0&#xff1a;\u5728\u6a21\u578b\u51c6\u5165\u62a5\u544a\u4e2d&#xff0c;\u5fc5\u987b\u540c\u6b65\u5c55\u793a\u201c\u5934\u90e8\u7c7b F1\u201d\u3001\u201c\u8170\u90e8\u7c7b F1\u201d\u548c\u201c\u957f\u5c3e\u7c7b 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