Applied Soft Computing Journal, 2019<\/p>\n\n\n
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<\u7814\u7a76\u80cc\u666f\u4e0e\u76ee\u7684><\/p>\n\n\n
\u96c6\u6210\u5b66\u4e60\u662f\u4e00\u79cd\u5c06\u591a\u4e2a\u5b66\u4e60\u5668\u7684\u9884\u6d4b\u7ed3\u679c\u7ed3\u5408\u8d77\u6765\u4ee5\u63d0\u9ad8\u9884\u6d4b\u6027\u80fd\u7684\u6280\u672f\u3002\u7136\u800c\uff0c\u96c6\u6210\u5b66\u4e60\u4e2d\u5b58\u5728\u4e00\u4e2a\u6311\u6218\uff1a\u5982\u4f55\u5e73\u8861\u5b66\u4e60\u8005\u4e4b\u95f4\u7684\u591a\u6837\u6027\u548c\u4e2a\u4f53\u51c6\u786e\u6027\u3002\u901a\u5e38\uff0c\u591a\u6837\u6027\u8d8a\u9ad8\uff0c\u4e2a\u4f53\u51c6\u786e\u6027\u5c31\u8d8a\u4f4e\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u8be5\u8bba\u6587\u63d0\u51fa\u4e86\u4e00\u4e2a\u65b0\u7684\u52a0\u6743\u96c6\u6210\u5b66\u4e60\u65b9\u6cd5\uff0c\u65e8\u5728\u540c\u65f6\u6700\u5927\u5316\u591a\u6837\u6027\u548c\u4e2a\u4f53\u51c6\u786e\u6027\u3002<\/p>\n\n\n
<\u521b\u65b0\u70b9><\/p>\n\n\n
\u8be5\u8bba\u6587\u7684\u4e3b\u8981\u521b\u65b0\u70b9\u5728\u4e8e\uff1a<\/p>\n\n\n
<\u7ed3\u8bba><\/p>\n\n\n
\u8be5\u8bba\u6587\u63d0\u51fa\u7684\u52a0\u6743\u96c6\u6210\u5b66\u4e60\u65b9\u6cd5\u5728UCI\u6570\u636e\u96c6\u548c\u4eba\u8138\u56fe\u50cf\u6570\u636e\u96c6\u4e0a\u7684\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u4e0e\u5176\u4ed6\u96c6\u6210\u65b9\u6cd5\u76f8\u6bd4\uff0c\u8be5\u65b9\u6cd5\u6709\u6548\u5730\u63d0\u9ad8\u4e86\u5206\u7c7b\u6027\u80fd\u3002<\/p>\n\n\n
<\u5b9e\u9a8c\u5185\u5bb9><\/p>\n\n\n
\u8be5\u8bba\u6587\u572830\u4e2aUCI\u6570\u636e\u96c6\u548c\u4eba\u8138\u56fe\u50cf\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u4e86\u5b9e\u9a8c\uff0c\u5e76\u5c06\u8be5\u65b9\u6cd5\u4e0e\u5176\u4ed6\u4e03\u79cd\u96c6\u6210\u65b9\u6cd5\u8fdb\u884c\u4e86\u6bd4\u8f83\uff0c\u5305\u62ecBagging\u3001AdaBoost\u3001WMV\u3001NBC\u3001EVEN\u3001MDM\u548cSCANN\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u8be5\u65b9\u6cd5\u5728\u5927\u591a\u6570\u6570\u636e\u96c6\u4e0a\u53d6\u5f97\u4e86\u6700\u4f73\u6027\u80fd\u3002<\/p>\n\n\n
<\u5bf9\u672c\u9886\u57df\u7684\u8d21\u732e><\/p>\n\n\n
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<\u4e3b\u8981\u5b9a\u7406><\/p>\n\n\n
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<\u5b58\u5728\u7684\u4e0d\u8db3><\/p>\n\n\n
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<\u672a\u6765\u7684\u5de5\u4f5c><\/p>\n\n\n
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\u603b\u7ed3\u8be5\u65b9\u6cd5\u7684\u4f18\u7f3a\u70b9\u3002<\/p>\n\n\n
\u5c55\u671b\u672a\u6765\u7684\u7814\u7a76\u65b9\u5411\u3002<\/p>\n\n\n
\u9644\u5f55\uff1a\u7b97\u6cd5<\/p>\n\n\n
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\u8bba\u6587\u4e2d\u63d0\u51fa\u7684\u53d8\u6362\u96c6\u6210\u5b66\u4e60 (TrEnL) \u7b97\u6cd5\u7684\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n
\u8f93\u5165\uff1a<\/p>\n\n\n
\u8f93\u51fa\uff1a<\/p>\n\n\n
\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n\n\n
\u6ce8\u610f\uff1a<\/p>\n\n\n
\u5e0c\u671b\u8fd9\u4e2a\u8be6\u7ec6\u7684\u6b65\u9aa4\u63cf\u8ff0\u80fd\u591f\u5e2e\u52a9\u60a8\u7406\u89e3 TrEnL \u7b97\u6cd5\u3002<\/p>\n\n\n
\u8fed\u4ee3\u4f18\u5316 \u662f TrEnL \u7b97\u6cd5\u7684\u6838\u5fc3\u6b65\u9aa4\uff0c\u7528\u4e8e\u6c42\u89e3\u76ee\u6807\u51fd\u6570 (13) \u4e2d\u7684\u6700\u4f73\u6743\u91cd\u5411\u91cf w \u548c\u8f85\u52a9\u5411\u91cf p\u3002\u8be5\u6b65\u9aa4\u91c7\u7528\u4ea4\u66ff\u65b9\u5411\u4e58\u5b50\u6cd5 (ADMM) \u8fdb\u884c\u4f18\u5316\uff0c\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n
1. \u56fa\u5b9a p\uff0c\u66f4\u65b0 w\uff1a<\/p>\n\n\n
\u5f53 p \u56fa\u5b9a\u65f6\uff0c\u76ee\u6807\u51fd\u6570 (13) \u53ef\u4ee5\u7b80\u5316\u4e3a\uff1a<\/p>\n\n\n
minw w^T (A – \u03bbD) w – 2b^T w\n<\/em><\/p>\n\n\n s.t. \u2211i^L w<\/em>i = 1, wi > 0\n<\/em><\/p>\n\n\n \u5176\u4e2d\uff1a<\/p>\n\n\n \u8fd9\u662f\u4e00\u4e2a\u5e26\u7ea6\u675f\u7684\u4e8c\u6b21\u89c4\u5212\u95ee\u9898\uff0c\u53ef\u4ee5\u4f7f\u7528\u62c9\u683c\u6717\u65e5\u4e58\u5b50\u6cd5\u5c06\u5176\u8f6c\u6362\u4e3a\u65e0\u7ea6\u675f\u95ee\u9898\u3002\u5f15\u5165\u62c9\u683c\u6717\u65e5\u4e58\u5b50 v \u548c u\uff0c\u5f97\u5230\u62c9\u683c\u6717\u65e5\u51fd\u6570\uff1a<\/p>\n\n\n \u039e(w, v, u, \u03c3) = F(w) – vh(w) + \u03c3\/2 h^2(w) + 1\/(2\u03c3) \u2211i^L { [max(0, u<\/em>i – \u03c3gi(w))]^2 – u<\/em>i^2 }<\/p>\n\n\n \u5176\u4e2d\uff1a<\/p>\n\n\n \u5bf9\u62c9\u683c\u6717\u65e5\u51fd\u6570 \u039e(w, v, u, \u03c3) \u6c42\u5bfc\uff0c\u5e76\u4ee4\u5bfc\u6570\u4e3a 0\uff0c\u5f97\u5230 w \u7684\u66f4\u65b0\u516c\u5f0f\uff1a<\/p>\n\n\n w(k+1) = (A – \u03bbD + \u03c311^T + \u2211i^L \u03c3Z(\u03c4<\/em>i)eie<\/em>i^T)^(-1) (b + v(k)1 + \u03c31 + \u2211i^L u<\/em>i(k)Z(\u03c4i)e<\/em>i)<\/p>\n\n\n \u5176\u4e2d\uff1a<\/p>\n\n\n 2. \u56fa\u5b9a w\uff0c\u66f4\u65b0 p\uff1a<\/p>\n\n\n \u5f53 w \u56fa\u5b9a\u65f6\uff0c\u76ee\u6807\u51fd\u6570 (13) \u53ef\u4ee5\u7b80\u5316\u4e3a\uff1a<\/p>\n\n\n min_p -2\/N p^TQw + 1\/N p^Tp<\/p>\n\n\n s.t. 0.5 < pn \u2264 1, n = 1, 2, …, N\n<\/em><\/p>\n\n\n \u8fd9\u4e5f\u662f\u4e00\u4e2a\u5e26\u7ea6\u675f\u7684\u4e8c\u6b21\u89c4\u5212\u95ee\u9898\uff0c\u540c\u6837\u53ef\u4ee5\u4f7f\u7528\u62c9\u683c\u6717\u65e5\u4e58\u5b50\u6cd5\u5c06\u5176\u8f6c\u6362\u4e3a\u65e0\u7ea6\u675f\u95ee\u9898\u3002\u5f15\u5165\u62c9\u683c\u6717\u65e5\u4e58\u5b50 \u03b3\uff0c\u5f97\u5230\u62c9\u683c\u6717\u65e5\u51fd\u6570\uff1a<\/p>\n\n\n L(p, \u03b3) = -2\/N p^TQw + 1\/N p^Tp + \u03b3^T(p – 1)<\/p>\n\n\n \u5bf9\u62c9\u683c\u6717\u65e5\u51fd\u6570 L(p, \u03b3) \u6c42\u5bfc\uff0c\u5e76\u4ee4\u5bfc\u6570\u4e3a 0\uff0c\u5f97\u5230 p \u7684\u66f4\u65b0\u516c\u5f0f\uff1a<\/p>\n\n\n u(k+1) = Qw(k+1) – \u03b3(k)<\/p>\n\n\n p(k+1) = (u(k+1) – 0.5 * 1)_+<\/p>\n\n\n \u5176\u4e2d\uff1a<\/p>\n\n\n 3. \u66f4\u65b0\u62c9\u683c\u6717\u65e5\u4e58\u5b50\uff1a<\/p>\n\n\n \u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u66f4\u65b0\u62c9\u683c\u6717\u65e5\u4e58\u5b50 v \u548c u\uff1a<\/p>\n\n\n v(k+1) = v(k) – \u03c3(1^T w(k+1) – 1)<\/p>\n\n\n u_i(k+1) = max(0, u_i(k) – \u03c3e_i^T w(k+1))<\/p>\n\n\n \u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u66f4\u65b0\u62c9\u683c\u6717\u65e5\u4e58\u5b50 \u03b3\uff1a<\/p>\n\n\n \u03b3(k+1) = \u03b3(k) – (p(k+1) – 1)<\/p>\n\n\n 4. \u8ba1\u7b97\u7ea6\u675f\u6761\u4ef6\u7684\u8bef\u5dee\uff1a<\/p>\n\n\n \u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u7ea6\u675f\u6761\u4ef6\u7684\u8bef\u5dee Estop\uff1a<\/p>\n\n\n Estop = sqrt((1^T w(k) – 1)^2 + \u2211i^L (max(e_i^T w(k), -u_i(k)\/\u03c3))^2)\n<\/em><\/p>\n\n\n 5. \u5224\u65ad\u662f\u5426\u505c\u6b62\u8fed\u4ee3\uff1a<\/p>\n\n\n \u5982\u679c Estop \u5c0f\u4e8e\u9608\u503c Emin \u6216\u8005\u8fed\u4ee3\u6b21\u6570 k \u5927\u4e8e\u6700\u5927\u8fed\u4ee3\u6b21\u6570 T\uff0c\u5219\u505c\u6b62\u8fed\u4ee3\uff0c\u5426\u5219\u7ee7\u7eed\u6267\u884c\u6b65\u9aa4 1 \u5230 4\u3002<\/p>\n\n\n \u6ce8\u610f\uff1a<\/p>\n\n\n \u5e0c\u671b\u8fd9\u4e2a\u8be6\u7ec6\u7684\u6b65\u9aa4\u63cf\u8ff0\u80fd\u591f\u5e2e\u52a9\u60a8\u7406\u89e3 TrEnL \u7b97\u6cd5\u7684\u8fed\u4ee3\u4f18\u5316\u8fc7\u7a0b\u3002<\/p>\n\n\n \u5728 TrEnL \u7b97\u6cd5\u4e2d\uff0c\u77e9\u9635 A \u548c\u5411\u91cf b \u7528\u4e8e\u66f4\u65b0\u6743\u91cd\u5411\u91cf w\u3002\u5b83\u4eec\u662f\u8fd9\u6837\u8ba1\u7b97\u7684\uff1a<\/p>\n\n\n \u5176\u4e2d\uff1a<\/p>\n\n\n \u77e9\u9635 A \u53ef\u4ee5\u770b\u4f5c\u662f\u5b66\u4e60\u5668\u6027\u80fd\u77e9\u9635 Q \u7684\u4e00\u79cd\u52a0\u6743\u5f62\u5f0f\u3002\u5b83\u5c06\u6bcf\u4e2a\u5b66\u4e60\u5668\u7684\u6027\u80fd\u4e0e\u5176\u5728\u6240\u6709\u5b66\u4e60\u5668\u4e2d\u7684\u76f8\u5bf9\u91cd\u8981\u6027\u8fdb\u884c\u52a0\u6743\u3002<\/p>\n\n\n \u5176\u4e2d\uff1a<\/p>\n\n\n \u5411\u91cf b \u53ef\u4ee5\u770b\u4f5c\u662f\u5b66\u4e60\u5668\u6027\u80fd\u77e9\u9635 Q \u548c\u671f\u671b\u6982\u7387\u5411\u91cf p \u7684\u4e00\u79cd\u52a0\u6743\u7ec4\u5408\u3002\u5b83\u8868\u793a\u6240\u6709\u5b66\u4e60\u5668\u5bf9\u6bcf\u4e2a\u6837\u672c\u7684\u9884\u6d4b\u7ed3\u679c\u4e0e\u671f\u671b\u6982\u7387\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n\n\n \u8fd9\u6837\u8ba1\u7b97 A \u548c b \u7684\u539f\u7406\u662f\uff0c\u5e0c\u671b\u901a\u8fc7\u6700\u5c0f\u5316\u4ee5\u4e0b\u76ee\u6807\u51fd\u6570\u6765\u627e\u5230\u6700\u4f73\u7684\u6743\u91cd\u5411\u91cf w\uff1a<\/p>\n\n\n w^T A w – 2b^T w<\/p>\n\n\n \u8fd9\u4e2a\u76ee\u6807\u51fd\u6570\u53ef\u4ee5\u89e3\u91ca\u4e3a\uff1a<\/p>\n\n\n \u56e0\u6b64\uff0c\u6700\u5c0f\u5316\u8fd9\u4e2a\u76ee\u6807\u51fd\u6570\u5c31\u76f8\u5f53\u4e8e\u627e\u5230\u4e00\u7ec4\u6743\u91cd\uff0c\u4f7f\u5f97\u6240\u6709\u5b66\u4e60\u5668\u7684\u52a0\u6743\u6027\u80fd\u6700\u5927\u5316\uff0c\u540c\u65f6\u6240\u6709\u5b66\u4e60\u5668\u7684\u9884\u6d4b\u7ed3\u679c\u4e0e\u671f\u671b\u6982\u7387\u4e4b\u95f4\u7684\u52a0\u6743\u5dee\u5f02\u6700\u5c0f\u5316\u3002<\/p>\n\n\n \u7b80\u800c\u8a00\u4e4b\uff0c\u8fd9\u6837\u8ba1\u7b97 A \u548c b \u7684\u76ee\u7684\u662f\u4e3a\u4e86\u5728 TrEnL \u7b97\u6cd5\u7684\u8fed\u4ee3\u4f18\u5316\u8fc7\u7a0b\u4e2d\uff0c\u627e\u5230\u4e00\u7ec4\u6700\u4f73\u7684\u6743\u91cd\uff0c\u4f7f\u5f97\u96c6\u6210\u5b66\u4e60\u5668\u7684\u6027\u80fd\u548c\u591a\u6837\u6027\u90fd\u5f97\u5230\u6700\u5927\u5316\u3002<\/p>\n\n\n QTQ \u662f\u4e00\u4e2a\u77e9\u9635\u8fd0\u7b97\uff0c\u5176\u4e2d Q \u662f\u4e00\u4e2a\u77e9\u9635\uff0cQT \u662f Q \u7684\u8f6c\u7f6e\u77e9\u9635\u3002\u8fd9\u4e2a\u8ba1\u7b97\u7684\u610f\u4e49\u53d6\u51b3\u4e8e\u77e9\u9635 Q \u7684\u5177\u4f53\u542b\u4e49\u3002<\/p>\n\n\n \u5728 TrEnL \u7b97\u6cd5\u4e2d\uff0cQ \u662f\u5b66\u4e60\u5668\u7684\u6027\u80fd\u77e9\u9635\uff0c\u5176\u5927\u5c0f\u4e3a N x L\uff0c\u5176\u4e2d N \u662f\u8bad\u7ec3\u6837\u672c\u7684\u6570\u91cf\uff0cL \u662f\u5b66\u4e60\u5668\u7684\u6570\u91cf\u3002\u56e0\u6b64\uff0cQTQ \u7684\u5927\u5c0f\u4e3a L x L\u3002<\/p>\n\n\n QTQ \u7684\u8ba1\u7b97\u53ef\u4ee5\u7406\u89e3\u4e3a\uff1a<\/p>\n\n\n \u5c06 Q \u7684\u6bcf\u4e00\u5217\uff08\u4ee3\u8868\u4e00\u4e2a\u5b66\u4e60\u5668\uff09\u4e0e\u5176\u81ea\u8eab\u8fdb\u884c\u5185\u79ef\u8fd0\u7b97\u3002<\/p>\n\n\n \u5c06\u6240\u6709\u5185\u79ef\u7684\u7ed3\u679c\u7ec4\u6210\u4e00\u4e2a\u65b0\u7684\u77e9\u9635\u3002<\/p>\n\n\n \u56e0\u6b64\uff0cQTQ \u7684\u5bf9\u89d2\u7ebf\u5143\u7d20\u8868\u793a\u6bcf\u4e2a\u5b66\u4e60\u5668\u81ea\u8eab\u7684\u6027\u80fd\uff0c\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20\u8868\u793a\u4e0d\u540c\u5b66\u4e60\u5668\u4e4b\u95f4\u7684\u6027\u80fd\u76f8\u4f3c\u6027\u3002<\/p>\n\n\n \u5728 TrEnL \u7b97\u6cd5\u7684\u76ee\u6807\u51fd\u6570\u4e2d\uff0cQTQ \u88ab\u7528\u6765\u8861\u91cf\u6240\u6709\u5b66\u4e60\u5668\u7684\u52a0\u6743\u6027\u80fd\u3002\u7531\u4e8e QTQ \u7684\u5bf9\u89d2\u7ebf\u5143\u7d20\u8868\u793a\u6bcf\u4e2a\u5b66\u4e60\u5668\u81ea\u8eab\u7684\u6027\u80fd\uff0c\u56e0\u6b64 QTQ \u53ef\u4ee5\u7528\u6765\u786e\u4fdd\u6240\u6709\u5b66\u4e60\u5668\u90fd\u5bf9\u6700\u7ec8\u7684\u96c6\u6210\u7ed3\u679c\u505a\u51fa\u8d21\u732e\u3002<\/p>\n\n\n \u6b64\u5916\uff0c\u7531\u4e8e QTQ \u7684\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20\u8868\u793a\u4e0d\u540c\u5b66\u4e60\u5668\u4e4b\u95f4\u7684\u6027\u80fd\u76f8\u4f3c\u6027\uff0c\u56e0\u6b64 QTQ \u4e5f\u53ef\u4ee5\u7528\u6765\u9f13\u52b1\u5b66\u4e60\u5668\u4e4b\u95f4\u7684\u591a\u6837\u6027\u3002\u5982\u679c\u4e24\u4e2a\u5b66\u4e60\u5668\u7684\u6027\u80fd\u975e\u5e38\u76f8\u4f3c\uff0c\u90a3\u4e48\u5b83\u4eec\u5728 QTQ \u4e2d\u5bf9\u5e94\u7684\u975e\u5bf9\u89d2\u7ebf\u5143\u7d20\u5c31\u4f1a\u5f88\u5927\u3002\u4e3a\u4e86\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\uff0c\u7b97\u6cd5\u4f1a\u503e\u5411\u4e8e\u964d\u4f4e\u8fd9\u4e24\u4e2a\u5b66\u4e60\u5668\u7684\u6743\u91cd\uff0c\u4ece\u800c\u63d0\u9ad8\u96c6\u6210\u5b66\u4e60\u5668\u7684\u591a\u6837\u6027\u3002<\/p>\n\n\n \u603b\u800c\u8a00\u4e4b\uff0c\u5728 TrEnL \u7b97\u6cd5\u4e2d\uff0cQTQ \u7684\u8ba1\u7b97\u610f\u4e49\u5728\u4e8e\uff1a<\/p>\n\n\n \u8861\u91cf\u6240\u6709\u5b66\u4e60\u5668\u7684\u52a0\u6743\u6027\u80fd\uff0c\u786e\u4fdd\u6240\u6709\u5b66\u4e60\u5668\u90fd\u5bf9\u6700\u7ec8\u7684\u96c6\u6210\u7ed3\u679c\u505a\u51fa\u8d21\u732e\u3002<\/p>\n\n\n 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\u8ba1\u7b97\u77e9\u9635 A \u548c\u5411\u91cf b \u7684\u539f\u7406<\/h2>\n\n\n
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QTQ \u8fd9\u4e2a\u8ba1\u7b97\u7684\u610f\u4e49\u662f\u4ec0\u4e48\uff1f<\/h2>\n\n\n