{"id":216,"date":"2016-11-24T17:40:59","date_gmt":"2016-11-24T09:40:59","guid":{"rendered":"http:\/\/ayonel.me\/?p=216"},"modified":"2016-12-30T14:43:28","modified_gmt":"2016-12-30T06:43:28","slug":"python-nformation-gain","status":"publish","type":"post","link":"https:\/\/ayonel.malash.net\/index.php\/2016\/11\/24\/python-nformation-gain\/","title":{"rendered":"python\u8ba1\u7b97\u4fe1\u606f\u589e\u76ca (information gain)"},"content":{"rendered":"

\u5728\u6587\u672c\u5206\u7c7b\u4e2d\u6709\u8fd9\u6837\u4e00\u4e2a\u573a\u666f\uff0c\u5f53\u6211\u4eec\u5df2\u7ecf\u5206\u597d\u8bcd\uff0c\u5e76\u6784\u9020\u51fa\u8bcd\u9891\u5411\u91cf\u540e\uff0c\u8fd9\u4e2a\u5411\u91cf\u4f1a\u5f88\u5927\uff0c\u7ecf\u5e38\u4f1a\u591a\u8fbe\u51e0\u4e07\u7ef4\uff0c\u751a\u81f3\u5341\u51e0\u4e07\u7ef4\u3002\u8fd9\u79cd\u89c4\u6a21\u7684\u6a21\u578b\u5982\u679c\u8981\u7528SVM\u7b49\u8f83\u9ad8\u7ea7\u7684\u673a\u5668\u5b66\u4e60\u8fdb\u884c\u8bad\u7ec3\u7684\u8bdd\uff0c\u90a3\u7b80\u76f4\u662f\u6162\u7684\u8981\u6b7b\uff0c\u6df1\u5ea6\u5b66\u4e60\u5c31\u518d\u522b\u8c08\u4e86\u3002\u4e3a\u4e86\u8f83\u5c11\u5411\u91cf\u7ef4\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528\u4e00\u4e9b\u65b9\u6cd5\uff0c\u6bd4\u5982\u5728\u8bcd\u5411\u91cf\u4e2d\u8fc7\u6ee4\u6389\u8bcd\u9891\u5c0f\u4e8eN\u7684\u8bcd\uff0c\u8fd9\u4e2aN\u53ef\u4ee5\u81ea\u5df1\u5b9a\uff0c\u4f46\u4e00\u822c\u53d6\u503c\u6bd4\u8f83\u5c0f\u3002\u91c7\u7528\u8fd9\u79cd\u65b9\u6cd5\u80fd\u6709\u6548\u964d\u4f4e\u5411\u91cf\u7ef4\u5ea6\uff0c\u4f46\u662f\u8fd8\u662f\u4e0d\u591f\u3002\u6211\u4eec\u4e0d\u80fd\u4e3a\u4e86\u964d\u4f4e\u5411\u91cf\u7ef4\u5ea6\u5230\u4e00\u5b9a\u7684\u7a0b\u5ea6\u800c\u4e0d\u65ad\u5730\u589e\u5927N\u503c\uff0c\u56e0\u4e3a\u8fd9\u79cd\u8fc7\u6ee4\u6389\u4f4e\u9891\u6b21\u7684\u65b9\u6cd5\uff0c\u5bf9\u5411\u91cf\u7ef4\u5ea6\u7684\u51cf\u5c11\u662f\u968f\u7740N\u7684\u589e\u5927\u800c\u9010\u6b65\u964d\u4f4e\u7684\uff0c\u6bd4\u5982\u8bf4\uff1a\u5c06N=1\uff0c\u4f60\u53ef\u4ee5\u8fc7\u6ee4\u638910000\u4e2a\u5355\u8bcd\uff1b\u63a5\u7740N=2\uff0c\u4f60\u8fc7\u6ee4\u6389\u4e8615000\u4e2a\u5355\u8bcd\uff1bN=3\uff0c\u8fc7\u6ee4\u638916000\u4e2a\u5355\u8bcd\uff1bN=4\uff0c\u8fc7\u6ee4\u6389\u4e8616800\u4e2a\u5355\u8bcd\u3002\u6240\u4ee5\u8fd9\u79cd\u65b9\u6cd5\u9002\u7528\u4e8e\u7c97\u7cd9\u5730\u964d\u7ef4\u3002\u6211\u4eec\u53ef\u4ee5\u5728\u539f\u59cb\u6570\u636e\u96c6\u4e0a\u5229\u7528\u8fd9\u79cd\u65b9\u6cd5\u5148\u8fc7\u6ee4\u4e00\u6ce2\u8bcd\u3002\u7136\u540e\u518d\u60f3\u522b\u7684\u65b9\u6cd5\u3002<\/p>\n

\u90a3\u4e48\u600e\u6837\u624d\u80fd\u5c06\u5411\u91cf\u7684\u7ef4\u5ea6\u964d\u5230\u6211\u4eec\u60f3\u8981\u7684\u5927\u5c0f\uff0c\u800c\u4e0d\u4f1a\u5bf9\u6574\u4e2a\u7cfb\u7edf\u7684\u4fe1\u606f\u4ea7\u751f\u91cd\u5927\u5f71\u54cd\u5462\uff1f\u8fd9\u4e2a\u95ee\u9898\u5c31\u662f\u7279\u5f81\u9009\u62e9\u7684\u95ee\u9898\u3002
\n\u7279\u5f81\u9009\u62e9\u67092\u4e2a\u5f88\u660e\u663e\u7684\u4f18\u70b9\uff1a
\n1. \u51cf\u5c11\u7279\u5f81\u6570\u91cf\u3001\u964d\u7ef4\uff0c\u4f7f\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u66f4\u5f3a\uff0c\u51cf\u5c11\u8fc7\u62df\u5408
\n2. \u589e\u5f3a\u5bf9\u7279\u5f81\u548c\u7279\u5f81\u503c\u4e4b\u95f4\u7684\u7406\u89e3<\/p>\n

\u4e00\u822c\u5bf9\u4e8e\u6587\u672c\u5206\u7c7b\u6709\u4e24\u79cd\u6700\u5e38\u7528\u7684\u4fe1\u606f\u9009\u62e9\u65b9\u6cd5\u3002\u4e00\u4e2a\u662f\u5361\u65b9\u68c0\u9a8c\uff0c\u53e6\u4e00\u4e2a\u662f\u4fe1\u606f\u589e\u76ca\u3002\u4f46\u51e1\u662f\u7279\u5f81\u9009\u62e9\uff0c\u603b\u662f\u5728\u5c06\u7279\u5f81\u7684\u91cd\u8981\u7a0b\u5ea6\u91cf\u5316\u4e4b\u540e\u518d\u8fdb\u884c\u9009\u62e9\uff0c\u800c\u5982\u4f55\u91cf\u5316\u7279\u5f81\u7684\u91cd\u8981\u6027\uff0c\u5c31\u6210\u4e86\u5404\u79cd\u65b9\u6cd5\u95f4\u6700\u5927\u7684\u4e0d\u540c\u3002\u5f00\u65b9\u68c0\u9a8c\u4e2d\u4f7f\u7528\u7279\u5f81\u4e0e\u7c7b\u522b\u95f4\u7684\u5173\u8054\u6027\u6765\u8fdb\u884c\u8fd9\u4e2a\u91cf\u5316\uff0c\u5173\u8054\u6027\u8d8a\u5f3a\uff0c\u7279\u5f81\u5f97\u5206\u8d8a\u9ad8\uff0c\u8be5\u7279\u5f81\u8d8a\u5e94\u8be5\u88ab\u4fdd\u7559\u3002<\/p>\n

\u5728\u4fe1\u606f\u589e\u76ca\u4e2d\uff0c\u91cd\u8981\u6027\u7684\u8861\u91cf\u6807\u51c6\u5c31\u662f\u770b\u7279\u5f81\u80fd\u591f\u4e3a\u5206\u7c7b\u7cfb\u7edf\u5e26\u6765\u591a\u5c11\u4fe1\u606f\uff0c\u5e26\u6765\u7684\u4fe1\u606f\u8d8a\u591a\uff0c\u8be5\u7279\u5f81\u8d8a\u91cd\u8981\u3002\u672c\u6587\u53ea\u9488\u5bf9\u4fe1\u606f\u589e\u76ca\uff0c\u5361\u65b9\u68c0\u9a8c\u8bf7\u81ea\u884c\u8c37\u6b4c\u5ea6\u5a18\u3002<\/p>\n

\u5173\u4e8e\u4fe1\u606f\u589e\u76ca\uff0c\u5927\u725bJasper<\/a>\u6709\u4e00\u7bc7\u5341\u5206\u7cbe\u5f69\u7684\u535a\u6587<\/a>\u6765\u8fdb\u884c\u4ecb\u7ecd\uff0c\u5176\u8ba1\u7b97\u65b9\u6cd5Jasper\u5df2\u7ecf\u8bf4\u5f97\u5341\u5206\u6e05\u695a\u4e86\u3002\u5efa\u8bae\u4f60\u770b\u5b8c\u8fd9\u7bc7\u6587\u7ae0\uff0c\u518d\u6765\u7ee7\u7eed\u9605\u8bfb\u672c\u6587\u3002<\/p>\n

\u4fe1\u606f\u589e\u76ca\u6700\u540e\u7684\u63a8\u5bfc\u516c\u5f0f\u4e3a
\n\u6211\u4eec\u73b0\u5728\u8981\u7528python\u6765\u5b9e\u73b0\u4fe1\u606f\u589e\u76ca\u7684\u8ba1\u7b97\u3002
\n\u5047\u8bbe\u6211\u4eec\u67094\u7bc7\u6587\u6863\uff0c\u6bcf\u7bc7\u6587\u6863\u90fd\u5df2\u7ecf\u5206\u597d\u8bcd\u4e86\uff1a<\/p>\n

\u6587\u68631\uff1a \u9c9c\u82b1 \u4f53\u80b2
\n\u6587\u68632\uff1a \u592a\u9633 \u5927\u8c61 \u4f53\u80b2
\n\u6587\u68633:  \u5927\u8c61<\/div><\/div>\n

\u5047\u8bbe\u6211\u4eec\u8bcd\u7684\u7d22\u5f15\u662f\uff1a<\/p>\n

[\u9c9c\u82b1\uff0c\u592a\u9633\uff0c\u5927\u8c61\uff0c\u4f53\u80b2]<\/div><\/div>\n

\u90a3\u4e48\u6211\u4eec\u7684\u6587\u6863\u6784\u9020\u597d\u7684\u8bcd\u9891\u5411\u91cf\u5206\u522b\u662f\uff1a<\/p>\n

\u6587\u68631\uff1a[1,0,0,1]:
\n\u6587\u68632\uff1a[0,1,1,1]
\n\u6587\u68633\uff1a[0,0,1,0]<\/div><\/div>\n

\u5047\u8bbe3\u7bc7\u6587\u6863\u7684\u5206\u7c7b\u5206\u522b\u662f\uff1a\u6587\u68631\u548c\u6587\u68632\u5c5e\u4e8e\u201c0\u201d\u7c7b\uff0c\u6587\u68633\u5c5e\u4e8e\u201c1\u201d\u7c7b\u3002<\/p>\n

\u90a3\u4e48\u6211\u4eec\u7a0b\u5e8f\u7684\u8f93\u5165\u5c31\u662fX\uff0cy\uff1a
\nX\u4ee3\u8868\u8bcd\u9891\u5411\u91cf\u7ec4\u6210\u7684\u77e9\u9635<\/p>\n

[[1,0,0,1],
\n [0,1,1,1],
\n [0,0,1,0]]<\/div><\/div>\n

y\u4ee3\u8868\u6807\u7b7e\u5411\u91cf<\/p>\n

[0,0,1]<\/div><\/div>\n

\u6211\u4eec\u5229\u7528numpy\u5305\u4e2d\u7684\u77e9\u9635\u6765\u5305\u88c5X\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u63d0\u4f9b\u8bb8\u591a\u65b9\u4fbf\u7684\u9ad8\u7ea7\u51fd\u6570\u3002
\n\u4e0b\u9762\u5c31\u8d34\u4e0a\u4ee3\u7801\uff0c\u4ee3\u7801\u91cc\u6709\u6ce8\u91ca\uff0c\u6709\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u597d\u597d\u7814\u7a76\u4e00\u4e0b\uff0c\u5982\u679c\u4f60\u60f3\u62ff\u6765\u76f4\u63a5\u7528\u7684\u8bdd\uff0c\u4e5f\u662f\u6ca1\u95ee\u9898\u7684\u3002\u4ee3\u7801\u7684\u6548\u7387\u5e94\u8be5\u8fd8\u662f\u53ef\u4ee5\u7684\uff0c\u5176\u4e2d\u6709\u4e00\u4e2a\u6bd4\u8f83\u5de7\u5999\u7684\u77e9\u9635\u7684\u8f6c\u79e9\u3002
\n\u53ef\u4ee5\u597d\u597d\u7406\u89e3\u4e00\u4e0b\uff1a<\/p>\n

#coding: utf-8<\/span>
\nimport<\/span> numpy as<\/span> np
\n'''
\n    \u8ba1\u7b97\u4fe1\u606f\u589e\u76ca
\n    powerd by ayonel
\n'''<\/span>
\nclass<\/span> InformationGain:
\n    def<\/span> __init__<\/span>(<\/span>self<\/span>,<\/span> X,<\/span> y)<\/span>:
\n        self<\/span>.X<\/span> =<\/span> X
\n        self<\/span>.y<\/span> =<\/span> y
\n        self<\/span>.totalSampleCount<\/span> =<\/span> X.shape<\/span>[<\/span>0<\/span>]<\/span>      # \u6837\u672c\u603b\u6570<\/span>
\n        self<\/span>.totalSystemEntropy<\/span> =<\/span> 0<\/span>             # \u7cfb\u7edf\u603b\u71b5<\/span>
\n        self<\/span>.totalClassCountDict<\/span> =<\/span> {<\/span>}<\/span>           # \u5b58\u50a8\u6bcf\u4e2a\u7c7b\u522b\u7684\u6837\u672c\u6570\u91cf\u662f\u591a\u5c11<\/span>
\n        self<\/span>.nonzeroPosition<\/span> =<\/span> X.T<\/span>.nonzero<\/span>(<\/span>)<\/span>    # \u5c06X\u8f6c\u7f6e\u4e4b\u540e\u8f93\u51fa\u975e\u96f6\u503c\u7684\u4f4d\u7f6e<\/span>
\n        self<\/span>.igResult<\/span> =<\/span> [<\/span>]<\/span>                      # \u4fdd\u5b58\u7ed3\u679c\u7684list<\/span>
\n        self<\/span>.wordExistSampleCount<\/span> =<\/span> 0<\/span>
\n        self<\/span>.wordExistClassCountDict<\/span> =<\/span> {<\/span>}<\/span>
\n        self<\/span>.iter<\/span>(<\/span>)<\/span>
\n
\n
\n    # \u5c06\u7ed3\u679c\u5217\u8868\u6392\u5e8f\u8f93\u51fa<\/span>
\n    def<\/span> get_result(<\/span>self<\/span>)<\/span>:
\n        return<\/span> self<\/span>.igResult<\/span>
\n
\n    # \u8ba1\u7b97\u7cfb\u7edf\u603b\u71b5<\/span>
\n    def<\/span> cal_total_system_entropy(<\/span>self<\/span>)<\/span>:
\n        # \u8ba1\u7b97\u6bcf\u4e2a\u7c7b\u522b\u5404\u6709\u591a\u5c11\u4e2a<\/span>
\n        for<\/span> label in<\/span> self<\/span>.y<\/span>:
\n            if<\/span> label not<\/span> in<\/span> self<\/span>.totalClassCountDict<\/span>:
\n                self<\/span>.totalClassCountDict<\/span>[<\/span>label]<\/span> =<\/span> 1<\/span>
\n            else<\/span>:
\n                self<\/span>.totalClassCountDict<\/span>[<\/span>label]<\/span> +=<\/span> 1<\/span>
\n        for<\/span> cls in<\/span> self<\/span>.totalClassCountDict<\/span>:
\n            probs =<\/span> self<\/span>.totalClassCountDict<\/span>[<\/span>cls]<\/span> \/ float<\/span>(<\/span>self<\/span>.totalSampleCount<\/span>)<\/span>
\n            self<\/span>.totalSystemEntropy<\/span> -=<\/span> probs * np.log<\/span>(<\/span>probs)<\/span>
\n
\n
\n    # \u904d\u5386nonzeroPosition\u65f6\uff0c\u9010\u6b65\u8ba1\u7b97\u51fa\u6bcf\u4e2aword\u7684\u4fe1\u606f\u589e\u76ca<\/span>
\n    def<\/span> iter<\/span>(<\/span>self<\/span>)<\/span>:
\n        self<\/span>.cal_total_system_entropy<\/span>(<\/span>)<\/span>
\n
\n        pre =<\/span> 0<\/span>
\n        for<\/span> i in<\/span> range<\/span>(<\/span>len<\/span>(<\/span>self<\/span>.nonzeroPosition<\/span>[<\/span>0<\/span>]<\/span>)<\/span>)<\/span>:
\n            if<\/span> i !=<\/span> 0<\/span> and<\/span> self<\/span>.nonzeroPosition<\/span>[<\/span>0<\/span>]<\/span>[<\/span>i]<\/span> !=<\/span> pre:
\n                for<\/span> notappear in<\/span> range<\/span>(<\/span>pre+1<\/span>,<\/span> self<\/span>.nonzeroPosition<\/span>[<\/span>0<\/span>]<\/span>[<\/span>i]<\/span>)<\/span>:  # \u5982\u679c\u4e00\u4e2a\u8bcd\u5728\u6574\u4e2a\u6837\u672c\u96c6\u4e2d\u90fd\u672a\u51fa\u73b0\uff0c\u5219\u76f4\u63a5\u8d4b\u4e3a0<\/span>
\n                    self<\/span>.igResult<\/span>.append<\/span>(<\/span>0.0<\/span>)<\/span>
\n                ig =<\/span> self<\/span>.cal_information_gain<\/span>(<\/span>)<\/span>
\n                self<\/span>.igResult<\/span>.append<\/span>(<\/span>ig)<\/span>
\n                self<\/span>.wordExistSampleCount<\/span> =<\/span> 0<\/span>
\n                self<\/span>.wordExistClassCountDict<\/span> =<\/span> {<\/span>}<\/span>
\n                pre =<\/span> self<\/span>.nonzeroPosition<\/span>[<\/span>0<\/span>]<\/span>[<\/span>i]<\/span>
\n            self<\/span>.wordExistSampleCount<\/span> +=<\/span> 1<\/span>
\n            yclass =<\/span> self<\/span>.y<\/span>[<\/span>self<\/span>.nonzeroPosition<\/span>[<\/span>1<\/span>]<\/span>[<\/span>i]<\/span>]<\/span>  # \u6c42\u5f97\u5f53\u524d\u6837\u672c\u7684\u6807\u7b7e<\/span>
\n            if<\/span> yclass not<\/span> in<\/span> self<\/span>.wordExistClassCountDict<\/span>:
\n                self<\/span>.wordExistClassCountDict<\/span>[<\/span>yclass]<\/span> =<\/span> 1<\/span>
\n            else<\/span>:
\n                self<\/span>.wordExistClassCountDict<\/span>[<\/span>yclass]<\/span> +=<\/span> 1<\/span>
\n        # \u8ba1\u7b97\u6700\u540e\u4e00\u4e2a\u5355\u8bcd\u7684ig<\/span>
\n        ig =<\/span> self<\/span>.cal_information_gain<\/span>(<\/span>)<\/span>
\n        self<\/span>.igResult<\/span>.append<\/span>(<\/span>ig)<\/span>
\n
\n    # \u8ba1\u7b97ig\u7684\u4e3b\u8981\u51fd\u6570<\/span>
\n    def<\/span> cal_information_gain(<\/span>self<\/span>)<\/span>:
\n        x_exist_entropy =<\/span> 0<\/span>
\n        x_nonexist_entropy =<\/span> 0<\/span>
\n
\n        for<\/span> cls in<\/span> self<\/span>.wordExistClassCountDict<\/span>:
\n            probs =<\/span> self<\/span>.wordExistClassCountDict<\/span>[<\/span>cls]<\/span> \/ float<\/span>(<\/span>self<\/span>.wordExistSampleCount<\/span>)<\/span>
\n            x_exist_entropy -=<\/span> probs * np.log<\/span>(<\/span>probs)<\/span>
\n
\n            probs =<\/span> (<\/span>self<\/span>.totalClassCountDict<\/span>[<\/span>cls]<\/span> - self<\/span>.wordExistClassCountDict<\/span>[<\/span>cls]<\/span>)<\/span> \/ float<\/span>(<\/span>self<\/span>.totalSampleCount<\/span> - self<\/span>.wordExistSampleCount<\/span>)<\/span>
\n            if<\/span> probs ==<\/span> 0<\/span>: #\u8be5\u5355\u8bcd\u5728\u6bcf\u6761\u6837\u672c\u4e2d\u90fd\u51fa\u73b0\u4e86\uff0c\u867d\u7136\u8be5\u51e0\u7387\u5f88\u5c0f<\/span>
\n                x_nonexist_entropy =<\/span> 0<\/span>
\n            else<\/span>:
\n                x_nonexist_entropy -=<\/span> probs*np.log<\/span>(<\/span>probs)<\/span>
\n
\n        for<\/span> cls in<\/span> self<\/span>.totalClassCountDict<\/span>:
\n            if<\/span> cls not<\/span> in<\/span> self<\/span>.wordExistClassCountDict<\/span>:
\n                probs =<\/span> self<\/span>.totalClassCountDict<\/span>[<\/span>cls]<\/span> \/ float<\/span>(<\/span>self<\/span>.totalSampleCount<\/span> - self<\/span>.wordExistSampleCount<\/span>)<\/span>
\n                x_nonexist_entropy -=<\/span> probs*np.log<\/span>(<\/span>probs)<\/span>
\n
\n        # \u5408\u5e76\u4e24\u9879\uff0c\u8ba1\u7b97\u51faig<\/span>
\n        ig =<\/span> self<\/span>.totalSystemEntropy<\/span> - (<\/span>(<\/span>self<\/span>.wordExistSampleCount<\/span>\/float<\/span>(<\/span>self<\/span>.totalSampleCount<\/span>)<\/span>)<\/span>*x_exist_entropy +
\n                                        (<\/span>(<\/span>self<\/span>.totalSampleCount<\/span>-self<\/span>.wordExistSampleCount<\/span>)<\/span>\/float<\/span>(<\/span>self<\/span>.totalSampleCount<\/span>)<\/span>*x_nonexist_entropy)<\/span>)<\/span>
\n        return<\/span> ig
\nif<\/span> __name__ ==<\/span> '__main__'<\/span>:
\n    X =<\/span> np.array<\/span>(<\/span>[<\/span>[<\/span>1<\/span>,<\/span>0<\/span>,<\/span>0<\/span>,<\/span>1<\/span>]<\/span>,<\/span>[<\/span>0<\/span>,<\/span>1<\/span>,<\/span>1<\/span>,<\/span>1<\/span>]<\/span>,<\/span>[<\/span>0<\/span>,<\/span>0<\/span>,<\/span>1<\/span>,<\/span>0<\/span>]<\/span>]<\/span>)<\/span>
\n    y =<\/span> [<\/span>0<\/span>,<\/span>0<\/span>,<\/span>1<\/span>]<\/span>
\n    ig =<\/span> InformationGain(<\/span>X,<\/span> y)<\/span>
\n    print<\/span>(<\/span>ig.get_result<\/span>(<\/span>)<\/span>)<\/span><\/div><\/div>\n

\u4ee5\u4e0a\u7a0b\u5e8f\u8fd0\u884c\u7ed3\u679c\uff1a<\/p>\n

[0.17441604792151594, 0.17441604792151594, 0.17441604792151594, 0.63651416829481278]<\/div><\/div>\n

\u4e0a\u9762\u7684\u7ed3\u679c\u4ee3\u8868\u7740
\n\u9c9c\u82b1\u7684\u4fe1\u606f\u589e\u76ca\uff1a0.17441604792151594
\n\u592a\u9633\u7684\u4fe1\u606f\u589e\u76ca\uff1a0.17441604792151594
\n\u5927\u8c61\u7684\u4fe1\u606f\u589e\u76ca\uff1a0.17441604792151594
\n\u4f53\u80b2\u7684\u4fe1\u606f\u589e\u76ca\uff1a0.63651416829481278<\/p>\n","protected":false},"excerpt":{"rendered":"

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