{"id":9007,"date":"2023-10-09T15:21:27","date_gmt":"2023-10-09T07:21:27","guid":{"rendered":"\/?p=9007"},"modified":"2023-10-09T15:21:27","modified_gmt":"2023-10-09T07:21:27","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e5%8d%8f%e6%96%b9%e5%b7%aecovariance%ef%bc%9f%ef%bc%88%e5%bb%b6%e4%bc%b8%e5%88%b0-%e5%8d%8f%e6%96%b9%e5%b7%ae%e7%9f%a9%e9%98%b5%e3%80%81%e5%a4%9a%e5%85%83%e9%ab%98","status":"publish","type":"post","link":"\/?p=9007","title":{"rendered":"\u4ec0\u4e48\u662f\u534f\u65b9\u5dee(covariance)\uff1f\uff08\u5ef6\u4f38\u5230 \u534f\u65b9\u5dee\u77e9\u9635\u3001\u591a\u5143\u9ad8\u65af\u5206\u5e03\u3001PCA\uff09"},"content":{"rendered":"<p>\u534f\u65b9\u5dee(covariance )\u662f\u4e00\u4e2a\u7edf\u8ba1\u91cf\uff0c\u662f\u5bf9\u4e00\u4e2a\u6837\u672c\u7684\u67d0\u4e00\u7edf\u8ba1\u7279\u6027\u7ed9\u51fa\u7684\u4e00\u4e2a\u4f30\u7b97\u91cf\u3002<\/p>\n<p>\u5e38\u89c1\u7edf\u8ba1\u91cf<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/ada563671853b31581d4cb82586a383c.png\" alt=\"img\" \/><\/p>\n<p>\u5747\u503c\u4f30\u7b97\u7684\u662f\u6837\u672c\u96c6\u5408\u7684\u5e73\u5747\u6c34\u5e73\u3002<\/p>\n<p>\u65b9\u5dee\u4f30\u7b97\u7684\u662f\u6837\u672c\u96c6\u5408\u7684\u6563\u5e03\u5ea6\uff0c\u5355\u5143\u7ef4\u5ea6\u504f\u79bb\u5176\u5747\u503c\u7684\u7a0b\u5ea6\u3002<\/p>\n<h4>\u90a3\u534f\u65b9\u5dee(covariance)\u5462\uff1f<\/h4>\n<p>\u5982\u679c\u662f\u4e00\u7ef4\u6837\u672c\u4e0d\u5b58\u5728\u534f\u65b9\u5dee(covariance)\uff0c<\/p>\n<p>\u5982\u679c\u662f\u4e8c\u7ef4\uff08\u591a\u7ef4\uff09\u6837\u672c\u5462\uff1f\u6bd4\u5982\u7edf\u8ba1\u591a\u4e2a\u5b66\u79d1\u7684\u8003\u8bd5\u6210\u7ee9\u3002<\/p>\n<p>\u4eff\u7167\u65b9\u5dee\u7684\u5b9a\u4e49\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/bc4edb806e34854df39bd4550c2a8479.jpeg\" alt=\"img\" \/><\/p>\n<p>\u6765\u5ea6\u91cf\u5404\u4e2a\u7ef4\u5ea6\u504f\u79bb\u5176\u5747\u503c\u7684\u7a0b\u5ea6\uff0c\u534f\u65b9\u5dee(covariance)\u53ef\u4ee5\u8fd9\u4e48\u6765\u5b9a\u4e49\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/e561249f59f6e071860de253ebf3274f.png\" alt=\"img\" \/><\/p>\n<p>\u76f4\u89c9\u7406\u89e3\u4e00\u4e0b\u5c31\u662f\uff1a\u5982\u679c\u6709X,Y\u4e24\u4e2a\u53d8\u91cf\uff0c\u6bcf\u4e2a\u65f6\u523b(\u6216\u70b9)\u7684\u201cX\u503c\u4e0e\u5176\u5747\u503c\u4e4b\u5dee\u201d\u4e58\u4ee5\u201cY\u503c\u4e0e\u5176\u5747\u503c\u4e4b\u5dee\u201d\u5f97\u5230\u4e00\u4e2a\u4e58\u79ef\uff0c\u518d\u5bf9\u8fd9\u6bcf\u65f6\u523b\u7684\u4e58\u79ef\u6c42\u548c\u5e76\u6c42\u51fa\u5747\u503c\uff08\u5176\u5b9e\u662f\u6c42\u201c\u671f\u671b\u201d\uff0c\u4f46\u5c31\u4e0d\u5f15\u7533\u592a\u591a\u65b0\u6982\u5ff5\u4e86\uff0c\u7b80\u5355\u8ba4\u4e3a\u5c31\u662f<a href=\"https:\/\/so.csdn.net\/so\/search?q=\u6c42\u5747\u503c&amp;spm=1001.2101.3001.7020\">\u6c42\u5747\u503c<\/a>\u4e86\uff09\u3002<\/p>\n<p>\u53ef\u4ee5\u901a\u4fd7\u7684\u7406\u89e3\u4e3a\uff1a\u4e24\u4e2a\u53d8\u91cf\u5728\u53d8\u5316\u8fc7\u7a0b\u4e2d\u662f\u540c\u65b9\u5411\u53d8\u5316\uff1f\u8fd8\u662f\u53cd\u65b9\u5411\u53d8\u5316\uff1f\u540c\u5411\u6216\u53cd\u5411\u7a0b\u5ea6\u5982\u4f55\uff1f\u4f60\u53d8\u5927\uff0c\u540c\u65f6\u6211\u4e5f\u53d8\u5927\uff0c\u8bf4\u660e\u4e24\u4e2a\u53d8\u91cf\u662f\u540c\u5411\u53d8\u5316\u6b63\u76f8\u5173\u7684\uff0c\u8fd9\u65f6\u534f\u65b9\u5dee\u5c31\u662f\u6b63\u7684\u3002<\/p>\n<blockquote>\n<p>\u4ece\u6570\u503c\u6765\u770b\uff0c\u534f\u65b9\u5dee\u7684\u6570\u503c\u8d8a\u5927\uff0c\u4e24\u4e2a\u53d8\u91cf\u540c\u5411\uff08\u6b63\u76f8\u5173\uff09\u7a0b\u5ea6\u4e5f\u5c31\u8d8a\u5927\u3002\u53cd\u4e4b\u4ea6\u7136\u3002<\/p>\n<\/blockquote>\n<h4>variance\u548ccovariance\u7684\u5b9a\u4e49\u6bd4\u8f83<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/050902ec4f954466b0bb71519a330743.png\" alt=\"img\" \/><\/p>\n<h4>\u8fd8\u6709\u4e00\u4e2a\u5c31\u662f<a href=\"https:\/\/so.csdn.net\/so\/search?q=\u534f\u65b9\u5dee\u77e9\u9635&amp;spm=1001.2101.3001.7020\">\u534f\u65b9\u5dee\u77e9\u9635<\/a>\uff08Covariance matrix\uff09<\/h4>\n<p>\u534f\u65b9\u5dee\u77e9\u9635\u662f\u7528\u4e8e\u63cf\u8ff0\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u4e4b\u95f4<a href=\"https:\/\/so.csdn.net\/so\/search?q=\u7ebf\u6027\u76f8\u5173\u6027&amp;spm=1001.2101.3001.7020\">\u7ebf\u6027\u76f8\u5173\u6027<\/a>\u7684\u77e9\u9635\u3002<br \/>\n\u5bf9\u4e24\u4e2a\u968f\u673a\u53d8\u91cfX\u548cY,\u534f\u65b9\u5dee\u77e9\u9635\u5b9a\u4e49\u4e3a:<br \/>\nCov(X, Y) = E[(X - E(X))(Y - E(Y))^T]<\/p>\n<p>\u5176\u4e2d,E(X)\u548cE(Y)\u5206\u522b\u8868\u793aX\u548cY\u7684\u671f\u671b(\u5747\u503c)\u3002<\/p>\n<p>\u5728<a href=\"https:\/\/baike.baidu.com\/item\/\u6982\u7387\u8bba\/829122?fromModule=lemma_inlink\">\u6982\u7387\u8bba<\/a>\u548c\u7edf\u8ba1\u5b66\u4e2d\uff0c\u534f\u65b9\u5dee\u7528\u4e8e\u8861\u91cf\u4e24\u4e2a\u53d8\u91cf\u7684\u603b\u4f53\u8bef\u5dee\u3002\u800c<a href=\"https:\/\/baike.baidu.com\/item\/\u65b9\u5dee\/3108412?fromModule=lemma_inlink\">\u65b9\u5dee<\/a>\u662f\u534f\u65b9\u5dee\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\uff0c\u5373\u5f53\u4e24\u4e2a\u53d8\u91cf\u662f\u76f8\u540c\u7684\u60c5\u51b5<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20231009151752672.png\" alt=\"\" \/><\/p>\n<p>\u4f8b\u5982,\u5bf9\u4e24\u4e2a\u4e8c\u7ef4\u968f\u673a\u53d8\u91cfX\u548cY:<br \/>\nX = [x1, x2]<br \/>\nY = [y1, y2]\u5219\u5176\u534f\u65b9\u5dee\u77e9\u9635\u4e3a:<br \/>\nCov(X, Y) =<br \/>\n[[Cov(x1, x1), Cov(x1, x2)],<br \/>\n[Cov(y1, x1), Cov(y1, x2)]]<\/p>\n<p>\u53ef\u4ee5\u770b\u51fa\u5bf9\u89d2\u7ebf\u5143\u7d20\u8868\u793ax1,x2\u548cy1,y2\u5404\u81ea\u7684\u65b9\u5dee,\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20\u8868\u793ax1\u4e0ey1,x1\u4e0ey2,x2\u4e0ey1,x2\u4e0ey2\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u3002<\/p>\n<p>\u6240\u4ee5,\u534f\u65b9\u5dee\u77e9\u9635\u6574\u4f53\u4e0a\u8868\u793a\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u5728\u5404\u7ef4\u5ea6\u4e0a\u4ee5\u53ca\u4e0d\u540c\u7ef4\u5ea6\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u3002<\/p>\n<h4><\/h4>\n<h4>\u5e94\u7528:\u534f\u65b9\u5dee\u77e9\u9635\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09<\/h4>\n<ul>\n<li>\u5c06X\u8f6c\u7f6e\u5e76\u4e0eX\u76f8\u4e58,\u7b49\u6548\u4e8e\u8ba1\u7b97X\u548cX\u5728\u6bcf\u4e2a\u7ef4\u5ea6\u4e0a\u5bf9\u5e94\u5750\u6807\u7684\u5185\u79ef\u3002<\/li>\n<li>\u5185\u79ef\u53cd\u6620\u4e86\u4e24\u4e2a\u5411\u91cf\u5728\u67d0\u4e2a\u7ef4\u5ea6\u4e0a\u7684\u76f8\u4f3c\u7a0b\u5ea6,\u8d8a\u76f8\u4f3c\u5185\u79ef\u8d8a\u5927\u3002<\/li>\n<li>\u56e0\u6b64$X_TX$\u7684\u6bcf\u4e2a\u5143\u7d20\u5c31\u662fX\u548cX\u5728\u8be5\u7ef4\u5ea6\u4e0a\u5750\u6807\u7684\u534f\u65b9\u5dee<\/li>\n<\/ul>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/62ef71f451044d298740f8faea9da7f6.png\" alt=\"img\" \/><\/p>\n<p><em>\u03a3\u662f\u5404\u4e3b\u6210\u5206\u5bf9\u6570\u636e\u65b9\u5dee\u7684\u8d21\u732e\uff0c\u4e5f\u5c31\u662f\u5404\u4e3b\u6210\u5206\u7684\u957f\u5ea6\u3002\u5b83\u4eec\u4e0d\u662f\u6743\u91cd\uff0c\u56e0\u4e3a\u5b83\u4eec\u4e0d\u4e00\u5b9a\u52a0\u8d77\u6765\u7b49\u4e8e1\u3002<\/em><\/p>\n<p><strong>\u5947\u5f02\u503c\u5206\u89e3\u53ef\u4ee5\u770b\u4f5c\u662f\u5bf9\u77e9\u9635S\u8fdb\u884c\u4e00\u4e2a\u65cb\u8f6c\u3001\u7f29\u653e\u548c\u518d\u65cb\u8f6c\u7684\u64cd\u4f5c\uff0c\u4f7f\u5f97S\u53d8\u6210\u4e00\u4e2a\u5bf9\u89d2\u77e9\u9635\u00b3\u3002\u8fd9\u6837\u53ef\u4ee5\u63d0\u53d6\u51faS\u7684\u4e3b\u8981\u7279\u5f81\uff0c\u4f8b\u5982\u65b9\u5411\u3001\u53d8\u5316\u7a0b\u5ea6\u548c\u7ebf\u6027\u76f8\u5173\u6027\u2074\u3002<\/strong><\/p>\n<h4>\u5e94\u7528\uff1a\u591a\u7ef4\u5ea6\u9ad8\u65af\u5206\u5e03<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTAwODczMzg=,size_16,color_FFFFFF,t_70.png\" alt=\"img\" \/><\/p>\n<p>\u591a\u7ef4\u9ad8\u65af\u5206\u5e03\u91cc\u9762\u6709\u4e24\u4e2a\u53c2\u6570\uff0c<\/p>\n<p>\u4e00\u4e2a\u662f<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/mu.png\" alt=\"\\mu\" \/> \uff0c\u53ef\u4ee5\u7528\u6240\u4ee5\u6837\u672c\u7684\u5747\u503c\u6765\u4f30\u8ba1\uff0c\u4ee3\u8868\u603b\u4f53\u6570\u636e\u7684\u5e73\u5747\u503c\u3002<\/p>\n<p>\u4e00\u4e2a\u662f\u2211\u2211\uff0c\u5c31\u662f\u524d\u9762\u7684\u534f\u65b9\u5dee\u77e9\u9635\uff0c\u4ee3\u8868\u4e0d\u540c\u7ef4\u5ea6\u7684\u76f8\u5173\u8054\u7a0b\u5ea6\u3002<\/p>\n<h4>\u5e94\u7528\uff1aPCA\u4e3b\u6210\u5206\u6790<\/h4>\n<p>\u672c\u8d28\u4e0a\u662f\u627e\u4e00\u4e2a\u66f4\u4f4e\u7ef4\u5ea6\u7684\u8868\u9762\uff08\u7a7a\u95f4\uff09\uff0c\u4f7f\u5f97\u6295\u5f71\u5230\u8fd9\u4e2a\u8868\u9762\u7684\u6570\u636e\u4e0e\u539f\u6570\u636e\u4e4b\u95f4\u7684\u8bef\u5dee\uff08\u8ddd\u79bb\uff09\u6700\u5c0f\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTAwODczMzg=,size_16,color_FFFFFF,t_70-1696835763320-51.png\" alt=\"img\" \/><\/p>\n<p>\u5b9e\u73b0\u7b97\u6cd5\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTAwODczMzg=,size_16,color_FFFFFF,t_70-1696835763320-52.png\" alt=\"img\" \/><\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTAwODczMzg=,size_16,color_FFFFFF,t_70-1696835763320-53.png\" alt=\"img\" \/><\/p>\n<p>\u2211\u2211 is Sigma is \u534f\u65b9\u5dee\u77e9\u9635\uff0c\u662fnxn\u65b9\u9635 \uff0c\u5728\u7ecf\u8fc7\u4e86normalization\u4e4b\u540e\u6c42\u5f97\u7684Sigma\uff0c\u672c\u8d28\u4e0a\u4ee3\u8868\u4e86\u6570\u636e\u96c6n\u4e2a\u7ef4\u5ea6\u7684\u76f8\u4e92\u5173\u7cfb\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTAwODczMzg=,size_16,color_FFFFFF,t_70-1696835763320-54.png\" alt=\"img\" \/><\/p>\n<p>\u5728\u7ecf\u8fc7svd\u5206\u89e3\u4e4b\u540e\uff0c\u6211\u4eec\u4e3b\u8981\u7528\u7684\u662fU\uff0c\u56e0\u4e3a\u6839\u636e<a href=\"https:\/\/blog.csdn.net\/u010087338\/article\/details\/114576013\">\u5f7b\u5e95\u7406\u89e3SVD\u5947\u5f02\u503c\u5206\u89e3<\/a>\uff0c\u6211\u4eec\u77e5\u9053U\u7684\u5217\u5411\u91cf\u662f Col\uff08 \u2211\u2211 \uff09\u7684\u4e00\u7ec4\u6807\u51c6\u6b63\u4ea4\u57fa\u3002<\/p>\n<p>\u8fd8\u6709\uff0cU\u7684\u5217\u5411\u91cf\u662f\u4ece\u5de6\u5230\u53f3\uff0c\u91cd\u8981\u6027\u9010\u6b65\u964d\u4f4e\u7684\uff0c\u6240\u4ee5\u8981\u964d\u5230k\u7ef4\uff0c\u53ea\u9700\u8981\u53d6U\u7684\u524dk\u4e2a\u5217\u5411\u91cf\uff0c\u8fd9\u6837\u5c31\u628a\u539f\u6765n\u7ef4\u7684\u5750\u6807\u7cfb\uff0c\u964d\u5230\u4e86k\u7ef4\u5355\u4f4d\u6b63\u4ea4\u7684\u5750\u6807\u7cfb\u3002<\/p>\n<p>\u800c\u65b0\u7684\u6570\u636e\u96c6\u7684\u503c\u5219\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTAwODczMzg=,size_16,color_FFFFFF,t_70-1696835763320-55.png\" alt=\"img\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u534f\u65b9\u5dee(covariance )\u662f\u4e00\u4e2a\u7edf\u8ba1\u91cf\uff0c\u662f\u5bf9\u4e00\u4e2a\u6837\u672c\u7684\u67d0\u4e00\u7edf\u8ba1\u7279\u6027\u7ed9\u51fa\u7684\u4e00\u4e2a\u4f30\u7b97\u91cf\u3002 \u5e38\u89c1\u7edf\u8ba1\u91cf \u5747\u503c\u4f30\u7b97\u7684\u662f\u6837\u672c\u96c6\u5408\u7684\u5e73\u5747\u6c34\u5e73\u3002   \u2026 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