{"id":832,"date":"2023-07-28T14:53:35","date_gmt":"2023-07-28T14:53:35","guid":{"rendered":"https:\/\/statorials.org\/cn\/mahalanobis-%e8%bf%9c%e7%a8%8b-python\/"},"modified":"2023-07-28T14:53:35","modified_gmt":"2023-07-28T14:53:35","slug":"mahalanobis-%e8%bf%9c%e7%a8%8b-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/mahalanobis-%e8%bf%9c%e7%a8%8b-python\/","title":{"rendered":"\u5982\u4f55\u5728 python \u4e2d\u8ba1\u7b97\u9a6c\u6c0f\u8ddd\u79bb"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u9a6c\u54c8\u62c9\u8bfa\u6bd4\u65af\u8ddd\u79bb<\/strong>\u662f\u591a\u5143\u7a7a\u95f4\u4e2d\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u5b83\u901a\u5e38\u7528\u4e8e\u68c0\u6d4b\u6d89\u53ca\u591a\u4e2a\u53d8\u91cf\u7684\u7edf\u8ba1\u5206\u6790\u4e2d\u7684\u5f02\u5e38\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u5728 Python \u4e2d\u8ba1\u7b97\u9a6c\u54c8\u62c9\u8bfa\u6bd4\u65af\u8ddd\u79bb\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1aPython \u4e2d\u7684\u9a6c\u54c8\u62c9\u8bfa\u6bd4\u65af\u8ddd\u79bb<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u4ee5\u4e0b\u6b65\u9aa4\u8ba1\u7b97 Python \u6570\u636e\u96c6\u4e2d\u6bcf\u4e2a\u89c2\u6d4b\u503c\u7684\u9a6c\u6c0f\u8ddd\u79bb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 1\uff1a\u521b\u5efa\u6570\u636e\u96c6\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u6211\u4eec\u5c06\u521b\u5efa\u4e00\u4e2a\u6570\u636e\u96c6\uff0c\u663e\u793a 20 \u540d\u5b66\u751f\u7684\u8003\u8bd5\u6210\u7ee9\uff0c\u4ee5\u53ca\u4ed6\u4eec\u5b66\u4e60\u6240\u7528\u7684\u5c0f\u65f6\u6570\u3001\u53c2\u52a0\u7684\u6a21\u62df\u8003\u8bd5\u6b21\u6570\u4ee5\u53ca\u4ed6\u4eec\u5f53\u524d\u8bfe\u7a0b\u7684\u6210\u7ee9\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n<span style=\"color: #107d3f;\">import<\/span> pandas <span style=\"color: #107d3f;\">as<\/span> pd<span style=\"color: #107d3f;\">\nimport<\/span> scipy <span style=\"color: #107d3f;\">as<\/span> stats\n\ndata = {'score': [91, 93, 72, 87, 86, 73, 68, 87, 78, 99, 95, 76, 84, 96, 76, 80, 83, 84, 73, 74],\n        'hours': [16, 6, 3, 1, 2, 3, 2, 5, 2, 5, 2, 3, 4, 3, 3, 3, 4, 3, 4, 4],\n        'prep': [3, 4, 0, 3, 4, 0, 1, 2, 1, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2],\n        'grade': [70, 88, 80, 83, 88, 84, 78, 94, 90, 93, 89, 82, 95, 94, 81, 93, 93, 90, 89, 89]\n        }\n\ndf = pd.DataFrame(data,columns=['score', 'hours', 'prep','grade'])\ndf.head()\n\n score hours prep grade\n0 91 16 3 70\n1 93 6 4 88\n2 72 3 0 80\n3 87 1 3 83\n4 86 2 4 88\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 2\uff1a\u8ba1\u7b97\u6bcf\u4e2a\u89c2\u6d4b\u503c\u7684\u9a6c\u6c0f\u8ddd\u79bb\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u7f16\u5199\u4e00\u4e2a\u7b80\u77ed\u7684\u51fd\u6570\u6765\u8ba1\u7b97\u9a6c\u6c0f\u8ddd\u79bb\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\"><span style=\"color: #008080;\">#create function to calculate Mahalanobis distance<\/span>\ndef<\/span> mahalanobis(x= <span style=\"color: #107d3f;\">None<\/span> , data= <span style=\"color: #107d3f;\">None<\/span> , cov= <span style=\"color: #107d3f;\">None<\/span> ):\n\n    x_mu = x - np.mean(data)\n    if not cov:\n        cov = np.cov(data.values.T)\n    inv_covmat = np.linalg.inv(cov)\n    left = np.dot(x_mu, inv_covmat)\n    mahal = np.dot(left, x_mu.T)\n    return mahal.diagonal()\n\n<span style=\"color: #107d3f;\"><span style=\"color: #008080;\">#create new column in dataframe that contains Mahalanobis distance for each row<\/span><\/span>\ndf['mahalanobis'] = mahalanobis(x=df, data=df[['score', 'hours', 'prep', 'grade']])\n\n<span style=\"color: #008080;\">#display first five rows of dataframe\n<\/span>df.head()\n\n score hours prep grade mahalanobis\n0 91 16 3 70 16.501963\n1 93 6 4 88 2.639286\n2 72 3 0 80 4.850797\n3 87 1 3 83 5.201261\n4 86 2 4 88 3.828734\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 3\uff1a\u8ba1\u7b97\u6bcf\u4e2a\u9a6c\u54c8\u62c9\u8bfa\u6bd4\u65af\u8ddd\u79bb\u7684 p \u503c\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u4e00\u4e9b\u9a6c\u54c8\u62c9\u8bfa\u6bd4\u65af\u8ddd\u79bb\u6bd4\u5176\u4ed6\u8ddd\u79bb\u5927\u5f97\u591a\u3002\u4e3a\u4e86\u786e\u5b9a\u4efb\u4f55\u8ddd\u79bb\u662f\u5426\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u5b83\u4eec\u7684 p \u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6bcf\u4e2a\u8ddd\u79bb\u7684 p \u503c\u8ba1\u7b97\u4e3a\u4e0e\u5177\u6709 k-1 \u81ea\u7531\u5ea6\u7684 Mahalanobis \u8ddd\u79bb\u7684\u5361\u65b9\u7edf\u8ba1\u91cf\u76f8\u5bf9\u5e94\u7684 p \u503c\uff0c\u5176\u4e2d k = \u53d8\u91cf\u6570\u3002\u56e0\u6b64\u5728\u672c\u4f8b\u4e2d\u6211\u4eec\u5c06\u4f7f\u7528\u81ea\u7531\u5ea6 4-1 = 3\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> scipy.stats <span style=\"color: #107d3f;\">import<\/span> chi2\n\n<span style=\"color: #008080;\">#calculate p-value for each mahalanobis distance<\/span> \ndf['p'] = 1 - chi2.cdf(df['mahalanobis'], 3)\n\n<span style=\"color: #008080;\">#display p-values for first five rows in dataframe<\/span>\ndf.head()\n\n score hours prep grade mahalanobis p\n0 91 16 3 70 16.501963 0.000895\n1 93 6 4 88 2.639286 0.450644\n2 72 3 0 80 4.850797 0.183054\n3 87 1 3 83 5.201261 0.157639\n4 86 2 4 88 3.828734 0.280562\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u901a\u5e38\uff0c<strong>\u5c0f\u4e8e 0.001 \u7684<\/strong>p \u503c\u88ab\u89c6\u4e3a\u5f02\u5e38\u503c\u3002<\/span><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u7b2c\u4e00\u4e2a\u89c2\u6d4b\u503c\u662f\u6570\u636e\u96c6\u4e2d\u7684\u5f02\u5e38\u503c\uff0c\u56e0\u4e3a\u5b83\u7684 p \u503c\u5c0f\u4e8e 0.001\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6839\u636e\u95ee\u9898\u7684\u4e0a\u4e0b\u6587\uff0c\u60a8\u53ef\u80fd\u51b3\u5b9a\u4ece\u6570\u636e\u96c6\u4e2d\u5220\u9664\u6b64\u89c2\u5bdf\u503c\uff0c\u56e0\u4e3a\u5b83\u662f\u5f02\u5e38\u503c\uff0c\u53ef\u80fd\u4f1a\u5f71\u54cd\u5206\u6790\u7ed3\u679c\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9a6c\u54c8\u62c9\u8bfa\u6bd4\u65af\u8ddd\u79bb\u662f\u591a\u5143\u7a7a\u95f4\u4e2d\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u5b83\u901a\u5e38\u7528\u4e8e\u68c0\u6d4b\u6d89\u53ca\u591a\u4e2a\u53d8\u91cf\u7684\u7edf\u8ba1\u5206\u6790\u4e2d\u7684\u5f02\u5e38\u503c\u3002 \u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u5728 [&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-832","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- 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