{"id":340,"date":"2024-08-13T17:26:52","date_gmt":"2024-08-13T09:26:52","guid":{"rendered":"https:\/\/www.xuzhe.tj.cn\/?p=340"},"modified":"2025-05-03T09:15:27","modified_gmt":"2025-05-03T01:15:27","slug":"bagging-is-a-small-data-set-phenomenon","status":"publish","type":"post","link":"https:\/\/www.xuzhe.tj.cn\/index.php\/2024\/08\/13\/bagging-is-a-small-data-set-phenomenon\/","title":{"rendered":"Bagging Is A Small-Data-Set Phenomenon \uff5c \u8bba\u6587\u7b14\u8bb0"},"content":{"rendered":"\n

\u8bba\u6587\u7b80\u4ecb<\/h2>\n\n\n

\u82f1\u6587\u9898\u76ee\uff1aBagging Is A Small-Data-Set Phenomenon<\/p>\n\n\n

\u4e2d\u6587\u9898\u76ee\uff1aBagging \u662f\u4e00\u79cd\u5c0f\u6570\u636e\u96c6\u73b0\u8c61<\/p>\n\n\n

\u4f5c\u8005\uff1aNitesh Chawla, Thomas E. Moore, Jr., Kevin W. Bowyer, Lawrence O. Hall, Clayton Springer, Philip Kegelmeyer<\/p>\n\n\n

\u53d1\u8868\u671f\u520a\u6216\u4f1a\u8bae\uff1aComputer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference<\/p>\n\n\n

\u53d1\u8868\u65e5\u671f\uff1a2001\u5e74<\/p>\n\n\n

\u5728\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0cBagging\u4e00\u76f4\u88ab\u8ba4\u4e3a\u662f\u63d0\u5347\u6a21\u578b\u6027\u80fd\u7684\u5229\u5668\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u5c0f\u6570\u636e\u96c6\u65f6\u6548\u679c\u663e\u8457\u3002\u7136\u800c\uff0c\u5f53\u9762\u5bf9\u6570\u767e\u4e07\u751a\u81f3\u6570\u5343\u4e07\u6761\u6570\u636e\u65f6\uff0cBagging\u662f\u5426\u4ecd\u7136\u80fd\u591f\u4fdd\u6301\u5176\u795e\u5947\u7684\u6548\u679c\uff1f\u5728\u8fd9\u7bc7\u8bba\u6587\u4e2d\uff0c\u7814\u7a76\u4eba\u5458Nitesh Chawla\u548c\u4ed6\u7684\u56e2\u961f\u5bf9\u8fd9\u4e00\u7ecf\u5178\u65b9\u6cd5\u63d0\u51fa\u4e86\u8d28\u7591\uff0c\u5e76\u63ed\u793a\u4e86\u5728\u5927\u6570\u636e\u96c6\u4e0a\uff0c\u7b80\u5355\u7684\u6570\u636e\u5212\u5206\u53ef\u80fd\u6bd4\u590d\u6742\u7684Bagging\u65b9\u6cd5\u66f4\u4e3a\u6709\u6548\u3002\u4ed6\u4eec\u7684\u7814\u7a76\u6311\u6218\u4e86\u4f20\u7edf\u89c2\u5ff5\uff0c\u5e26\u6765\u4e86\u5173\u4e8e\u5927\u6570\u636e\u5904\u7406\u7684\u65b0\u89c6\u89d2\u3002\u5982\u679c\u4f60\u5173\u5fc3\u5982\u4f55\u5728\u6570\u636e\u7206\u70b8\u7684\u65f6\u4ee3\u4e2d\u5b9e\u73b0\u9ad8\u6548\u7684\u6a21\u578b\u8bad\u7ec3\uff0c\u8fd9\u7bc7\u6587\u7ae0\u5c06\u4e3a\u4f60\u63ed\u793a\u4e00\u4e2a\u610f\u60f3\u4e0d\u5230\u7684\u7b54\u6848\u3002<\/p>\n\n\n\n

\u4ee5\u4e0b\u662f\u5bf9\u8be5\u8bba\u6587\u7684\u603b\u7ed3\uff1a<\/p>\n\n\n

<\u7814\u7a76\u80cc\u666f\u4e0e\u76ee\u7684><\/p>\n\n\n

\u968f\u7740\u6570\u636e\u96c6\u89c4\u6a21\u7684\u4e0d\u65ad\u6269\u5927\uff0c\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u5982Bagging\u5728\u5904\u7406\u8fd9\u4e9b\u5927\u6570\u636e\u96c6\u65f6\u9762\u4e34\u7740\u6311\u6218\u3002Bagging\u65b9\u6cd5\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u8868\u73b0\u826f\u597d\uff0c\u901a\u8fc7\u6709\u653e\u56de\u91c7\u6837\u521b\u5efa\u591a\u4e2a\u5206\u7c7b\u5668\u6765\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u8d85\u5927\u89c4\u6a21\u7684\u6570\u636e\u96c6\uff0cBagging\u53ef\u80fd\u7531\u4e8e\u9700\u8981\u5904\u7406\u5927\u91cf\u7684\u6570\u636e\u5305\u800c\u5bfc\u81f4\u6548\u7387\u4f4e\u4e0b\u3002\u8be5\u8bba\u6587\u7684\u7814\u7a76\u76ee\u7684\u662f\u63a2\u8ba8\u5728\u5927\u6570\u636e\u96c6\u7684\u80cc\u666f\u4e0b\uff0c\u7b80\u5355\u7684\u6570\u636e\u5212\u5206\u662f\u5426\u80fd\u591f\u63d0\u4f9b\u6bd4Bagging\u66f4\u597d\u7684\u6027\u80fd\uff0c\u4ee5\u53ca\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6Bagging\u7684\u54ea\u4e9b\u8981\u7d20\u662f\u5fc5\u8981\u7684\u3002<\/p>\n\n\n

<\u521b\u65b0\u70b9><\/p>\n\n\n

\u8be5\u8bba\u6587\u7684\u521b\u65b0\u70b9\u5728\u4e8e\u9996\u6b21\u7cfb\u7edf\u6027\u5730\u6bd4\u8f83\u4e86\u5728\u5927\u6570\u636e\u96c6\u4e0a\u4f7f\u7528\u7b80\u5355\u7684\u6570\u636e\u5212\u5206\u4e0e\u4f20\u7edfBagging\u65b9\u6cd5\u7684\u6548\u679c\u3002\u7814\u7a76\u8868\u660e\uff0c\u7b80\u5355\u7684\u5c06\u6570\u636e\u96c6\u5212\u5206\u4e3a\u4e0d\u76f8\u4ea4\u7684\u5b50\u96c6\u80fd\u591f\u5728\u4fdd\u6301\u6216\u63d0\u5347\u5206\u7c7b\u5668\u6027\u80fd\u7684\u540c\u65f6\uff0c\u663e\u8457\u51cf\u5c11\u8ba1\u7b97\u8d44\u6e90\u7684\u6d88\u8017\u3002\u6b64\u5916\uff0c\u4f5c\u8005\u8fd8\u63a2\u8ba8\u4e86\u4e0d\u540c\u7684Bagging\u53d8\u4f53\uff0c\u5982\u65e0\u91cd\u590d\u5c0f\u5305\u548c\u5206\u5272\u52a0\u5305\uff08bagged disjoint\uff09\u7684\u6548\u679c\uff0c\u4e3a\u5927\u6570\u636e\u96c6\u4e0a\u7684\u96c6\u6210\u5b66\u4e60\u63d0\u4f9b\u4e86\u65b0\u7684\u601d\u8def\u3002<\/p>\n\n\n

<\u7ed3\u8bba><\/p>\n\n\n

\u8bba\u6587\u7684\u7ed3\u8bba\u662f\uff0c\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\uff0c\u7b80\u5355\u7684\u6570\u636e\u5212\u5206\u65b9\u6cd5\u901a\u5e38\u80fd\u591f\u63d0\u4f9b\u6bd4\u4f20\u7edfBagging\u66f4\u597d\u7684\u6027\u80fd\u3002<\/strong>\u5c24\u5176\u662f\u5728\u6570\u636e\u96c6\u8fc7\u5927\u4ee5\u81f3\u4e8e\u65e0\u6cd5\u5728\u5355\u4e2a\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u5904\u7406\u7684\u60c5\u51b5\u4e0b\uff0c\u7b80\u5355\u7684\u5206\u5272\u7b56\u7565\u4e0d\u4ec5\u63d0\u9ad8\u4e86\u5206\u7c7b\u5668\u7684\u6027\u80fd\uff0c\u8fd8\u6bd4\u590d\u6742\u7684Bagging\u65b9\u6cd5\u66f4\u52a0\u9ad8\u6548\u3002\u6b64\u5916\uff0c\u7814\u7a76\u8868\u660e\uff0c\u968f\u7740\u6570\u636e\u96c6\u89c4\u6a21\u7684\u589e\u52a0\uff0c\u968f\u673a\u91cd\u590d\u91c7\u6837\u7684Bagging\u65b9\u6cd5\u7684\u4f18\u52bf\u9010\u6e10\u51cf\u5f31\uff0c\u800c\u7b80\u5355\u7684\u5206\u5272\u65b9\u6cd5\u5219\u8868\u73b0\u66f4\u52a0\u7a33\u5b9a\u3002<\/p>\n\n\n

<\u5b9e\u9a8c\u5185\u5bb9><\/p>\n\n\n

\u8bba\u6587\u901a\u8fc7\u4e09\u4e2a\u5b9e\u9a8c\u96c6\u7fa4\u5bf9\u4e0d\u540c\u65b9\u6cd5\u8fdb\u884c\u4e86\u9a8c\u8bc1\u3002\u9996\u5148\uff0c\u4f7f\u7528\u56db\u4e2a\u5c0f\u578b\u6570\u636e\u96c6\u6d4b\u8bd5\u4e86\u4e0d\u540c\u7684\u5206\u7c7b\u5668\u751f\u6210\u65b9\u6cd5\u3002\u7136\u540e\uff0c\u4f7f\u7528\u4e00\u4e2a\u5305\u542b\u8fd130\u4e07\u6837\u672c\u7684\u4e2d\u578b\u6570\u636e\u96c6\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u8fd9\u4e9b\u65b9\u6cd5\u7684\u6548\u679c\u3002\u6700\u540e\uff0c\u4f7f\u7528\u4e00\u4e2a\u5305\u542b360\u4e07\u6837\u672c\u7684\u5927\u578b\u6570\u636e\u96c6\uff0c\u8bc4\u4f30\u4e86\u6570\u636e\u5206\u5272\u5728\u8d85\u5927\u89c4\u6a21\u6570\u636e\u96c6\u4e0a\u7684\u8868\u73b0\u3002\u6bcf\u4e2a\u5b9e\u9a8c\u90fd\u901a\u8fc7\u4ea4\u53c9\u9a8c\u8bc1\u6765\u786e\u4fdd\u7ed3\u679c\u7684\u53ef\u9760\u6027\uff0c\u6bd4\u8f83\u4e86\u4e0d\u540c\u5206\u5272\u548cBagging\u65b9\u6cd5\u5728\u5206\u7c7b\u51c6\u786e\u6027\u548c\u8ba1\u7b97\u8d44\u6e90\u6d88\u8017\u4e0a\u7684\u8868\u73b0\u3002<\/p>\n\n\n

<\u5bf9\u672c\u9886\u57df\u7684\u8d21\u732e><\/p>\n\n\n

\u8be5\u7814\u7a76\u4e3a\u673a\u5668\u5b66\u4e60\u9886\u57df\u5c24\u5176\u662f\u5927\u6570\u636e\u96c6\u5904\u7406\u65b9\u6cd5\u63d0\u4f9b\u4e86\u91cd\u8981\u7684\u89c1\u89e3\u3002\u901a\u8fc7\u7cfb\u7edf\u6027\u5730\u6bd4\u8f83Bagging\u548c\u7b80\u5355\u5206\u5272\u65b9\u6cd5\u7684\u8868\u73b0\uff0c\u8bba\u6587\u4e3a\u5927\u89c4\u6a21\u6570\u636e\u5904\u7406\u63d0\u51fa\u4e86\u66f4\u52a0\u5b9e\u7528\u4e14\u6709\u6548\u7684\u7b56\u7565\uff0c\u6311\u6218\u4e86\u4f20\u7edfBagging\u5728\u6240\u6709\u6570\u636e\u96c6\u4e0a\u5747\u6709\u6548\u7684\u5047\u8bbe\u3002\u6b64\u7814\u7a76\u6210\u679c\u4e3a\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u96c6\u6210\u5b66\u4e60\u65b9\u6cd5\u5728\u5927\u6570\u636e\u80cc\u666f\u4e0b\u7684\u5e94\u7528\u63d0\u4f9b\u4e86\u65b0\u7684\u7406\u8bba\u652f\u6301\u548c\u5b9e\u8df5\u65b9\u5411\u3002<\/p>\n\n\n

<\u5b58\u5728\u7684\u4e0d\u8db3><\/p>\n\n\n

\u5c3d\u7ba1\u8be5\u7814\u7a76\u5c55\u793a\u4e86\u7b80\u5355\u6570\u636e\u5206\u5272\u5728\u5927\u6570\u636e\u96c6\u4e0a\u7684\u4f18\u8d8a\u6027\uff0c\u4f46\u5176\u65b9\u6cd5\u5728\u5904\u7406\u6570\u636e\u96c6\u9ad8\u5ea6\u4e0d\u5e73\u8861\u6216\u7c7b\u522b\u6570\u91cf\u6781\u591a\u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u80fd\u4f1a\u9762\u4e34\u6027\u80fd\u4e0b\u964d\u7684\u95ee\u9898\u3002\u6b64\u5916\uff0c\u8bba\u6587\u4e3b\u8981\u5173\u6ce8\u7684\u662f\u5206\u7c7b\u95ee\u9898\uff0c\u5bf9\u4e8e\u56de\u5f52\u6216\u5176\u4ed6\u7c7b\u578b\u7684\u9884\u6d4b\u4efb\u52a1\uff0c\u65b9\u6cd5\u7684\u6709\u6548\u6027\u8fd8\u6709\u5f85\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u3002<\/p>\n\n\n

<\u672a\u6765\u7684\u5de5\u4f5c><\/p>\n\n\n

\u672a\u6765\u7684\u7814\u7a76\u53ef\u4ee5\u6269\u5c55\u5230\u5176\u4ed6\u7c7b\u578b\u7684\u673a\u5668\u5b66\u4e60\u4efb\u52a1\uff0c\u5982\u56de\u5f52\u5206\u6790\u548c\u805a\u7c7b\uff0c\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u6570\u636e\u5206\u5272\u65b9\u6cd5\u7684\u9002\u7528\u6027\u3002\u540c\u65f6\uff0c\u53ef\u4ee5\u63a2\u7d22\u5728\u66f4\u52a0\u590d\u6742\u7684\u6570\u636e\u96c6\uff08\u5982\u5177\u6709\u65f6\u95f4\u5e8f\u5217\u7279\u5f81\u6216\u591a\u6a21\u6001\u7279\u5f81\u7684\u6570\u636e\u96c6\uff09\u4e0a\uff0c\u5982\u4f55\u4f18\u5316\u5206\u5272\u548cBagging\u7b56\u7565\u3002\u6b64\u5916\uff0c\u7814\u7a76\u8fd8\u53ef\u4ee5\u7ed3\u5408\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\uff0c\u8003\u5bdf\u5728\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u4e2d\uff0c\u6570\u636e\u5206\u5272\u4e0eBagging\u7684\u7ed3\u5408\u6548\u679c\u3002<\/p>\n\n\n

\u7ae0\u8282\u5185\u5bb9<\/h2>\n\n\n

\u4ee5\u4e0b\u662f\u5bf9\u8bba\u6587\u5404\u7ae0\u8282\u5185\u5bb9\u7684\u68b3\u7406\uff1a<\/p>\n\n\n

1. \u5f15\u8a00 (Introduction)<\/h3>\n\n\n

\u672c\u7ae0\u8282\u4ecb\u7ecd\u4e86Bagging\u65b9\u6cd5\u7684\u57fa\u7840\u539f\u7406\u548c\u5b83\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u7684\u6210\u529f\u5e94\u7528\uff0c\u540c\u65f6\u6307\u51fa\u4e86\u5728\u5927\u6570\u636e\u96c6\u80cc\u666f\u4e0b\uff0cBagging\u53ef\u80fd\u9762\u4e34\u7684\u95ee\u9898\u548c\u6311\u6218\u3002\u7814\u7a76\u7684\u76ee\u7684\u5c31\u662f\u63a2\u7d22\u5728\u5927\u6570\u636e\u96c6\u4e0a\uff0cBagging\u7684\u54ea\u4e9b\u5143\u7d20\u662f\u5fc5\u8981\u7684\uff0c\u4ee5\u53ca\u662f\u5426\u5b58\u5728\u66f4\u7b80\u5355\u7684\u65b9\u6cd5\u6765\u66ff\u4ee3Bagging \u3002<\/p>\n\n\n

\u5173\u952e\u5185\u5bb9\u7684\u6458\u5f55\u3001\u7ffb\u8bd1\u53ca\u8bc4\u8bba<\/h4>\n\n\n

1.<\/strong> <\/p>\n\n\n

\u539f\u6587\uff1a<\/strong>“Many data mining applications use data sets that are too large to be handled in the memory of the typical computer. One possible approach is to sub-sample the data in some manner. However, it can be difficult a priori to know how to sub-sample so that accuracy is not affected. Another possible approach is to partition the original data into smaller subsets, and form a committee of classifiers. One advantage of this approach is that the partition size can simply be set at whatever amount of the original data can be conveniently handled on the available system. Another advantage is that the committee potentially has better accuracy than a single classifier constructed on all the data.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong>\u8bb8\u591a\u6570\u636e\u6316\u6398\u5e94\u7528\u4f7f\u7528\u7684\u6570\u636e\u96c6\u8fc7\u4e8e\u5e9e\u5927\uff0c\u65e0\u6cd5\u5728\u5178\u578b\u8ba1\u7b97\u673a\u7684\u5185\u5b58\u4e2d\u5904\u7406\u3002\u4e00\u4e2a\u53ef\u80fd\u7684\u65b9\u6cd5\u662f\u5bf9\u6570\u636e\u8fdb\u884c\u67d0\u79cd\u5f62\u5f0f\u7684\u5b50\u91c7\u6837\u3002\u7136\u800c\uff0c\u4e8b\u5148\u5f88\u96be\u77e5\u9053\u5982\u4f55\u5b50\u91c7\u6837\u624d\u80fd\u4e0d\u5f71\u54cd\u51c6\u786e\u6027\u3002\u53e6\u4e00\u79cd\u53ef\u80fd\u7684\u65b9\u6cd5\u662f\u5c06\u539f\u59cb\u6570\u636e\u5212\u5206\u4e3a\u8f83\u5c0f\u7684\u5b50\u96c6\uff0c\u5e76\u5f62\u6210\u4e00\u4e2a\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u3002\u8be5\u65b9\u6cd5\u7684\u4e00\u4e2a\u4f18\u52bf\u5728\u4e8e\uff0c\u53ef\u4ee5\u6839\u636e\u7cfb\u7edf\u7684\u5b9e\u9645\u53ef\u5904\u7406\u6570\u636e\u91cf\u6765\u786e\u5b9a\u5212\u5206\u7684\u5927\u5c0f\u3002\u53e6\u4e00\u4e2a\u4f18\u52bf\u5728\u4e8e\uff0c\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u53ef\u80fd\u6bd4\u57fa\u4e8e\u6240\u6709\u6570\u636e\u6784\u5efa\u7684\u5355\u4e00\u5206\u7c7b\u5668\u5177\u6709\u66f4\u597d\u7684\u51c6\u786e\u6027\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong>\u8fd9\u4e00\u6bb5\u5f3a\u8c03\u4e86\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\u9762\u4e34\u7684\u6311\u6218\uff0c\u5e76\u63d0\u51fa\u4e86\u4e24\u79cd\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6848\u3002\u76f8\u6bd4\u4e8e\u5b50\u91c7\u6837\uff0c\u6570\u636e\u5212\u5206\u4e0e\u5f62\u6210\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u7684\u65b9\u6cd5\u4e0d\u4ec5\u5177\u6709\u7075\u6d3b\u6027\uff0c\u8fd8\u53ef\u80fd\u63d0\u9ad8\u5206\u7c7b\u7cbe\u5ea6\u3002\u8fd9\u4e3a\u63a5\u4e0b\u6765\u7814\u7a76\u66f4\u9ad8\u6548\u7684\u6570\u636e\u5904\u7406\u65b9\u6cd5\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n\n\n

2.<\/strong> <\/p>\n\n\n

\u539f\u6587\uff1a<\/strong>“In its typical form, bagging involves random sampling with replacement from the original pool of training data to create ‘bags’ of data for a committee of thirty to one hundred classifiers. Bagging has been shown to result in improved performance over a single classifier created on all of the original data. The success of bagging suggests that it might be a useful approach to creating a committee of classifiers for large data sets. We define large data sets as those which do not fit in the memory of a typical scientific computer. However, experience with bagging has primarily been in the context of ‘small’ data sets. If the original data set is too large to handle conveniently, then creating and processing thirty or more bags will of course present even greater problems.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong>\u5728\u5176\u5178\u578b\u5f62\u5f0f\u4e2d\uff0cBagging\u901a\u8fc7\u5bf9\u539f\u59cb\u8bad\u7ec3\u6570\u636e\u6c60\u8fdb\u884c\u6709\u653e\u56de\u7684\u968f\u673a\u91c7\u6837\u6765\u521b\u5efa\u6570\u636e\u201c\u5305\u201d\uff0c\u7528\u4e8e\u4e00\u4e2a\u5305\u542b\u4e09\u5341\u5230\u4e00\u767e\u4e2a\u5206\u7c7b\u5668\u7684\u59d4\u5458\u4f1a\u3002\u7814\u7a76\u8868\u660e\uff0cBagging\u53ef\u4ee5\u6bd4\u57fa\u4e8e\u6240\u6709\u539f\u59cb\u6570\u636e\u521b\u5efa\u7684\u5355\u4e00\u5206\u7c7b\u5668\u5e26\u6765\u66f4\u597d\u7684\u6027\u80fd\u3002Bagging\u7684\u6210\u529f\u8868\u660e\uff0c\u5b83\u53ef\u80fd\u662f\u4e3a\u5927\u6570\u636e\u96c6\u521b\u5efa\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u7684\u4e00\u79cd\u6709\u7528\u65b9\u6cd5\u3002\u6211\u4eec\u5c06\u5927\u6570\u636e\u96c6\u5b9a\u4e49\u4e3a\u90a3\u4e9b\u4e0d\u80fd\u9002\u5e94\u5178\u578b\u79d1\u5b66\u8ba1\u7b97\u673a\u5185\u5b58\u7684\u6570\u636e\u96c6\u3002\u7136\u800c\uff0cBagging\u7684\u5e94\u7528\u7ecf\u9a8c\u4e3b\u8981\u96c6\u4e2d\u5728\u201c\u5c0f\u201d\u6570\u636e\u96c6\u4e0a\u3002\u5982\u679c\u539f\u59cb\u6570\u636e\u96c6\u8fc7\u5927\u800c\u96be\u4ee5\u5904\u7406\uff0c\u90a3\u4e48\u521b\u5efa\u548c\u5904\u7406\u4e09\u5341\u4e2a\u6216\u66f4\u591a\u7684\u5305\u5c06\u5e26\u6765\u66f4\u5927\u7684\u95ee\u9898\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong>\u8fd9\u4e00\u6bb5\u6df1\u5165\u89e3\u91ca\u4e86Bagging\u65b9\u6cd5\u7684\u4f18\u70b9\u4ee5\u53ca\u5176\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u7684\u5e94\u7528\u6210\u529f\u3002\u7136\u800c\uff0c\u5f53\u5e94\u7528\u5230\u5927\u6570\u636e\u96c6\u65f6\uff0cBagging\u7684\u6709\u6548\u6027\u548c\u6548\u7387\u4f1a\u53d7\u5230\u8d28\u7591\uff0c\u56e0\u4e3a\u5904\u7406\u5927\u91cf\u7684\u6570\u636e\u5305\u4f1a\u5e26\u6765\u8ba1\u7b97\u4e0a\u7684\u8d1f\u62c5\u3002\u6b64\u6bb5\u6587\u5b57\u4e3a\u63a2\u8ba8Bagging\u65b9\u6cd5\u5728\u5927\u6570\u636e\u96c6\u4e0a\u7684\u5c40\u9650\u6027\u63d0\u4f9b\u4e86\u80cc\u666f\u4fe1\u606f\u3002<\/p>\n\n\n

3.<\/strong> <\/p>\n\n\n

\u539f\u6587\uff1a<\/strong>“This raises the question of which particulars of the bagging approach are essential in the context of large data sets. In this work, we show that simple partitioning of a large original data set into disjoint subsets results in better performance than creating bags of the same size.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong>\u8fd9\u5c31\u5f15\u53d1\u4e86\u4e00\u4e2a\u95ee\u9898\uff0c\u5373\u5728\u5927\u6570\u636e\u96c6\u7684\u80cc\u666f\u4e0b\uff0cBagging\u65b9\u6cd5\u7684\u54ea\u4e9b\u7ec6\u8282\u662f\u5fc5\u8981\u7684\u3002\u5728\u672c\u7814\u7a76\u4e2d\uff0c\u6211\u4eec\u8868\u660e\uff0c\u5c06\u5927\u89c4\u6a21\u539f\u59cb\u6570\u636e\u96c6\u7b80\u5355\u5730\u5212\u5206\u4e3a\u4e0d\u76f8\u4ea4\u7684\u5b50\u96c6\uff0c\u5176\u6027\u80fd\u4f18\u4e8e\u521b\u5efa\u76f8\u540c\u5927\u5c0f\u7684\u6570\u636e\u5305\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong>\u8fd9\u6bb5\u6587\u5b57\u660e\u786e\u63d0\u51fa\u4e86\u8bba\u6587\u7684\u7814\u7a76\u95ee\u9898\uff0c\u5373\u5728\u5927\u6570\u636e\u96c6\u7684\u80cc\u666f\u4e0b\uff0cBagging\u7684\u54ea\u4e9b\u5143\u7d20\u5bf9\u5176\u6548\u679c\u81f3\u5173\u91cd\u8981\u3002\u901a\u8fc7\u5b9e\u9a8c\uff0c\u8bba\u6587\u8868\u660e\uff0c\u7b80\u5355\u7684\u6570\u636e\u5212\u5206\u65b9\u6cd5\u53ef\u80fd\u6bd4\u590d\u6742\u7684Bagging\u66f4\u6709\u6548\u3002\u8fd9\u4e3a\u540e\u7eed\u7684\u5b9e\u9a8c\u548c\u7ed3\u679c\u8ba8\u8bba\u63d0\u4f9b\u4e86\u7406\u8bba\u4f9d\u636e\u3002<\/p>\n\n\n

2. \u6587\u732e\u7efc\u8ff0 (Literature Review)<\/h3>\n\n\n

\u8fd9\u4e00\u90e8\u5206\u7efc\u8ff0\u4e86Bagging\u53ca\u5176\u6539\u8fdb\u65b9\u6cd5\u5728\u5206\u7c7b\u5668\u6027\u80fd\u63d0\u5347\u4e0a\u7684\u7814\u7a76\u73b0\u72b6\uff0c\u5305\u62ecBreiman\u5bf9Bagging\u7684\u7ecf\u5178\u5de5\u4f5c\u548c\u5176\u4ed6\u7814\u7a76\u8005\u63d0\u51fa\u7684\u66ff\u4ee3\u7b56\u7565\u3002\u4f5c\u8005\u8fd8\u8ba8\u8bba\u4e86\u8fd9\u4e9b\u65b9\u6cd5\u5728\u4e0d\u540c\u7c7b\u578b\u6570\u636e\u96c6\u4e0a\u7684\u8868\u73b0\uff0c\u4ee5\u53ca\u5728\u5927\u6570\u636e\u96c6\u80cc\u666f\u4e0b\u53ef\u80fd\u5b58\u5728\u7684\u5c40\u9650\u6027 \u3002<\/p>\n\n\n

\u6458\u5f55\u7684\u5173\u952e\u5185\u5bb9\u3001\u7ffb\u8bd1\u53ca\u8bc4\u8bba<\/h4>\n\n\n

1. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Breiman\u2019s bagging has been shown to improve classifier accuracy. Bagging basically combines models learned on different samplings of a given dataset. According to Breiman, bagging exploits the instability in the classifiers, since perturbing the training set produces different classifiers using the same learning algorithm. Quinlan experimented with bagging on various datasets and found that bagging substantially improved accuracy. However, the experiments were performed on ‘small’ datasets, the largest one being 20,000 examples.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

Breiman \u7684Bagging\u65b9\u6cd5\u5df2\u88ab\u8bc1\u660e\u80fd\u591f\u63d0\u9ad8\u5206\u7c7b\u5668\u7684\u51c6\u786e\u6027\u3002Bagging \u57fa\u672c\u4e0a\u662f\u5c06\u4ece\u7ed9\u5b9a\u6570\u636e\u96c6\u7684\u4e0d\u540c\u91c7\u6837\u4e2d\u5b66\u4e60\u5230\u7684\u6a21\u578b\u7ed3\u5408\u8d77\u6765\u3002\u6839\u636e Breiman \u7684\u8bf4\u6cd5\uff0cBagging \u5229\u7528\u4e86\u5206\u7c7b\u5668\u7684\u4e0d\u7a33\u5b9a\u6027\uff0c\u56e0\u4e3a\u6270\u52a8\u8bad\u7ec3\u96c6\u4f1a\u4f7f\u7528\u76f8\u540c\u7684\u5b66\u4e60\u7b97\u6cd5\u751f\u6210\u4e0d\u540c\u7684\u5206\u7c7b\u5668\u3002Quinlan \u5728\u5404\u79cd\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u4e86 Bagging \u7684\u5b9e\u9a8c\uff0c\u53d1\u73b0 Bagging \u663e\u8457\u63d0\u9ad8\u4e86\u51c6\u786e\u6027\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u5b9e\u9a8c\u662f\u5728\u201c\u5c0f\u201d\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u7684\uff0c\u6700\u5927\u7684\u4e00\u4e2a\u6570\u636e\u96c6\u4e5f\u53ea\u6709 20,000 \u4e2a\u6837\u672c\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u6bb5\u8bdd\u5f3a\u8c03\u4e86 Bagging \u65b9\u6cd5\u5728\u63d0\u9ad8\u5206\u7c7b\u5668\u51c6\u786e\u6027\u65b9\u9762\u7684\u6709\u6548\u6027\uff0c\u4f46\u540c\u65f6\u4e5f\u6307\u51fa\u4e86\u5176\u5728\u5b9e\u9a8c\u89c4\u6a21\u4e0a\u7684\u5c40\u9650\u6027\uff0c\u4e3b\u8981\u662f\u96c6\u4e2d\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u9a8c\u8bc1\u3002\u8fd9\u4e3a\u8ba8\u8bba Bagging \u5728\u5927\u89c4\u6a21\u6570\u636e\u96c6\u4e0a\u7684\u5e94\u7528\u6548\u679c\u94fa\u57ab\u4e86\u80cc\u666f\uff0c\u6697\u793a\u4e86\u53ef\u80fd\u5b58\u5728\u7684\u6311\u6218\u3002<\/p>\n\n\n

2. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Domingos empirically tested two alternative theories supporting bagging: (1) bagging works because it approximates Bayesian model averaging or (2) it works because it shifts the priors to a more appropriate region in the decision space. The empirical results showed that bagging worked possibly because it counter-acts the inherent simplicity bias of the decision trees. That is, with M different bags, M different classifiers are learned, and together their output is more complex than that of the single learner.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

Domingos \u5b9e\u8bc1\u6d4b\u8bd5\u4e86\u4e24\u79cd\u652f\u6301 Bagging \u7684\u7406\u8bba\uff1a(1) Bagging \u6709\u6548\u662f\u56e0\u4e3a\u5b83\u8fd1\u4f3c\u4e8e\u8d1d\u53f6\u65af\u6a21\u578b\u5e73\u5747\u5316\uff0c\u6216 (2) \u5b83\u6709\u6548\u662f\u56e0\u4e3a\u5b83\u5c06\u5148\u9a8c\u6982\u7387\u8f6c\u79fb\u5230\u51b3\u7b56\u7a7a\u95f4\u4e2d\u66f4\u5408\u9002\u7684\u533a\u57df\u3002\u5b9e\u8bc1\u7ed3\u679c\u8868\u660e\uff0cBagging \u7684\u6709\u6548\u6027\u53ef\u80fd\u662f\u56e0\u4e3a\u5b83\u62b5\u6d88\u4e86\u51b3\u7b56\u6811\u56fa\u6709\u7684\u7b80\u5355\u6027\u504f\u5dee\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u901a\u8fc7 M \u4e2a\u4e0d\u540c\u7684\u6570\u636e\u5305\uff0c\u5b66\u4e60\u5230 M \u4e2a\u4e0d\u540c\u7684\u5206\u7c7b\u5668\uff0c\u5e76\u4e14\u5b83\u4eec\u7684\u8f93\u51fa\u7ec4\u5408\u5728\u4e00\u8d77\u6bd4\u5355\u4e2a\u5b66\u4e60\u5668\u7684\u8f93\u51fa\u66f4\u590d\u6742\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u6bb5\u8bdd\u63a2\u8ba8\u4e86 Bagging \u7684\u7406\u8bba\u57fa\u7840\uff0c\u5f3a\u8c03\u4e86 Bagging \u5982\u4f55\u901a\u8fc7\u589e\u52a0\u6a21\u578b\u590d\u6742\u6027\u6765\u6539\u8fdb\u51b3\u7b56\u6811\u7684\u6027\u80fd\u3002\u8fd9\u4e3a\u7406\u89e3 Bagging \u7684\u6838\u5fc3\u673a\u5236\u63d0\u4f9b\u4e86\u7406\u8bba\u652f\u6301\uff0c\u89e3\u91ca\u4e86\u5b83\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u6027\u6a21\u578b\u65f6\u7684\u4f18\u52bf\u3002<\/p>\n\n\n

3. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Chan and Stolfo compared arbiter and combiner strategies by applying a learning algorithm to disjoint subsets of data. Their experiments showed that the arbiter strategy better sustains the accuracy compared to the classifier learned on the entire data set. The combiner strategy showed a drop in accuracy with the increase in the number of subsets, which can be attributed to the lack of information content in the small subsets. However, a few cases resulted in an improvement in accuracy. We are interested in disjoint subsets of larger original data sets than in their work, and so there is reason to expect that accuracy can be maintained.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

Chan \u548c Stolfo \u901a\u8fc7\u5c06\u5b66\u4e60\u7b97\u6cd5\u5e94\u7528\u4e8e\u4e0d\u76f8\u4ea4\u7684\u6570\u636e\u5b50\u96c6\uff0c\u6bd4\u8f83\u4e86\u4ef2\u88c1\u5668\u7b56\u7565\u548c\u7ec4\u5408\u5668\u7b56\u7565\u3002\u4ed6\u4eec\u7684\u5b9e\u9a8c\u8868\u660e\uff0c\u4e0e\u5728\u6574\u4e2a\u6570\u636e\u96c6\u4e0a\u5b66\u4e60\u7684\u5206\u7c7b\u5668\u76f8\u6bd4\uff0c\u4ef2\u88c1\u5668\u7b56\u7565\u80fd\u591f\u66f4\u597d\u5730\u7ef4\u6301\u51c6\u786e\u6027\u3002\u7ec4\u5408\u5668\u7b56\u7565\u968f\u7740\u5b50\u96c6\u6570\u91cf\u7684\u589e\u52a0\uff0c\u51c6\u786e\u6027\u4e0b\u964d\uff0c\u8fd9\u53ef\u4ee5\u5f52\u56e0\u4e8e\u5c0f\u5b50\u96c6\u4fe1\u606f\u5185\u5bb9\u7684\u7f3a\u4e4f\u3002\u7136\u800c\uff0c\u5728\u5c11\u6570\u60c5\u51b5\u4e0b\uff0c\u51c6\u786e\u6027\u6709\u6240\u63d0\u9ad8\u3002\u6211\u4eec\u5bf9\u6bd4\u4ed6\u4eec\u7684\u5de5\u4f5c\uff0c\u5173\u6ce8\u66f4\u5927\u539f\u59cb\u6570\u636e\u96c6\u7684\u4e0d\u76f8\u4ea4\u5b50\u96c6\uff0c\u56e0\u6b64\u6709\u7406\u7531\u76f8\u4fe1\u51c6\u786e\u6027\u80fd\u591f\u7ef4\u6301\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u8ba8\u8bba\u4e86\u5c06\u6570\u636e\u5212\u5206\u4e3a\u4e0d\u76f8\u4ea4\u5b50\u96c6\u65f6\u7684\u4e0d\u540c\u7b56\u7565\u53ca\u5176\u5bf9\u5206\u7c7b\u5668\u6027\u80fd\u7684\u5f71\u54cd\u3002\u901a\u8fc7\u63a2\u8ba8\u4ef2\u88c1\u5668\u548c\u7ec4\u5408\u5668\u7b56\u7565\u7684\u6548\u679c\uff0c\u4e3a\u540e\u7eed\u7814\u7a76\u63d0\u4f9b\u4e86\u6bd4\u8f83\u89c6\u89d2\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u96c6\u65f6\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53ef\u80fd\u66f4\u6709\u4f18\u52bf\u3002<\/p>\n\n\n

\u8fd9\u4e9b\u6bb5\u843d\u5c55\u793a\u4e86 Bagging \u65b9\u6cd5\u7684\u7406\u8bba\u57fa\u7840\u548c\u5b9e\u9a8c\u9a8c\u8bc1\uff0c\u5f3a\u8c03\u4e86\u5b83\u5728\u63d0\u9ad8\u5206\u7c7b\u5668\u6027\u80fd\u65b9\u9762\u7684\u6709\u6548\u6027\u3002\u540c\u65f6\uff0c\u901a\u8fc7\u6bd4\u8f83\u4e0d\u540c\u7684\u6570\u636e\u5904\u7406\u7b56\u7565\uff0c\u63a2\u8ba8\u4e86\u5982\u4f55\u5728\u5927\u6570\u636e\u96c6\u4e0a\u4f18\u5316\u5206\u7c7b\u5668\u7684\u51c6\u786e\u6027\u548c\u7a33\u5b9a\u6027\u3002\u6587\u7ae0\u4e2d\u7684\u6587\u732e\u7efc\u8ff0\u4e3a\u8bfb\u8005\u63d0\u4f9b\u4e86\u80cc\u666f\u4fe1\u606f\uff0c\u5e76\u4e3a\u540e\u7eed\u5b9e\u9a8c\u548c\u7ed3\u679c\u5206\u6790\u5960\u5b9a\u4e86\u7406\u8bba\u57fa\u7840\u3002<\/p>\n\n\n

3. \u5b9e\u9a8c (Experiments)<\/h3>\n\n\n

\u8bba\u6587\u7684\u6838\u5fc3\u90e8\u5206\uff0c\u4ecb\u7ecd\u4e86\u4e09\u7ec4\u5b9e\u9a8c\uff0c\u5206\u522b\u4f7f\u7528\u4e86\u5c0f\u89c4\u6a21\u3001\u4e2d\u7b49\u89c4\u6a21\u548c\u5927\u89c4\u6a21\u6570\u636e\u96c6\u3002\u5b9e\u9a8c\u7684\u76ee\u7684\u662f\u6bd4\u8f83\u4e0d\u540c\u6570\u636e\u5212\u5206\u548cBagging\u53d8\u4f53\u5728\u5206\u7c7b\u5668\u6027\u80fd\u4e0a\u7684\u8868\u73b0 \u3002\u4f5c\u8005\u6d4b\u8bd5\u4e86\u56db\u79cd\u4e0d\u540c\u7684\u5206\u7c7b\u5668\u751f\u6210\u65b9\u6cd5\uff0c\u5305\u62ec\u4e0d\u76f8\u4ea4\u5b50\u96c6\u5212\u5206\uff08disjoint partitions\uff09\u548c\u5c0f\u5305\u5212\u5206\uff08small bags\uff09\u7b49 \u3002<\/p>\n\n\n

3.1. \u6570\u636e\u96c6\u548c\u5212\u5206\u65b9\u6cd5 (Datasets and Partitioning Methods)<\/h4>\n\n\n

\u63cf\u8ff0\u4e86\u4f7f\u7528\u7684\u6570\u636e\u96c6\u7684\u8be6\u7ec6\u4fe1\u606f\u4ee5\u53ca\u56db\u79cd\u5206\u7c7b\u5668\u751f\u6210\u65b9\u6cd5\u7684\u5177\u4f53\u6b65\u9aa4 \u3002<\/p>\n\n\n

3.2. \u57fa\u672c\u5206\u7c7b\u5668\u4e0e\u8ba1\u7b97\u7cfb\u7edf (Base Classifier and Computing Systems)<\/h4>\n\n\n

\u4ecb\u7ecd\u4e86\u7528\u4e8e\u5b9e\u9a8c\u7684\u5206\u7c7b\u5668\u7b97\u6cd5\uff08\u5982C4.5\u51b3\u7b56\u6811\uff09\u548c\u8ba1\u7b97\u73af\u5883\uff0c\u5305\u62ec\u5728\u8d85\u5927\u89c4\u6a21\u6570\u636e\u96c6\u4e0a\u4f7f\u7528\u7684\u5e76\u884c\u8ba1\u7b97\u7cfb\u7edf \u3002<\/p>\n\n\n

\u6458\u5f55\u7684\u5173\u952e\u5185\u5bb9\u3001\u7ffb\u8bd1\u53ca\u8bc4\u8bba<\/h4>\n\n\n

1. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Three sets of experiments were performed. The first uses four ‘small’ datasets, representative of those commonly used in pattern recognition and machine learning research. It compares four approaches to creating a committee of N classifiers, with each classifier created using (1\/N)-th of the training data. The performance of the approaches is also compared to that of ‘true bagging’ – bags of the same size as the pool of training data, randomly sampled with replacement. The point of this first set of experiments is to isolate the essential factor(s) leading to good performance in the committee of classifiers.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u8fdb\u884c\u4e86\u4e09\u7ec4\u5b9e\u9a8c\u3002\u7b2c\u4e00\u7ec4\u4f7f\u7528\u4e86\u56db\u4e2a\u201c\u5c0f\u201d\u6570\u636e\u96c6\uff0c\u4ee3\u8868\u4e86\u6a21\u5f0f\u8bc6\u522b\u548c\u673a\u5668\u5b66\u4e60\u7814\u7a76\u4e2d\u5e38\u7528\u7684\u6570\u636e\u96c6\u3002\u5b9e\u9a8c\u6bd4\u8f83\u4e86\u521b\u5efaN\u4e2a\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u7684\u56db\u79cd\u65b9\u6cd5\uff0c\u6bcf\u4e2a\u5206\u7c7b\u5668\u90fd\u4f7f\u75281\/N\u7684\u6570\u636e\u8bad\u7ec3\u96c6\u521b\u5efa\u3002\u8fd8\u5c06\u8fd9\u4e9b\u65b9\u6cd5\u7684\u6027\u80fd\u4e0e\u201c\u771f\u6b63\u7684Bagging\u201d\u8fdb\u884c\u4e86\u6bd4\u8f83\uff0c\u5373\u901a\u8fc7\u968f\u673a\u6709\u653e\u56de\u91c7\u6837\u521b\u5efa\u4e0e\u8bad\u7ec3\u6570\u636e\u6c60\u5927\u5c0f\u76f8\u540c\u7684\u6570\u636e\u5305\u3002\u7b2c\u4e00\u7ec4\u5b9e\u9a8c\u7684\u76ee\u7684\u662f\u9694\u79bb\u51fa\u5bfc\u81f4\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u6027\u80fd\u826f\u597d\u7684\u5173\u952e\u56e0\u7d20\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u6bb5\u5185\u5bb9\u8bf4\u660e\u4e86\u5b9e\u9a8c\u7684\u8bbe\u8ba1\u76ee\u6807\uff0c\u5373\u901a\u8fc7\u5bf9\u6bd4\u4e0d\u540c\u7684\u65b9\u6cd5\u6765\u627e\u51fa\u5728\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u4e2d\u8868\u73b0\u6700\u597d\u7684\u56e0\u7d20\u3002\u5b9e\u9a8c\u4e0d\u4ec5\u63a2\u8ba8\u4e86\u4f20\u7edfBagging\u65b9\u6cd5\uff0c\u8fd8\u6d89\u53ca\u4e86\u5176\u4ed6\u521b\u65b0\u7684\u6570\u636e\u5904\u7406\u65b9\u6cd5\uff0c\u4e3a\u7814\u7a76\u7684\u7ed3\u8bba\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n\n\n

2. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“The second set of experiments uses a ‘moderate’ size dataset of almost 300,000 examples. The same four approaches are evaluated on this data set. The point is to verify that the pattern of performance results observed with smaller data sets holds with a larger data set.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u7b2c\u4e8c\u7ec4\u5b9e\u9a8c\u4f7f\u7528\u4e86\u4e00\u4e2a\u5305\u542b\u8fd130\u4e07\u4e2a\u6837\u672c\u7684\u201c\u4e2d\u7b49\u201d\u89c4\u6a21\u6570\u636e\u96c6\u3002\u5bf9\u8be5\u6570\u636e\u96c6\u8bc4\u4f30\u4e86\u76f8\u540c\u7684\u56db\u79cd\u65b9\u6cd5\u3002\u76ee\u7684\u662f\u9a8c\u8bc1\u5728\u8f83\u5c0f\u6570\u636e\u96c6\u4e0a\u89c2\u5bdf\u5230\u7684\u6027\u80fd\u6a21\u5f0f\u662f\u5426\u5728\u8f83\u5927\u6570\u636e\u96c6\u4e0a\u4e5f\u6210\u7acb\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u901a\u8fc7\u5f15\u5165\u4e2d\u7b49\u89c4\u6a21\u7684\u6570\u636e\u96c6\uff0c\u5b9e\u9a8c\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u4e86\u4e0d\u540c\u65b9\u6cd5\u5728\u89c4\u6a21\u66f4\u5927\u7684\u6570\u636e\u96c6\u4e0a\u7684\u8868\u73b0\u3002\u8fd9\u6709\u52a9\u4e8e\u5224\u65ad\u65b9\u6cd5\u7684\u9002\u7528\u8303\u56f4\uff0c\u4ee5\u53ca\u5b83\u4eec\u5728\u4e0d\u540c\u6570\u636e\u89c4\u6a21\u4e0a\u7684\u4e00\u81f4\u6027\u3002<\/p>\n\n\n

3. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“The last experiment uses a ‘large’ dataset of approximately 3.6 million examples to investigate the degree of performance improvement that the disjoint partitioning approach can achieve over a classifier built on all the original data.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u6700\u540e\u4e00\u7ec4\u5b9e\u9a8c\u4f7f\u7528\u4e86\u4e00\u4e2a\u5927\u7ea6360\u4e07\u4e2a\u6837\u672c\u7684\u201c\u5927\u578b\u201d\u6570\u636e\u96c6\uff0c\u65e8\u5728\u7814\u7a76\u4e0d\u76f8\u4ea4\u5212\u5206\u65b9\u6cd5\u76f8\u5bf9\u4e8e\u5728\u6240\u6709\u539f\u59cb\u6570\u636e\u4e0a\u6784\u5efa\u7684\u5206\u7c7b\u5668\u80fd\u591f\u5b9e\u73b0\u7684\u6027\u80fd\u63d0\u5347\u7a0b\u5ea6\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u5f15\u5165\u4e86\u5927\u89c4\u6a21\u6570\u636e\u96c6\u7684\u5b9e\u9a8c\uff0c\u63a2\u8ba8\u4e86\u4e0d\u76f8\u4ea4\u5212\u5206\u5728\u8d85\u5927\u6570\u636e\u96c6\u4e0a\u7684\u8868\u73b0\u3002\u8fd9\u4e3a\u7814\u7a76\u63d0\u4f9b\u4e86\u5e7f\u6cdb\u7684\u6570\u636e\u89c4\u6a21\u80cc\u666f\uff0c\u4f7f\u5f97\u7814\u7a76\u7ed3\u679c\u5177\u6709\u66f4\u9ad8\u7684\u666e\u904d\u6027\u3002<\/p>\n\n\n

4. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“For the experiments on the small and moderate size datasets, release 8 of the C4.5 decision tree system was run on standard SUN workstations. The one run of the large dataset to produce a single classifier was done on a 64-processor SGI IRE64 with 32 GB of main memory at Sandia National Labs, also using the standard C4.5 release 8. Creating the one decision tree on the large dataset took approximately thirty days on the SGI.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u5bf9\u4e8e\u5c0f\u578b\u548c\u4e2d\u7b49\u89c4\u6a21\u6570\u636e\u96c6\u7684\u5b9e\u9a8c\uff0cC4.5\u51b3\u7b56\u6811\u7cfb\u7edf\u7684\u7b2c8\u7248\u8fd0\u884c\u5728\u6807\u51c6\u7684SUN\u5de5\u4f5c\u7ad9\u4e0a\u3002\u5bf9\u4e8e\u5927\u578b\u6570\u636e\u96c6\u7684\u5b9e\u9a8c\uff0c\u4f7f\u7528\u4e86\u4f4d\u4e8eSandia\u56fd\u5bb6\u5b9e\u9a8c\u5ba4\u768464\u5904\u7406\u5668SGI IRE64\u8ba1\u7b97\u673a\uff0c\u914d\u5907\u4e8632GB\u5185\u5b58\uff0c\u540c\u6837\u4f7f\u7528\u4e86\u6807\u51c6\u7684C4.5\u7b2c8\u7248\u3002\u5728\u5927\u578b\u6570\u636e\u96c6\u4e0a\u521b\u5efa\u4e00\u4e2a\u51b3\u7b56\u6811\u5927\u7ea6\u82b1\u8d39\u4e86\u4e09\u5341\u5929\u7684\u65f6\u95f4\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u6bb5\u6587\u5b57\u5c55\u793a\u4e86\u4e0d\u540c\u6570\u636e\u96c6\u5b9e\u9a8c\u6240\u9700\u7684\u8ba1\u7b97\u8d44\u6e90\uff0c\u5c24\u5176\u662f\u5927\u578b\u6570\u636e\u96c6\u7684\u8ba1\u7b97\u590d\u6742\u6027\u3002\u5b83\u7a81\u51fa\u4e86\u5728\u5904\u7406\u8d85\u5927\u89c4\u6a21\u6570\u636e\u96c6\u65f6\uff0c\u8ba1\u7b97\u8d44\u6e90\u7684\u9700\u6c42\u53ef\u80fd\u6781\u5176\u9ad8\u6602\uff0c\u9a8c\u8bc1\u4e86\u7814\u7a76\u4e2d\u6240\u63d0\u51fa\u7684\u65b9\u6cd5\u5728\u4e0d\u540c\u8ba1\u7b97\u73af\u5883\u4e0b\u7684\u9002\u7528\u6027\u548c\u6548\u7387\u3002<\/p>\n\n\n

4. \u7ed3\u679c (Results)<\/h3>\n\n\n

\u672c\u7ae0\u8282\u5c55\u793a\u4e86\u5b9e\u9a8c\u7684\u7ed3\u679c\uff0c\u5305\u62ec\u5404\u4e2a\u6570\u636e\u96c6\u548c\u5212\u5206\u65b9\u6cd5\u5728\u5206\u7c7b\u51c6\u786e\u6027\u4e0a\u7684\u5bf9\u6bd4\u3002\u7ed3\u679c\u8868\u660e\uff0c\u7b80\u5355\u7684\u4e0d\u76f8\u4ea4\u5b50\u96c6\u5212\u5206\u65b9\u6cd5\u5728\u5927\u6570\u636e\u96c6\u4e0a\u5f80\u5f80\u4f18\u4e8e\u4f20\u7edf\u7684Bagging \u3002<\/p>\n\n\n

\u6458\u5f55\u7684\u5173\u952e\u5185\u5bb9\u3001\u7ffb\u8bd1\u53ca\u8bc4\u8bba<\/h4>\n\n\n

1. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Figures 2 through 5 summarize the experimental comparison of the different approaches on the small datasets detailed in Table 1. The plots compare the performance of two, four, six, and eight disjoint partitions (D) to that of C4.5 on the complete data set, and to classifier committees formed using the other three approaches (DB, SB, NRSB). Results are shown as the paired average difference across the ten folds in the ten-fold cross-validation, with standard error indicated.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u56fe2\u5230\u56fe5\u603b\u7ed3\u4e86\u5728\u88681\u4e2d\u8be6\u7ec6\u5217\u51fa\u7684\u5c0f\u578b\u6570\u636e\u96c6\u4e0a\u4e0d\u540c\u65b9\u6cd5\u7684\u5b9e\u9a8c\u6bd4\u8f83\u3002\u8fd9\u4e9b\u56fe\u8868\u6bd4\u8f83\u4e86\u4f7f\u7528\u4e24\u4e2a\u3001\u56db\u4e2a\u3001\u516d\u4e2a\u548c\u516b\u4e2a\u4e0d\u76f8\u4ea4\u5212\u5206\uff08D\uff09\u7684\u6027\u80fd\uff0c\u5e76\u4e0e\u4f7f\u7528\u6574\u4e2a\u6570\u636e\u96c6\u8bad\u7ec3\u7684C4.5\u4ee5\u53ca\u5176\u4ed6\u4e09\u79cd\u65b9\u6cd5\uff08DB\u3001SB\u3001NRSB\uff09\u7ec4\u6210\u7684\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u7684\u6027\u80fd\u8fdb\u884c\u4e86\u5bf9\u6bd4\u3002\u7ed3\u679c\u663e\u793a\u4e3a\u5341\u6298\u4ea4\u53c9\u9a8c\u8bc1\u4e2d\u5341\u4e2a\u6298\u53e0\u7684\u914d\u5bf9\u5e73\u5747\u5dee\u5f02\uff0c\u5e76\u6ce8\u660e\u4e86\u6807\u51c6\u8bef\u5dee\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u89e3\u91ca\u4e86\u5b9e\u9a8c\u7ed3\u679c\u7684\u8868\u793a\u65b9\u5f0f\uff0c\u91cd\u70b9\u5728\u4e8e\u5c55\u793a\u4e0d\u540c\u6570\u636e\u5212\u5206\u65b9\u6cd5\u548c\u4f20\u7edfBagging\u65b9\u6cd5\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u7684\u6027\u80fd\u5dee\u5f02\u3002\u901a\u8fc7\u5341\u6298\u4ea4\u53c9\u9a8c\u8bc1\u6765\u8bc4\u4f30\u8fd9\u4e9b\u65b9\u6cd5\u7684\u8868\u73b0\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u6d88\u9664\u5076\u7136\u6027\u8bef\u5dee\uff0c\u786e\u4fdd\u7ed3\u679c\u7684\u53ef\u9760\u6027\u548c\u7a33\u5065\u6027\u3002<\/p>\n\n\n

2. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“From examining the sequence of plots it is clear that disjoint partitions generally, but not always, beat small bags. It appears to make little difference whether the small bags are created by sampling with or without replacement. The ‘bagged disjoints’ appear to generally perform slightly better than the simple disjoints, but then the training sets for the individual decision trees are slightly larger.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u4ece\u8fd9\u4e9b\u56fe\u8868\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u4e0d\u76f8\u4ea4\u5212\u5206\u901a\u5e38\uff08\u4f46\u5e76\u975e\u603b\u662f\uff09\u4f18\u4e8e\u5c0f\u5305\u3002\u5c0f\u5305\u662f\u901a\u8fc7\u6709\u653e\u56de\u8fd8\u662f\u65e0\u653e\u56de\u91c7\u6837\u521b\u5efa\u7684\uff0c\u4f3c\u4e4e\u5dee\u522b\u4e0d\u5927\u3002\u201c\u888b\u88c5\u4e0d\u76f8\u4ea4\u201d\u65b9\u6cd5\u901a\u5e38\u6bd4\u7b80\u5355\u7684\u4e0d\u76f8\u4ea4\u65b9\u6cd5\u8868\u73b0\u7a0d\u597d\uff0c\u4f46\u8fd9\u65f6\u4e2a\u522b\u51b3\u7b56\u6811\u7684\u8bad\u7ec3\u96c6\u7a0d\u5927\u4e00\u4e9b\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u8ba8\u8bba\u4e86\u4e0d\u76f8\u4ea4\u5212\u5206\u548c\u5c0f\u5305\u5728\u5b9e\u9a8c\u4e2d\u7684\u8868\u73b0\uff0c\u6307\u51fa\u4e86\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u4e0d\u76f8\u4ea4\u5212\u5206\u4f18\u4e8e\u5c0f\u5305\uff0c\u5e76\u4e14\u888b\u88c5\u4e0d\u76f8\u4ea4\u65b9\u6cd5\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u5347\u6027\u80fd\u3002\u8fd9\u4e9b\u7ed3\u679c\u8868\u660e\uff0cBagging\u65b9\u6cd5\u4e2d\u7684\u968f\u673a\u91c7\u6837\u5e76\u975e\u603b\u662f\u6709\u4f18\u52bf\uff0c\u7279\u522b\u662f\u5728\u5904\u7406\u5927\u578b\u6570\u636e\u96c6\u65f6\u3002<\/p>\n\n\n

3. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Because it uses constant-size bags as the number of classifiers in the committee grows larger, ‘true bagging’ should naturally outperform any of the four approaches. Data points for ‘true bagging’ performance are given in Table 2. However, the point is that true bagging is simply not a practical option for ‘large’ datasets.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u7531\u4e8e\u201c\u771f\u6b63\u7684Bagging\u201d\u4f7f\u7528\u56fa\u5b9a\u5927\u5c0f\u7684\u6570\u636e\u5305\uff0c\u968f\u7740\u5206\u7c7b\u5668\u6570\u91cf\u7684\u589e\u52a0\uff0c\u5176\u6027\u80fd\u81ea\u7136\u5e94\u8be5\u4f18\u4e8e\u5176\u4ed6\u56db\u79cd\u65b9\u6cd5\u3002\u88682\u4e2d\u7ed9\u51fa\u4e86\u201c\u771f\u6b63\u7684Bagging\u201d\u6027\u80fd\u7684\u6570\u636e\u70b9\u3002\u7136\u800c\uff0c\u5173\u952e\u5728\u4e8e\u5bf9\u4e8e\u201c\u5927\u201d\u6570\u636e\u96c6\u6765\u8bf4\uff0c\u771f\u6b63\u7684Bagging\u6839\u672c\u4e0d\u662f\u4e00\u4e2a\u5b9e\u7528\u7684\u9009\u62e9\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u5f3a\u8c03\u4e86\u5728\u7406\u8bba\u4e0a\uff0c\u771f\u6b63\u7684Bagging\u5728\u6027\u80fd\u4e0a\u53ef\u80fd\u4f18\u4e8e\u5176\u4ed6\u65b9\u6cd5\uff0c\u4f46\u5b83\u5728\u5927\u6570\u636e\u96c6\u4e0a\u7684\u5e94\u7528\u53d7\u5230\u5b9e\u9645\u8ba1\u7b97\u8d44\u6e90\u7684\u9650\u5236\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5c3d\u7ba1Bagging\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u8868\u73b0\u826f\u597d\uff0c\u4f46\u5b83\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\u7684\u9ad8\u8ba1\u7b97\u6210\u672c\u4f7f\u5176\u4e0d\u9002\u7528\u3002<\/p>\n\n\n

4. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“The average accuracy of a single classifier trained on (1\/8)-th of the large dataset is 74.1 %. A single decision tree created using all the data performs substantially better than this, 78.6% versus 74.1%. At the same time, a committee of eight classifiers created on (1\/8)-ths of the data performs substantially better than a single tree created on all the data, 81.8% versus 78.6%.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u5728\u5927\u6570\u636e\u96c6\u76841\/8\u90e8\u5206\u4e0a\u8bad\u7ec3\u7684\u5355\u4e2a\u5206\u7c7b\u5668\u7684\u5e73\u5747\u51c6\u786e\u7387\u4e3a74.1%\u3002\u4f7f\u7528\u6240\u6709\u6570\u636e\u521b\u5efa\u7684\u5355\u4e2a\u51b3\u7b56\u6811\u6027\u80fd\u660e\u663e\u66f4\u597d\uff0c\u4e3a78.6%\u5bf974.1%\u3002\u540c\u65f6\uff0c\u7531\u6570\u636e\u76841\/8\u90e8\u5206\u521b\u5efa\u7684\u516b\u4e2a\u5206\u7c7b\u5668\u7ec4\u6210\u7684\u59d4\u5458\u4f1a\u7684\u6027\u80fd\u660e\u663e\u4f18\u4e8e\u4f7f\u7528\u6240\u6709\u6570\u636e\u521b\u5efa\u7684\u5355\u4e2a\u51b3\u7b56\u6811\uff0c\u4e3a81.8%\u5bf978.6%\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u7ed3\u679c\u663e\u793a\uff0c\u5c3d\u7ba1\u5355\u4e2a\u51b3\u7b56\u6811\u5728\u5168\u6570\u636e\u4e0a\u7684\u6027\u80fd\u8f83\u597d\uff0c\u4f46\u901a\u8fc7\u5c06\u6570\u636e\u5212\u5206\u4e3a\u591a\u4e2a\u90e8\u5206\u5e76\u5f62\u6210\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u5206\u7c7b\u51c6\u786e\u6027\u3002\u8fd9\u8bc1\u660e\u4e86\u5206\u7c7b\u5668\u96c6\u6210\u65b9\u6cd5\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\u7684\u4f18\u52bf\uff0c\u7279\u522b\u662f\u5f53\u8ba1\u7b97\u8d44\u6e90\u6709\u9650\u65f6\uff0c\u5206\u5272\u7b56\u7565\u53ef\u4ee5\u63d0\u9ad8\u6574\u4f53\u6a21\u578b\u7684\u6027\u80fd \u3002<\/p>\n\n\n

5. \u7ed3\u8bba\u4e0e\u8ba8\u8bba (Conclusions and Discussion)<\/h3>\n\n\n

\u603b\u7ed3\u4e86\u5b9e\u9a8c\u7ed3\u679c\uff0c\u5f97\u51fa\u4e86\u51e0\u4e2a\u91cd\u8981\u7684\u7ed3\u8bba\uff0c\u5305\u62ec\u4e0d\u76f8\u4ea4\u5b50\u96c6\u5212\u5206\u5728\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u96c6\u65f6\u7684\u4f18\u8d8a\u6027\u3002\u4f5c\u8005\u8fd8\u8ba8\u8bba\u4e86\u8fd9\u4e9b\u53d1\u73b0\u5bf9\u5b9e\u9645\u5e94\u7528\u7684\u5f71\u54cd\uff0c\u5e76\u63d0\u51fa\u4e86\u672a\u6765\u53ef\u80fd\u7684\u7814\u7a76\u65b9\u5411 \u3002<\/p>\n\n\n

\u6458\u5f55\u7684\u5173\u952e\u5185\u5bb9\u3001\u7ffb\u8bd1\u53ca\u8bc4\u8bba<\/h4>\n\n\n

1. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“The results support several important conclusions. The overall conclusion is that datasets too large to handle practically in the memory of the typical computer are appropriately handled by simple partitioning to form a committee of classifiers. More specifically, a committee created using disjoint partitions can be expected to outperform a committee created using the same number and size of bootstrap aggregates (‘bags’). Also, the performance of the committee of classifiers can be expected to exceed that of a single classifier built from all the data.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e9b\u7ed3\u679c\u652f\u6301\u51e0\u4e2a\u91cd\u8981\u7684\u7ed3\u8bba\u3002\u603b\u4f53\u7ed3\u8bba\u662f\uff0c\u5bf9\u4e8e\u90a3\u4e9b\u8fc7\u4e8e\u5e9e\u5927\u800c\u65e0\u6cd5\u5728\u5178\u578b\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u5b9e\u9645\u5904\u7406\u7684\u6570\u636e\u96c6\uff0c\u901a\u8fc7\u7b80\u5355\u7684\u5212\u5206\u6765\u521b\u5efa\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u662f\u5408\u9002\u7684\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u4f7f\u7528\u4e0d\u76f8\u4ea4\u5212\u5206\u521b\u5efa\u7684\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u9884\u8ba1\u5c06\u4f18\u4e8e\u4f7f\u7528\u76f8\u540c\u6570\u91cf\u548c\u5927\u5c0f\u7684Bootstrap\u805a\u5408\uff08\u201c\u888b\u201d\uff09\u521b\u5efa\u7684\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u3002\u6b64\u5916\uff0c\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u7684\u6027\u80fd\u9884\u8ba1\u5c06\u8d85\u8fc7\u4ece\u6240\u6709\u6570\u636e\u4e2d\u6784\u5efa\u7684\u5355\u4e00\u5206\u7c7b\u5668\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u603b\u7ed3\u4e86\u8bba\u6587\u7684\u6838\u5fc3\u53d1\u73b0\uff0c\u5373\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\uff0c\u7b80\u5355\u7684\u6570\u636e\u5212\u5206\u65b9\u6cd5\u5728\u521b\u5efa\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u65b9\u9762\u5177\u6709\u660e\u663e\u4f18\u52bf\u3002\u8fd9\u4e00\u7ed3\u8bba\u5177\u6709\u91cd\u8981\u7684\u5b9e\u9645\u610f\u4e49\uff0c\u56e0\u4e3a\u5b83\u8868\u660e\uff0c\u5728\u8d44\u6e90\u6709\u9650\u7684\u60c5\u51b5\u4e0b\uff0c\u7b80\u5355\u7684\u5212\u5206\u7b56\u7565\u53ef\u4ee5\u6709\u6548\u66ff\u4ee3\u66f4\u590d\u6742\u7684Bagging\u65b9\u6cd5\uff0c\u4ece\u800c\u63d0\u9ad8\u6a21\u578b\u7684\u6027\u80fd\u3002<\/p>\n\n\n

2. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Results obtained here seem to support the position that bagging results depend simply on obtaining a ‘diverse’ set of classifiers. Building classifiers on disjoint partitions of the data provides a set of classifiers that meet this requirement. Each individual classifier performs similarly, but correctly classifies a (partially) different set of examples.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u91cc\u83b7\u5f97\u7684\u7ed3\u679c\u4f3c\u4e4e\u652f\u6301\u8fd9\u6837\u4e00\u79cd\u89c2\u70b9\uff0c\u5373Bagging\u7684\u6548\u679c\u4e3b\u8981\u4f9d\u8d56\u4e8e\u83b7\u5f97\u4e00\u7ec4\u201c\u591a\u6837\u5316\u201d\u7684\u5206\u7c7b\u5668\u3002\u57fa\u4e8e\u6570\u636e\u7684\u4e0d\u76f8\u4ea4\u5212\u5206\u6784\u5efa\u5206\u7c7b\u5668\u63d0\u4f9b\u4e86\u4e00\u7ec4\u7b26\u5408\u8fd9\u4e00\u8981\u6c42\u7684\u5206\u7c7b\u5668\u3002\u6bcf\u4e2a\u5355\u72ec\u7684\u5206\u7c7b\u5668\u8868\u73b0\u76f8\u4f3c\uff0c\u4f46\u6b63\u786e\u5206\u7c7b\u4e86\u4e00\u7ec4\uff08\u90e8\u5206\uff09\u4e0d\u540c\u7684\u6837\u672c\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u6bb5\u5f3a\u8c03\u4e86Bagging\u65b9\u6cd5\u6210\u529f\u7684\u5173\u952e\u5728\u4e8e\u5206\u7c7b\u5668\u7684\u591a\u6837\u6027\u3002\u901a\u8fc7\u4e0d\u76f8\u4ea4\u7684\u5212\u5206\u6765\u6784\u5efa\u5206\u7c7b\u5668\u96c6\u5408\uff0c\u8bba\u6587\u8bc1\u660e\u4e86\u8fd9\u4e00\u65b9\u6cd5\u53ef\u4ee5\u6709\u6548\u5730\u6ee1\u8db3\u8fd9\u4e00\u9700\u6c42\uff0c\u4ece\u800c\u63d0\u5347\u6a21\u578b\u7684\u603b\u4f53\u6027\u80fd\u3002\u8fd9\u8fdb\u4e00\u6b65\u5f3a\u5316\u4e86\u7b80\u5355\u5212\u5206\u7b56\u7565\u5728\u5927\u6570\u636e\u96c6\u5904\u7406\u4e2d\u7684\u4f18\u52bf\u3002<\/p>\n\n\n

3. \u539f\u6587\uff1a<\/strong><\/p>\n\n\n

“Some researchers have suggested that many large-dataset problems can be solved using only a fraction of the data, perhaps by simple sub-sampling. Classical pattern recognition would suggest that this question is more appropriately viewed in terms of the density of training sample population in the feature space, rather than simply the size of the dataset.”<\/p>\n\n\n

\u7ffb\u8bd1\uff1a<\/strong><\/p>\n\n\n

\u4e00\u4e9b\u7814\u7a76\u8005\u5efa\u8bae\uff0c\u8bb8\u591a\u5927\u6570\u636e\u96c6\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u4ec5\u4f7f\u7528\u90e8\u5206\u6570\u636e\u6765\u89e3\u51b3\uff0c\u53ef\u80fd\u901a\u8fc7\u7b80\u5355\u7684\u5b50\u91c7\u6837\u3002\u7ecf\u5178\u7684\u6a21\u5f0f\u8bc6\u522b\u4f1a\u5efa\u8bae\u8fd9\u4e2a\u95ee\u9898\u66f4\u9002\u5408\u4ece\u7279\u5f81\u7a7a\u95f4\u4e2d\u8bad\u7ec3\u6837\u672c\u5206\u5e03\u7684\u5bc6\u5ea6\u89d2\u5ea6\u6765\u770b\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u6570\u636e\u96c6\u7684\u5927\u5c0f\u3002<\/p>\n\n\n

\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n

\u8fd9\u4e00\u6bb5\u63d0\u51fa\u4e86\u7ecf\u5178\u6a21\u5f0f\u8bc6\u522b\u4e2d\u7684\u89c2\u70b9\uff0c\u5373\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\uff0c\u4ec5\u4ec5\u5173\u6ce8\u6570\u636e\u96c6\u7684\u5927\u5c0f\u53ef\u80fd\u4e0d\u8db3\u4ee5\u89e3\u51b3\u95ee\u9898\uff0c\u5fc5\u987b\u8003\u8651\u5230\u8bad\u7ec3\u6837\u672c\u5728\u7279\u5f81\u7a7a\u95f4\u4e2d\u7684\u5206\u5e03\u5bc6\u5ea6\u3002\u8fd9\u8868\u660e\uff0c\u5c3d\u7ba1\u5b50\u91c7\u6837\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u7b56\u7565\uff0c\u4f46\u5728\u5904\u7406\u590d\u6742\u95ee\u9898\u65f6\uff0c\u53ef\u80fd\u9700\u8981\u66f4\u6df1\u5165\u7684\u5206\u6790\u548c\u66f4\u590d\u6742\u7684\u65b9\u6cd5\u6765\u786e\u4fdd\u6a21\u578b\u7684\u6709\u6548\u6027 \u3002<\/p>\n\n\n

\u8fd9\u4e9b\u6bb5\u843d\u5c55\u793a\u4e86\u8bba\u6587\u5728\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u96c6\u65f6\u7684\u5173\u952e\u53d1\u73b0\u548c\u7406\u8bba\u4f9d\u636e\uff0c\u5f3a\u8c03\u4e86\u7b80\u5355\u6570\u636e\u5212\u5206\u5728\u521b\u5efa\u5206\u7c7b\u5668\u59d4\u5458\u4f1a\u4e2d\u7684\u4f18\u8d8a\u6027\uff0c\u540c\u65f6\u63a2\u8ba8\u4e86Bagging\u65b9\u6cd5\u7684\u6838\u5fc3\u539f\u7406\u3002\u901a\u8fc7\u8fd9\u4e9b\u7ed3\u8bba\uff0c\u8bba\u6587\u4e3a\u5728\u8d44\u6e90\u53d7\u9650\u7684\u73af\u5883\u4e0b\u5904\u7406\u5927\u6570\u636e\u96c6\u63d0\u4f9b\u4e86\u65b0\u7684\u601d\u8def\u3002<\/p>\n\n\n

\u81f4\u8c22 (Acknowledgments)<\/h3>\n\n\n

\u611f\u8c22\u652f\u6301\u8fd9\u9879\u7814\u7a76\u7684\u673a\u6784\u548c\u4eba\u5458 \u3002<\/p>\n\n\n

\u53c2\u8003\u6587\u732e (References)<\/h3>\n\n\n

\u5217\u51fa\u4e86\u8bba\u6587\u4e2d\u5f15\u7528\u7684\u6240\u6709\u6587\u732e\uff0c\u6db5\u76d6\u4e86Bagging\u65b9\u6cd5\u3001\u6570\u636e\u5212\u5206\u7b56\u7565\u3001\u4ee5\u53ca\u5927\u6570\u636e\u96c6\u5904\u7406\u76f8\u5173\u7684\u7814\u7a76 \u3002<\/p>\n\n\n

\u4e00\u4e9b\u95ee\u9898<\/h2>\n\n\n

\u8bba\u6587\u4e2d\u7684 \u5c0f\u578b\u3001\u4e2d\u578b\u3001\u5927\u578b \u662f\u5982\u4f55\u5b9a\u4e49\u7684\uff0c\u4ee5\u53ca\u5404\u7c7b\u578b\u6570\u636e\u96c6\u7684\u6570\u96c6\u91cf\u8303\u56f4<\/h3>\n\n\n

\u5728\u8fd9\u7bc7\u8bba\u6587\u4e2d\uff0c\u6570\u636e\u96c6\u88ab\u5212\u5206\u4e3a\u5c0f\u578b\u3001\u4e2d\u578b\u548c\u5927\u578b\uff0c\u5177\u4f53\u7684\u5b9a\u4e49\u548c\u6837\u672c\u91cf\u8303\u56f4\u5982\u4e0b\uff1a<\/p>\n\n\n

\u5c0f\u578b\u6570\u636e\u96c6\uff08Small Datasets\uff09<\/h4>\n\n\n

\u5b9a\u4e49\u548c\u6837\u672c\u91cf\u8303\u56f4\uff1a<\/strong>\u5c0f\u578b\u6570\u636e\u96c6\u901a\u5e38\u662f\u6307\u90a3\u4e9b\u53ef\u4ee5\u8f7b\u677e\u5904\u7406\u4e14\u5e38\u7528\u4e8e\u6a21\u5f0f\u8bc6\u522b\u548c\u673a\u5668\u5b66\u4e60\u7814\u7a76\u7684\u6807\u51c6\u6570\u636e\u96c6\u3002\u8bba\u6587\u4e2d\u4f7f\u7528\u7684\u56db\u4e2a\u5c0f\u578b\u6570\u636e\u96c6\u5305\u62ec\u6765\u81eaUCI\u6570\u636e\u4ed3\u5e93\u7684\u7ecf\u5178\u6570\u636e\u96c6\uff0c\u5982Pendigits\uff0810,992\u4e2a\u6837\u672c\uff0c10\u4e2a\u7c7b\uff09\u548cSatimage\uff086,435\u4e2a\u6837\u672c\uff0c6\u4e2a\u7c7b\uff09\u7b49\u3002<\/p>\n\n\n

\u6837\u672c\u91cf\uff1a<\/strong>– Pendigits \u6570\u636e\u96c6\uff1a10,992 \u4e2a\u6837\u672c– Satimage \u6570\u636e\u96c6\uff1a6,435 \u4e2a\u6837\u672c– Mammography \u6570\u636e\u96c6\uff1a11,183 \u4e2a\u6837\u672c<\/p>\n\n\n

\u4e2d\u578b\u6570\u636e\u96c6\uff08Moderate Datasets\uff09<\/h4>\n\n\n

\u5b9a\u4e49\u548c\u6837\u672c\u91cf\u8303\u56f4\uff1a<\/strong>\u4e2d\u578b\u6570\u636e\u96c6\u6307\u7684\u662f\u90a3\u4e9b\u6bd4\u5c0f\u578b\u6570\u636e\u96c6\u66f4\u5927\uff0c\u4f46\u4ecd\u53ef\u5728\u6807\u51c6\u8ba1\u7b97\u73af\u5883\u4e2d\u5904\u7406\u7684\u6570\u636e\u96c6\u3002\u8bba\u6587\u4e2d\u63d0\u5230\u7684\u4e2d\u578b\u6570\u636e\u96c6\u662f\u4e00\u4e2a\u7528\u4e8e\u9884\u6d4b\u86cb\u767d\u8d28\u4e8c\u7ea7\u7ed3\u6784\u7684\u6570\u636e\u96c6\uff0c\u5305\u542b\u8fd130\u4e07\u4e2a\u6837\u672c\u3002<\/p>\n\n\n

\u6837\u672c\u91cf\uff1a<\/strong>– \u86cb\u767d\u8d28\u4e8c\u7ea7\u7ed3\u6784\u9884\u6d4b\u6570\u636e\u96c6\uff1a\u5927\u7ea6299,186 \u4e2a\u6837\u672c<\/p>\n\n\n

\u5927\u578b\u6570\u636e\u96c6\uff08Large Datasets\uff09<\/h4>\n\n\n

\u5b9a\u4e49\u548c\u6837\u672c\u91cf\u8303\u56f4\uff1a<\/strong>\u5927\u578b\u6570\u636e\u96c6\u662f\u6307\u90a3\u4e9b\u65e0\u6cd5\u5728\u5178\u578b\u8ba1\u7b97\u673a\u5185\u5b58\u4e2d\u65b9\u4fbf\u5904\u7406\u7684\u5927\u89c4\u6a21\u6570\u636e\u96c6\u3002\u8bba\u6587\u4f7f\u7528\u7684\u4e00\u4e2a\u5927\u578b\u6570\u636e\u96c6\u6765\u81ea\u86cb\u767d\u8d28\u6570\u636e\u5e93\uff08PDB\uff09\uff0c\u5305\u542b\u7ea6360\u4e07\u4e2a\u6837\u672c\u3002<\/p>\n\n\n

\u6837\u672c\u91cf\uff1a<\/strong>– \u86cb\u767d\u8d28\u6570\u636e\u5e93\u6570\u636e\u96c6\uff1a\u7ea63,679,152 \u4e2a\u6837\u672c<\/p>\n\n\n

\u8ba1\u7b97\u8d44\u6e90\u9700\u6c42\uff1a<\/strong>– \u5927\u578b\u6570\u636e\u96c6\u7684\u8bad\u7ec3\u9700\u8981\u5728\u9ad8\u5ea6\u5e76\u884c\u7684\u8ba1\u7b97\u73af\u5883\u4e0b\u8fdb\u884c\uff0c\u4f8b\u5982\u4f7f\u7528\u591a\u5904\u7406\u5668\u7684\u8d85\u7ea7\u8ba1\u7b97\u673a\u3002\u8fd9\u79cd\u5927\u89c4\u6a21\u6570\u636e\u96c6\u7684\u5904\u7406\u65f6\u95f4\u8f83\u957f\uff0c\u4f8b\u5982\u6784\u5efa\u4e00\u4e2a\u51b3\u7b56\u6811\u53ef\u80fd\u9700\u8981\u6570\u5341\u5929\u65f6\u95f4 \u3002<\/p>\n\n\n

\u8fd9\u4e9b\u5b9a\u4e49\u548c\u6837\u672c\u91cf\u8303\u56f4\u8bf4\u660e\u4e86\u4e0d\u540c\u89c4\u6a21\u6570\u636e\u96c6\u5728\u5b9e\u9a8c\u4e2d\u7684\u5e94\u7528\u80cc\u666f\uff0c\u5e76\u5f3a\u8c03\u4e86\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\u6240\u9700\u7684\u8ba1\u7b97\u8d44\u6e90\u548c\u65b9\u6cd5\u7684\u4e0d\u540c\u3002<\/p>\n\n\n

\u8bf7\u89e3\u91ca \u6b64\u8bba\u6587\u7684\u9898\u76ee\u201cBagging \u662f\u4e00\u79cd\u5c0f\u6570\u636e\u96c6\u73b0\u8c61 \u201d<\/h3>\n\n\n

\u8bba\u6587\u7684\u9898\u76ee\u201cBagging Is A Small-Data-Set Phenomenon\u201d\uff08Bagging \u662f\u4e00\u79cd\u5c0f\u6570\u636e\u96c6\u73b0\u8c61\uff09\u610f\u5728\u5f3a\u8c03Bagging\u65b9\u6cd5\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u7684\u6709\u6548\u6027\uff0c\u4f46\u5728\u5927\u6570\u636e\u96c6\u4e0a\u53ef\u80fd\u5e76\u4e0d\u5177\u5907\u540c\u6837\u7684\u4f18\u52bf\u3002<\/p>\n\n\n

\u89e3\u91ca\uff1a<\/p>\n\n\n

    \n
  1. Bagging\u65b9\u6cd5\u7684\u80cc\u666f<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n

    Bagging\uff08Bootstrap Aggregating\uff09\u662f\u4e00\u79cd\u96c6\u6210\u5b66\u4e60\u65b9\u6cd5\uff0c\u901a\u8fc7\u4ece\u539f\u59cb\u6570\u636e\u96c6\u4e2d\u968f\u673a\u6709\u653e\u56de\u5730\u62bd\u53d6\u591a\u4e2a\u5b50\u96c6\uff08\u79f0\u4e3a\u201c\u5305\u201d\uff09\uff0c\u7136\u540e\u5728\u6bcf\u4e2a\u5b50\u96c6\u4e0a\u8bad\u7ec3\u4e00\u4e2a\u5206\u7c7b\u5668\uff0c\u6700\u7ec8\u901a\u8fc7\u6295\u7968\u7b49\u673a\u5236\u7ed3\u5408\u8fd9\u4e9b\u5206\u7c7b\u5668\u7684\u8f93\u51fa\uff0c\u4ee5\u63d0\u9ad8\u6a21\u578b\u7684\u603b\u4f53\u6027\u80fd\u3002Bagging\u4e3b\u8981\u662f\u4e3a\u4e86\u5e94\u5bf9\u6a21\u578b\u7684\u4e0d\u7a33\u5b9a\u6027\uff08\u5982\u51b3\u7b56\u6811\uff09\uff0c\u901a\u8fc7\u589e\u52a0\u6a21\u578b\u7684\u591a\u6837\u6027\u6765\u63d0\u9ad8\u9884\u6d4b\u7684\u51c6\u786e\u6027\u3002<\/p>\n\n\n

      \n
    1. \u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u7684\u8868\u73b0<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n

      \u7814\u7a76\u8868\u660e\uff0cBagging\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u80fd\u591f\u663e\u8457\u63d0\u9ad8\u5206\u7c7b\u5668\u7684\u51c6\u786e\u6027\u3002\u539f\u56e0\u5728\u4e8e\uff0c\u968f\u673a\u62bd\u6837\u4ea7\u751f\u7684\u591a\u4e2a\u6570\u636e\u5305\u53ef\u4ee5\u901a\u8fc7\u4e0d\u540c\u7684\u8bad\u7ec3\u6570\u636e\u6765\u51cf\u5c11\u6a21\u578b\u7684\u8fc7\u62df\u5408\uff0c\u4ece\u800c\u63d0\u5347\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002\u56e0\u6b64\uff0c\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\uff0cBagging\u65b9\u6cd5\u7279\u522b\u6709\u6548\u3002<\/p>\n\n\n

        \n
      1. \u5728\u5927\u6570\u636e\u96c6\u4e0a\u7684\u5c40\u9650\u6027<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n

        \u7136\u800c\uff0c\u8bba\u6587\u901a\u8fc7\u5b9e\u9a8c\u53d1\u73b0\uff0cBagging\u5728\u5904\u7406\u5927\u6570\u636e\u96c6\u65f6\u5e76\u6ca1\u6709\u8868\u73b0\u51fa\u540c\u6837\u7684\u4f18\u52bf\u3002\u5bf9\u4e8e\u5927\u6570\u636e\u96c6\uff0cBagging\u65b9\u6cd5\u7684\u8ba1\u7b97\u5f00\u9500\u548c\u8d44\u6e90\u9700\u6c42\u975e\u5e38\u9ad8\uff0c\u56e0\u4e3a\u521b\u5efa\u548c\u5904\u7406\u591a\u4e2a\u6570\u636e\u5305\u9700\u8981\u5927\u91cf\u7684\u8ba1\u7b97\u8d44\u6e90\u548c\u65f6\u95f4\u3002\u6b64\u5916\uff0c\u5927\u6570\u636e\u96c6\u672c\u8eab\u7684\u6837\u672c\u91cf\u548c\u591a\u6837\u6027\u5df2\u7ecf\u5f88\u9ad8\uff0c\u901a\u8fc7Bagging\u8fdb\u4e00\u6b65\u589e\u52a0\u591a\u6837\u6027\u5bf9\u6a21\u578b\u6027\u80fd\u7684\u63d0\u5347\u53d8\u5f97\u6709\u9650\uff0c\u751a\u81f3\u53ef\u80fd\u7531\u4e8e\u8d44\u6e90\u9650\u5236\u5bfc\u81f4\u6548\u7387\u4f4e\u4e0b\u3002<\/strong><\/p>\n\n\n

        \u8bba\u6587\u8fd8\u8868\u660e\uff0c\u7b80\u5355\u7684\u6570\u636e\u5212\u5206\uff08\u5982\u4e0d\u76f8\u4ea4\u5212\u5206\uff09\u5728\u5927\u6570\u636e\u96c6\u4e0a\u53ef\u4ee5\u6bd4Bagging\u66f4\u6709\u6548\uff0c\u56e0\u4e3a\u5b83\u907f\u514d\u4e86\u5197\u4f59\u7684\u6570\u636e\u5904\u7406\uff0c\u540c\u65f6\u4ecd\u7136\u80fd\u591f\u63d0\u4f9b\u8db3\u591f\u7684\u6a21\u578b\u591a\u6837\u6027\u3002<\/p>\n\n\n

        \u56e0\u6b64\uff0c\u8bba\u6587\u9898\u76ee\u201cBagging \u662f\u4e00\u79cd\u5c0f\u6570\u636e\u96c6\u73b0\u8c61\u201d\u4f20\u8fbe\u7684\u6838\u5fc3\u89c2\u70b9\u662f\uff1aBagging\u65b9\u6cd5\u7684\u6709\u6548\u6027\u4e3b\u8981\u4f53\u73b0\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\uff0c\u800c\u5728\u5927\u6570\u636e\u96c6\u80cc\u666f\u4e0b\uff0c\u5176\u4f18\u52bf\u4e0d\u518d\u660e\u663e\uff0c\u751a\u81f3\u53ef\u80fd\u4e0d\u5982\u66f4\u7b80\u5355\u7684\u5212\u5206\u65b9\u6cd5\u3002\u8fd9\u4e2a\u9898\u76ee\u7a81\u51fa\u4e86\u7814\u7a76\u7684\u5173\u952e\u53d1\u73b0\uff0c\u6311\u6218\u4e86Bagging\u5728\u5927\u6570\u636e\u96c6\u5e94\u7528\u4e2d\u7684\u9002\u7528\u6027\uff0c\u5e76\u4e3a\u5bfb\u627e\u66f4\u6709\u6548\u7684\u5904\u7406\u5927\u6570\u636e\u96c6\u7684\u65b9\u6cd5\u63d0\u51fa\u4e86\u65b0\u7684\u65b9\u5411\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u8bba\u6587\u7b80\u4ecb \u82f1\u6587\u9898\u76ee\uff1aBagging Is A Small-D…<\/p>\n","protected":false},"author":1,"featured_media":507,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[27],"class_list":["post-340","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-26","tag-ensemble-learning"],"_links":{"self":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/340","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/comments?post=340"}],"version-history":[{"count":3,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/340\/revisions"}],"predecessor-version":[{"id":508,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/340\/revisions\/508"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media\/507"}],"wp:attachment":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media?parent=340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/categories?post=340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/tags?post=340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}