{"id":1643,"date":"2023-07-25T13:22:41","date_gmt":"2023-07-25T13:22:41","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%85%b0%e7%89%b9%e6%8c%87%e6%95%b0\/"},"modified":"2023-07-25T13:22:41","modified_gmt":"2023-07-25T13:22:41","slug":"%e5%85%b0%e7%89%b9%e6%8c%87%e6%95%b0","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%85%b0%e7%89%b9%e6%8c%87%e6%95%b0\/","title":{"rendered":"\u4ec0\u4e48\u662f\u5170\u5fb7\u6307\u6570\uff1f \uff08\u5b9a\u4e49\u548c\u793a\u4f8b\uff09"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u5170\u5fb7\u6307\u6570<\/strong>\u662f\u4e00\u79cd\u6bd4\u8f83\u4e24\u79cd\u4e0d\u540c\u805a\u7c7b\u65b9\u6cd5\u7ed3\u679c\u76f8\u4f3c\u5ea6\u7684\u65b9\u6cd5\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5170\u5fb7\u6307\u6570\u901a\u5e38\u8868\u793a\u4e3a<em>R<\/em> \uff0c\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>R<\/em> = (a+b) \/ ( <sub>nC<\/sub> <sub>2<\/sub> )<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>a\uff1a<\/strong>\u6839\u636e\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\uff0c\u4e00\u5bf9\u5143\u7d20\u5c5e\u4e8e\u540c\u4e00\u7c07\u7684\u6b21\u6570\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b\uff1a<\/strong>\u6839\u636e\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\uff0c\u4e00\u5bf9\u5143\u7d20\u5c5e\u4e8e\u4e0d\u540c\u7c07\u7684\u6b21\u6570\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n<\/sub> C <sub>2<\/sub> \uff1a<\/strong> <em>n \u4e2a<\/em>\u5143\u7d20\u7684\u96c6\u5408\u4e2d\u65e0\u5e8f\u5bf9\u7684\u6570\u91cf\u3002<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Rand \u7d22\u5f15\u59cb\u7ec8\u91c7\u7528 0 \u5230 1 \u4e4b\u95f4\u7684\u503c\uff0c\u5176\u4e2d\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>0\uff1a<\/strong>\u8868\u793a\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\u5bf9\u4e00\u5bf9\u5143\u7d20\u7684\u805a\u7c7b\u4e0d\u4e00\u81f4\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1\uff1a<\/strong>\u8868\u793a\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\u5728\u6bcf\u5bf9\u5143\u7d20\u7684\u805a\u7c7b\u4e0a\u5b8c\u5168\u4e00\u81f4\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u5982\u4f55\u8ba1\u7b97\u7b80\u5355\u6570\u636e\u96c6\u7684\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\u4e4b\u95f4\u7684 Rand \u6307\u6570\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1a\u5982\u4f55\u8ba1\u7b97\u5170\u5fb7\u6307\u6570<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u6709\u4ee5\u4e0b\u7531\u4e94\u4e2a\u5143\u7d20\u7ec4\u6210\u7684\u6570\u636e\u96c6\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u6570\u636e\u96c6\uff1a{A\u3001B\u3001C\u3001D\u3001E}<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u4f7f\u7528\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\u5c06\u6bcf\u4e2a\u5143\u7d20\u653e\u5165\u4ee5\u4e0b\u805a\u7c7b\u4e2d\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u65b9\u6cd5 1 \u805a\u7c7b\uff1a{1, 1, 1, 2, 2}<\/span><\/li>\n<li><span style=\"color: #000000;\">\u805a\u7c7b\u65b9\u6cd52\uff1a{1,1,2,2,3}<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u8ba1\u7b97\u8fd9\u4e9b\u805a\u7c7b\u65b9\u6cd5\u4e4b\u95f4\u7684\u5170\u5fb7\u6307\u6570\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u5199\u4e0b\u4e94\u5143\u7d20\u6570\u636e\u96c6\u4e2d\u6240\u6709\u53ef\u80fd\u7684\u65e0\u5e8f\u5bf9\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u65e0\u5e8f\u5bf9\uff1a{A, B}, {A, C}, {A, D}, {A, E}, {B, C}, {B, D}, {B, E}, {C, D } , {C, E}, {D, E}<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6709<strong>10 \u4e2a<\/strong>\u65e0\u5e8f\u5bf9\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97<strong>a<\/strong> \uff0c\u5b83\u8868\u793a\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\u4e2d\u5c5e\u4e8e\u540c\u4e00\u7c07\u7684\u65e0\u5e8f\u5bf9\u7684\u6570\u91cf\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">{AB}<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c a = <strong>1<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97<strong>b<\/strong> \uff0c\u5b83\u8868\u793a\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\u4e2d\u5c5e\u4e8e\u4e0d\u540c\u7c07\u7684\u65e0\u5e8f\u5bf9\u7684\u6570\u91cf\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">{A\uff0cD}\uff0c{A\uff0cE}\uff0c{B\uff0cD}\uff0c{B\uff0cE}\uff0c{C\uff0cE}<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0cb = <strong>5<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa\u5170\u5fb7\u6307\u6570\u5982\u4e0b\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><em>R<\/em> = (a+b) \/ ( <sub>nC<\/sub> <sub>2<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em> = (1+5) \/ 10<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em> = 6\/10<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5170\u5fb7\u6307\u6570\u4e3a<strong>0.6<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5982\u4f55\u8ba1\u7b97R\u4e2d\u7684\u5170\u5fb7\u6307\u6570<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<strong>\u5316\u77f3<\/strong>\u5305\u4e2d\u7684<strong>rand.index()<\/strong>\u51fd\u6570\u6765\u8ba1\u7b97 R \u4e2d\u4e24\u79cd\u805a\u7c7b\u65b9\u6cd5\u4e4b\u95f4\u7684 Rand \u6307\u6570\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #993300;\">library<\/span> (fossil)\n\n<span style=\"color: #008080;\">#define clusters\n<\/span>method1 &lt;- c(1, 1, 1, 2, 2)\nmethod2 &lt;- c(1, 1, 2, 2, 3)\n\n<span style=\"color: #008080;\">#calculate Rand index between clustering methods\n<\/span>rand. <span style=\"color: #3366ff;\">index<\/span> (method1, method2)\n\n[1] 0.6\n<\/strong><\/span><\/pre>\n<p><span style=\"color: #000000;\">\u5170\u5fb7\u6307\u6570\u4e3a<strong>0.6<\/strong> \u3002\u8fd9\u5bf9\u5e94\u4e8e\u6211\u4eec\u624b\u52a8\u8ba1\u7b97\u7684\u503c\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5982\u4f55\u5728 Python \u4e2d\u8ba1\u7b97 Rand \u6307\u6570<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u5728Python\u4e2d\u5b9a\u4e49\u4ee5\u4e0b\u51fd\u6570\u6765\u8ba1\u7b97\u4e24\u4e2a\u7c07\u4e4b\u95f4\u7684Rand\u6307\u6570\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">special<\/span> <span style=\"color: #008000;\">import<\/span> comb\n\n<span style=\"color: #008080;\">#define Rand index function\n<\/span><span style=\"color: #008000;\">def<\/span> <span style=\"color: #993300;\">rand_index<\/span> (actual, pred):\n\n    tp_plus_fp = comb(np. <span style=\"color: #3366ff;\">bincount<\/span> (actual), 2). <span style=\"color: #3366ff;\">sum<\/span> ()\n    tp_plus_fn = comb(np. <span style=\"color: #3366ff;\">bincount<\/span> (pred), 2). <span style=\"color: #3366ff;\">sum<\/span> ()\n    A = np. <span style=\"color: #3366ff;\">c_<\/span> [(actual, pred)]\n    tp = sum(comb( <span style=\"color: #3366ff;\">np.bincount<\/span> (A[A[:, 0] == i, 1]), 2) <span style=\"color: #3366ff;\">.sum<\/span> ()\n             <span style=\"color: #008000;\">for<\/span> i <span style=\"color: #008000;\">in<\/span> set(actual))\n    fp = tp_plus_fp - tp\n    fn = tp_plus_fn - tp\n    tn = comb(len(A), 2) - tp - fp - fn\n    <span style=\"color: #008000;\">return<\/span> (tp + tn) \/ (tp + fp + fn + tn)\n\n<span style=\"color: #008080;\">#calculate Rand index\n<\/span>rand_index([1, 1, 1, 2, 2], [1, 1, 2, 2, 3])\n\n0.6<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u5170\u5fb7\u6307\u6570\u7ed3\u679c\u4e3a<strong>0.6<\/strong> \u3002\u8fd9\u5bf9\u5e94\u4e8e\u524d\u9762\u793a\u4f8b\u4e2d\u8ba1\u7b97\u7684\u503c\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/cn\/k-\u8868\u793a\u5728-r-\u4e2d\u5206\u7ec4\/\" target=\"_blank\" rel=\"noopener\">K \u5747\u503c\u805a\u7c7b\u7b80\u4ecb<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/r-\u4e2d\u7684-k-\u4e2a\u4e2d\u5fc3\u70b9\/\" target=\"_blank\" rel=\"noopener\">K-Medoids \u805a\u7c7b\u7b80\u4ecb<\/a><br \/>\u5c42\u6b21\u805a\u7c7b\u7b80\u4ecb<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5170\u5fb7\u6307\u6570\u662f\u4e00\u79cd\u6bd4\u8f83\u4e24\u79cd\u4e0d\u540c\u805a\u7c7b\u65b9\u6cd5\u7ed3\u679c\u76f8\u4f3c\u5ea6\u7684\u65b9\u6cd5\u3002 \u5170\u5fb7\u6307\u6570\u901a\u5e38\u8868\u793a\u4e3aR \uff0c\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a R = (a+b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1643","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin 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