{"id":3192,"date":"2022-02-27T13:08:17","date_gmt":"2022-02-27T05:08:17","guid":{"rendered":"https:\/\/egonlin.com\/?p=3192"},"modified":"2022-02-27T13:10:03","modified_gmt":"2022-02-27T05:10:03","slug":"%e7%ac%ac%e4%ba%8c%e8%8a%82%ef%bc%9a%e7%89%b9%e5%be%81%e9%80%89%e6%8b%a9","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3192","title":{"rendered":"\u7b2c\u4e8c\u8282\uff1a\u7279\u5f81\u9009\u62e9"},"content":{"rendered":"

\u7279\u5f81\u9009\u62e9<\/h1>\n

  \u7279\u5f81\u5de5\u7a0b\u5728\u5de5\u4e1a\u4e0a\u6709\u8fd9\u4e48\u4e00\u53e5\u5e7f\u4e3a\u6d41\u4f20\u7684\u8bdd\uff1a\u6570\u636e\u548c\u7279\u5f81\u51b3\u5b9a\u4e86\u673a\u5668\u5b66\u4e60\u7684\u4e0a\u9650\uff0c\u800c\u6a21\u578b\u548c\u7b97\u6cd5\u53ea\u662f\u903c\u8fd1\u8fd9\u4e2a\u4e0a\u9650\u800c\u5df2\u3002\u63a5\u4e0b\u6765\u5c06\u7ed9\u4f60\u4ecb\u7ecd\u7279\u5f81\u5de5\u7a0b\u7684\u7b2c\u4e00\u4e2a\u5206\u652f\uff0c\u7279\u5f81\u9009\u62e9\u3002<\/p>\n

  \u5bf9\u4e8e\u4e00\u4e2a\u5b66\u4e60\u4efb\u52a1\u6765\u8bf4\uff0c\u5982\u679c\u67d0\u4e00\u4e2a\u7279\u5f81\u548c\u6211\u4eec\u7684\u5b66\u4e60\u4efb\u52a1\u6ca1\u6709\u592a\u5927\u5173\u7cfb\uff0c\u6211\u4eec\u628a\u5b83\u79f0\u4e4b\u4e3a\u65e0\u5173\u7279\u5f81(irrelevant feature)\uff0c\u5982\u4e2a\u4eba\u957f\u76f8\u548c\u8d22\u5bcc\u81ea\u7531\uff1b\u5982\u679c\u67d0\u4e00\u4e2a\u7279\u5f81\u548c\u6211\u4eec\u7684\u5b66\u4e60\u4efb\u52a1\u6709\u592a\u5927\u5173\u7cfb\uff0c\u6211\u4eec\u628a\u5b83\u79f0\u4e4b\u4e3a\u76f8\u5173\u7279\u5f81(relevant feature)\uff0c\u800c\u6211\u4eec\u63a5\u4e0b\u6765\u8981\u8bb2\u7684\u7279\u5f81\u9009\u62e9(feature select)\u5219\u662f\u8981\u4ece\u7ed9\u5b9a\u7684\u539f\u751f\u7279\u5f81\u96c6\u5408\u6c47\u603b\u9009\u51fa\u76f8\u5173\u7279\u5f81\u7684\u5b50\u96c6\uff0c\u5373\u7b5b\u9009\u6389\u65e0\u5173\u7279\u5f81\u3002<\/p>\n

  \u7b5b\u9009\u6389\u65e0\u5173\u7279\u5f81\u4e00\u822c\u662f\u5728\u8bad\u7ec3\u6a21\u578b\u4e4b\u524d\uff0c\u6240\u4ee5\u7279\u5f81\u9009\u62e9\u4e5f\u5c5e\u4e8e\u6784\u5efa\u673a\u5668\u5b66\u4e60\u7cfb\u7edf\u4e2d\u7684\u6570\u636e\u9884\u5904\u7406\u3002<\/p>\n

\u7279\u5f81\u9009\u62e9\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. \u7279\u5f81\u9009\u62e9\u7684\u7528\u5904<\/li>\n
  2. \u8fc7\u6ee4\u5f0f\u7279\u5f81\u9009\u62e9<\/li>\n
  3. \u5305\u88f9\u5f0f\u7279\u5f81\u9009\u62e9<\/li>\n
  4. \u5d4c\u5165\u5f0f\u7279\u5f81\u9009\u62e9<\/li>\n
  5. \u9ad8\u7ea7\u7279\u5f81\u9009\u62e9<\/li>\n<\/ol>\n

    \u7279\u5f81\u9009\u62e9\u5f15\u5165<\/h1>\n

      \u5982\u679c\u6211\u4eec\u6709\u4e00\u4e2a\u5b66\u4e60\u4efb\u52a1\u662f\u4e3a\u4e86\u5206\u6790\u4e00\u4e2a\u4eba\u5177\u5907\u4ec0\u4e48\u6761\u4ef6\u66f4\u53ef\u80fd\u8d22\u5bcc\u81ea\u7531\uff0c\u8ba9\u6211\u4eec\u60f3\u8c61\u4e00\u4e0b\uff0c\u867d\u7136\u4f60\u53ef\u80fd\u60f3\u8c61\u4e0d\u5230\uff0c\u6211\u5c31\u76f4\u8bf4\u4e86\uff0c\u8fd9\u4e2a\u793e\u4f1a\u4e0a\u8d22\u5bcc\u81ea\u7531\u7684\u4eba\u4e2a\u4eba\u957f\u76f8\u4e00\u822c\u822c\u7684\u6709\u5f88\u591a\uff1b\u4e2a\u4eba\u957f\u76f8\u633a\u6f02\u4eae\u7684\u5982\u660e\u661f\u4e5f\u4f1a\u6709\u5f88\uff1b\u4e2a\u4eba\u957f\u76f8\u76f8\u6bd4\u8f83\u4e0d\u968f\u65f6\u4ee3\u6f6e\u6d41\u7684\u4e5f\u4f1a\u6709\uff0c\u8fd9\u53ef\u4ee5\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u8868\u660e\u4e2a\u4eba\u662f\u5426\u80fd\u8d22\u5bcc\u81ea\u7531\u548c\u4e2a\u4eba\u957f\u76f8\u6ca1\u6709\u5173\u7cfb\u3002<\/p>\n

      \u4f46\u662f\u6211\u4eec\u53ef\u80fd\u518d\u5bf9\u4e2a\u4eba\u6761\u4ef6\u6570\u636e\u6316\u6398\u7684\u65f6\u5019\uff0c\u628a\u8fd9\u4e00\u4e2a\u7279\u5f81\u4e5f\u5f53\u505a\u5f71\u54cd\u6a21\u578b\u51c6\u786e\u5ea6\u7684\u6761\u4ef6\u4e4b\u4e00\uff0c\u5982\u679c\u53ea\u6709\u51e0\u4e2a\u7ef4\u5ea6\u7684\u7279\u5f81\uff0c\u6216\u51e0\u4e2a\u65e0\u5173\u7279\u5f81\uff0c\u6211\u4eec\u8ba1\u7b97\u673a\u53ef\u4ee5\u5e94\u4ed8\u7684\u8fc7\u6765\uff0c\u4f46\u662f\u5982\u679c\u51fa\u73b0\u7ef4\u6570\u707e\u96be\u7684\u65f6\u5019\uff0c\u6bcf\u591a\u4e00\u4e2a\u65e0\u5173\u7279\u5f81\u5bf9\u6211\u4eec\u7684\u8ba1\u7b97\u673a\u6765\u8bf4\uff0c\u8ba1\u7b97\u91cf\u90fd\u662f\u5e9e\u5927\u7684\uff0c\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u5c31\u5f97\u8003\u8651\u8fc7\u6ee4\u6389\u8fd9\u4e9b\u53ef\u80fd\u65e0\u610f\u4e49\u7684\u7279\u5f81\u4e86\uff0c\u6bd5\u7adf\u82e5\u5c06\u7eb7\u7e41\u590d\u6742\u7684\u56e0\u7d20\u62bd\u4e1d\u5265\u8327\uff0c\u53ea\u7559\u4e0b\u5173\u952e\u56e0\u7d20\uff0c\u771f\u76f8\u5f80\u5f80\u5bb9\u6613\u770b\u6e05\u3002<\/p>\n

      \u4e0a\u8ff0\u6240\u8bf4\u7684\u957f\u76f8\u53ef\u80fd\u662f\u901a\u8fc7\u6211\u4eec\u8ba4\u77e5\u5224\u65ad\u51fa\u6765\u7684\uff0c\u5de5\u4e1a\u4e0a\u53ef\u6ca1\u6709\u8fd9\u4e48\u591a\u53ef\u4ee5\u901a\u8fc7\u8ba4\u77e5\u5224\u65ad\u51fa\u6765\u7684\u65e0\u5173\u7279\u5f81\uff0c\u800c\u6211\u4eec\u6240\u8981\u8bb2\u8ff0\u7684\u7279\u5f81\u9009\u62e9\u5e72\u7684\u5c31\u662f\u8fd9\u4ef6\u4e8b\u3002<\/p>\n

    \u7279\u5f81\u9009\u62e9\u8be6\u89e3<\/h1>\n

    \u65e0\u5173\u7279\u5f81\u548c\u5197\u4f59\u7279\u5f81<\/h2>\n

      \u4e0a\u4e00\u8282\u8bb2\u5230\u4e86\u7279\u5f81\u9009\u62e9\u7684\u4efb\u52a1\u662f\u5c3d\u53ef\u80fd\u7684\u8fc7\u6ee4\u6389\u65e0\u5173\u7279\u5f81\uff0c\u4f46\u662f\u9664\u4e86\u65e0\u5173\u7279\u5f81\u4e4b\u5916\uff0c\u6709\u65f6\u5019\u6211\u4eec\u8fd8\u4f1a\u78b0\u5230\u5197\u4f59\u7279\u5f81(redundant feature)\u3002<\/p>\n

      \u5197\u4f59\u7279\u5f81\u53ef\u4ee5\u7406\u89e3\u4e3a\u53ef\u4ee5\u4ece\u5176\u4ed6\u7279\u5f81\u4e2d\u63a8\u6f14\u51fa\u6765\u7684\u7279\u5f81\uff0c\u6bd4\u5982\u6211\u4eec\u6b63\u5728\u8003\u8651\u7acb\u65b9\u4f53\u5bf9\u8c61\uff0c\u5982\u679c\u6211\u4eec\u6709\u4e86\u7acb\u65b9\u4f53\u5730\u9762\u5bbd$a$\u548c\u5e95\u9762\u957f$b$\u8fd9\u4e24\u4e2a\u7279\u5f81\uff0c\u5982\u679c\u518d\u7ed9\u6211\u4eec\u7acb\u65b9\u4f53\u5e95\u9762\u7684\u9762\u79ef$S$\u7684\u8bdd\uff0c\u5219\u8fd9\u4e2a\u9762\u79ef$S$\u5373\u4e3a\u5197\u4f59\u7279\u5f81\u3002\u4f46\u662f\u5982\u679c\u6211\u4eec\u7684\u5b66\u4e60\u4efb\u52a1\u662f\u4e3a\u4e86\u8ba1\u7b97\u4e00\u4e2a\u7acb\u65b9\u4f53\u7684\u4f53\u79ef$V$\uff0c\u901a\u8fc7\u7acb\u65b9\u4f53\u4f53\u79ef\u516c\u5f0f\u53ef\u4ee5\u77e5\u9053\u7ed9\u6211\u4eec$S$\u6bd4\u7ed9\u6211\u4eec$a$\u548c$b$\u66f4\u597d\uff0c\u56e0\u4e3a\u7ed9\u4e86$a$\u548c$b$\u6211\u4eec\u8fd8\u9700\u8981\u8ba1\u7b97\u51fa$S$\u3002\u5bf9\u4e8e\u8fd9\u79cd\u5197\u4f59\u7279\u5f81\u53ef\u4ee5\u8003\u8651\u7279\u5f81\u4e0e\u7279\u5f81\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u3002<\/p>\n

      \u8fd8\u6709\u4e00\u79cd\u5197\u4f59\u7279\u5f81\uff0c\u5982\u5b66\u751f\u7684\u6210\u7ee9\u53ea\u5206\u4e3a\u53ca\u683c\u548c\u4e0d\u53ca\u683c\uff0c\u6709\u65f6\u5019\u6211\u4eec\u53ef\u4ee5\u53ea\u8003\u8651\u53ca\u683c\u7684\u5b66\u751f\u60c5\u51b5\uff0c\u56e0\u4e3a\u6ca1\u8003\u8651\u5230\u53ca\u683c\u60c5\u51b5\u7684\u5b66\u751f\u5c31\u662f\u4e0d\u53ca\u683c\uff0c\u8fd9\u6837\u4e5f\u53ef\u4ee5\u9002\u5f53\u7684\u8fdb\u884c\u7279\u5f81\u9009\u62e9\u3002<\/p>\n

    \u8fc7\u6ee4\u5f0f\u7279\u5f81\u9009\u62e9<\/h2>\n

      \u8fc7\u6ee4\u5f0f\u9009\u62e9\u4e3b\u8981\u662f\uff0c\u901a\u8fc7\u4e0d\u540c\u7684\u65b9\u6cd5\u53bb\u68c0\u6d4b\u7279\u5f81\u4e0e\u6837\u672c\u4e4b\u95f4\u7684\u76f8\u5173\u5ea6\uff0c\u7136\u540e\u4f9d\u636e\u4e0d\u540c\u65b9\u6cd5\u7684\u68c0\u9a8c\u89c4\u5219\u7b5b\u9009\u7279\u5f81\u3002\u5bf9\u7279\u5f81\u8fc7\u6ee4\u4e4b\u540e\u518d\u8bad\u7ec3\u6a21\u578b\u3002<\/p>\n

    \u5361\u65b9\u68c0\u9a8c<\/h3>\n

      \u5361\u65b9\u68c0\u9a8c\u53ef\u4ee5\u68c0\u9a8c\u67d0\u4e2a\u7279\u5f81\u5206\u5e03\u4e0e\u8f93\u51fa\u503c\u5206\u5e03\u4e4b\u95f4\u7684\u76f8\u5173\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u7ed9\u5b9a\u5361\u65b9\u503c\u9608\u503c\uff0c\u9009\u62e9\u8fc7\u6ee4\u6389\u5361\u65b9\u503c\u8f83\u5927\u7684\u90e8\u5206\u7279\u5f81\u3002\u901a\u8fc7\u4e5f\u53ef\u4ee5\u901a\u8fc7p\u503c\u5224\u65ad\uff0cp\u503c\u4e3a\u7ed3\u679c\u4e3a\u53ef\u4fe1\u7a0b\u5ea6\u7684\u4e00\u4e2a\u9012\u51cf\u6307\u6807\uff0cp\u503c\u8d8a\u5927\uff0c\u6211\u4eec\u8d8a\u4e0d\u80fd\u8ba4\u4e3a\u6837\u672c\u4e2d\u53d8\u91cf\u7684\u5173\u8054\u662f\u603b\u4f53\u4e2d\u5404\u53d8\u91cf\u5173\u8054\u7684\u53ef\u9760\u6307\u6807\u3002<\/p>\n

    # \u5361\u65b9\u68c0\u9a8c\u793a\u4f8b\nimport numpy as np\nfrom sklearn.feature_selection import SelectKBest\nfrom sklearn.feature_selection import chi2\n\nX = [[0, 2, 0, 3], [0, 1, 4, 3], [0, 1, 1, 3]]\ny = np.array([[2], [4], [5]])<\/code><\/pre>\n
    # \u4f7f\u7528SelectKBest\u8fdb\u884c\u7279\u5f81\u9009\u62e9\nselector = SelectKBest(score_func=chi2, k=4)\nselector = selector.fit(X, y)\nprint('\u5361\u65b9\u503c:{}'.format(selector.scores_))<\/code><\/pre>\n
    \u5361\u65b9\u503c:[nan 0.5 5.2 0. ]<\/code><\/pre>\n
    # \u76f4\u63a5\u4f7f\u7528chi2\u7c7b\u83b7\u53d6chi_values\u503c\nchi_value, p_value = chi2(X, y)\nprint('\u5361\u65b9\u503c:{}\\np\u503c:{}'.format(chi_value, p_value))<\/code><\/pre>\n
    \u5361\u65b9\u503c:[nan 0.5 5.2 0. ]\np\u503c:[       nan 0.77880078 0.07427358 1.        ]<\/code><\/pre>\n
    \u65b9\u5dee\u8fc7\u6ee4<\/h3>\n
      \u9996\u5148\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa\u6240\u6709\u7279\u5f81\u7684\u65b9\u5dee$D(x_i)\\quad(i=1,2,\\cdots,n)$\uff0c\u7136\u540e\u7ed9\u5b9a\u4e00\u4e2a\u65b9\u5dee\u9608\u503c$\\epsilon$\uff0c\u5982\u679c$D(x_i)>\\epsilon$\uff0c\u5219\u8be5\u4fdd\u7559\u8be5\u7279\u5f81\uff0c\u53cd\u4e4b\uff0c\u8fc7\u6ee4\u6389\u8be5\u7279\u5f81\u3002\u4e00\u822c\u65b9\u5dee\u5c0f\u4e8e1\uff0c\u7279\u5f81\u5bf9\u6a21\u578b\u7684\u4f5c\u7528\u53ef\u80fd\u5e76\u4e0d\u5927\uff1b\u5982\u679c\u65b9\u5dee\u4e3a0\uff0c\u5373\u6240\u6709\u6837\u672c\u7684\u7279\u5f81\u53d6\u503c\u90fd\u662f\u4e00\u6837\u7684\uff0c\u5219\u8be5\u7279\u5f81\u4e00\u5b9a\u662f\u65e0\u7528\u7684\uff0c\u53ef\u4ee5\u76f4\u63a5\u820d\u5f03\u3002\u540c\u7406\u53ef\u4ee5\u4f7f\u7528from sklearn.feature_selection import SelectKBest<\/code>\u9009\u62e9\u7279\u5f81\uff0c\u6b64\u5904\u4e0d\u591a\u8d58\u8ff0\u3002<\/p>\n
    # \u65b9\u5dee\u8fc7\u6ee4\u793a\u4f8b\nfrom sklearn.feature_selection import VarianceThreshold\n\nX = [[0, 2, 0, 3], [0, 1, 4, 3], [0, 1, 1, 3]]\nselector = VarianceThreshold()<\/code><\/pre>\n
    print('\u901a\u8fc7\u65b9\u5dee\u8fc7\u6ee4\u7279\u5f81:\\n{}'.format(selector.fit_transform(X, y)))<\/code><\/pre>\n
    \u901a\u8fc7\u65b9\u5dee\u8fc7\u6ee4\u7279\u5f81:\n[[2 0]\n [1 4]\n [1 1]]<\/code><\/pre>\n
    \u76f8\u5173\u7cfb\u6570\u8fc7\u6ee4<\/h3>\n
      \u66fe\u7ecf\u5728\u7ebf\u6027\u56de\u5f52\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u8fc7\u8be5\u65b9\u6cd5\u3002\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u8bad\u7ec3\u96c6\u4e2d\u6837\u672c\u7279\u5f81\u4e0e\u8f93\u51fa\u503c\u4e4b\u95f4\u7684\u76f8\u5173\u5ea6\uff0c\u9009\u62e9\u76f8\u5173\u5ea6\u8f83\u5927\u7684\u90e8\u5206\u7279\u5f81\uff0c\u6b64\u5904\u6211\u4e48\u9009\u62e9pearsonr\u7cfb\u6570\u4e3e\u4f8b\u3002<\/p>\n
      \u5bf9\u4e8epearsonr\u7cfb\u6570\uff0c\u5b83\u8861\u91cf\u7684\u662f\u53d8\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u76f8\u5173\u6027\uff0c\u53d6\u503c\u8303\u56f4\u4e3a$[-1,1]$\uff0c\u5176\u4e2d1\u4ee3\u8868\u53d8\u91cf\u5b8c\u5168\u6b63\u76f8\u5173\uff0c-1\u4ee3\u8868\u5b8c\u5168\u8d1f\u76f8\u5173\u3002<\/p>\n
    # \u76f8\u5173\u7cfb\u6570\u8fc7\u6ee4\u793a\u4f8b\nimport numpy as np\nimport scipy as sc\n\na = [1, 2, 3, 4]\nb = [2, 3, 6, 9]\nc = [-2, -4, -6, -7]\na = np.array(a)\nb = np.array(b)\nc = np.array(c)<\/code><\/pre>\n
    print('a\u548cb\u4e4b\u95f4\u7684\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570:{}'.format(sc.stats.pearsonr(a, b)[0]))\nprint('a\u548cc\u4e4b\u95f4\u7684\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570:{}'.format(sc.stats.pearsonr(a, c)[0]))<\/code><\/pre>\n
    a\u548cb\u4e4b\u95f4\u7684\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570:0.9797958971132713\na\u548cc\u4e4b\u95f4\u7684\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570:-0.9897782665572894<\/code><\/pre>\n
    F\u68c0\u9a8c<\/h3>\n
      F\u68c0\u9a8c\uff0c\u6700\u5e38\u7528\u7684\u522b\u540d\u53eb\u505a\u8054\u5408\u5047\u8bbe\u68c0\u9a8c(joint hypotheses test)\uff0c\u6b64\u5916\u4e5f\u79f0\u65b9\u5dee\u6bd4\u7387\u68c0\u9a8c\u3001\u65b9\u5dee\u9f50\u6027\u68c0\u9a8c\uff0c\u901a\u4ea7\u5982\u5361\u65b9\u68c0\u9a8c\uff0c\u7ed9\u5b9aF\u503c\u9608\u503c\uff0c\u9009\u62e9F\u503c\u8f83\u5927\u7684\u90e8\u5206\u7279\u5f81\u3002F\u68c0\u9a8c\u53ef\u4ee5\u68c0\u9a8c\u5206\u7c7b\u548c\u56de\u5f52\u95ee\u9898\uff0c\u5728scikit-learn\u5e93\u4e2d\u5206\u522b\u5bf9\u5e94from sklearn.feature_selection import f_classif<\/code>\u548cfrom sklearn.feature_selection import f_regression<\/code>\u6b64\u5904\u53ea\u7ed9\u51fa\u56de\u5f52\u95ee\u9898\u7684\u4ee3\u7801\uff0c\u5e76\u4e14\u540c\u7406\u53ef\u4ee5\u4f7f\u7528from sklearn.feature_selection import SelectKBest<\/code>\u9009\u62e9\u7279\u5f81\uff0c\u6b64\u5904\u4e0d\u591a\u8d58\u8ff0\u3002<\/p>\n
    # F\u68c0\u9a8c\u793a\u4f8b\nimport numpy as np\nfrom sklearn.feature_selection import f_classif\nfrom sklearn.feature_selection import f_regression\n\nX = [[1, 2, 4, 3], [2, 1, 4, 3], [3, 1, 1, 4]]\ny = np.array([[2], [4], [5]]).ravel()<\/code><\/pre>\n
    f_value, p_value = f_regression(X, y)\nprint('f_value:{}\\np_value:{}'.format(f_value, p_value))<\/code><\/pre>\n
    f_value:[27.          8.33333333  1.33333333  1.33333333]\np_value:[0.12103772 0.21229562 0.45437105 0.45437105]<\/code><\/pre>\n
    \u4e92\u4fe1\u606f\u8fc7\u6ee4<\/h3>\n
      \u4e92\u4fe1\u606f\u5373\u4fe1\u606f\u589e\u76ca\uff0c\u4e92\u4fe1\u606f\u503c\u8d8a\u5927\uff0c\u8bf4\u660e\u8be5\u7279\u5f81\u548c\u8f93\u51fa\u503c\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u8d8a\u5927\uff0c\u5373\u7b5b\u9009\u6389\u4e92\u4fe1\u606f\u503c\u8f83\u5c0f\u7684\u7279\u5f81\u3002\u4e00\u822c\u53ef\u4ee5\u8ba1\u7b97\u5206\u7c7b\u548c\u56de\u5f52\u95ee\u9898\u4e2d\u7279\u5f81\u4e0e\u8f93\u51fa\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\uff0c\u5728scikit-learn\u5e93\u4e2d\u5206\u522b\u5bf9\u5e94from sklearn.feature_selection import mutual_info_classif<\/code>\u548cfrom sklearn.feature_selection import mutual_info_regression<\/code>\uff0c\u6b64\u5904\u53ea\u7ed9\u51fa\u56de\u5f52\u95ee\u9898\u7684\u4ee3\u7801\uff0c\u5e76\u4e14\u540c\u7406\u53ef\u4ee5\u4f7f\u7528from sklearn.feature_selection import SelectKBest<\/code>\u9009\u62e9\u7279\u5f81\uff0c\u6b64\u5904\u4e0d\u591a\u8d58\u8ff0\u3002<\/p>\n
    # \u4e92\u4fe1\u606f\u8fc7\u6ee4\u793a\u4f8b\nimport numpy as np\nfrom sklearn.feature_selection import mutual_info_regression\nfrom sklearn.feature_selection import mutual_info_classif\n\nX = [[1., 2., 4., 3.], [2., 1., 4., 3.], [3., 1., 1., 4.]]\ny = np.array([[2.], [4.], [5.]]).ravel()<\/code><\/pre>\n
    mi = mutual_info_regression(X, y, n_neighbors=1)\nprint('mi:{}'.format(mi))<\/code><\/pre>\n
    mi:[0.5        0.16666667 0.         0.16666667]<\/code><\/pre>\n
    \u5305\u88f9\u5f0f\u7279\u5f81\u9009\u62e9<\/h2>\n
      \u5305\u88f9\u5f0f\u9009\u62e9\u5e76\u4e0d\u662f\u76f4\u63a5\u5bf9\u7279\u5f81\u8fdb\u884c\u9009\u62e9\uff0c\u800c\u662f\u628a\u6700\u7ec8\u5c06\u8981\u4f7f\u7528\u7684\u5b66\u4e60\u5668\u7684\u6027\u80fd\u4f5c\u4e3a\u7279\u5f81\u5b50\u96c6\u7684\u8bc4\u4ef7\u6807\u51c6\uff0c\u5373\u9009\u62e9\u6700\u6709\u5229\u4e8e\u5b66\u4e60\u5668\u6027\u80fd\u7684\u7279\u5f81\u5b50\u96c6\u3002<\/p>\n
      \u5305\u88f9\u5f0f\u9009\u62e9\u4ece\u5b66\u4e60\u5668\u6027\u80fd\u4e0a\u770b\uff0c\u8f83\u4e8e\u8fc7\u6ee4\u5f0f\u7279\u5f81\u9009\u62e9\u4f1a\u66f4\u597d\uff0c\u4f46\u662f\u7531\u4e8e\u662f\u4ece\u4e0d\u540c\u7684\u5b66\u4e60\u5668\u4e2d\u9009\u62e9\u6700\u4f18\u7684\u5b66\u4e60\u5668\uff0c\u9700\u8981\u8bad\u7ec3\u591a\u4e2a\u5b66\u4e60\u5668\uff0c\u56e0\u6b64\u8ba1\u7b97\u673a\u7684\u8ba1\u7b97\u5f00\u9500\u8f83\u4e8e\u8fc7\u6ee4\u5f0f\u7279\u5f81\u9009\u62e9\u4f1a\u5927\u5f88\u591a\u3002<\/p>\n
    \u9012\u5f52\u7279\u5f81\u6d88\u9664<\/h3>\n
      \u9012\u5f52\u7279\u5f81\u6d88\u9664\u53ef\u4ee5\u7406\u89e3\u6210\uff0c\u6ca1\u8bad\u7ec3\u4e00\u6b21\u6a21\u578b\uff0c\u6d88\u9664\u82e5\u5e72\u4e2a\u6743\u503c\u7cfb\u6570\u8f83\u5c0f\u7684\u7279\u5f81\uff0c\u7136\u540e\u57fa\u4e8e\u65b0\u7684\u7279\u5f81\u503c\u8fdb\u884c\u4e0b\u4e00\u8f6e\u8bad\u7ec3\uff0c\u4e0d\u65ad\u91cd\u590d\u4e0a\u8ff0\u7684\u8fc7\u7a0b\u3002<\/p>\n
      \u6211\u4eec\u4ee5\u8f83\u4e3a\u7ecf\u5178\u7684SVM-REF\u4e3e\u4f8b\uff0cSVM\u5728\u7b2c\u4e00\u8f6e\u8bad\u7ec3\u7684\u65f6\u5019\uff0c\u5f97\u5230\u8d85\u5e73\u9762$S=w^Tx+b=0$\uff0c\u5982\u679c\u6bcf\u4e2a\u8bad\u7ec3\u6570\u636e\u6709$n$\u4e2a\u7279\u5f81\uff0c\u5219SVM-REF\u4f1a\u6d88\u9664$n$\u4e2a\u7279\u5f81\u4e2d${w_i}^2,\\quad(i=1,2,\\cdots,n)$\u6700\u5c0f\u7684\u7279\u5f81\uff0c\u56e0\u6b64\u7279\u5f81\u6570\u5c06\u53d8\u6210$n-1$\u4e2a\uff0c\u7136\u540e\u5bf9\u8bad\u7ec3\u96c6\u7ee7\u7eed\u8bad\u7ec3\uff0c\u4f7f\u7528\u4e0a\u8ff0\u65b9\u6cd5\u5c06\u7279\u5f81\u53d8\u6210$n-2$\u4e2a\u2026\u2026<\/p>\n
      \u5728scikit-learn\u5e93\u4e2d\u53ef\u4ee5\u4f7f\u7528from sklearn.feature_selection import RFE<\/code>\u548cfrom sklearn.feature_selection import RFECV<\/code>\u65b9\u6cd5\u7528\u4e8e\u9012\u5f52\u7279\u5f81\u6d88\u9664\uff0c\u6b64\u5904\u4f7f\u7528CV\u65b9\u6cd5\u8ba9\u6a21\u578b\u81ea\u52a8\u6d88\u9664\u6307\u5b9a\u4e2a\u6570\u7684\u7279\u5f81\u3002<\/p>\n
    # \u9012\u5f52\u7279\u5f81\u6d88\u9664\u793a\u4f8b\nfrom sklearn.datasets import make_friedman1\nfrom sklearn.feature_selection import RFECV\nfrom sklearn.svm import SVR\n\n# \u751f\u621010\u7ef4\u7279\u5f81\u768450\u4e2a\u6837\u672c\nX, y = make_friedman1(n_samples=50, n_features=10, random_state=0)\nestimator = SVR(kernel="linear")\nselector = RFECV(estimator, step=1, cv=4)\nselector = selector.fit(X, y)<\/code><\/pre>\n
    print('\u7279\u5f81\u4e2a\u6570:{}'.format(selector.n_features_))<\/code><\/pre>\n
    \u7279\u5f81\u4e2a\u6570:6<\/code><\/pre>\n
    print('\u88ab\u9009\u5b9a\u7684\u7279\u5f81:{}'.format(selector.support_))<\/code><\/pre>\n
    \u88ab\u9009\u5b9a\u7684\u7279\u5f81:[ True  True  True  True  True False False False  True False]<\/code><\/pre>\n
    print('\u7279\u5f81\u6392\u540d:{}'.format(selector.ranking_))<\/code><\/pre>\n
    \u7279\u5f81\u6392\u540d:[1 1 1 1 1 5 3 2 1 4]<\/code><\/pre>\n
    \u5d4c\u5165\u5f0f\u7279\u5f81\u9009\u62e9<\/h2>\n
      \u5d4c\u5165\u5f0f\u7279\u5f81\u9009\u62e9\u662f\u5c06\u7279\u5f81\u9009\u62e9\u8fc7\u7a0b\u4e0e\u5b66\u4e60\u5668\u8bad\u7ec3\u8fc7\u7a0b\u878d\u4e3a\u4e00\u4f53\uff0c\u5373\u4e24\u8005\u5728\u540c\u4e00\u4e2a\u4f18\u5316\u8fc7\u7a0b\u4e2d\u5b8c\u6210\u3002\u5d4c\u5165\u5f0f\u7279\u5f81\u4e00\u822c\u9700\u8981\u80fd\u5f97\u5230\u7279\u5f81\u6743\u91cd\u7cfb\u6570\u6216\u7279\u5f81\u91cd\u8981\u5ea6\u7684\u5b66\u4e60\u5668\uff0c\u4e5f\u5c31\u662f\u8bf4\u5982\u7ebf\u6027\u56de\u5f52\u3001\u903b\u8f91\u56de\u5f52\u3001\u51b3\u7b56\u6811\u3001\u968f\u673a\u68ee\u6797\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u5d4c\u5165\u5f0f\u7279\u5f81\u9009\u7684\u5b66\u4e60\u5668\u3002<\/p>\n
      \u901a\u5e38\u4f7f\u7528\u6700\u591a\u7684\u662fL1\u6b63\u5219\u5316\u548cL2\u6b63\u5219\u5316\uff0c\u5728\u7ebf\u6027\u56de\u5f52\u7684\u6b63\u5219\u5316\u4e2d\u8bb2\u5230\uff0cL1\u548cL2\u6b63\u5219\u5316\u53ef\u4ee5\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\uff0c\u4f46\u662fL1\u548cL2\u6b63\u5219\u5316\u6709\u65f6\u5019\u4e5f\u88ab\u7528\u6765\u505a\u7279\u5f81\u9009\u62e9\u3002\u5f53\u6b63\u5219\u5316\u7cfb\u6570\u8d8a\u5927\u7684\u65f6\u5019\uff0c\u5bf9\u6a21\u578b\u7684\u60e9\u7f5a\u529b\u5ea6\u4e5f\u8d8a\u5927\uff0c\u56e0\u6b64\u4f1a\u5bfc\u81f4\u7279\u5f81\u7684\u6743\u91cd\u7cfb\u6570\u53d8\u62100\uff0c\u8fd9\u6837\u7279\u5f81\u5bf9\u4e8e\u6a21\u578b\u800c\u8a00\u5c31\u6ca1\u6709\u610f\u4e49\u4e86\uff0c\u56e0\u6b64\u4fbf\u8fbe\u5230\u4e86\u7279\u5f81\u9009\u62e9\u7684\u76ee\u7684\u3002<\/p>\n
      \u5728scikit-learn\u5e93\u4e2d\u53ef\u4ee5\u4f7f\u7528from sklearn.feature_selection import SelectFromModel<\/code>\u6765\u9009\u62e9\u7279\u5f81\uff0c\u6b64\u5904\u4f7f\u7528L1\u6b63\u5219\u5316\u548c\u968f\u673a\u68ee\u6797\u4e3e\u4f8b\u3002<\/p>\n
    # \u5d4c\u5165\u5f0f\u9009\u62e9\u793a\u4f8b\nfrom sklearn.datasets import make_friedman1\nfrom sklearn.linear_model import Lasso\nfrom sklearn.ensemble import RandomForestRegressor\nfrom sklearn.feature_selection import SelectFromModel\n\nX, y = make_friedman1(n_samples=100, n_features=10, random_state=0)\n\n# \u6709\u7cfb\u6570\u7684\u7ebf\u6027\u6a21\u578b\u4e2d\uff0cL1\u6b63\u5219\u5316\u53ef\u751f\u6210\u4e00\u4e2a\u7a00\u758f\u77e9\u9635\nlasso = Lasso()\nlasso.fit(X, y)\nmodel = SelectFromModel(lasso)\nnew_X = model.fit(X, y)\nprint('L1\u6b63\u5219\u5316:{}'.format(new_X.get_support()))\n\n# \u65e0\u7cfb\u6570\u7684\u6a21\u578b\u4e2d\uff0c\u6839\u636e\u91cd\u8981\u6027\u7b5b\u9009\u65e0\u5173\u7279\u5f81\nrf = RandomForestRegressor(n_estimators=10)\nrf.fit(X, y)\nmodel = SelectFromModel(rf)\nnew_X = model.fit(X, y)\nprint('\u968f\u673a\u68ee\u6797:{}'.format(new_X.get_support()))<\/code><\/pre>\n
    L1\u6b63\u5219\u5316:[False False False  True False False False False False False]\n\u968f\u673a\u68ee\u6797:[ True False False  True False False False False False False]<\/code><\/pre>\n
    \u9ad8\u7ea7\u7279\u5f81\u5bfb\u627e<\/h2>\n
      \u9ad8\u7ea7\u7279\u5f81\u53ef\u4ee5\u7406\u89e3\u6210\uff0c\u8bad\u7ec3\u6570\u636e\u7279\u5f81\u6ca1\u6709\u7ed9\u6211\u4eec\u7684\u4fe1\u606f\uff0c\u5c31\u90a3\u5197\u4f59\u7279\u5f81\u4e2d\u7684\u4f8b\u5b50\u4e3e\u4f8b\uff0c\u5982\u679c\u5f97\u5230\u4e86\u6b63\u65b9\u4f53\u7684\u8fb9\u957f$a$\uff0c\u8fdb\u800c\u53ef\u4ee5\u5f97\u5230\u6b63\u65b9\u4f53\u7684\u67d0\u4e00\u4e2a\u9762\u7684\u8868\u9762\u79ef$S=a^2$\uff0c\u8fdb\u800c\u53c8\u53ef\u4ee5\u5f97\u5230\u7acb\u65b9\u4f53\u7684\u4f53\u79ef$V=a^3$\uff0c\u8fdb\u800c\u53ef\u4ee5\u5f97\u5230\u2026\u4e5f\u5c31\u662f\u8bf4\uff0c\u9ad8\u7ea7\u7279\u5f81\u53ef\u4ee5\u4e00\u76f4\u627e\u4e0b\u53bb\u3002\u8fd9\u4e5f\u4e00\u5b9a\u7a0b\u5ea6\u8bf4\u660e\u4e86\u5197\u4f59\u7279\u5f81\u6709\u65f6\u5019\u4e5f\u53ef\u80fd\u662f\u6709\u76ca\u7279\u5f81\uff0c\u6240\u4ee5\u5bf9\u5197\u4f59\u7279\u5f81\u505a\u5904\u7406\u4e5f\u9700\u8981\u591a\u591a\u8003\u8651\u3002<\/p>\n
      \u5728Kaggle\u4e4b\u7c7b\u7684\u7b97\u6cd5\u7ade\u8d5b\u4e2d\uff0c\u9ad8\u5206\u56e2\u961f\u4e3b\u8981\u4f7f\u7528\u7684\u65b9\u6cd5\u9664\u4e86\u96c6\u6210\u5b66\u4e60\u7b97\u6cd5\uff0c\u5269\u4e0b\u7684\u4e3b\u8981\u5c31\u662f\u5728\u5bfb\u627e\u9ad8\u7ea7\u7279\u5f81\u3002\u6240\u4ee5\u5bfb\u627e\u9ad8\u7ea7\u7279\u5f81\u4e00\u822c\u662f\u6a21\u578b\u4f18\u5316\u7684\u5fc5\u8981\u6b65\u9aa4\u4e4b\u4e00\u3002\u4f46\u662f\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u7b2c\u4e00\u6b21\u5efa\u7acb\u6a21\u578b\u7684\u65f6\u5019\uff0c\u6211\u4eec\u53ef\u4ee5\u5148\u4e0d\u5bfb\u627e\u9ad8\u7ea7\u7279\u5f81\uff0c\u5f97\u5230\u4ee5\u540e\u57fa\u51c6\u6a21\u578b\u540e\uff0c\u518d\u5bfb\u627e\u9ad8\u7ea7\u7279\u5f81\u8fdb\u884c\u4f18\u5316\u3002<\/p>\n
    \u5bfb\u627e\u9ad8\u7ea7\u7279\u5f81\u7684\u65b9\u6cd5<\/h3>\n
      \n
    1. \u82e5\u5e72\u9879\u7279\u5f81\u52a0\u548c\uff1a \u80a1\u7968\u4ea4\u6613\u4e2d\u5f97\u5230\u67d0\u53ea\u80a1\u7968\u7684\u6bcf\u5468\u7684\u603b\u4ef7\u683c<\/li>\n
    2. \u82e5\u5e72\u9879\u7279\u5f81\u4e4b\u5dee\uff1a \u80a1\u7968\u4ea4\u6613\u4e2d\u5f97\u5230\u67d0\u53ea\u80a1\u7968\u7684\u4e24\u5929\u7684\u5dee\u989d<\/li>\n
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      \u5c0f\u7ed3<\/h1>\n
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