{"id":63048,"date":"2025-08-04T16:21:56","date_gmt":"2025-08-04T08:21:56","guid":{"rendered":"https:\/\/swarma.org\/?p=63048"},"modified":"2025-08-04T16:21:56","modified_gmt":"2025-08-04T08:21:56","slug":"%e5%9f%ba%e4%ba%8e%e5%8f%af%e9%80%86%e6%80%a7%e7%9a%84%e5%9b%a0%e6%9e%9c%e6%b6%8c%e7%8e%b0%e7%90%86%e8%ae%ba%ef%bd%9c%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=63048","title":{"rendered":"\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff5c\u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u662f\u4e00\u79cd\u91cf\u5316\u56e0\u679c\u6d8c\u73b0\u7684\u65b0\u6846\u67b6\uff0c\u8be5\u65b9\u6cd5\u57fa\u4e8e\u5947\u5f02\u503c\u5206\u89e3\uff0c\u63d0\u51fa\u4e86\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff08\u0393<\/span><\/span>\u03b1<\/span><\/sub>\uff09\u7684\u6982\u5ff5\uff0c\u7528\u4e8e\u91cf\u5316\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\u63a5\u8fd1\u53ef\u9006\u52a8\u529b\u5b66\u7684\u7a0b\u5ea6\uff0c\u8be5\u6307\u6807\u5728\u79bb\u6563\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u548c\u8fde\u7eed\u7684\u5177\u6709\u9ad8\u65af\u566a\u58f0\u7684\u8fde\u7eed\u9a6c\u5c14\u79d1\u592b\u7cfb\u7edf\u90fd\u6709\u76f8\u5e94\u7684\u8868\u8fbe\u65b9\u5f0f\u4e0e\u7269\u7406\u542b\u4e49\uff1b\u4e0e\u6b64\u540c\u65f6\uff0c\u8be5\u7406\u8bba\u8fd8\u63d0\u51fa\u4e86\u4e00\u79cd\u4e0d\u4f9d\u8d56\u4e8e\u7c97\u7c92\u5316\u65b9\u6848\u5c31\u80fd\u76f4\u63a5\u6839\u636e\u52a8\u529b\u5b66\u7684\u5947\u5f02\u503c\u8c31\u5224\u65ad\u56e0\u679c\u6d8c\u73b0\u662f\u5426\u53d1\u751f\u7684\u65b9\u6cd5\u3002\u7ecf\u8fc7\u7406\u8bba\u63a8\u5bfc\u548c\u6570\u503c\u5b9e\u9a8c\u8bc1\u660e\uff0c\u5728\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u5224\u65ad\u548c\u91cf\u5316\u95ee\u9898\u4e0a\uff0c\u57fa\u4e8e\u8fd1\u4f3c\u53ef\u9006\u6027\u6307\u6807\u7684\u56e0\u679c\u6d8c\u73b0\u5224\u65ad\u4e0eErik Hoel\u7b49\u4eba\u63d0\u51fa\u7684\u57fa\u4e8e\u6709\u6548\u4fe1\u606f\uff08EI\uff09\u6307\u6807\u6700\u5927\u5316\u7684\u56e0\u679c\u6d8c\u73b0\u5224\u65ad\u662f\u7b49\u6548\u7684\uff0c\u4e14log<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/sub><\/span>\u548cEI\u662f\u5b58\u5728\u7740\u6e10\u8fd1\u8fd1\u4f3c\u7ebf\u6027\u7684\u5173\u7cfb\uff1b\u800c\u5728\u8fde\u7eed\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u4e2d\uff0c\u7814\u7a76\u8005\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4e00\u4e2a\u8fd1\u4f3c\u7684\u7ebf\u6027\u5173\u7cfb\u516c\u5f0f\u4ee5\u8868\u8fbe\u4e24\u79cd\u6307\u6807\u7684\u8054\u7cfb\u3002\u6b64\u5916\uff0c\u8be5\u7406\u8bba\u8fd8\u63d0\u51fa\u4e86\u57fa\u4e8e\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\u7684\u65b0\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u5e76\u901a\u8fc7\u5b9e\u9a8c\u8bc1\u660e\u4e86\u8be5\u65b9\u6cd5\u7684\u6709\u6548\u6027\u3002<\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/span><\/span><\/strong><\/p>\n


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\u4e3a\u4e86\u7cfb\u7edf\u68b3\u7406\u56e0\u679c\u6d8c\u73b0\u6700\u65b0\u8fdb\u5c55\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u56e0\u679c\u6d8c\u73b0\u7cfb\u5217\u8bfb\u4e66\u4f1a\uff0c\u76ee\u524d\u5df2\u7ecf\u6301\u7eed\u5230\u300c\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u5982\u679c\u4f60\u5bf9\u8fd9\u4e00\u8bdd\u9898\u611f\u5174\u8da3\uff0c\u975e\u5e38\u63a8\u8350\u4f60\u52a0\u5165\u793e\u533a\uff01<\/span><\/span><\/strong><\/span><\/strong><\/p>\n


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\u201c\u96c6\u667a\u767e\u79d1\u7cbe\u9009\u201d\u662f\u4e00\u4e2a\u957f\u671f\u4e13\u680f\uff0c\u6301\u7eed\u4e3a\u5927\u5bb6\u63a8\u9001\u590d\u6742\u6027\u79d1\u5b66\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8d44\u6e90\u4fe1\u606f\u3002\u4f5c\u4e3a\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u96c6\u667a\u767e\u79d1\u5e0c\u671b\u6253\u9020\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u6700\u5168\u9762\u7684\u767e\u79d1\u5168\u4e66\uff0c\u6b22\u8fce\u5bf9\u590d\u6742\u6027\u79d1\u5b66\u611f\u5174\u8da3\u3001\u70ed\u7231\u77e5\u8bc6\u6574\u7406\u548c\u5206\u4eab\u7684\u670b\u53cb\u52a0\u5165\uff0c\u6587\u672b\u53ef\u4ee5\u626b\u7801\u62a5\u540d\u52a0\u5165\u767e\u79d1\u5fd7\u613f\u8005\uff01<\/span><\/strong><\/span><\/strong><\/p>\n


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\u2191\u2191\u2191\u626b\u7801\u76f4\u8fbe\u767e\u79d1\u8bcd\u6761<\/span><\/p>\n

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\u5173\u952e\u8bcd\uff1a\u56e0\u679c\u6d8c\u73b0\uff0c\u6709\u6548\u4fe1\u606f\uff0c\u5143\u80de\u81ea\u52a8\u673a<\/span><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
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\u9f9a\u94ed\u5eb7\u3001\u5218\u51ef\u5a01<\/span> <\/span><\/span><\/span>| \u4f5c\u8005<\/span><\/span><\/p>\n

\u5f20\u6c5f\u3001\u738b\u5fd7\u9e4f <\/span><\/span><\/span>| \u6574\u7406\u3001\u5ba1\u6821<\/span><\/span><\/section>\n


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\u76ee\u5f55<\/span><\/strong><\/p>\n

1. <\/span>\u5386\u53f2\u7b80\u4ecb<\/span><\/span><\/span><\/span><\/span><\/span><\/section>\n
2. \u57fa\u672c\u6982\u5ff5<\/span><\/span><\/span><\/span><\/section>\n

2.1\t\u4e25\u683c\u7684\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span><\/p>\n

2.1.1\t\u79bb\u6563\u52a8\u529b\u5b66<\/span><\/span><\/p>\n

2.1.2\t\u8fde\u7eed\u52a8\u529b\u5b66<\/span><\/span><\/p>\n

2.2\tTPM\u77e9\u9635\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span><\/p>\n

2.2.1\t\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/span><\/p>\n

2.2.2\t\u5f52\u4e00\u5316<\/span><\/span><\/p>\n

2.2.3\t\u5177\u4f53\u4f8b\u5b50<\/span><\/span><\/p>\n

2.3\t\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span><\/p>\n

2.3.1\t\u7ef4\u5ea6\u5e73\u5747<\/span><\/span><\/p>\n

2.3.2\t\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/span><\/p>\n

3. \u6709\u6548\u4fe1\u606f\uff08EI\uff09\u4e0e\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span><\/p>\n

3.1\t\u79bb\u6563\u72b6\u6001\u60c5\u5f62<\/span><\/span><\/p>\n

3.1.1\t\u4e0eEI\u7684\u76f8\u4f3c\u6027<\/span><\/span><\/p>\n

3.1.2\t\u4e0eEI\u7684\u4e0d\u540c<\/span><\/span><\/p>\n

3.2\t\u8fde\u7eed\u53d8\u91cf\u60c5\u5f62<\/span><\/span><\/p>\n

3.2.1\t\u6709\u6548\u4fe1\u606f\u4e0e\u8fd1\u4f3c\u53ef\u9006\u6027<\/span><\/span><\/p>\n

4. \u79bb\u6563TPM\u57fa\u4e8eSVD\uff08\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff09\u7684\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/p>\n

4.1\t\u6e05\u6670\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/p>\n

4.2\t\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/p>\n

4.3\tTPM\u77e9\u9635\u7684\u7c97\u7c92\u5316\u65b9\u6cd5<\/span><\/span><\/p>\n

4.4\t\u4e0e\u57fa\u4e8e\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u5173\u7cfb<\/span><\/span><\/p>\n

4.5\t\u5177\u4f53\u6848\u4f8b<\/span><\/span><\/p>\n

4.5.1\t\u5e03\u5c14\u7f51\u7edc<\/span><\/span><\/p>\n

4.5.2\t\u590d\u6742\u7f51\u7edc<\/span><\/span><\/p>\n

4.5.3\t\u5143\u80de\u81ea\u52a8\u673a<\/span><\/span><\/p>\n

5. \u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u57fa\u4e8eSVD\u7684\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/p>\n

5.1\t\u56e0\u679c\u6d8c\u73b0\u7684\u91cf\u5316\u6307\u6807<\/span><\/span><\/p>\n

5.1.1\t\u4e0e\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u5b9a\u91cf\u5316\u7684\u5173\u7cfb<\/span><\/span><\/p>\n

5.2\t\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u57fa\u4e8eSVD\u7684\u7c97\u7c92\u5316\u7b56\u7565<\/span><\/span><\/p>\n

5.2.1\t\u7b2c\u4e00\u6b65<\/span><\/span><\/p>\n

5.2.2\t\u7b2c\u4e8c\u6b65<\/span><\/span><\/p>\n

5.3\t\u8fde\u7eed\u7cfb\u7edf\u5177\u4f53\u6848\u4f8b<\/span><\/span><\/p>\n

5.3.1\t\u589e\u957f\u6a21\u578b<\/span><\/span><\/p>\n

5.3.2\t\u79bb\u6563\u5316\u5e03\u6717\u8fd0\u52a8<\/span><\/span><\/p>\n

5.3.3\tSIR\u6a21\u578b<\/span><\/span><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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1. \u5386\u53f2\u7b80\u4ecb<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

\u56e0\u679c\u6d8c\u73b0\uff08causal emergence\uff09\u662f\u6307\u52a8\u529b\u7cfb\u7edf\u4e2d\u7684\u4e00\u7c7b\u7279\u6b8a\u7684\u6d8c\u73b0\u73b0\u8c61\uff0c\u5373\u7cfb\u7edf\u5728\u5b8f\u89c2\u5c3a\u5ea6\u4f1a\u5c55\u73b0\u51fa\u66f4\u5f3a\u7684\u56e0\u679c\u7279\u6027\u3002\u7279\u522b\u7684\uff0c\u5bf9\u4e8e\u4e00\u7c7b\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u7cfb\u7edf\u6765\u8bf4\uff0c\u5728\u5bf9\u5176\u72b6\u6001\u7a7a\u95f4\u8fdb\u884c\u9002\u5f53\u7684\u7c97\u7c92\u5316\u4ee5\u540e\uff0c\u6240\u5f62\u6210\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u4f1a\u5c55\u73b0\u51fa\u6bd4\u5fae\u89c2\u66f4\u5f3a\u7684\u56e0\u679c\u7279\u6027\u2014\u2014\u5373\u66f4\u5927\u7684\u6709\u6548\u4fe1\u606f\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u8be5\u7cfb\u7edf\u53d1\u751f\u4e86\u56e0\u679c\u6d8c\u73b0<\/span><\/span>[1]<\/span><\/span>[2]<\/span><\/span>\u30022013\u5e74\uff0cHoel\u7b49\u4eba<\/span><\/span>[1]<\/span><\/span>\u6700\u65e9\u63d0\u51fa\u4e86\u57fa\u4e8e\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff0c\u8be5\u7406\u8bba\u5229\u7528\u6709\u6548\u4fe1\u606f\uff08Effective Information\uff0c\u7b80\u79f0EI\uff09\u6765\u5ea6\u91cf\u4e00\u4e2a\u52a8\u529b\u5b66\u7684\u56e0\u679c\u6548\u5e94\uff0c\u5e76\u7528\u8fd9\u4e00\u5ea6\u91cf\u6765\u91cf\u5316\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u6d8c\u73b0\u73b0\u8c61\u30022020\u5e74\uff0cRosas\u7b49<\/span><\/span>[3]<\/span><\/span>\u53c8\u4ece\u4fe1\u606f\u7406\u8bba\u89c6\u89d2\u51fa\u53d1\uff0c\u63d0\u51fa\u4e00\u79cd\u57fa\u4e8e\u4fe1\u606f\u5206\u89e3\u65b9\u6cd5\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff0c\u8be5\u7406\u8bba\u7528\u534f\u540c\u4fe1\u606f\u6216\u8005\u7279\u6709\u4fe1\u606f\u6765\u5b9a\u91cf\u523b\u753b\u6d8c\u73b0\u30022023\u5e74\uff0cBarnett\u7b49\u4eba<\/span><\/span>[4]<\/span><\/span>\u57fa\u4e8e\u8f6c\u79fb\u71b5\uff0c\u901a\u8fc7\u5224\u65ad\u5b8f\u89c2\u52a8\u529b\u5b66\u4e0e\u5fae\u89c2\u52a8\u529b\u5b66\u7684\u89e3\u8026\u7a0b\u5ea6\u6765\u5224\u65ad\u6d8c\u73b0\u7684\u53d1\u751f\uff0c\u5c06\u56e0\u679c\u6d8c\u73b0\u523b\u753b\u4e3a\u5b8f\u89c2\u7684\u53d8\u91cf\u4e0e\u5fae\u89c2\u7684\u53d8\u91cf\u76f8\u4e92\u72ec\u7acb\u7684\u73b0\u8c61\u3002<\/span><\/span><\/span><\/p>\n

\u7136\u800c\uff0c\u73b0\u6709\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u5b58\u5728\u7740\u4e00\u5b9a\u7684\u5c40\u9650\u6027\u3002\u4f8b\u5982\uff0c\u57fa\u4e8e\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u662f\u4e00\u4e2a\u4f9d\u8d56\u4e8e\u7c97\u7c92\u5316\u65b9\u6848\u7684\u7406\u8bba\uff0c\u4e0d\u540c\u7684\u7c97\u7c92\u5316\u7b56\u7565\u4f1a\u5f97\u5230\u5b8c\u5168\u4e0d\u540c\u7684\u56e0\u679c\u6d8c\u73b0\u5224\u65ad\u7ed3\u679c\u3002\u5c3d\u7ba1\u8fd9\u4e00\u5c40\u9650\u53ef\u4ee5\u901a\u8fc7\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f<\/span><\/span>[5]<\/span><\/span>\u9009\u53d6\u7c97\u7c92\u5316\u7b56\u7565\u5f97\u5230\u4e00\u5b9a\u7a0b\u5ea6\u7684\u89e3\u51b3\uff0c\u4f46\u662f\u8be5\u4f18\u5316\u95ee\u9898\u8fd8\u662f\u5f88\u96be\u6c42\u89e3\u3002Rosas\u7b49\u4eba\u63d0\u51fa\u4e86\u7528\u534f\u540c\u4fe1\u606f\u91cf\u5316\u6d8c\u73b0\u7684\u65b9\u6cd5<\/span><\/span>[3]<\/span><\/span>\uff0c\u4f46\u662f\u8fd9\u79cd\u8ba1\u7b97\u6d89\u53ca\u5230\u591a\u4e2a\u53d8\u91cf\u7684\u6240\u6709\u7ec4\u5408\uff0c\u56e0\u800c\u8ba1\u7b97\u91cf\u4f1a\u968f\u7740\u53d8\u91cf\u6570\u7684\u589e\u52a0\u800c\u5448\u73b0\u6307\u6570\u589e\u957f\u3002Rosas\u8fdb\u4e00\u6b65\u63d0\u51fa\u4e86\u8fd1\u4f3c\u8ba1\u7b97\u65b9\u6848\uff0c\u4f46\u662f\u8be5\u65b9\u6cd5\u4e0eErik Hoel\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u4e00\u6837\uff0c\u9700\u8981\u4e8b\u5148\u6307\u5b9a\u7c97\u7c92\u5316\u65b9\u6848\u6216\u6d8c\u73b0\u53d8\u91cf<\/span><\/span>[3]<\/span><\/span>\u3002\u540c\u6837\u5730\uff0cSeth\u7b49\u4eba\u66f4\u65e9\u63d0\u51fa\u7684\u7528\u683c\u5170\u6770\u56e0\u679c\u91cf\u5316\u6d8c\u73b0\u7406\u8bba\u4e5f\u9700\u8981\u5728\u7c97\u7c92\u5316\u65b9\u6848\u7ed9\u5b9a\u7684\u60c5\u51b5\u4e0b\u5c55\u5f00\u8ba8\u8bba<\/span><\/span>[4]<\/span><\/span>\u3002\u5bf9\u4e8e\u7c97\u7c92\u5316\u65b9\u6848\u7684\u8fc7\u5206\u4f9d\u8d56\u4f1a\u4f7f\u5f97\u8fd9\u4e9b\u91cf\u5316\u6d8c\u73b0\u7406\u8bba\u5728\u4e0d\u540c\u7a0b\u5ea6\u4e0a\u4f9d\u8d56\u4e8e\u89c2\u5bdf\u8005\u7684\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u56e0\u800c\u4e0d\u80fd\u5b8c\u5168\u53cd\u6620\u7cfb\u7edf\u52a8\u529b\u5b66\u7684\u6027\u8d28\u3002\u90a3\u4e48\uff0c\u662f\u5426\u5b58\u5728\u7740\u4e00\u79cd\u4e0d\u4f9d\u8d56\u4e8e\u7c97\u7c92\u5316\u65b9\u6848\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u5462\uff1f<\/span><\/span><\/span><\/p>\n

2024\u5e74\uff0c\u5f20\u6c5f\u7b49\u4eba<\/span><\/span>[6]<\/span><\/span>\u57fa\u4e8e\u5947\u5f02\u503c\u5206\u89e3\uff0c\u63d0\u51fa\u4e86\u4e00\u5957\u65b0\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3002\u8be5\u7406\u8bba\u7684\u6838\u5fc3\u601d\u60f3\u662f\u6307\u51fa\u6240\u8c13\u7684\u56e0\u679c\u6d8c\u73b0\u5176\u5b9e\u7b49\u4ef7\u4e8e\u52a8\u529b\u5b66\u53ef\u9006\u6027\u7684\u6d8c\u73b0\u3002\u7ed9\u5b9a\u4e00\u4e2a\u7cfb\u7edf\u7684\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\uff0c\u901a\u8fc7\u5bf9\u5b83\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\uff0c\u5c06\u5947\u5f02\u503c\u7684<\/span><\/span>\u03b1<\/span><\/span>\u6b21\u65b9\u4e4b\u548c\u5b9a\u4e49\u4e3a\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\u7684\u8fd1\u4f3c\u53ef\u9006\u6027\u5ea6\u91cf\uff08<\/span><\/span>\"image.png\"<\/span><\/sub>\uff09\uff0c\u8fd9\u91cc<\/span><\/span><\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/sub>\u4e3a\u5947\u5f02\u503c\uff0c<\/span><\/span>\u03b1<\/span><\/span>\u4e3a\u4e00\u4e2a\u53c2\u6570\uff0c\u7528\u4ee5\u523b\u753b\u6700\u7ec8\u6307\u6807\u504f\u5411\u4e8e\u8861\u91cf\u786e\u5b9a\u6027\u6216\u7b80\u5e76\u6027\u7684\u7a0b\u5ea6\uff0c\u901a\u5e38\u6211\u4eec\u53d6<\/span><\/span>\u03b1<\/span><\/span>=<\/span><\/span>1<\/span><\/span>\uff0c\u8868\u793a\u5e73\u6743\u8003\u8651\u786e\u5b9a\u6027\u6216\u7b80\u5e76\u6027\u5bf9\u6700\u7ec8\u53ef\u9006\u6027\u5ea6\u91cf\u7684\u5f71\u54cd\u3002\u8be5\u6307\u6807\u4e0e\u6709\u6548\u4fe1\u606f\u5177\u6709\u9ad8\u5ea6\u7684\u76f8\u5173\u6027\uff0c\u56e0\u800c\u4e5f\u53ef\u4ee5\u7528\u4e8e\u523b\u753b\u52a8\u529b\u5b66\u7684\u56e0\u679c\u6548\u5e94\u5f3a\u5ea6\u3002\u6839\u636e\u5947\u5f02\u503c\u7684\u8c31\uff0c\u8be5\u65b9\u6cd5\u53ef\u4ee5\u5728\u4e0d\u663e\u5f0f\u5b9a\u4e49\u7c97\u7c92\u5316\u65b9\u6848\u7684\u6761\u4ef6\u4e0b\uff0c\u76f4\u63a5\u5b9a\u4e49\u6240\u8c13<\/span><\/span>\u6e05\u6670\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/b>\uff08clear causal emergence\uff09\u548c<\/span><\/span>\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/b>\uff08vague causal emergence\uff09\u7684\u6982\u5ff5\u3002<\/span><\/span><\/span><\/p>\n

\u76f4\u89c2\u5730\u8bf4\uff0c\u5982\u679c\u5c06\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\u770b\u4f5c\u662f\u4e00\u4e2a\u901a\u4fe1\u4fe1\u9053\uff0c\u90a3\u4e48\uff0c\u6bcf\u4e00\u72b6\u6001\u4e0b\u7684\u6982\u7387\u8f6c\u79fb\u5c31\u770b\u4f5c\u662f\u4e00\u4e2a\u4fe1\u606f\u901a\u8def\uff08information pathway\uff09\uff0c\u4e8e\u662f\u8be5\u7cfb\u7edf\u53d1\u751f\u56e0\u679c\u6d8c\u73b0\u5c31\u7b49\u4ef7\u4e8e\u7cfb\u7edf\u4e2d\u5b58\u5728\u7740\u5197\u4f59\u7684\u4fe1\u606f\u901a\u8def\u2014\u2014\u5b58\u5728\u7740\u4e00\u4e9b\u72b6\u6001\u8f6c\u79fb\u4e0e\u5176\u5b83\u72b6\u6001\u8f6c\u79fb\u76f8\u4f3c\u6216\u7ebf\u6027\u76f8\u5173\uff0c\u800c\u6d88\u9664\u8fd9\u4e9b\u5197\u4f59\u901a\u8def\u7684\u6700\u597d\u529e\u6cd5\u5c31\u662f\u5229\u7528SVD\u627e\u5230\u7b49\u4e8e\u96f6\u6216\u63a5\u8fd1\u4e8e\u96f6\u7684\u5947\u5f02\u503c\u4ee5\u53ca\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\uff0c\u8fd9\u5b9e\u9645\u4e0a\u6b63\u662f\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u7cbe\u9ad3\u6240\u5728\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc1\u660e\uff0c\u6700\u5927\u5316\u5b8f\u89c2\u52a8\u529b\u5b66\u6709\u6548\u4fe1\u606f\u7684\u7c97\u7c92\u5316\u65b9\u6848\u8fd1\u4f3c\u7b49\u4ef7\u4e8e\u5c06\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u5411\u8f83\u5927\u5947\u5f02\u503c\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\u65b9\u5411\u505a\u6295\u5f71\u7684\u7c97\u7c92\u5316\u65b9\u6848\u3002\u800c\u4e14\uff0c\u7cfb\u7edf\u6240\u80fd\u8fbe\u5230\u7684\u6700\u5927\u4fe1\u606f\u4f20\u8f93\u6548\u7387\u7684\u63d0\u5347\uff08\u5f52\u4e00\u5316\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff09\uff0c\u5c31\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u56e0\u679c\u6d8c\u73b0\u7684\u5f3a\u5ea6\u3002<\/span><\/span><\/p>\n

2025\u5e74\uff0c\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba<\/span><\/span>[7]<\/span><\/span>\u53c8\u88ab\u6210\u529f\u5730\u62d3\u5c55\u5230\u4e86\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u4e4b\u4e2d\uff08<\/span><\/span><\/span>X<\/span><\/span>t<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span>=<\/span><\/span>a<\/span><\/span>0<\/span><\/span><\/sub>+<\/span><\/span>A<\/span><\/span>X<\/span><\/span>t<\/span><\/span><\/sub>+<\/span><\/span>\u03be<\/span><\/span>t<\/span><\/span><\/sub>\uff09\u3002\u5bf9\u4e8e\u4e00\u4e2a\u5177\u6709\u9ad8\u65af\u566a\u58f0\u7684\u8fed\u4ee3\u52a8\u529b\u7cfb\u7edf\uff0c\u6211\u4eec\u53ef\u4ee5\u7c7b\u6bd4\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u8ba1\u7b97\u5947\u5f02\u503c\u7684\u65b9\u6cd5\uff0c\u5229\u7528\u6cdb\u51fd\u5206\u6790\u548c\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u5f97\u5230\u9891\u57df\u7a7a\u95f4\u4e2d\u8fde\u7eed\u52a8\u529b\u7cfb\u7edf\u7684\u53ef\u9006\u6027\u5ea6\u91cf\u6307\u6807<\/span><\/span>\"image.png\"<\/span><\/sub>\u3002\u800c\u4e0e\u79bb\u6563\u72b6\u6001\u7a7a\u95f4\u4e0d\u540c\uff0c\u5bf9\u4e8e\u8fde\u7eed\u7684\u7a7a\u95f4\uff0c\u65e0\u8bba\u72b6\u6001\u7a7a\u95f4\u7684\u7ef4\u6570<\/span><\/span>n<\/span><\/span>\u53d6\u591a\u5c11<\/span><\/span>R<\/span><\/span>n<\/span><\/span><\/sup>\u4e4b\u95f4\u72b6\u6001\u6570\u91cf\u90fd\u662f\u65e0\u7a77\u7684\uff0c\u72b6\u6001\u7a7a\u95f4\u7684\u52bf\uff08\u53cd\u5e94\u96c6\u5408\u4e2d\u70b9\u7684\u6570\u91cf\uff09\u4e5f\u90fd\u662f\u76f8\u540c\u9636\u7684\u65e0\u7a77\u5927\uff0c\u56e0\u6b64\u6211\u4eec\u65e0\u6cd5\u76f4\u63a5\u4ece\u72b6\u6001\u4e0a\u8fdb\u884c\u7ea6\u51cf\uff0c\u800c\u9700\u8981\u628a\u6d8c\u73b0\u7684\u7814\u7a76\u5bf9\u8c61\uff0c\u4ece\u6982\u7387\u7a7a\u95f4\u8f6c\u79fb\u5230\u53d8\u91cf\u7a7a\u95f4\uff0c\u800c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6070\u597d\u4e0e\u6b63\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635\u7684\u9006\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u4e0e\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635\u7684\u9006\u77e9\u9635<\/span><\/span>A<\/span><\/span>T<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>A<\/span><\/span>\u90fd\u6b63\u76f8\u5173\uff0c\u4e24\u4e2a\u534f\u65b9\u5dee\u77e9\u9635\u5728\u4e00\u8d77\u53ef\u4ee5\u53cd\u6620\u53d8\u91cf\u7a7a\u95f4\u5728\u52a8\u529b\u5b66\u610f\u4e49\u4e0b\u7684\u53ef\u9006\u6027\u3002\u5728\u53d8\u91cf\u7a7a\u95f4\uff0c\u56e0\u679c\u6d8c\u73b0\u7684\u542b\u4e49\u5373\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u4e2d\u5b58\u5728\u7740\u5197\u4f59\u7684\u7ef4\u5ea6\uff0c\u800c\u901a\u8fc7\u7c97\u7c92\u5316\u65b9\u6848\u5c06\u52a8\u529b\u5b66\u5411\u8f83\u5927\u5947\u5f02\u503c\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\u4e0a\u6295\u5f71\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u83b7\u5f97\u6700\u5927\u5316\u7684\u7ef4\u5ea6\u5e73\u5747\u53ef\u9006\u6027\u7684\u63d0\u5347\uff0c\u8fd9\u4e00\u6f5c\u5728\u7684\u63d0\u5347\u80fd\u529b\u5c31\u53ef\u4ee5\u88ab\u5b9a\u4e49\u4e3a\u56e0\u679c\u6d8c\u73b0\u7684\u5b9a\u91cf\u5316\u5ea6\u91cf\u3002\u56e0\u6b64\u5728\u6ee1\u8db3\u9ad8\u65af\u566a\u58f0\u7684\u8fde\u7eed\u53d8\u91cf\u7a7a\u95f4\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5728\u4e0d\u663e\u5f0f\u5b9a\u4e49\u7c97\u7c92\u5316\u65b9\u6848\u7684\u6761\u4ef6\u4e0b\uff0c\u76f4\u63a5\u5b9a\u4e49\u6240\u8c13<\/span><\/span>\u6e05\u6670\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/b>\u548c<\/span><\/span>\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/b>\u3002<\/span><\/span><\/span><\/p>\n

\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u4e0e\u5df2\u6709\u7684\u5176\u4ed6\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u6700\u5927\u7684\u533a\u522b\u5c31\u662f\u4e0d\u9700\u8981\u6307\u5b9a\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u4ec5\u4ece\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u6216\u9ad8\u65af\u8fed\u4ee3\u7cfb\u7edf\u7684\u5947\u5f02\u503c\u8c31\u5c31\u80fd\u5224\u65ad\u56e0\u679c\u6d8c\u73b0\u7684\u53d1\u751f\uff0c\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u89c4\u907f\u4e86\u56e0\u679c\u6d8c\u73b0\u7ed3\u679c\u4f9d\u8d56\u4e8e\u7c97\u7c92\u5316\u7b56\u7565\u7684\u95ee\u9898\u548c\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u96be\u4ee5\u4f18\u5316\u6c42\u89e3\u7684\u95ee\u9898\u3002\u5176\u6b21\uff0c\u8fd9\u5957\u7406\u8bba\u6307\u51fa\u4e00\u4e2a\u52a8\u529b\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u7279\u6027\u4ec5\u4ec5\u662f\u7cfb\u7edf\u7ebf\u6027\u5316\u7b97\u7b26\u7684\u5947\u5f02\u503c\u8c31\u51b3\u5b9a\u7684\uff0c\u56e0\u800c\u662f\u4e00\u5957\u66f4\u52a0\u53cd\u6620\u7cfb\u7edf\u52a8\u529b\u5b66\u7279\u6027\u672c\u8eab\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3002<\/span><\/span><\/p>\n


<\/span><\/span><\/h1>\n

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<\/span><\/section>\n

<\/span><\/section>\n
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<\/section>\n<\/section>\n<\/section>\n
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2. \u57fa\u672c\u6982\u5ff5<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

\u4e0b\u9762\u8be6\u7ec6\u4ecb\u7ecd\u8be5\u7406\u8bba\u7684\u57fa\u672c\u6982\u5ff5\uff0c\u5206\u522b\u662f\u52a8\u529b\u5b66\u53ef\u9006\u6027\u3001\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u3001\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u548c\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/span><\/p>\n

2.1 \u4e25\u683c\u7684\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span><\/span><\/h2>\n

2.1.1 \u79bb\u6563\u52a8\u529b\u5b66<\/span><\/span><\/span><\/h3>\n

\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u9a6c\u5c14\u53ef\u592b\u94fe<\/span><\/span>\u03c7<\/span><\/span>\u548c\u5bf9\u5e94\u7684<\/span><\/span>\u8f6c\u79fb\u6982\u7387\u77e9\u9635(Transitional Probability Matrix\uff0c\u7b80\u79f0TPM)<\/span><\/span><\/b> P \uff0c\u5982\u679cP\u540c\u65f6\u6ee1\u8db3\uff1a<\/span><\/span><\/span><\/p>\n

1. P\u662f\u53ef\u9006\u77e9\u9635\uff0c\u5373\u5b58\u5728\u77e9\u9635<\/span><\/span>P<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\uff0c\u4f7f\u5f97<\/span><\/span>P<\/span><\/span>P<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>=<\/span><\/span>I<\/span><\/span>\uff0c<\/span><\/span><\/span>I<\/span><\/span>\u4e3a\u5355\u4f4d\u77e9\u9635\uff1b<\/span><\/span><\/p>\n

2. P<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup>\u4e5f\u662f\u53e6\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe<\/span><\/span><\/span>\u03c7<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u7684\u6709\u6548TPM\uff0c<\/span><\/span><\/span><\/p>\n

\u5219<\/span><\/span>\u03c7<\/span><\/span>\u548cP\u53ef\u4ee5\u79f0\u4e3a<\/span><\/span>\u4e25\u683c\u52a8\u529b\u5b66\u53ef\u9006\u7684<\/span><\/span><\/b>\u3002<\/span><\/span><\/span><\/p>\n

\u5173\u4e8e\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u5b9a\u7406\uff1a<\/span><\/span><\/p>\n

\u5b9a\u74061<\/span>\uff1a<\/span><\/span><\/b>\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u9a6c\u5c14\u79d1\u592b\u94fe<\/span><\/span>\u03c7<\/span><\/span>\u548c\u5bf9\u5e94\u7684TPM P\uff0c\u5f53\u4e14\u4ec5\u5f53P\u662f\u7f6e\u6362\u77e9\u9635(Permutation Matrix)\u7684\u65f6\u5019\uff0cP\u662f\u4e25\u683c\u52a8\u529b\u5b66\u53ef\u9006\u7684\u3002<\/span><\/span><\/span><\/p>\n

\u6240\u8c13\u7684\u7f6e\u6362\u77e9\u9635\u662f\u6307\u6bcf\u4e00\u4e2a\u884c\u5411\u91cf\u90fd\u662f\u72ec\u70ed\u5411\u91cf\uff08one-hot vector\uff0c\u5373\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u662f1\uff0c\u5176\u4f59\u5143\u7d20\u5747\u4e3a\u96f6\u7684\u5411\u91cf\uff09\uff0c\u6bcf\u4e24\u4e2a\u884c\u5411\u91cf\u90fd\u4e0d\u76f8\u540c\u3002<\/span><\/span><\/p>\n

2.1.2 \u8fde\u7eed\u52a8\u529b\u5b66<\/span><\/span><\/span><\/h3>\n

TPM\u77e9\u9635\u4e0a\u57fa\u4e8eSVD\u7684\u56e0\u679c\u6d8c\u73b0\u867d\u7136\u80fd\u5f97\u5230\u4e0d\u4f9d\u8d56\u7c97\u7c92\u5316\u7b56\u7565\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u4f46\u662f\u4e5f\u5b58\u5728\u4e00\u4e2a\u5f0a\u7aef\uff0c\u5c31\u662f\u53ea\u80fd\u91cf\u5316\u79bb\u6563\u6761\u4ef6\u6982\u7387\u7a7a\u95f4\u7684\u56e0\u679c\u6548\u5e94\u5f3a\u5ea6\u548c\u56e0\u679c\u6d8c\u73b0\u3002\u7531\u4e8e\u79bb\u6563\u6982\u7387\u7a7a\u95f4\u548c\u8fde\u7eed\u6982\u7387\u7a7a\u95f4\u5177\u6709\u672c\u8d28\u7684\u4e0d\u540c\uff0c\u5bf9\u4e8e\u8fde\u7eed\u6982\u7387\u7a7a\u95f4\u7684\u57fa\u4e8eSVD\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u6211\u4eec\u9700\u8981\u5355\u72ec\u8fdb\u884c\u5206\u6790\u3002\u8fd9\u91cc\uff0c\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u5177\u6709\u4ee3\u8868\u6027\u7684\u8fde\u7eed\u53d8\u91cf\u7684\u52a8\u529b\u7cfb\u7edf\uff0c\u8fd9\u5c31\u662f\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\uff0c\u5f15\u5165\u5b83\u7684\u57fa\u4e8eSVD\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba<\/span><\/span>[7]<\/span><\/span>\u3002<\/span><\/span><\/span><\/p>\n

\u9ad8\u65af\u566a\u58f0\u7684\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u53ef\u4ee5\u5199\u6210\uff1a<\/span><\/span><\/p>\n

X<\/span><\/span>\ud835\udc61+1<\/span><\/sub>=a<\/span><\/span>0<\/span><\/sub>+\ud835\udc34\u22c5\ud835\udc4b<\/span><\/span>\ud835\udc61<\/span><\/sub>+\u03be<\/span><\/span><\/span>\ud835\udc61<\/span><\/sub> \uff081\uff09<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d<\/span><\/span>\ud835\udc4b<\/span><\/span>\ud835\udc61<\/span><\/span><\/sub>\u662ft\u65f6\u523b\u7684\u72b6\u6001\u5411\u91cf, \u7ef4\u6570\u4e3a<\/span><\/span>n<\/span><\/span>\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e3at\u65f6\u523b\u7684\u566a\u97f3\u53d8\u91cf\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u662f\u5b83\u7684\u534f\u65b9\u5dee\u77e9\u9635\u3002\u8fd9\u662f\u4e00\u79cd\u6700\u7b80\u5355\u7684\u8fde\u7eed\u72b6\u6001\u7a7a\u95f4\u7684\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u8981\u5c06SVD\u65b9\u6cd5\u6269\u5c55\u5230\u8fd9\u7c7b\u7cfb\u7edf\u4e0a\u3002<\/span><\/span><\/span><\/p>\n

\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\uff08\u5f0f<\/span><\/span>1<\/span><\/span><\/b>\uff09 \uff0c\u5982\u679c\u5b83\u540c\u65f6\u6ee1\u8db3\uff1a<\/span><\/span><\/span><\/p>\n

1. A\u662f\u53ef\u9006\u77e9\u9635\uff0c\u5373\u5b58\u5728\u77e9\u9635<\/span><\/span>A<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\uff0c\u4f7f\u5f97<\/span><\/span>A<\/span><\/span>A<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>=<\/span><\/span>I<\/span><\/span>\uff0c<\/span><\/span><\/span>I<\/span><\/span>\u4e3a\u5355\u4f4d\u77e9\u9635\uff1b<\/span><\/span><\/p>\n

2. \u6b63\u9006\u5411\u52a8\u529b\u5b66\u534f\u65b9\u5dee\u77e9\u9635\u6ee1\u8db3<\/span><\/span>(<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>)<\/span><\/span>\u2192<\/span><\/span>0<\/span><\/span>,<\/span><\/span>\u03a3<\/span><\/span>\u2192<\/span><\/span>0<\/span><\/span>\uff1b<\/span><\/span><\/span><\/p>\n

\u5219<\/span><\/span>X<\/span><\/span>\ud835\udc61<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/span><\/sub>=<\/span><\/span><\/span>a<\/span><\/span>0<\/span><\/span><\/sub>+<\/span><\/span>\ud835\udc34<\/span><\/span>\u22c5<\/span><\/span>\ud835\udc4b<\/span><\/span>\ud835\udc61<\/span><\/span><\/sub>+<\/span><\/span>\u03be<\/span><\/span>\ud835\udc61<\/span><\/span><\/sub>\u53ef\u4ee5\u79f0\u4e3a<\/span><\/span>\u4e25\u683c\u52a8\u529b\u5b66\u53ef\u9006\u7684<\/span><\/span><\/b>\uff0c\u6b64\u65f6\u52a8\u529b\u5b66\u7b49\u4ef7\u4e8e\u4e00\u4e00\u6620\u5c04<\/span><\/span>X<\/span><\/span>\ud835\udc61<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span>=<\/span><\/span>a<\/span><\/span>0<\/span><\/span><\/sub>+<\/span><\/span>\ud835\udc34<\/span><\/span>\u22c5<\/span><\/span>\ud835\udc4b<\/span><\/span>\ud835\udc61<\/span><\/span><\/sub>\u3002<\/span><\/span><\/span><\/p>\n

\u4e0d\u96be\u53d1\u73b0\uff0c\u4e25\u683c\u53ef\u9006\u7684\u60c5\u51b5\u4e0b\uff0c\u52a8\u529b\u7cfb\u7edf\u53ef\u4ee5\u76f4\u63a5\u5199\u6210\u53ef\u9006\u6620\u5c04<\/span><\/span><\/p>\n

<\/section>\n

\u5176\u9006\u52a8\u529b\u5b66\u4e3a\uff1a<\/span><\/span><\/p>\n

<\/span><\/p>\n

\u6b64\u65f6<\/span><\/span>\ud835\udc4b<\/span><\/span>\ud835\udc61<\/span><\/span><\/sub>\u548c<\/span><\/span>\ud835\udc4b<\/span><\/span>t<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span>\u53ef\u4ee5\u76f8\u4e92\u5efa\u7acb\u4e00\u4e00\u6620\u5c04\u3002\u800c<\/span><\/span>A<\/span><\/span>\u4e0d\u53ef\u9006\u6216\u5b58\u5728\u566a\u58f0<\/span><\/span>\"image.png\"<\/span><\/sub>\u7684\u60c5\u51b5\u4e0b\uff0c\u4f1a\u9020\u6210\u6620\u5c04\u7684\u4e0d\u53ef\u9006\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u80fd\u901a\u8fc7\u8fd1\u4f3c\u53ef\u9006\u6027\u6765\u5ea6\u91cf\u4ee5\u4e0a\u4e24\u79cd\u60c5\u51b5\u7684\u53ef\u9006\u6027\u3002\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u5f53\u566a\u58f0\u534f\u65b9\u5dee\u540c\u65f6\u6ee1\u8db3<\/span><\/span>\u03a3<\/span><\/span>\u2192<\/span><\/span>0<\/span><\/span>, <\/span><\/span>A<\/span><\/span>\u2020<\/span><\/span><\/sup>\u03a3<\/span><\/span>(<\/span><\/span>A<\/span><\/span>\u2020<\/span><\/span><\/sup>)<\/span><\/span>T<\/span><\/span><\/sup>\u2192<\/span><\/span>0<\/span><\/span>\uff0c\u5373\u6b63\u5411\u52a8\u529b\u5b66\u548c\u9006\u5411\u52a8\u529b\u5b66\u7684\u566a\u58f0\u534f\u65b9\u5dee\u77e9\u9635\u5747\u63a5\u8fd10\u7684\u65f6\u5019\uff0c\u6574\u4e2a\u52a8\u529b\u5b66\u53ef\u4ee5\u8fd1\u4f3c\u4e3a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u548c<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u6b64\u65f6<\/span><\/span>\ud835\udc4b<\/span><\/span>\ud835\udc61<\/span><\/span><\/sub>\u548c<\/span><\/span>\ud835\udc4b<\/span><\/span>t<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span>\u4e4b\u95f4\u7684\u7684\u6761\u4ef6\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u5199\u6210\u72c4\u62c9\u514b\u5206\u5e03<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u9006\u8fc7\u7a0b\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u4f7f\u52a8\u529b\u7cfb\u7edf\u7684\u53ef\u9006\u6027\u8fbe\u5230\u6700\u5f3a\u3002\u56e0\u6b64\u6211\u4eec\u53ea\u8981\u5bfb\u627e\u4e00\u79cd\u540c\u65f6\u5305\u542b<\/span><\/span>\u03a3<\/span><\/span>\u548c<\/span><\/span>A<\/span><\/span>\u2020<\/span><\/span><\/sup><\/span>\u03a3<\/span><\/span>(<\/span><\/span>A<\/span><\/span>\u2020<\/span><\/span><\/sup>)<\/span><\/span>T<\/span><\/span><\/sup>\u7684\u6307\u6807\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5ea6\u91cf\u8fd1\u4f3c\u53ef\u9006\u6027\u3002\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635\u7684\u9006\u77e9\u9635<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u548c\u6b63\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635\u7684\u9006\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u5171\u540c\u5f71\u54cd\u4e86\u8fd1\u4f3c\u53ef\u9006\u6027\u7684\u5927\u5c0f\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\uff0c\u6b63\u5411\u3001\u9006\u5411\u7684\u534f\u65b9\u5dee\u90fd\u5f88\u5c0f\uff0c\u6216\u975e\u6ee1\u79e9\u3001\u75c5\u6001\uff08\u5bf9\u5e94\u7ef4\u5ea6\u867d\u7136\u53d6\u503c\u975e0\uff0c\u4f46\u76f8\u6bd4\u5176\u4ed6\u7ef4\u5ea6\u76f8\u5dee\u8fc7\u4e8e\u60ac\u6b8a\uff09\u7684\u77e9\u9635\u5bf9\u6a21\u578b\u6574\u4f53\u5f71\u54cd\u8f83\u5c0f\u7684\u65f6\u5019\uff0c\u7cfb\u7edf\u52a8\u529b\u5b66\u6709\u66f4\u5f3a\u7684\u53ef\u9006\u6027\u3002<\/span><\/span><\/span><\/p>\n

2.2 TPM\u77e9\u9635\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span><\/span><\/p>\n

\u7eaf\u7cb9\u7684\u7f6e\u6362\u77e9\u9635\u5728\u6240\u6709\u53ef\u80fd\u7684TPM\u4e2d\u975e\u5e38\u7a00\u5c11\uff0c\u6240\u4ee5\u5927\u591a\u6570\u7684TPM\u5e76\u4e0d\u662f\u4e25\u683c\u52a8\u529b\u5b66\u53ef\u9006\u7684\u3002\u56e0\u6b64\uff0c\u9700\u8981\u4e00\u4e2a\u6307\u6807\u6765\u523b\u753b\u4efb\u610f\u4e00\u4e2aTPM\u63a5\u8fd1\u52a8\u529b\u5b66\u53ef\u9006\u7684\u7a0b\u5ea6\u3002\u8003\u8651P\u7684\u79e9\u4e3ar\uff0c\u5f53\u4e14\u4ec5\u5f53r<N\uff08N\u4e3a\u77e9\u9635\u7684\u7ef4\u6570\uff09\u7684\u65f6\u5019\uff0cP\u662f\u4e0d\u53ef\u9006\u7684\uff1b\u4e14P\u8d8a\u9000\u5316\u5bf9\u5e94\u7740\u8d8a\u5c0f\u7684r\u3002\u7136\u800c\uff0c\u975e\u9000\u5316\uff08\u6ee1\u79e9\uff09\u7684\u77e9\u9635P\u5e76\u4e0d\u603b\u662f\u52a8\u529b\u5b66\u53ef\u9006\u7684\uff0c\u56e0\u4e3a\uff1a<\/span><\/span><\/p>\n

1. \u5c3d\u7ba1<\/span><\/span>P<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u5b58\u5728\uff0c<\/span><\/span>P<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u5e76\u4e0d\u4e00\u5b9a\u662f\u6ee1\u8db3\u5f52\u4e00\u5316\u6761\u4ef6\u7684\u5408\u6cd5TPM\uff08\u5373\u77e9\u9635\u4e2d\u6bcf\u4e2a\u5143\u7d20\u90fd\u5927\u4e8e\u7b49\u4e8e0\uff0c\u5c0f\u4e8e\u7b49\u4e8e1\uff0c\u4e14\u6bcf\u4e00\u884c\u6ee1\u8db3\u52a0\u548c\u4e3a1\u7684\u6761\u4ef6\uff09\uff1b<\/span><\/span><\/span>
<\/span><\/span><\/p>\n

2. \u5982\u524d\u6240\u8ff0\uff0c\u82e5P\u6ee1\u8db3\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff0c\u5219P\u5fc5\u4e3a\u7f6e\u6362\u77e9\u9635\u3002<\/span><\/span><\/p>\n

\u6240\u6709\u7f6e\u6362\u77e9\u9635\u7684\u884c\u5411\u91cf\u90fd\u662f\u72ec\u70ed\u5411\u91cf\u3002\u8fd9\u4e00\u7279\u6027\u53ef\u4ee5\u88ab\u77e9\u9635P\u7684\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u8303\u6570\uff08Frobenius norm\uff09\u523b\u753b\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5f53\u4e14\u4ec5\u5f53P\u7684\u884c\u5411\u91cf\u662f\u72ec\u70ed\u5411\u91cf\u7684\u65f6\u5019\uff0c\u77e9\u9635P\u7684\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u8303\u6570\u53d6\u6700\u5927\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u7531\u77e9\u9635P\u7684\u79e9r\u548c\u77e9\u9635\u7684\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u8303\u6570\u627e\u5230P\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u4e0e\u77e9\u9635\u5947\u5f02\u503c\u4e4b\u95f4\u7684\u8054\u7cfb\u3002<\/span><\/span><\/p>\n

\u9996\u5148\uff0c\u77e9\u9635\u7684\u79e9\u53ef\u4ee5\u88ab\u5199\u4f5c\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/sub>\u662f\u77e9\u9635P\u7684\u7b2ci\u4e2a\u5947\u5f02\u503c\uff0c<\/span><\/span><\/span>N<\/span><\/span>\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u6570\u3002<\/span><\/span><\/p>\n

\u7d27\u63a5\u7740\uff0c\u77e9\u9635\u7684\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u8303\u6570\u53ef\u4ee5\u88ab\u5199\u4f5c\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u8fd9\u4e5f\u662f\u6240\u6709\u5947\u5f02\u503c\u7684\u5e73\u65b9\u548c\u3002\u53ef\u4ee5\u770b\u51fa\u77e9\u9635\u7684\u79e9\u548c\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u8303\u6570\u90fd\u4e0e\u5947\u5f02\u503c\u76f8\u8054\u7cfb\u3002<\/span><\/span><\/p>\n

\u7531\u4e8e\u7edd\u5927\u90e8\u5206\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\uff08TPM\uff09\u90fd\u4e0d\u662f\u7f6e\u6362\u77e9\u9635\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u6307\u6807\u6765\u523b\u753b\u4e00\u4e2aTPM\u9760\u8fd1\u53ef\u9006\u7684\u7f6e\u6362\u77e9\u9635\u7a0b\u5ea6\u7684\u6307\u6807\uff0c\u8fd9\u5c31\u662f\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u3002 \u5047\u8bbe\u9a6c\u5c14\u79d1\u592b\u94fe\u7684TPM\u4e3aP\uff0c\u5947\u5f02\u503c\u4e3a<\/span><\/span>(<\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/sub>\u2265<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/sub>\u2265<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>\u2265<\/span><\/span>\u03c3<\/span><\/span>N<\/span><\/span><\/sub>\u2265<\/span><\/span>0<\/span><\/span>)<\/span><\/span>\uff0c\u90a3\u4e48\u77e9\u9635P\u7684<\/span><\/span>\u03b1<\/span><\/span>\u9636\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u5b9a\u4e49\u4e3a\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span>\u03b1<\/span><\/span>\u2208<\/span><\/span>(<\/span><\/span>0<\/span><\/span>,<\/span><\/span>2<\/span><\/span>)<\/span><\/span>\u662f\u53c2\u6570\u3002<\/span><\/span><\/span><\/p>\n

\u5b9e\u9645\u4e0a\uff0c\u5f53<\/span><\/span>\u03b1<\/span><\/span>\u2265<\/span><\/span>1<\/span><\/span>\u65f6\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u662fP\u7684\u6c99\u6ed5\u8303\u6570\uff08Schatten norm\uff09\uff1b\u5f53<\/span><\/span>0<\/span><\/span><<\/span><\/span>\u03b1<\/span><\/span><<\/span><\/span>1<\/span><\/span>\u65f6\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u662fP\u7684\u51c6\u8303\u6570\uff08quasinorm\uff09<\/span><\/span>[8]<\/span><\/span>[9]<\/span><\/span>[10]<\/span><\/span>[11]<\/span><\/span>\u3002\u4f7f\u7528\u8fd9\u4e2a\u5b9a\u4e49\u6765\u523b\u753b\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u662f\u5408\u7406\u7684\uff0c\u56e0\u4e3a\u5b8c\u5168\u52a8\u529b\u5b66\u53ef\u9006\u6027\u53ef\u4ee5\u901a\u8fc7\u6700\u5927\u5316<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6765\u5f97\u5230\u3002<\/span><\/span><\/span><\/p>\n

\u6211\u4eec\u53ef\u4ee5\u8bc1\u660e\u5982\u4e0b\u7ed3\u8bba\uff1a\u5bf9\u4e8e\u4efb\u610f<\/span><\/span><\/span>\u03b1<\/span><\/span>\u2208<\/span><\/span>(<\/span><\/span>0<\/span><\/span>,<\/span><\/span>2<\/span><\/span>)<\/span><\/span>\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span>\u7684\u6700\u5927\u503c\u662fN\uff0c\u5f53\u4e14\u4ec5\u5f53P\u662f\u7f6e\u6362\u77e9\u9635\u7684\u65f6\u5019\u80fd\u53d6\u5230\u8be5\u6700\u5927\u503c\u3002<\/span><\/span><\/span><\/p>\n

2.2.1 \u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/span><\/span><\/h3>\n

\u901a\u8fc7\u8c03\u6574\u53c2\u6570<\/span><\/span>\u03b1<\/span><\/span>\u2208<\/span><\/span>(<\/span><\/span>0<\/span><\/span>,<\/span><\/span>2<\/span><\/span>)<\/span><\/span>\uff0c\u53ef\u4ee5\u4f7f<\/span><\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u66f4\u597d\u5730\u53cd\u6620P\u7684\u786e\u5b9a\u6027\u6216\u8005\u7b80\u5e76\u6027\u3002\u5f53<\/span><\/span>\u03b1<\/span><\/span>\u2192<\/span><\/span>0<\/span><\/span>,<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6536\u655b\u5230P\u7684\u79e9\uff0c\u8fd9\u7c7b\u4f3c\u4e8eEI\u5b9a\u4e49\u4e2d\u7684\u975e\u7b80\u5e76\u6027\u9879\uff0c\u56e0\u4e3a\u968f\u7740P\u8d8a\u6765\u8d8a\u9000\u5316\uff0cr\u8d8a\u6765\u8d8a\u5c0f\u3002\u7136\u800c\uff0c\u5b9a\u4e49\u4e0d\u5141\u8bb8<\/span><\/span>\u03b1<\/span><\/span>\u7cbe\u786e\u4e3a\u96f6\uff0c\u56e0\u4e3ar\u4e0d\u662fP\u7684\u8fde\u7eed\u51fd\u6570\uff0c\u800c\u4e14\u6700\u5927\u5316\u79e9\u4e0d\u7b49\u4e8e\u7f6e\u6362\u77e9\u9635\u3002\u540c\u6837\uff0c\u5f53<\/span><\/span>\u03b1<\/span><\/span>\u2192<\/span><\/span>2<\/span><\/span>\u65f6\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6536\u655b\u5230<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4f46\u662f\u5b9a\u4e49\u4e0d\u5141\u8bb8<\/span><\/span>\u03b1<\/span><\/span>\u53d62\uff0c\u56e0\u4e3a<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/sub><\/span>=<\/span><\/span><\/sub>2<\/span><\/sub><\/span>\u7684\u6700\u5927\u5316\u5e76\u4e0d\u610f\u5473\u7740P\u662f\u53ef\u9006\u7684\u3002<\/span><\/span>|<\/span><\/span>|<\/span><\/span>P<\/span><\/span>|<\/span><\/span>|<\/span><\/span>F<\/span><\/span><\/sub>\u4e0eEI\u5b9a\u4e49\u4e2d\u7684\u786e\u5b9a\u6027\u9879\u5177\u6709\u53ef\u6bd4\u6027\uff0c\u56e0\u4e3a\u5f53P\u5177\u6709\u8d8a\u6765\u8d8a\u591a\u7684\u72ec\u70ed\u5411\u91cf\uff0cP\u4e2d\u7684\u6700\u5927\u8f6c\u79fb\u6982\u7387\u4e5f\u4f1a\u53d8\u5f97\u66f4\u5927\uff0c\u610f\u5473\u7740\u52a8\u529b\u5b66\u53d8\u5f97\u66f4\u52a0\u53ef\u9006\u3002<\/span><\/span><\/span><\/p>\n

\u5728\u5b9e\u8df5\u4e2d\uff0c\u6211\u4eec\u603b\u662f\u53d6<\/span><\/span>\u03b1<\/span><\/span>=<\/span><\/span>1<\/span><\/span>\u6765\u5e73\u8861<\/span><\/span>\u0393<\/span><\/span>\u6d4b\u91cf\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\u7684\u503e\u5411\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/sub><\/span>=<\/span><\/span><\/sub>1<\/span><\/sub><\/span>\u88ab\u79f0\u4e3a\u6838\u8303\u6570<\/span><\/span>[11]<\/span><\/span>[12]<\/span><\/span>\u3002\u4e3a\u7b80\u4fbf\uff0c\u4e0b\u6587\u4e2d\u5c06<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/sub><\/span>=<\/span><\/span><\/sub>1<\/span><\/sub><\/span>\u8bb0\u4f5c<\/span><\/span>\u0393<\/span><\/span>\u3002<\/span><\/span><\/span><\/p>\n

2.2.2 \u5f52\u4e00\u5316<\/span><\/span><\/span><\/h3>\n

\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u53d7\u77e9\u9635\u7684\u5927\u5c0f\u5f71\u54cd\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5bf9\u5176\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u5f97\u5230<\/span><\/span>\u03b3<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6765\u523b\u753b\u4e0e\u5927\u5c0f\u65e0\u5173\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff0c\u8fd9\u6837\u53ef\u4ee5\u66f4\u65b9\u4fbf\u5730\u5728\u4e0d\u540c\u5927\u5c0f\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u4e4b\u95f4\u8fdb\u884c\u6bd4\u8f83\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5bb9\u6613\u8bc1\u660e\uff0c<\/span><\/span>\u03b3<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u603b\u662f\u5c0f\u4e8e1\u5927\u4e8e0\u3002<\/span><\/span><\/span><\/p>\n

2.2.3 \u5177\u4f53\u4f8b\u5b50<\/span><\/span><\/span><\/h3>\n

\u5728\u4e0b\u56fe\u4e2d\uff0c\u4f5c\u8005\u7ed9\u51fa\u4e86\u56db\u4e2a\u5177\u4f53\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u4f8b\u5b50\uff0c\u8be5\u9a6c\u6c0f\u94fe\u7684\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u5982\u4e0b\u56fe\u6240\u793a\u3002\u6211\u4eec\u53ef\u4ee5\u5bf9\u6bd4\u8be5\u9a6c\u6c0f\u94fe\u7684<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\u548c\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff08\u56fe\u4e2d\u7684<\/span><\/span>\u0393<\/span><\/span>\uff0c\u5373<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/sub><\/span>=<\/span><\/span><\/sub>1<\/span><\/sub><\/span>\uff09\u3002\u5bf9\u6bd4\u56fe(a)\uff0c(b)\uff0c\u6211\u4eec\u53d1\u73b0\u5bf9\u4e8e\u4e0d\u540c\u7684\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\uff0c<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\u964d\u4f4e\u7684\u65f6\u5019\uff0c<\/span><\/span>\u0393<\/span><\/span>\u4e5f\u540c\u6b65\u964d\u4f4e\u3002\u8fdb\u4e00\u6b65\uff0c\u56fe(c)\u548c(d)\u662f\u5bf9\u6bd4\u7c97\u7c92\u5316\u524d\u540e\u7684\u6548\u679c\uff0c\u5176\u4e2d\u56fe(d)\u662f\u5bf9\u56fe(c)\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u7684\u7c97\u7c92\u5316\uff08\u5c06\u524d\u4e09\u4e2a\u72b6\u6001\u5f52\u5e76\u4e3a\u4e00\u4e2a\u5b8f\u89c2\u6001\uff09\u3002\u7531\u4e8e\u5b8f\u89c2\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u56fe(d)\u662f\u4e00\u4e2a\u786e\u5b9a\u6027\u7cfb\u7edf\uff0c\u56e0\u6b64\uff0c\u5f52\u4e00\u5316\u540e\u7684<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\uff0c<\/span><\/span>e<\/span><\/span>f<\/span><\/span>f<\/span><\/span>\u2261<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\/<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>N<\/span><\/span>\u548c\u5f52\u4e00\u5316\u540e\u7684<\/span><\/span><\/span>\u0393<\/span><\/span>\uff1a<\/span><\/span>\u03b3<\/span><\/span>\u2261<\/span><\/span>\u0393<\/span><\/span>\/<\/span><\/span>N<\/span><\/span>\u90fd\u8fbe\u5230\u4e86\u6700\u5927\u503c1\u3002<\/span><\/span><\/span><\/p>\n

\"Gamma\u4f8b\u5b50.png\"<\/section>\n

2.3 \u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span><\/span><\/h2>\n

TPM\u77e9\u9635\u53ef\u4ee5\u901a\u8fc7SVD\u5206\u89e3\u76f4\u63a5\u5f97\u5230\u5947\u5f02\u503c\u8c31\uff0c\u5728\u72b6\u6001\u7a7a\u95f4\u4e2d\u57fa\u4e8e\u4e0d\u540c\u72b6\u6001\u5bf9\u5e94\u7684\u5947\u5f02\u503c\uff0c\u8fdb\u884c\u56e0\u679c\u6d8c\u73b0\u7684\u8ba1\u7b97\uff0c\u53ea\u8981\u72b6\u6001\u662f\u79bb\u6563\u7684\uff0c\u4e0d\u7ba1\u662f\u6709\u9650\u7684\u8fd8\u662f\u53ef\u6570\u7684\uff0c\u90fd\u53ef\u4ee5\u8fdb\u884c\u56e0\u679c\u6d8c\u73b0\u7684\u8ba1\u7b97\u3002\u4f46\u662f\u8fde\u7eed\u7a7a\u95f4\u4e0a\u7684\u52a8\u529b\u7cfb\u7edf\u7684\u72b6\u6001\u6570\u91cf\u4e0d\u53ef\u6570\u4e14\u662f\u65e0\u7a77\u591a\u7684\uff0c\u65e0\u6cd5\u7528\u540c\u6837\u7684\u65b9\u6cd5\u524a\u51cf\u5947\u5f02\u503c\u6570\u91cf\u3002\u56e0\u4e3a\u672c\u8d28\u4e0a\u8fde\u7eed\u7a7a\u95f4\u4e4b\u95f4\u7684\u52bf\u662f\u76f8\u540c\u7684\uff0c\u65e0\u7a77\u96c6\u53ef\u4ee5\u4e0e\u5176\u771f\u5b50\u96c6\u5f62\u6210\u4e00\u4e00\u6620\u5c04\uff0c\u56e0\u6b64\u65e0\u8bba\u600e\u4e48\u5220\u51cf\u72b6\u6001\u6570\u91cf\uff0c\u5269\u4f59\u7684\u72b6\u6001\u6570\u91cf\u4f9d\u7136\u662f\u65e0\u7a77\u591a\u7684\uff0c\u8fd9\u5c31\u5982\u540c\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u70b9\u5176\u5b9e\u548c\u5e73\u9762\u4e0a\u4e00\u6837\u591a\u7c7b\u4f3c\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\uff0c\u6211\u4eec\u9700\u8981\u7528\u65b0\u7684\u65b9\u6cd5\u8fdb\u884c\u56e0\u679c\u6d8c\u73b0\u7684\u5224\u65ad\u548c\u5b9a\u91cf\u5316\uff0c\u5373\u4ece\u72b6\u6001\u7a7a\u95f4\u7684\u5947\u5f02\u503c\u53d8\u4e3a\u6b27\u6c0f\u7a7a\u95f4\u7684\u5947\u5f02\u503c\u3002TPM\u77e9\u9635\u672c\u8d28\u4e0a\u662f\u79bb\u6563\u6761\u4ef6\u6982\u7387<\/span><\/span>p<\/span><\/span>(<\/span><\/span>x<\/span><\/span>t<\/span><\/sub><\/span><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span><\/span>|<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>)<\/span><\/span>\u6784\u6210\u7684\u77e9\u9635\uff0c\u77e9\u9635\u7684\u7b2ci\u884c\u7b2cj\u5217\u4ee3\u8868<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>=<\/span><\/span>i<\/span><\/span>\u7684\u6761\u4ef6\u4e0b<\/span><\/span>x<\/span><\/span>t<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span>=<\/span><\/span>j<\/span><\/span>\u7684\u6982\u7387\uff0c\u56e0\u6b64\u4ece\u6761\u4ef6\u6982\u7387\u7684\u89d2\u5ea6\u7c7b\u6bd4\u5230\u8fde\u7eed\u7cfb\u7edf\uff0c\u9ad8\u65af\u8fed\u4ee3\u7cfb\u7edf\u7684\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u4e3a\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5728\u79bb\u6563\u60c5\u51b5\u4e0b\uff0c\u7531\u4e8e<\/span><\/span>\ud835\udc43<\/span><\/span>\u7684\u5947\u5f02\u503c\u7684\u5e73\u65b9\u4e3a\u77e9\u9635<\/span><\/span>\ud835\udc43<\/span><\/span>\u22c5<\/span><\/span>\ud835\udc43<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u7684\u7279\u5f81\u503c\uff0c\u6545\u8ba1\u7b97\u8fde\u7eed\u60c5\u51b5\u4e0b\u7684<\/span><\/span>\ud835\udc43<\/span><\/span>\u22c5<\/span><\/span>\ud835\udc43<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u5bf9\u5e94\u4e3a\u51fd\u6570\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u53ef\u4ee5\u770b\u5230\uff0c\u7531\u4e8e<\/span><\/span><\/span>K<\/span><\/span>(<\/span><\/span>x<\/span><\/span>,<\/span><\/span>y<\/span><\/span>)<\/span><\/span>\u4ec5\u4ec5\u662f<\/span><\/span>x<\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>\u7684\u51fd\u6570\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06<\/span><\/span>x<\/span><\/span>\u2212<\/span><\/span>y<\/span><\/span>\u547d\u540d\u4e3a\u4e00\u4e2a\u65b0\u7684\u53d8\u91cf<\/span><\/span>z<\/span><\/span>\uff0c\u65b0\u7684\u51fd\u6570<\/span><\/span>K<\/span><\/span>\u5373\u4e3a\u4e00\u4e2a\u5173\u4e8e<\/span><\/span>z<\/span><\/span>\u7684\u4e00\u5143\u51fd\u6570\u3002<\/span><\/span><\/p>\n

\u56e0\u6b64\uff0c<\/span><\/span>\ud835\udc5d<\/span><\/span>(<\/span><\/span>\ud835\udc66<\/span><\/span>|<\/span><\/span>\ud835\udc65<\/span><\/span>)<\/span><\/span>\u7684\u5947\u5f02\u503c\u5e73\u65b9\u5c31\u662f\u7b97\u5b50<\/span><\/span>\u039a<\/span><\/span>\u7684\u7279\u5f81\u503c\u3002\u5047\u8bbe<\/span><\/span>\u039a<\/span><\/span>\u7684\u7279\u5f81\u503c\u4e3a<\/span><\/span>\u03b6<\/span><\/span>2<\/span><\/span><\/sup>\uff0c\u7279\u5f81\u51fd\u6570\u4e3a\uff1a<\/span><\/span>\u03c8<\/span><\/span>(<\/span><\/span>\ud835\udc67<\/span><\/span>)<\/span><\/span>\uff0c \u5219\u6839\u636e\u7279\u5f81\u503c\u548c\u7279\u5f81\u51fd\u6570\u7684\u5b9a\u4e49\u6709\uff1a<\/span><\/span>
<\/span><\/span><\/p>\n

<\/section>\n

\u57fa\u4e8e\u5176\u7279\u6b8a\u7ed3\u6784\uff0c\u53ef\u5bf9\u5176\u8fdb\u884c\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u5f97\u5230\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u6240\u4ee5\u6700\u7ec8\u6211\u4eec\u53ef\u4ee5\u5728\u65b0\u7684\u9891\u7387\u7a7a\u95f4\u4e2d\uff0c\u627e\u5230\u4e00\u79cd\u7c7b\u4f3c\u4e8e\u5947\u5f02\u503c\u8c31\u7684\u51fd\u6570\uff0c\u6211\u4eec\u79f0\u4e3a\u9ad8\u65af\u5206\u5e03\u7684\u5947\u5f02\u51fd\u6570\uff0c<\/span><\/span>\u03b1<\/span><\/span>\u4e58\u65b9\u540e\u5f97\u5230\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u8fd9\u91cc\uff0c<\/span><\/span>p<\/span><\/span>d<\/span><\/span>e<\/span><\/span>t<\/span><\/span>\u4ee3\u8868\u4f2a\u884c\u5217\u5f0f\uff0c<\/span><\/span>\u2020<\/span><\/span>\u4ee3\u8868Moore-Penrose\u4f2a\u9006\u8fd0\u7b97\u3002\u7531\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u5176\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u6307\u6807<\/span><\/span>\u0393<\/span><\/span>\ud835\udefc<\/span><\/span><\/sub>\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u53ef\u89c1\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u548c\u6b63\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u5171\u540c\u5f71\u54cd\u4e86\u8fd1\u4f3c\u53ef\u9006\u6027\u7684\u5927\u5c0f\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\uff0c\u5fc5\u987b\u4e24\u4e2a\u534f\u65b9\u5dee\u90fd\u5f88\u5c0f\uff0c\u975e\u6ee1\u79e9\u6216\u75c5\u6001\u7684\u7ef4\u5ea6\u5f71\u54cd\u8f83\u5c0f\u7684\u65f6\u5019\uff0c\u7cfb\u7edf\u52a8\u529b\u5b66\u624d\u6709\u66f4\u5f3a\u7684\u53ef\u9006\u6027\u3002<\/span><\/span><\/span><\/p>\n

2.3.1 \u7ef4\u5ea6\u5e73\u5747<\/span><\/span><\/span><\/h3>\n

\u8fdb\u4e00\u6b65\uff0c\u53ef\u4ee5\u53ef\u9006\u6027\u6307\u6807\u53d6\u5bf9\u6570\u5e76\u53bb\u6389\u5e38\u6570\u9879\uff0c\u5f97\u5230\u7ef4\u5ea6\u5e73\u5747\u7684\u6307\u6807<\/span><\/span><\/p>\n

<\/section>\n

\u8fd9\u91cc\uff0c<\/span><\/span>\ud835\udc60<\/span><\/span>\ud835\udc56<\/span><\/span><\/sub>\u4e3a\u77e9\u9635<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u7684\u7b2c<\/span><\/span>i<\/span><\/span>\u4e2a\u5947\u5f02\u503c\uff0c<\/span><\/span>\ud835\udf05<\/span><\/span>\ud835\udc56<\/span><\/span><\/sub>\u4e3a\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u7684\u7b2ci\u4e2a\u5947\u5f02\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5206\u6790\u8fd9\u4e24\u4e2a\u5947\u5f02\u503c\u6784\u6210\u7684\u8054\u5408\u8c31\uff0c\u5373\u53ef\u5b9a\u91cf\u523b\u753b\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u7279\u6027\u4e86\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u628a\u539f\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u7684\u5947\u5f02\u503c\u5206\u89e3\u8f6c\u53d8\u4e3a\u4e86\u5bf9<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u548c<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u8fd9\u4e24\u4e2a\u77e9\u9635\u7684\u5947\u5f02\u503c\u5206\u89e3\u95ee\u9898\u3002\u5176\u4e2d\uff0c<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u4e3a\u6b63\u5411\u52a8\u529b\u5b66\uff0c\u5373<\/span><\/span>p<\/span><\/span>(<\/span><\/span>x<\/span><\/span>t<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span>|<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>)<\/span><\/span>=<\/span><\/span>N<\/span><\/span>(<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>,<\/span><\/span>\u03a3<\/span><\/span>)<\/span><\/span>\u7684\u534f\u65b9\u5dee\u77e9\u9635\u4e4b\u9006\uff0c\u800c<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u5219\u662f<\/span><\/span>p<\/span><\/span>(<\/span><\/span>x<\/span><\/span>t<\/span><\/sub><\/span>+<\/span><\/span><\/sub>1<\/span><\/sub><\/span>|<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>)<\/span><\/span>\u7684\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635\u3002<\/span><\/span><\/span><\/p>\n

2.3.2 \u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/span><\/span><\/h3>\n

\u5728\u79bb\u6563\u72b6\u6001\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u901a\u8fc7\u8c03\u6574\u53c2\u6570<\/span><\/span>\u03b1<\/span><\/span>\u2208<\/span><\/span>(<\/span><\/span>0<\/span><\/span>,<\/span><\/span>2<\/span><\/span>]<\/span><\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f<\/span><\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u66f4\u597d\u5730\u53cd\u6620P\u7684\u786e\u5b9a\u6027\u6216\u8005\u7b80\u5e76\u6027\u5bf9\u6700\u7ec8\u53ef\u9006\u6027\u7684\u5f71\u54cd\u3002\u7c7b\u4f3c\u7684\uff0c\u5728\u8fde\u7eed\u53d8\u91cf\u60c5\u5f62\uff0c\u5f53<\/span><\/span>\u03b1<\/span><\/span>\u2192<\/span><\/span>0<\/span><\/span>, <\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6536\u655b\u5230<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u6b64\u65f6<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u2192<\/span><\/sub><\/span>0<\/span><\/sub><\/span>\u53ea\u7531\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635\u51b3\u5b9a\uff0c\u800c\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u76f4\u63a5\u5f71\u54cd\u7cfb\u7edf\u7684\u7b80\u5e76\u6027\u3002\u7136\u800c\uff0c\u5b9a\u4e49\u4e0d\u5141\u8bb8<\/span><\/span>\u03b1<\/span><\/span>\u7cbe\u786e\u4e3a\u96f6\uff0c\u8fd9\u6837\u4f1a\u5bfc\u81f4\u6307\u6807\u8d8b\u4e8e\u65e0\u7a77\u3002<\/span><\/span><\/span><\/p>\n

\u540c\u6837\uff0c\u5f53<\/span><\/span>\u03b1<\/span><\/span>=<\/span><\/span>2<\/span><\/span>\u65f6\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6536\u655b\u5230<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u534f\u65b9\u5dee\u77e9\u9635\u7684\u9006\u7684\u884c\u5217\u5f0f\u8d8a\u5927\uff0c\u4ee3\u8868\u65b9\u5dee\u8d8a\u5927\uff0c\u4e5f\u5c31\u662f\u52a8\u529b\u5b66\u7684\u4e0d\u786e\u5b9a\u6027\u8d8a\u5f3a\uff0c\u8fd9\u4e5f\u53ef\u4ee5\u5bfc\u81f4\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u66f4\u52a0\u53ef\u9006\u3002\u56e0\u6b64\uff0c\u5f53<\/span><\/span><\/span>\u03b1<\/span><\/span>\u4ece0\u52302\u8fde\u7eed\u8fc7\u5ea6\u65f6\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u5c31\u4f1a\u4ece\u7531\u7eaf\u7cb9\u523b\u753b\u7b80\u5e76\u6027\u6307\u6807\uff0c\u9010\u6e10\u8fc7\u6e21\u5230\u523b\u753b\u4e0d\u786e\u5b9a\u6027\u7684\u6307\u6807\u3002 \u5728\u5b9e\u8df5\u4e2d\uff0c\u6211\u4eec\u603b\u662f\u53d6<\/span><\/span>\u03b1<\/span><\/span>=<\/span><\/span>1<\/span><\/span>\u6765\u5e73\u8861<\/span><\/span>\u0393<\/span><\/span>\u6d4b\u91cf\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\u7684\u7efc\u5408\u5f71\u54cd\u3002<\/span><\/span><\/span><\/p>\n


<\/span><\/span><\/h1>\n

\n
\n
\n
\n
\n

<\/span><\/section>\n

<\/span><\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n
\n

3. \u6709\u6548\u4fe1\u606f\uff08EI\uff09\u4e0e\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

3.1 \u79bb\u6563\u72b6\u6001\u60c5\u5f62<\/span><\/span><\/span><\/h2>\n

\u8fd1\u4f3c\u53ef\u9006\u6027\u548c\u6709\u6548\u4fe1\u606f\u5b58\u5728\u7740\u5bc6\u5207\u7684\u5173\u7cfb\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4e0b\u9762\u7684\u5b9a\u7406\u548c\u6570\u503c\u6a21\u62df\u770b\u51fa\u3002<\/span><\/span><\/p>\n

\u9996\u5148\uff0c\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u4e0eEI\u6709\u7740\u76f8\u540c\u7684\u6700\u5927\u503c<\/span><\/span><\/p>\n

\u5b9a\u74062<\/span>\uff1a<\/span><\/span><\/b>\u5bf9\u4e8e\u4efb\u610f TPM P \u548c <\/span><\/span>\u03b1<\/span><\/span>\u2208<\/span><\/span>(<\/span><\/span>0<\/span><\/span>,<\/span><\/span>2<\/span><\/span>)<\/span><\/span>\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u7684\u5bf9\u6570\u548cEI\u90fd\u6709\u76f8\u540c\u7684\u6700\u5c0f\u503c0\u548c\u4e00\u4e2a\u5171\u540c\u7684\u6781\u5c0f\u503c\u70b9\uff08\u5f53<\/span><\/span>\"image.png\"<\/span><\/sub>\u65f6\u53d6\u5230\uff09\uff0c\u5176\u4e2d<\/span><\/span>\ud835\udfd9<\/span><\/span>1<\/span><\/span>\u662f\u51681\u77e9\u9635\u3002\u5b83\u4eec\u8fd8\u6709\u76f8\u540c\u7684\u6700\u5927\u503c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>N<\/span><\/span>\uff0c\u6700\u5927\u503c\u70b9\u5bf9\u5e94\u4e8eP\u662f\u4e00\u4e2a\u7f6e\u6362\u77e9\u9635\u3002<\/span><\/span><\/span><\/p>\n

\u56e0\u6b64\u5f53P\u662f\u53ef\u9006\u7684\uff08\u7f6e\u6362\u77e9\u9635\uff09\u65f6\uff0c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u548cEI\u53ef\u4ee5\u8fbe\u5230\u6700\u5927\u503c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>N<\/span><\/span>\u3002\u5f53<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5b83\u4eec\u4e5f\u53ef\u4ee5\u8fbe\u5230\u6700\u5c0f\u503c0\u3002\u7136\u800c\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc1\u660e<\/span><\/span>\"image.png\"<\/span><\/sub>\u5e76\u4e0d\u662fEI\u7684\u552f\u4e00\u6700\u5c0f\u70b9\uff0c\u5bf9\u4e8e\u4efb\u4f55\u6ee1\u8db3<\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/sub>=<\/span><\/span>P<\/span><\/span>j<\/span><\/span><\/sub>,<\/span><\/span>\u2200<\/span><\/span>i<\/span><\/span><\/sub>\u2208<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>N<\/span><\/span>]<\/span><\/span>\u7684TPM\u90fd\u80fd\u4f7fEI=0\u3002\u5176\u6b21EI\u7684\u4e0a\u9650\u548c\u4e0b\u9650\u90fd\u662f<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u7684\u7ebf\u6027\u9879\u3002<\/span><\/span><\/span><\/p>\n

\u5176\u6b21\uff0c<\/span><\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6784\u6210\u4e86EI\u7684\u4e0a\u4e0b\u754c\u3002<\/span><\/span><\/p>\n

\u5b9a\u74063<\/span>\uff1a<\/span><\/span>\u5bf9\u4e8e\u4efb\u4f55TPM P\uff0c\u5176\u6709\u6548\u4fe1\u606fEI\u7684\u4e0a\u9650\u4e3a<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4e0b\u9650\u4e3a<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u2212<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>N<\/span><\/span>.<\/span><\/span><\/span><\/p>\n

\u56e0\u6b64\uff0c\u6709\u5982\u4e0b\u4e0d\u7b49\u5f0f\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u5b9e\u9645\u4e0a\uff0cEI\u6709\u4e00\u4e2a\u66f4\u4e25\u683c\u7684\u4e0a\u9650\uff0c<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\u2264<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\uff0c\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\u867d\u7136\u5df2\u7ecf\u5728\u591a\u4e2a\u7cfb\u7edf\u4e2d\u89c2\u5bdf\u5230\uff0c\u4f46\u76ee\u524d\u5c1a\u4e0d\u80fd\u4ece\u7406\u8bba\u4e0a\u8bc1\u660e\u5b83\u7684\u6210\u7acb\u3002<\/span><\/span><\/span><\/p>\n

\u6211\u4eec\u53d1\u73b0\u5728\u8bb8\u591a\u4f8b\u5b50\u4e2d\uff0cEI\u548c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u5177\u6709\u8fd1\u4f3c\u7ebf\u6027\u5173\u7cfb\uff0c\u56e0\u6b64\uff0c\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u731c\u60f3\u5b58\u5728\u5982\u4e0b\u8fd1\u4f3c\u5173\u7cfb\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5728\u79bb\u6563\u72b6\u6001\u7a7a\u95f4\u60c5\u51b5\u4e0b\uff0c\u8be5\u8fd1\u4f3c\u5173\u7cfb\u867d\u7136\u4e0d\u80fd\u4ece\u7406\u8bba\u4e0a\u8bc1\u660e\uff0c\u4f46\u5374\u53ef\u4ee5\u901a\u8fc7\u591a\u4e2a\u6570\u503c\u4f8b\u5b50\u52a0\u4ee5\u8bc1\u660e\u3002<\/span><\/span><\/span><\/p>\n

3.1.1 \u4e0eEI\u7684\u76f8\u4f3c\u6027<\/span><\/span><\/span><\/h3>\n

\u6839\u636e\u524d\u6587\uff0cEI\u7684\u4e0a\u754c\u548c\u4e0b\u754c\u5206\u522b\u662f<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u7684\u7ebf\u6027\u9879\u3002\u7531\u6b64\u8fd8\u53ef\u4ee5\u63a8\u6d4b\u4e24\u8005\u5177\u6709\u8fd1\u4f3c\u5173\u7cfb\uff1a<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\u223c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u3002\u4e0b\u9762\u901a\u8fc7\u6570\u503c\u6a21\u62df\u8bf4\u660e\u8fd9\u4e00\u70b9\u3002\u5177\u4f53\u7684\u505a\u6cd5\u662f\u968f\u673a\u751f\u6210\u4e00\u4e9b\u968f\u673a\u7684TPM\uff0c\u8ba1\u7b97\u5b83\u4eec\u7684EI\u548c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\uff0c\u5e76\u7ed8\u5236\u6563\u70b9\u56fe\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u5c06\u5c55\u793a\u4e09\u79cd\u4e0d\u540c\u7684\u968f\u673aTPM\u7684\u751f\u6210\u65b9\u5f0f\u4e0b\u7684\u7ed3\u8bba\u3002<\/span><\/span><\/span><\/p>\n

<\/span><\/span><\/p>\n

\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u5728\u7531\u4e09\u79cd\u4e0d\u540c\u65b9\u6cd5\u751f\u6210\u7684\u5404\u79cd\u5f52\u4e00\u5316\u7684TPM \u4e0a\u6bd4\u8f83\u4e86<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u548c EI\u7684\u5173\u7cfb\uff0c\u8fd9\u4e09\u79cd\u5173\u7cfb\u5305\u62ec\uff1a1\uff09\u8f6f\u5316\u7f6e\u6362\u77e9\u9635\uff08\u56fea\uff09\uff1b2\uff09\u8f6f\u5316\u9000\u5316\u77e9\u9635\uff08\u56feb\uff09\uff1b3\uff09\u5b8c\u5168\u968f\u673a\u77e9\u9635\uff08\u56fec\uff09\u3002<\/span><\/span><\/span><\/p>\n

\u56fe(a)\u3001(b)\u548c(c)\u8868\u660e\uff0c\u5728\u8fd9\u4e9b\u4f8b\u5b50\u4e2d\u90fd\u89c2\u5bdf\u5230\u4e86\u6b63\u76f8\u5173\u6027\uff0c\u5e76\u4e14\u5728N \u226b 1 \u65f6\uff0c<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\u223c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>.<\/span><\/span>\u7684\u8fd1\u4f3c\u5173\u7cfb\u5f97\u5230\u4e86\u8bc1\u5b9e\u3002\u5728(a) \u548c (b) \u4e2d\u53ef\u4ee5\u660e\u663e\u89c2\u5bdf\u5230\u8fd9\u79cd\u5173\u7cfb\uff0c\u4f46\u5728(b) \u4e2d\uff0c\u7531\u4e8e\u8986\u76d6\u4e86\u6709\u9650\u7684<\/span><\/span>\u0393<\/span><\/span>\u503c\u533a\u57df\uff0c\u8fd9\u79cd\u5173\u7cfb\u9000\u5316\u4e3a\u8fd1\u4f3c\u7ebf\u6027\u5173\u7cfb\u3002<\/span><\/span><\/span><\/p>\n

\u56fe(a)\u548c(b)\u4e2d\u7528\u7ea2\u8272\u865a\u7ebf\u8868\u793a\u4e86 EI \u7684\u4e0a\u4e0b\u9650\u3002\u4e0d\u8fc7\uff0c\u5728\u56fe(c\uff09\u4e2d\uff0c\u7531\u4e8e\u6240\u6709\u70b9\u90fd\u96c6\u4e2d\u5728\u4e00\u4e2a\u5c0f\u533a\u57df\u5185\uff0c\u56e0\u6b64\u770b\u4e0d\u5230\u7406\u8bba\u8fb9\u754c\u7ebf\u3002\u6839\u636e\u7ecf\u9a8c\uff0c\u56fe\u4e2d\u7070\u8272\u65ad\u7ebf\u6240\u793a\u7684<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u7684\u4e0a\u9650\u66f4\u4e3a\u4e25\u683c\u3002\u56e0\u6b64\u53ef\u4ee5\u63a8\u6d4b <\/span><\/span>E<\/span><\/span>I<\/span><\/span>\u2264<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u8fd9\u4e00\u65b0\u5173\u7cfb\u662f\u6210\u7acb\u7684\uff0c\u4f46\u5176\u4e25\u5bc6\u6027\u6709\u5f85\u8bc1\u660e\u3002<\/span><\/span><\/span><\/p>\n

\u4ee5\u4e0b\u662f\u8fd9\u4e09\u79cd\u751f\u6210TPM\u65b9\u5f0f\u7684\u5177\u4f53\u751f\u6210\u6b65\u9aa4\uff1a<\/span><\/span><\/p>\n

\u8f6f\u5316\u7f6e\u6362\u77e9\u9635\uff1a<\/span><\/span><\/span><\/p>\n

1\uff09\u968f\u673a\u751f\u6210\u4e00\u4e2aN\u9636\u7f6e\u6362\u77e9\u9635P\uff1b<\/span><\/span><\/p>\n

2\uff09\u5bf9\u4e8eP\u4e2d\u7684\u6bcf\u4e2a\u884c\u5411\u91cf<\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/sub>\uff0c\u5047\u8bbe1\u5143\u7d20\u7684\u4f4d\u7f6e\u662f<\/span><\/span>j<\/span><\/span>i<\/span><\/span><\/sub>\uff0c\u6211\u4eec\u5c06<\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/sub>\u7684\u6240\u6709\u6761\u76ee\u586b\u5165\u4f4d\u4e8e<\/span><\/span>j<\/span><\/span>i<\/span><\/span><\/sub>\u5904\u7684\u9ad8\u65af\u5206\u5e03\u4e2d\u5fc3\u7684\u6982\u7387\uff0c\u5373<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5176\u4e2d\uff0c<\/span><\/span>\u03c3<\/span><\/span>\u662f\u8f6f\u5316\u7a0b\u5ea6\u7684\u81ea\u7531\u53c2\u6570\uff0c\u5982\u679c<\/span><\/span>\u03c3<\/span><\/span>\u2192<\/span><\/span>\u221e<\/span><\/span>\u5219<\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/sub>\u53d8\u4e3a\u4e86\u4e00\u4e2a\u5168\u90e8\u75311\/N\u6784\u6210\u7684\u5411\u91cf\uff0c\u5982\u679c<\/span><\/span>\u03c3<\/span><\/span>\u2192<\/span><\/span>0<\/span><\/span>\u5219<\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/sub>\u9000\u5316\u4e3a\u72ec\u70ed\u5411\u91cf\uff1b<\/span><\/span><\/span><\/p>\n

3) \u5c06<\/span><\/span>\"image.png\"<\/span><\/sub>\u9664\u4ee5\u65b0\u7684\u884c\u5411\u91cf\uff0c\u4f7f\u5176\u5f52\u4e00\u5316\uff0c\u8fd9\u6837\u4fee\u6539\u540e\u7684\u77e9\u9635<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>\u4e5f\u662f\u4e00\u4e2a\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u3002<\/span><\/span><\/span><\/p>\n

\u8f6f\u5316\u9000\u5316\u77e9\u9635\uff1a<\/span><\/span><\/span><\/p>\n

\u751f\u6210\u65b9\u5f0f\u4e0e\u8f6f\u5316\u7f6e\u6362\u77e9\u9635\u975e\u5e38\u76f8\u4f3c\uff0c\u4f46\u539f\u59cb\u77e9\u9635P\u4e0d\u662f\u7f6e\u6362\u77e9\u9635\uff0c\u800c\u662f\u9000\u5316\u77e9\u9635\u3002\u9000\u5316\u610f\u5473\u7740\u6709\u4e00\u4e9b\u884c\u5411\u91cf\u662f\u76f8\u540c\u7684\uff0c\u76f8\u540c\u884c\u5411\u91cf\u7684\u6570\u91cf\u7528N – r\u8868\u793a\uff0c\u5b83\u662f\u53d7\u63a7\u53d8\u91cf\uff0c\u5176\u4e2dr\u662fP\u7684\u79e9\u3002\u901a\u8fc7\u8c03\u6574N-r\uff0c\u6211\u4eec\u53ef\u4ee5\u63a7\u5236TPM\u7684\u9000\u5316\u7a0b\u5ea6\u3002<\/span><\/span><\/p>\n

\u5b8c\u5168\u968f\u673a\u77e9\u9635\uff1a<\/span><\/span><\/span><\/p>\n

1)<\/span><\/span><\/b> \u4ece[0, 1]\u4e0a\u7684\u5747\u5300\u5206\u5e03\u4e2d\u62bd\u53d6\u4e00\u4e2a\u884c\u968f\u673a\u5411\u91cf\uff1b<\/span><\/span><\/span><\/p>\n

2)<\/span><\/span><\/b> \u5bf9\u8be5\u884c\u5411\u91cf\u8fdb\u884c\u5f52\u4e00\u5316\u5904\u7406\uff0c\u4f7f\u751f\u6210\u7684\u77e9\u9635\u662f\u4e00\u4e2aTPM\u3002<\/span><\/span><\/span>
<\/span><\/span><\/p>\n

\u8fdb\u4e00\u6b65\uff0c\u6587\u732e<\/span><\/span>[6]<\/span><\/span>\u8fd8\u5728\u5927\u5c0f\u4e3aN=2 \u7684\u6700\u7b80\u5355\u53c2\u6570\u5316TPM\u4e2d\u5f97\u5230\u4e86EI\u548c<\/span><\/span>\u0393<\/span><\/span>\u7684\u89e3\u6790\u89e3\uff0c\u5e76\u5c55\u793a\u4e86EI\u548c<\/span><\/span>\u0393<\/span><\/span>\u4e0e\u53c2\u6570p\u548cq\u7684\u5173\u7cfb\u3002\u5176\u4e2dp\u548cq\u7528\u4e8e\u751f\u6210\u6700\u7b80\u5355\u7684<\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span>2<\/span><\/span>\u9a6c\u5c14\u79d1\u592b\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4e0b\u56fe(a)\u8868\u793a<\/span><\/span>\u0393<\/span><\/span>\u968fp\u548cq\u7684\u53d8\u5316\uff0c\u56fe(b)\u8868\u793aEI\u968fp\u548cq \u7684\u53d8\u5316\u3002(a)\u548c(b)\u4e4b\u95f4\u7684\u5dee\u5f02\u663e\u800c\u6613\u89c1\uff1a1\uff09\u5f53<\/span><\/span>p<\/span><\/span>\u2248<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>\u65f6\uff0c<\/span><\/span>\u0393<\/span><\/span>\u6709\u4e00\u4e2a\u6700\u5c0f\u503c\u7684\u5cf0\uff0c\u4f46EI\u6ca1\u6709\uff1b2\uff09\u89c2\u5bdf\u5230EI \u2248 0\u65f6\u7684\u533a\u57df\u66f4\u5bbd\uff0c\u800c<\/span><\/span>\u0393<\/span><\/span>\u2248<\/span><\/span>1<\/span><\/span>\u65f6\u7684\u533a\u57df\u8981\u5c0f\u5f97\u591a\uff1b3\uff09\u89c2\u5bdf\u5230<\/span><\/span>\u0393<\/span><\/span>\u6709\u4e00\u4e2a\u4ece0\u5230\u6700\u5927\u503cN=2\u7684\u6e10\u8fdb\u8fc7\u6e21\uff0c\u4f46EI\u6ca1\u6709\u3002 \u56e0\u6b64\uff0c\u6211\u4eec\u5f97\u51fa\u7ed3\u8bba\uff0cEI\u548c<\/span><\/span>\u0393<\/span><\/span>\u5728\u5404\u79cdTPM\u4e0a\u9ad8\u5ea6\u76f8\u5173\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n

3.1.2 \u4e0eEI\u7684\u4e0d\u540c<\/span><\/span><\/span><\/h3>\n

\u9996\u5148\uff0cEI \u901a\u8fc7KL\u6563\u5ea6\u6765\u91cf\u5316\u6bcf\u4e2a\u884c\u5411\u91cf\u4e0eP\u7684\u5e73\u5747\u884c\u5411\u91cf\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u8861\u91cf\u7684\u662f\u884c\u5411\u91cf\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u3002\u76f8\u53cd\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u8bc4\u4f30\u7684\u662f\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff0c\u7279\u522b\u662f\u5f53<\/span><\/span>\u03b1<\/span><\/span>\u63a5\u8fd1 0 \u65f6\uff0c\u8fd9\u4e0e\u884c\u5411\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u76f8\u4e92\u4f9d\u8d56\u6027\u76f8\u5173\u3002\u867d\u7136\u884c\u5411\u91cf\u7684\u7ebf\u6027\u76f8\u4e92\u4f9d\u8d56\u6027\u8868\u660e\u5b83\u4eec\u7684\u76f8\u4f3c\u6027\u2014\u2014\u8fd9\u610f\u5473\u7740\u4e24\u4e2a\u76f8\u540c\u7684\u884c\u5411\u91cf\u662f\u7ebf\u6027\u76f8\u5173\u7684\uff0c\u4f46\u53cd\u4e4b\u5219\u4e0d\u4e00\u5b9a\u6210\u7acb\u3002\u56e0\u6b64\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u4e0d\u4ec5\u6355\u83b7\u4e86\u884c\u5411\u91cf\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\uff0c\u800c\u4e14\u8fd8\u6355\u83b7\u4e86P\u4e0e\u52a8\u529b\u5b66\u53ef\u9006\u77e9\u9635\u7684\u63a5\u8fd1\u5ea6\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cEI\u65e0\u6cd5\u5b8c\u6210\u8fd9\u4e2a\u4efb\u52a1\u3002<\/span><\/span><\/span><\/p>\n

\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u6570\u503c\u5b9e\u9a8c\u6765\u9a8c\u8bc1\u8fd9\u4e00\u70b9\uff1a\u53ef\u4ee5\u901a\u8fc7\u5c06\u7ebf\u6027\u76f8\u5173\u884c\u5411\u91cf\u4e0e\u7ebf\u6027\u72ec\u7acb\u884c\u5411\u91cf\u6df7\u5408\u6765\u521b\u5efaTPM\uff0c\u5176\u4e2d\u72ec\u7acb\u5411\u91cf\u7684\u6570\u91cf\u6216\u7b49\u7ea7\u662f\u53d7\u63a7\u53c2\u6570\u3002\u9996\u5148\uff0c\u751f\u6210r\u4e2a\u72ec\u7acb\u7684\u72ec\u70ed\u5411\u91cf\uff0c\u7136\u540e\u8f6f\u5316\u8fd9\u4e9b\u884c\u5411\u91cf\uff0c\u8f6f\u5316\u7a0b\u5ea6\u7531<\/span><\/span>\u03c3<\/span><\/span>\u63a7\u5236\u3002\u968f\u540e\uff0c\u901a\u8fc7\u5c06\u8fd9\u4e9b\u8f6f\u5316\u7684\u72ec\u70ed\u5411\u91cf\u4e0e\u968f\u673a\u9009\u62e9\u7684\u7ebf\u6027\u7cfb\u6570\u7ebf\u6027\u7ec4\u5408\u6765\u521b\u5efa\u989d\u5916\u7684\u884c\u5411\u91cf\u3002\u7136\u540e\u91cf\u5316<\/span><\/span>\u0393<\/span><\/span>\u548c EI \u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5f88\u660e\u663e\uff0c\u5bf9\u4e8e\u8f83\u5c0f\u7684r\u503c\uff0c\u968f\u7740<\/span><\/span>\u03c3<\/span><\/span>\u7684\u589e\u52a0\uff0c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u548c EI \u4e4b\u95f4\u7684\u5dee\u5f02\u4f1a\u51cf\u5c0f\uff0c\u56e0\u4e3a P \u7684\u7ebf\u6027\u4f9d\u8d56\u6027\u968f\u7740\u5411\u91cf\u53d8\u5f97\u66f4\u52a0\u660e\u663e\u800c\u589e\u5f3a\u3002\u8fd9\u5f3a\u8c03\u4e86\u7ebf\u6027\u76f8\u5173\u6027\u5e76\u4e0d\u7b49\u4e8e\u884c\u5411\u91cf\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u3002\u7136\u800c\uff0c\u968f\u7740\u72ec\u7acb\u884c\u5411\u91cf\u6570\u91cf\u7684\u589e\u52a0\uff0c\u5982\u679c<\/span><\/span>\u03c3<\/span><\/span>\u4fdd\u6301\u5f88\u5c0f\uff0cP\u4f1a\u6536\u655b\u5230\u7f6e\u6362\u77e9\u9635\u3002\u56e0\u6b64\uff0cEI \u548c<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u90fd\u8fbe\u5230\u4e86\u76f8\u540c\u7684\u6700\u5927\u503c\u3002\u8fd9\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u5f53r\u5f88\u5927\u65f6\uff0c\u5dee\u5f02\u66f2\u7ebf\u4f1a\u51fa\u73b0\u8f7b\u5fae\u7684\u98a0\u7c38\u3002<\/span><\/span><\/span><\/p>\n

\u5176\u6b21\uff0c\u5373\u4f7f\u5728\u6240\u6709\u884c\u5411\u91cf\u76f8\u540c\u7684\u60c5\u51b5\u4e0b\uff0cEI \u548c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u4e4b\u95f4\u4e5f\u5b58\u5728\u663e\u8457\u7684\u533a\u522b\uff0c\u5bfc\u81f4 EI= 0 \u800c<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u800c\u8fd9\u662f\u4e00\u4e2a\u53ef\u4ee5\u968f<\/span><\/span>\"image.png\"<\/span><\/sub>\u53d8\u5316\u7684\u91cf\u3002\u8fd9\u79cd\u5dee\u5f02\u610f\u5473\u7740\uff0c\u4e0e EI \u4e0d\u540c\uff0c<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u53ef\u4ee5\u63d0\u4f9b\u6709\u5173\u884c\u5411\u91cf\u7684\u66f4\u5168\u9762\u7684\u89c1\u89e3\uff0c\u8d85\u8d8a\u5176\u4e0e\u5e73\u5747\u884c\u5411\u91cf\u7684\u76f8\u4f3c\u6027\u3002<\/span><\/span><\/span><\/p>\n

3.2 \u8fde\u7eed\u53d8\u91cf\u60c5\u5f62<\/span><\/span><\/span><\/h2>\n

\u548cTPM\u6709\u6240\u4e0d\u540c\uff0c\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u4e0b\uff0c\u52a8\u529b\u5b66\u8fd1\u4f3c\u53ef\u9006\u6027\u548c\u7ef4\u5ea6\u5e73\u5747\u6709\u6548\u4fe1\u606f\u7684\u5173\u7cfb\uff0c\u53ef\u4ee5\u76f4\u63a5\u6c42\u51fa\u8fd1\u4f3c\u7684\u89e3\u6790\u89e3\uff0c\u8fd9\u662f\u56e0\u4e3a\u5b83\u4eec\u90fd\u53ef\u4ee5\u7528\u52a8\u529b\u5b66\u53c2\u6570\u77e9\u9635<\/span><\/span>A<\/span><\/span>\u548c\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u7684\u7ebf\u6027\u51fd\u6570\u8868\u793a\u3002\u8fd9\u4e3b\u8981\u662f\u7531\u4e8e\u6b64\u65f6\u6982\u7387\u7a7a\u95f4\u662f\u8fde\u7eed\u7a7a\u95f4\uff0c\u65e0\u8bba\u5220\u51cf\u591a\u5c11\u4e2a\u8fde\u7eed\u7684\u533a\u95f4\uff0c\u53ea\u8981\u6ca1\u6709\u79bb\u6563\u5316\uff0c\u72b6\u6001\u6570\u91cf\u90fd\u662f\u65e0\u7a77\uff0c\u56e0\u6b64\u6211\u4eec\u8981\u4ece\u72b6\u6001\u7a7a\u95f4\u7684\u7814\u7a76\u8f6c\u5316\u4e3a\u5bf9\u6b27\u6c0f\u7a7a\u95f4\u7684\u7814\u7a76\uff0c\u56e0\u4e3a\u6b27\u6c0f\u7a7a\u95f4\u6709\u9762\u79ef\u3001\u4f53\u79ef\u7684\u6982\u5ff5\uff0c\u5bf9\u7ef4\u5ea6\u7684\u7ea6\u51cf\u4f1a\u5bfc\u81f4\u9ad8\u7ef4\u7acb\u65b9\u4f53\u7684\u4f53\u79ef\u51cf\u5c0f\uff0c\u4f7f\u52a8\u529b\u5b66\u7684\u56e0\u679c\u6548\u5e94\u5f3a\u5ea6\u53d1\u751f\u6539\u53d8\u3002<\/span><\/span><\/span><\/p>\n

3.2.1 \u6709\u6548\u4fe1\u606f\u4e0e\u8fd1\u4f3c\u53ef\u9006\u6027<\/span><\/span><\/span><\/h3>\n

\u5f53\u9006\u5411\u52a8\u529b\u5b66<\/span><\/span>\"image.png\"<\/span><\/sub>\u63a5\u8fd1\u4e00\u4e2a\u6807\u51c6\u5316\u7684\u6b63\u6001\u5206\u5e03<\/span><\/span>A<\/span><\/span>\u2020<\/span><\/span><\/sup>\u03a3<\/span><\/span>(<\/span><\/span>A<\/span><\/span>\u2020<\/span><\/span><\/sup>)<\/span><\/span>T<\/span><\/span><\/sup>\u2248<\/span><\/span>I<\/span><\/span>n<\/span><\/span>\u7684\u65f6\u5019, <\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u548c\u7ef4\u5ea6\u5e73\u5747\u7684\u6709\u6548\u4fe1\u606f\u6ee1\u8db3\u5173\u7cfb\u4e3a\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span>ln<\/span><\/span>\u2061<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u662f\u5bf9\u8fd1\u4f3c\u53ef\u9006\u6027\u53d6\u5bf9\u6570\u540e\u5f97\u5230\u7684\u53ef\u9006\u4fe1\u606f\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u662f\u4e0e<\/span><\/span>A<\/span><\/span>\u548c<\/span><\/span>\u03a3<\/span><\/span>\u65e0\u5173\u7684\u5e38\u6570\u9879\u3002\u5f53<\/span><\/span>\"image.png\"<\/span><\/sub>\u662f\u4e00\u4e2a\u6807\u51c6\u5316\u7684\u6b63\u6001\u5206\u5e03, \u4e14<\/span><\/span>A<\/span><\/span>\u2208<\/span><\/span>R<\/span><\/span>m<\/span><\/sup><\/span>\u00d7<\/span><\/span><\/sup>n<\/span><\/sup><\/span>\u662f\u53ef\u9006\u77e9\u9635\u7684\u65f6\u5019\uff0c\u7b49\u53f7\u6210\u7acb\u3002<\/span><\/span><\/span><\/p>\n


<\/span><\/span><\/h1>\n

\n
\n
\n
\n
\n

<\/span><\/section>\n

<\/span><\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n
\n

4. \u79bb\u6563TPM<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n

\u57fa\u4e8eSVD\uff08\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff09\u7684\u56e0\u679c\u6d8c\u73b0<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

4.1 \u6e05\u6670\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/span><\/h2>\n

\u5bf9\u4e8e\u5177\u6709TPM P\u7684\u7ed9\u5b9a\u9a6c\u5c14\u53ef\u592b\u94fe<\/span><\/span>\u03c7<\/span><\/span>\uff0c\u5982\u679c<\/span><\/span>r<\/span><\/span>\u2261<\/span><\/span>r<\/span><\/span>a<\/span><\/span>n<\/span><\/span>k<\/span><\/span>(<\/span><\/span>P<\/span><\/span>)<\/span><\/span><<\/span><\/span>N<\/span><\/span>\uff0c\u5219\u8be5\u7cfb\u7edf\u4e2d\u4f1a\u51fa\u73b0\u660e\u663e\u7684\u56e0\u679c\u6d8c\u73b0\u3002\u4e14\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u4e3a\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

4.2 \u6a21\u7cca\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/span><\/p>\n

\u5bf9\u4e8e\u5177\u6709\u4efb\u610f\u7684\u9a6c\u5c14\u53ef\u592b\u94fe<\/span><\/span>\u03c7<\/span><\/span>\uff0c\u5176\u6982\u7387\u8f6c\u79fb\u77e9\u9635\uff08TPM\uff09\u4e3aP\uff0c\u5047\u8bbe\u5176\u5947\u5f02\u503c\u4e3a<\/span><\/span>(<\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/sub>\u2265<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/sub>\u2265<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>\u2265<\/span><\/span>\u03c3<\/span><\/span>N<\/span><\/span><\/sub>\u2265<\/span><\/span>0<\/span><\/span>)<\/span><\/span>\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u5b9e\u503c<\/span><\/span>\u03f5<\/span><\/span>\u2208<\/span><\/span>[<\/span><\/span>0<\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/sub>]<\/span><\/span>\uff0c\u5982\u679c\u5b58\u5728\u6574\u6570<\/span><\/span>i<\/span><\/span>\u2208<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>N<\/span><\/span>)<\/span><\/span>\uff0c\u4f7f\u5f97<\/span><\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/sub>><\/span><\/span>\u03f5<\/span><\/span>\uff0c\u5219\u7cfb\u7edf\u4e2d\u51fa\u73b0\u4e86\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\uff0c\u5176\u6a21\u7cca\u7a0b\u5ea6\u4e3a<\/span><\/span>\u03f5<\/span><\/span>\u3002\u800c\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u4e3a\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>=<\/span><\/span>m<\/span><\/span>a<\/span><\/span>x<\/span><\/span>{<\/span><\/span>i<\/span><\/span>|<\/span><\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/sub>><\/span><\/span>\u03f5<\/span><\/span>}<\/span><\/span><\/span><\/p>\n

\u8fd9\u4e9b\u5b9a\u4e49\u4e0e\u4efb\u4f55\u7c97\u7c92\u5316\u65b9\u6cd5\u65e0\u5173\uff0c\u5b83\u4ee3\u8868\u4e86\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u5b66\u7684\u5185\u5728\u5ba2\u89c2\u5c5e\u6027\u3002\u56e0\u6b64\uff0c\u6e05\u6670\u548c\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u90fd\u53ef\u4ee5\u5ba2\u89c2\u5730\u91cf\u5316\u3002\u5f53<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>0<\/span><\/span>\u65f6\uff0c\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u662f\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u7684\u7279\u4f8b\uff0c\u7279\u522b\u662f\u5f53\u5947\u5f02\u503c\u53ef\u4ee5\u5206\u6790\u6c42\u89e3\u65f6\uff0c\u5b83\u5177\u6709\u7406\u8bba\u4ef7\u503c\u3002\u6b64\u5916\uff0c\u5bf9\u56e0\u679c\u6d8c\u73b0\u53d1\u751f\u7684\u5224\u65ad\u4e0e<\/span><\/span>\u03b1<\/span><\/span>\u65e0\u5173\uff0c\u56e0\u4e3a\u5b83\u53ea\u4e0e\u79e9\u6709\u5173\u3002\u56e0\u6b64\uff0c\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u7684\u6982\u5ff5\u4ec5\u7531P\u51b3\u5b9a\uff0c\u662f\u65e0\u53c2\u6570\u7684\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5fc5\u987b\u7ed9\u51fa\u9608\u503c<\/span><\/span>\u03f5<\/span><\/span>\uff0c\u56e0\u4e3a\u5947\u5f02\u503c\u53ef\u80fd\u65e0\u9650\u8d8b\u8fd1\u4e8e0\uff0c\u4f46P\u662f\u6ee1\u79e9\u7684\u3002\u53ef\u4ee5\u6839\u636e\u5947\u5f02\u503c\u9891\u8c31\u4e2d\u7684\u660e\u663e\u622a\u6b62\u70b9\u6765\u9009\u62e9<\/span><\/span>\u03f5<\/span><\/span>\u3002\u82e5<\/span><\/span>\u03f5<\/span><\/span>\u975e\u5e38\u5c0f\uff08\u6bd4\u5982<\/span><\/span>\u03f5<\/span><\/span><<\/span><\/span>10<\/span><\/span>\u2212<\/span><\/sup><\/span>10<\/span><\/sup><\/span>\uff09\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u8bf4\u56e0\u679c\u6d8c\u73b0\u5927\u81f4\u53d1\u751f\u3002\u5bf9\u4e8e\u4efb\u610f<\/span><\/span>\u03f5<\/span><\/span>\u2265<\/span><\/span>0<\/span><\/span>,<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>(<\/span><\/span>\u03f5<\/span><\/span>)<\/span><\/span>\u2208<\/span><\/span>[<\/span><\/span>0<\/span><\/span>,<\/span><\/span>N<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span>]<\/span><\/span>\uff0c\u53ea\u6709\u5f53<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>(<\/span><\/span>\u03f5<\/span><\/span>)<\/span><\/span>><\/span><\/span>0<\/span><\/span>\u65f6\uff0c\u624d\u4f1a\u51fa\u73b0\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/span><\/span><\/p>\n

\u8fd9\u91cc\u6211\u4eec\u4e0d\u96be\u770b\u51fa\uff0c\u56e0\u679c\u6d8c\u73b0\u73b0\u8c61\u7684\u672c\u8d28\u5728\u4e8e\u6982\u7387\u8f6c\u79fb\u77e9\u9635P\u4e0b\u5b58\u5728\u5197\u4f59\u7684\u4fe1\u606f\u901a\u8def\uff0c\u8fd9\u4e9b\u901a\u8def\u662f\u4e0d\u53ef\u9006\u7684\uff0c\u7531\u5bf9\u5e94\u4e8e\u96f6\u6216\u63a5\u8fd1\u96f6\u5947\u5f02\u503c\u7684\u5947\u5f02\u5411\u91cf\u8868\u793a\u3002\u56e0\u679c\u6d8c\u73b0\u7684\u91cf\u5316\u672c\u8d28\u4e0a\uff0c\u662f\u901a\u8fc7\u6d4b\u91cf\u5f53\u8fd9\u4e9b\u5197\u4f59\u4fe1\u9053\u88ab\u6f5c\u5728\u7684\u6700\u4f73\u7c97\u7c92\u5ea6\u5316\u7b56\u7565\u53bb\u9664\u65f6\u5e73\u5747\u53ef\u9006\u6027\u6216\u4fe1\u606f\u4f20\u8f93\u6548\u7387\u7684\u6f5c\u5728\u6700\u4f18\u7ed3\u679c\u6765\u5b9e\u73b0\u7684\u3002<\/span><\/span><\/p>\n

4.3 TPM\u77e9\u9635\u7684\u7c97\u7c92\u5316\u65b9\u6cd5<\/span><\/span><\/span><\/h2>\n

\u867d\u7136\u65e0\u9700\u7c97\u7c92\u5316\u4e5f\u80fd\u5b9a\u4e49\u548c\u91cf\u5316\u6e05\u6670\u6216\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\uff0c\u4f46\u5728\u4e00\u4e9b\u573a\u5408\uff0c\u6211\u4eec\u4ecd\u7136\u9700\u8981\u5bf9\u539f\u59cb\u7cfb\u7edf\u8fdb\u884c\u66f4\u7b80\u5355\u7684\u7c97\u7c92\u5316\u63cf\u8ff0\uff0c\u4ee5\u4fbf\u4e0e\u901a\u8fc7\u6700\u5927\u5316EI\u5f97\u51fa\u7684\u7ed3\u679c\u8fdb\u884c\u6bd4\u8f83\u3002\u56e0\u6b64\uff0c\u6587\u7ae0<\/span><\/span>[6]<\/span><\/span>\u63d0\u4f9b\u4e86\u4e00\u79cd\u57fa\u4e8e\u5947\u5f02\u503c\u5206\u89e3\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\uff0c\u4ee5\u83b7\u5f97\u5b8f\u89c2\u5c42\u9762\u7684\u7b80\u5316TPM\u3002\u5176\u57fa\u672c\u601d\u60f3\u662f\u5c06P\u4e2d\u7684\u884c\u5411\u91cf <\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/sub>,<\/span><\/span>\u2200<\/span><\/span>i<\/span><\/span><\/sub>\u2208<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>N<\/span><\/span>]<\/span><\/span>\u6295\u5f71\u5230<\/span><\/span>P<\/span><\/span>\u7684\u51e0\u4e2a\u8f83\u5927\u5947\u5f02\u503c\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\u6240\u5f20\u6210\u7684\u5b50\u7a7a\u95f4\u4e0a\uff0c\u4ece\u800c\u4fdd\u7559P\u7684\u4e3b\u8981\u4fe1\u606f\uff0c\u5e76\u4fdd\u6301<\/span><\/span>\u0393<\/span><\/span>\u4e0d\u53d8\u3002<\/span><\/span><\/span><\/p>\n

\u8be5\u65b9\u6cd5\u7684\u57fa\u672c\u601d\u8def\u662f\u5c06P\u4e2d\u7684\u6240\u6709\u884c\u5411\u91cf<\/span><\/span>P<\/span><\/span>i<\/span><\/span>\u89c6\u4e3a\u7ef4\u6570\u4e3aN\u7684\u6570\u636e\u5411\u91cf\uff0c\u7136\u540e\u9996\u5148\u5bf9\u8fd9\u4e9b\u884c\u5411\u91cf\u8fdb\u884cPCA\u964d\u7ef4\uff0c\u5176\u6b21\u5c06\u5176\u805a\u7c7b\u4e3ar\u4e2a\u7c07\uff0c\u5176\u4e2dr\u662f\u6839\u636e\u5947\u5f02\u503c\u8c31\u7684\u9608\u503c<\/span><\/span>\u03f5<\/span><\/span>\u622a\u53d6\u7684\u3002\u6709\u4e86\u8fd9\u4e2a\u805a\u7c7b\u65b9\u6848\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u6307\u5b9aTPM\u7684\u7b80\u5316\u8fc7\u7a0b\u3002\u6587\u7ae0<\/span><\/span>[6]<\/span><\/span>\u7ed9\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u7a33\u6001\u5206\u5e03\u548c\u5bf9\u5e94\u7684\u6d41\u77e9\u9635\u7684\u7b80\u5316TPM\u7684\u65b9\u6848\u3002\u5177\u4f53\u5730\uff0c\u5c31\u662f\u5c06P\u5bf9\u5e94\u7684\u7a33\u6001\u6d41\u77e9\u9635F\u6309\u7167\u805a\u7c7b\u65b9\u6848\u8fdb\u884c\u72b6\u6001\u5f52\u5e76\uff0c\u5e76\u5c06\u88ab\u5f52\u5e76\u4e3a\u4e00\u7c7b\u7684\u5217\u4e0a\u7684\u6d41\u91cf\u8fdb\u884c\u76f8\u52a0\uff0c\u4ece\u800c\u5f97\u5230\u4e00\u4e2a\u7b80\u5316\u7684<\/span><\/span><\/span>r<\/span><\/span>\u00d7<\/span><\/span>r<\/span><\/span>\u7ef4\u5ea6\u7684\u6d41\u77e9\u9635<\/span><\/span>F<\/span><\/span>\u2032<\/span><\/span>\uff0c\u7136\u540e\u5c06\u5176\u5f52\u4e00\u5316\u5f97\u5230\u7c97\u7c92\u5316\u540e\u7684TPM\uff1a<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>\u3002\u8fd9\u6837\u505a\u7684\u597d\u5904\u662f\u4e3a\u4e86\u4fdd\u8bc1\u72b6\u6001\u5f52\u5e76\u8fc7\u7a0b\u4e2d\u7684\u6d41\u91cf\u5b88\u6052\uff08\u7531\u4e8e\u9a6c\u5c14\u53ef\u592b\u94fe\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u79cd\u968f\u673a\u6e38\u8d70\u7684\u7c92\u5b50\u6d41\uff0c\u56e0\u6b64\u8fd9\u79cd\u6d41\u5e94\u8be5\u5728\u7c97\u7c92\u5316\u7684\u8fc7\u7a0b\u4e2d\u4fdd\u6301\u6d41\u91cf\u5b88\u6052\uff09\u3002<\/span><\/span><\/p>\n

1)<\/span><\/span><\/b> \u5bf9P\u8fdb\u884cSVD\u5206\u89e3\uff08\u5047\u8bbeP\u662f\u4e0d\u53ef\u5f52\u7ea6\u7684\uff0c\u4e14\u5177\u6709\u5468\u671f\u6027\uff0c\u4ece\u800c\u5b58\u5728\u5e73\u7a33\u5206\u5e03\uff09\uff1a<\/span><\/span><\/span><\/p>\n

P<\/span><\/span>=<\/span><\/span>U<\/span><\/span>\u22c5<\/span><\/span>\u03a3<\/span><\/span>\u22c5<\/span><\/span>V<\/span><\/span>T<\/span><\/span><\/sup>,<\/span><\/span><\/span><\/p>\n

\u5176\u4e2d\uff0c<\/span><\/span>U<\/span><\/span>\u548c<\/span><\/span>V<\/span><\/span>\u662f\u4e24\u4e2a\u5c3a\u5bf8\u4e3aN\u00d7N\u7684\u6b63\u4ea4\u5f52\u4e00\u5316\u77e9\u9635\uff0c<\/span><\/span>\u03a3<\/span><\/span>=<\/span><\/span>d<\/span><\/span>i<\/span><\/span>a<\/span><\/span>g<\/span><\/span>(<\/span><\/span>\u03c3<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>\u03c3<\/span><\/span>N<\/span><\/span><\/sub>)<\/span><\/span> \u662f\u4e00\u4e2a\u5bf9\u89d2\u77e9\u9635\uff0c\u5305\u542b\u6240\u6709\u6709\u5e8f\u5947\u5f02\u503c\u3002<\/span><\/span><\/span><\/p>\n

2)<\/span><\/span><\/b>\u9009\u62e9\u4e00\u4e2a<\/span><\/span>\u03f5<\/span><\/span>\u4f5c\u4e3a\u9608\u503c\u6765\u622a\u65ad\u5947\u5f02\u503c\u8c31\uff0c\u5e76\u5f97\u5230<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>\u4f5c\u4e3a\u4fdd\u7559\u72b6\u6001\u7684\u4e2a\u6570\uff1b<\/span><\/span><\/span><\/p>\n

3)<\/span><\/span><\/b>\u901a\u8fc7\u8ba1\u7b97<\/span><\/span>\"image.png\"<\/span><\/sub>\u5bf9P\u4e2d\u7684\u6240\u6709<\/span><\/span>P<\/span><\/span>i<\/span><\/span>\u8fdb\u884c\u964d\u7ef4\uff0c\u5176\u4e2d<\/span><\/span>V<\/span><\/span>N<\/span><\/sub><\/span>\u00d7<\/span><\/span><\/sub>r<\/span><\/span><\/sub>\u03f5<\/span><\/sub><\/span>\u7531<\/span><\/span>P<\/span><\/span>\u22c5<\/span><\/span>P<\/span><\/span>T<\/span><\/span><\/sup>\u7684\u524d<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>\u4e2a\u7279\u5f81\u5411\u91cf\u6784\u6210\uff1b<\/span><\/span><\/span><\/p>\n

4)<\/span><\/span><\/b> \u901a\u8fc7 K-means \u7b97\u6cd5\u5c06<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e2d\u7684\u6240\u6709\u884c\u5411\u91cf\u805a\u7c7b\u4e3ar\u7ec4\uff0c\u5f97\u5230\u6295\u5f71\u77e9\u9635<\/span><\/span>\u03a6<\/span><\/span>\uff0c\u5176\u5b9a\u4e49\u4e3a:<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5bf9<\/span><\/span>\u2200<\/span><\/span>i<\/span><\/span>,<\/span><\/span>r<\/span><\/span>\u2208<\/span><\/span>[<\/span><\/span>1<\/span><\/span>,<\/span><\/span>N<\/span><\/span>]<\/span><\/span>\u90fd\u6210\u7acb\u3002<\/span><\/span><\/span><\/p>\n

5)<\/span><\/span><\/b> \u5229\u7528<\/span><\/span>\u03a6<\/span><\/span>\u548cP\u5f97\u5230\u65b0\u7684TPM\u3002<\/span><\/span><\/span><\/p>\n

\u4e3a\u4e86\u8bf4\u660e\u5982\u4f55\u83b7\u5f97\u7b80\u5316\u7684TPM\uff0c\u9996\u5148\u5b9a\u4e49\u4e00\u4e2a\u77e9\u9635\uff0c\u79f0\u4e3a\u7a33\u6001\u6d41\u77e9\u9635\uff0c\u5982\u4e0b\u6240\u793a <\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d\uff0c<\/span><\/span>\u03bc<\/span><\/span>\u662fP\u7684\u7a33\u6001\u5206\u5e03\uff0c\u5373\u6ee1\u8db3<\/span><\/span>P<\/span><\/span>\u22c5<\/span><\/span>\u03bc<\/span><\/span>=<\/span><\/span>\u03bc<\/span><\/span>\u3002<\/span><\/span><\/span><\/p>\n

\u5176\u6b21\uff0c\u6211\u4eec\u5c06\u6839\u636e <\/span><\/span>\u03a6<\/span><\/span>\u548c<\/span><\/span>F<\/span><\/span>\u5f97\u5230\u7c97\u7c92\u5316\u540e\u7684\u7a33\u6001\u6d41\u77e9\u9635\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d\uff0cF’\u662f\u7c97\u7c92\u5316\u540e\u7684\u5e73\u7a33\u6d41\u77e9\u9635\u3002\u5728\u5f52\u5e76\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4fdd\u6301\u6240\u6709\u77e9\u9635\u4e0a\u7684\u6d41\u91cf\u603b\u91cf\u662f\u4e0d\u53d8\u7684\u3002<\/span><\/span><\/span><\/p>\n

\u6700\u540e\uff0c\u7c97\u7c92\u5316\u540e\u7684TPM\u53ef\u76f4\u63a5\u901a\u8fc7\u5f52\u4e00\u5316\u6bcf\u4e00\u884c\u5f97\u5230\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u5c06N\u4e2a<\/span><\/span>\"image.png\"<\/span><\/sub>\u62fc\u5728\u4e00\u8d77\u5c31\u80fd\u5f97\u5230\u6700\u7ec8\u7684TPM\u3002<\/span><\/span><\/p>\n

\u53ef\u4ee5\u8bc1\u660e\uff0c\u8fd9\u6837\u7684\u7c97\u7c92\u5316\u65b9\u6848\u53ef\u4ee5\u4fdd\u8bc1\u8ba9\u7c97\u7c92\u5316\u64cd\u4f5c\u548c\u65f6\u95f4\u6f14\u5316\u64cd\u4f5c\u5177\u6709\u53ef\u4ea4\u6362\u7684\u6027\u8d28\uff08\u8bc1\u660e\u53ef\u4ee5\u53c2\u8003<\/span><\/span>[6]<\/span><\/span>\uff09\u3002<\/span><\/span><\/span><\/p>\n

4.4 \u4e0e\u57fa\u4e8e\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u5173\u7cfb<\/span><\/span><\/span><\/h2>\n

\u4e0a\u8ff0\u6709\u5173\u56e0\u679c\u6d8c\u73b0\u7684\u5b9a\u4e49\u4ee5\u53ca\u76f8\u5e94\u7684\u57fa\u4e8e\u52a8\u529b\u5b66\u53ef\u9006\u6027\u7684\u5408\u7406\u6027\u6765\u6e90\u4e8e\u8fd9\u5957SVD\u65b9\u6848\u5b9a\u4e49\u7684\u56e0\u679c\u6d8c\u73b0\u4e0e\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u5b9a\u4e49\u7684\u5bc6\u5207\u5173\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc1\u660e\uff0c\u8981\u60f3\u83b7\u5f97\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u7c97\u7c92\u5316\u7b56\u7565\u4e5f\u8fd1\u4f3c\u7b49\u4ef7\u4e8e\u662f\u5411\u6700\u5927\u5947\u5f02\u503c\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\u65b9\u5411\u6295\u5f71\u7684\u7b56\u7565\u3002\u5728Erik Hoel\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u7684\u6846\u67b6\u5185\uff0c\u7ed9\u5b9a\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u5b66\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u5927\u5c0f\u4f9d\u8d56\u4e8e\u7c97\u7c92\u5316\u7b56\u7565\u7684\u9009\u62e9\uff0c\u53ef\u4ee5\u901a\u8fc7\u5b8f\u89c2\u52a8\u529b\u5b66\u7684EI\u6700\u5927\u5316\u5bfb\u627e\u6700\u4f18\u7684\u7c97\u7c92\u5316\u7b56\u7565\u3002\u7531\u4e8e\u5bf9\u4e8e\u79bb\u6563\u7684\u9a6c\u5c14\u53ef\u592b\u94fe\u6765\u8bf4\uff0c\u7c97\u7c92\u5316\u7b56\u7565\u5f80\u5f80\u90fd\u662f\u6bd4\u8f83\u4e25\u683c\u76840\u62161\u6784\u6210\u7684\u5411\u91cf\uff0c\u56e0\u6b64\u5e76\u4e0d\u80fd\u7b80\u5355\u5730\u6839\u636e\u5947\u5f02\u5411\u91cf\u6765\u76f4\u63a5\u6295\u5f71\uff0c\u4f46\u662f\u5982\u679c\u7c97\u7c92\u5316\u7b56\u7565\u5c3d\u53ef\u80fd\u5730\u4e0e\u6700\u5927\u7684\u51e0\u4e2a\u5947\u5f02\u5411\u91cf\u5e73\u884c\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8ba9\u7c97\u7c92\u5316\u540e\u52a8\u529b\u5b66\u7684EI\u5c3d\u53ef\u80fd\u66f4\u5927\uff0c\u56e0\u6b64\u6700\u5927\u5316EI\u7684\u5fc5\u8981\u6761\u4ef6\u8fd1\u4f3c\u53ef\u4ee5\u8ba4\u4e3a\u5c31\u662f\u5f80\u6700\u5927\u5947\u5f02\u503c\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\u7a7a\u95f4\u505a\u6295\u5f71\u3002\u4e0b\u9762\u7ed9\u51fa\u8f83\u4e3a\u4e25\u683c\u7684\u63a8\u5bfc\uff1a<\/span><\/span><\/p>\n

\u5bf9\u4e8e\u79bb\u6563\u7684\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a<\/span><\/span>N<\/span><\/span>\u00d7<\/span><\/span>r<\/span><\/span>\u805a\u7c7b\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\u5b9a\u4e49\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u5176\u4e2d\u5411\u91cf<\/span><\/span>\u03a6<\/span><\/span>i<\/span><\/span><\/sub>\u2208<\/span><\/span>R<\/span><\/span>N<\/span><\/span><\/sup>\u8868\u793a\u7b2ci\u4e2a\u805a\u7c7b\u4e2d\u5305\u542b\u7684\u5143\u7d20\uff0c\u5f53\u7b2cj\u4e2a\u5fae\u89c2\u6001\u5c5e\u4e8e\u7b2ci\u4e2a\u5b8f\u89c2\u6001\uff0c\u5219<\/span><\/span>\u03a6<\/span><\/span>i<\/span><\/sub><\/span>,<\/span><\/span><\/sub>j<\/span><\/sub><\/span>=<\/span><\/span>1<\/span><\/span>\uff0c\u5426\u5219\u4e3a0\u3002<\/span><\/span><\/span><\/p>\n

\u7531\u4e8e\u6bcf\u4e2a\u5fae\u89c2\u72b6\u6001\u5bf9\u5e94\u4e8e\u552f\u4e00\u7684\u5b8f\u89c2\u72b6\u6001\uff0c\u56e0\u6b64\u6240\u6709\u5411\u91cf<\/span><\/span>\u03a6<\/span><\/span>i<\/span><\/span><\/sub>\uff0c\u5f7c\u6b64\u4e4b\u95f4\u90fd\u662f\u76f8\u4e92\u6b63\u4ea4\u7684\u3002\u56e0\u6b64\uff0c\u7c97\u7c92\u5316\u540e\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635\uff08TPM\uff09\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>\u662f\u7c97\u7c92\u5316\u4e4b\u540e\u7684TPM\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u662f\u5f52\u4e00\u5316\u77e9\u9635\uff0c\u53ef\u4ee5\u4f7f\u5f97<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>\u4f9d\u7136\u4fdd\u6301\u884c\u89c4\u4e00\u5316\u3002<\/span><\/span><\/span>\u03a6<\/span><\/span>\u8fd9\u79cd\u7c97\u7c92\u5316\u65b9\u6cd5\u901a\u8fc7\u5c06<\/span><\/span>P<\/span><\/span>\u4e2d\u4e0d\u540c\u5217\u7684\u6982\u7387\u76f8\u52a0\u5e76\u5bf9\u6240\u6709\u884c\u8fdb\u884c\u5e73\u5747\uff0c\u5c06\u5fae\u89c2\u6001\u538b\u7f29\u4e3a\u5b8f\u89c2\u6001\u3002<\/span><\/span><\/span><\/p>\n

\u4e0d\u8fc7\uff0c\u8fd9\u79cd\u7c97\u7c92\u5316\u7b56\u7565\u5f97\u5230\u7684\u8868\u8fbe\u5f0f\u4e0d\u662f\u5bf9\u79f0\u7684\u5f62\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u7a0d\u4f5c\u6539\u53d8\uff0c\u5c06<\/span><\/span>\u03a6<\/span><\/span>\u7684\u6bcf\u4e00\u884c\u9664\u4ee5\u5176\u8303\u6570\u6765\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u5373\u8bbe\u65b0\u7684\u7c97\u7c92\u5316\u5411\u91cf\u53ef\u5199\u4e3a\uff1a<\/span><\/span>\u03d5<\/span><\/span>i<\/span><\/span><\/sub>=<\/span><\/span>\u03a6<\/span><\/span>i<\/span><\/span><\/sub>\/<\/span><\/span>|<\/span><\/span>\u03a6<\/span><\/span>i<\/span><\/span><\/sub>|<\/span><\/span>\uff0c\u8fd9\u91cc\u5b9a\u4e49<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4e8e\u662f\uff0c\u6211\u4eec\u4fbf\u80fd\u591f\u5c06\u7c97\u7c92\u5316\u540e\u7684TPM\u8fd1\u4f3c\u5199\u4e3a\u4e00\u79cd\u5bf9\u79f0\u7684\u4e58\u79ef\u5f62\u5f0f\uff1a<\/span><\/span><\/span>
<\/span><\/p>\n

<\/section>\n

\u8fdb\u4e00\u6b65\uff0c\u6211\u4eec\u53ef\u4ee5\u5bf9P\u77e9\u9635\u8fdb\u884cSVD\u5206\u89e3\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u4ece\u800c\u5f97\u5230\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u5c06\u8be5\u5f0f\u4ee3\u5165<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>\u2248<\/span><\/span>\u03d5<\/span><\/span>T<\/span><\/span><\/sup>P<\/span><\/span>\u03d5<\/span><\/span><\/span>\uff0c\u5f97\u5230\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u8fdb\u4e00\u6b65\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e<\/span><\/span>\u0393<\/span><\/span>\u7684\u5b9a\u4e49\u548c\u5b83\u7684\u4e0b\u754c\uff0c\u5f97\u5230\uff1a<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u56e0\u6b64\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u5411<\/span><\/span>\u03d5<\/span><\/span>j<\/span><\/span><\/sub>\u4e0e\u5947\u5f02\u5411\u91cf<\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/sub>\u5e73\u884c\uff0c\u4f7f\u5f97\u5bf9\u4e8e\u6240\u6709i\u2264r\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u5230\u6700\u5927\u5316\uff0c\u76f8\u5f53\u4e8e\u4e3a<\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/sub>\u7684\u65b9\u5411\u5206\u914d\u66f4\u591a\u7684\u6982\u7387\u8d28\u91cf\u3002<\/span><\/span><\/span><\/p>\n

\u6545\u800c\uff0c\u901a\u8fc7\u5411\u4f7f\u5f97\u7c97\u7c92\u5316\u5411\u91cf\u4e0e<\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/sub>\u8fd1\u4f3c\u5e73\u884c\uff0c\u6211\u4eec\u53ef\u4ee5\u6700\u5927\u5316<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>(<\/span><\/span>P<\/span><\/span>\u2032<\/span><\/span>)<\/span><\/span>\u3002\u56e0\u4e3a<\/span><\/span>log<\/span><\/span>\u2061<\/span><\/span>(<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>)<\/span><\/span>\u223c<\/span><\/span>E<\/span><\/span>I<\/span><\/span>\uff0c\u6240\u4ee5\u5728\u6700\u5927\u5316<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u7684\u540c\u65f6\uff0c\u4e5f\u5c31\u6700\u5927\u5316\u4e86EI\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u9009\u62e9\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u4e3a\u5947\u5f02\u503c\u6700\u5927\u7684\u5947\u5f02\u5411\u91cf\u65b9\u5411\u5206\u914d\u66f4\u591a\u7684\u6982\u7387\u8d28\u91cf\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u8fd1\u4f3c\u6700\u5927\u5316EI\u3002<\/span><\/span><\/span><\/p>\n

\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u7c97\u7c92\u5316\u7b56\u7565\u03a6\u7684\u7ea6\u675f\uff08\u4f8b\u5982\uff0c\u5b8f\u89c2\u52a8\u529b\u5b66TPM\u7684\u5206\u7ec4\u548c\u5f52\u4e00\u5316\uff09\u4f1a\u963b\u6b62<\/span><\/span>\u03d5<\/span><\/span>j<\/span><\/span><\/sub>\u4e0e\u5947\u5f02\u5411\u91cf\u5b8c\u7f8e\u5bf9\u9f50\u3002\u56e0\u6b64\uff0c\u57fa\u4e8eSVD\u7684\u7c97\u7c92\u5316\u7b56\u7565\u53ea\u662f\u6700\u5927\u5316EI\u7684\u8fd1\u4f3c\u5fc5\u8981\u6761\u4ef6\u3002<\/span><\/span><\/span><\/p>\n

4.5 \u5177\u4f53\u6848\u4f8b<\/span><\/span><\/span><\/h2>\n

\u4f7f\u7528\u57fa\u4e8e\u53ef\u9006\u6027\u548cSVD\u5206\u89e3\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u5141\u8bb8\u6211\u4eec\u76f4\u63a5\u91cf\u5316\u4e00\u4e2a\u5b9e\u9645\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u73b0\u8c61\u3002\u4e0b\u9762\u5206\u522b\u9488\u5bf9\u5e03\u5c14\u7f51\u7edc\u548c\u590d\u6742\u7f51\u7edc\u8fdb\u884c\u8bf4\u660e\u3002<\/span><\/span><\/p>\n

4.5.1 \u5e03\u5c14\u7f51\u7edc<\/span><\/span><\/span><\/h3>\n

\u4e0b\u9762\u57fa\u4e8eHoel\u7b49\u4eba\u7684\u8bba\u6587<\/span><\/span>[13]<\/span><\/span>[14]<\/span><\/span>\u4e2d\u63d0\u51fa\u7684\u51e0\u79cd\u5e03\u5c14\u7f51\u7edc\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u5b66\u6765\u6d4b\u8bd5\u6e05\u6670\u548c\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u7684\u5b9a\u4e49\u3002<\/span><\/span><\/span><\/p>\n

\u4e0b\u56fe(a)-(i)\u5206\u522b\u663e\u793a\u4e86\u4ece\u5177\u6709\u76f8\u540c\u8282\u70b9\u673a\u5236\u7684\u76f8\u540c\u5e03\u5c14\u7f51\u7edc\u6a21\u578b\u751f\u6210\u7684\u7528\u4e8e\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u548c\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u7684TPM\u7684\u4e24\u4e2a\u793a\u4f8b\u3002\u56fe(c) \u8868\u793a\u901a\u8fc7\u7c97\u7c92\u5316(a)\u5f97\u5230\u7684\u65b0\u5e03\u5c14\u7f51\u7edc\uff0c\u7c97\u7c92\u5316\u7b56\u7565\u662f\u4ece (f) \u548c (i) \u7684 TPM \u4e2d\u63d0\u53d6\u7684\u3002\u56fe(d)\u4e2d\u7684TPM\u76f4\u63a5\u6e90\u81ea\u56fe(a)\u548c(b)\u4e2d\u7684\u5e03\u5c14\u7f51\u7edc\u53ca\u5176\u8282\u70b9\u673a\u5236\u3002\u5b83\u4eec\u7684\u5947\u5f02\u503c\u8c31\u5206\u522b\u5982\u56fe(e)\u548c(h)\u6240\u793a\u3002(d)\u4e2d\u7684\u4f8b\u5b50\u53ea\u67094\u4e2a\u975e\u96f6\u5947\u5f02\u503c\uff0c\u5947\u5f02\u503c\u8c31\u5982\u56fe(e)\u6240\u793a\uff0c\u56e0\u6b64\uff0c\u51fa\u73b0\u660e\u663e\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u4e14\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u4e3a<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>=<\/span><\/span>0.75<\/span><\/span>\u3002 \u8fd9\u4e00\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u5224\u65ad\u4e0e\u53c2\u8003\u6587\u732e<\/span><\/span>[13]<\/span><\/span>\u76f8\u540c\u3002(f) \u548c (i) \u5206\u522b\u662f\u5bf9 (d) \u548c (g) \u4e2d\u7684\u539f\u59cb TPM \u5e94\u7528\u7c97\u7c92\u5316\u65b9\u6cd5\u540e\u7f29\u51cf\u7684TPM\u548c\u6295\u5f71\u77e9\u9635\u3002<\/span><\/span><\/span><\/p>\n

\u56fe(g)\u4e2d\u7684TPM\u53ef\u4ee5\u663e\u793a\u51fa\u6a21\u7cca\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u8fd9\u662f\u5728(d)\u4e2d\u7684TPM\u4e0a\u6dfb\u52a0\u5f3a\u5ea6\u4e3a\uff08std = 0.03\uff09\u7684\u968f\u673a\u9ad8\u65af\u566a\u58f0\u540e\u5f97\u5230\u7684\u3002\u56e0\u6b64\uff0c\u5947\u5f02\u9891\u8c31\u5982\u56fe(h)\u6240\u793a\u3002\u6211\u4eec\u9009\u62e9<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>0.2<\/span><\/span>\u4f5c\u4e3a\u9608\u503c\uff0c\u8fd9\u6837\u5c31\u53ea\u5269\u4e0b4\u4e2a\u5927\u7684\u5947\u5f02\u503c\u3002\u56e0\u679c\u6d8c\u73b0\u7a0b\u5ea6\u4e3a\u0394<\/span><\/span>\u0393(0.2)<\/span><\/span>=<\/span><\/span>0.69<\/span><\/span>\u3002<\/span><\/span>\u03f5<\/span><\/span>\u503c\u662f\u6839\u636e\u56fe(h)\u4e2d\u7684\u5947\u5f02\u503c\u9891\u8c31\u9009\u62e9\u7684\uff0c\u5728\u56fe(h)\u4e2d\u53ef\u4ee5\u89c2\u5bdf\u5230\u6307\u6570\u4e3a3\u548c<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>0.2<\/span><\/span>\u65f6\u6709\u4e00\u4e2a\u660e\u663e\u7684\u5206\u754c\u70b9\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u4e0b\u56fe\u663e\u793a\u4e86\u53e6\u4e00\u4e2a\u66f4\u590d\u6742\u7684\u5e03\u5c14\u7f51\u7edc\u6a21\u578b\u7684\u660e\u663e\u56e0\u679c\u6d8c\u73b0\u4f8b\u5b50\uff0c\u8be5\u6a21\u578b\u6765\u81ea\u53c2\u8003\u6587\u732e<\/span><\/span>[13]<\/span><\/span><\/sup>\uff0c\u5176\u4e2d\u5177\u6709\u76f8\u540c\u8282\u70b9\u673a\u5236\u76846\u4e2a\u8282\u70b9\u53ef\u5f52\u7c7b\u4e3a3\u4e2a\u8d85\u7ea7\u8282\u70b9\uff0c\u4ee5\u663e\u793a\u56e0\u679c\u6d8c\u73b0\u3002(a)\u4e3a6\u8282\u70b912\u6761\u8fb9\u7684\u5e03\u5c14\u7f51\u7edc\u6a21\u578b\u3002 (b)\u662f\u6839\u636e(e)\u4e2d\u7684TPM\u5f97\u51fa\u7684\u7c97\u7c92\u5316\u540e\u7684\u5e03\u5c14\u7f51\u7edc\u6a21\u578b\u3002\u539f\u59cb\u5e03\u5c14\u7f51\u7edc\u6a21\u578b\u7684\u76f8\u5e94TPM\u5982\u56fe(c)\u6240\u793a\u3002\u5947\u5f02\u503c\u8c31\u5982\u56fe(d\uff09\u6240\u793a\uff0c\u5176\u4e2d\u67098\u4e2a\u975e\u96f6\u503c\u3002\u8fd9\u4e2a\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u4e3a<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>=<\/span><\/span>2.23<\/span><\/span>\u3002\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u5224\u65ad\u4e0e<\/span><\/span>[13]<\/span><\/span><\/sup>\u76f8\u540c\u3002(e) \u662f\u5bf9(c)\u7684\u7c97\u7c92\u5316\u3002(f) \u662f\u6839\u636e\u57fa\u4e8e SVD \u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u5f97\u5230\u7684\u4ece\u5fae\u89c2\u72b6\u6001\u5230\u5b8f\u89c2\u72b6\u6001\u7684\u6295\u5f71\u77e9\u9635\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n

4.5.2 \u590d\u6742\u7f51\u7edc<\/span><\/span><\/span><\/h3>\n

\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u91cf\u5316\u53ef\u5e94\u7528\u4e8e\u590d\u6742\u7f51\u7edc\uff0c\u5982\u4e0b\u56fe\u6240\u793a\u3002\u56fe\uff08a)-(c\uff09\u663e\u793a\u4e86\u7531\u968f\u673a\u5757\u6a21\u578b\uff08SBM\uff09\u751f\u6210\u7684\u5177\u6709\u4e09\u7ec4\u53c2\u6570\uff08\u5185\u90e8\u8fde\u63a5\u6982\u7387\uff09\u7684\u590d\u6742\u7f51\u7edc\u7684\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u4f8b\u5b50\u3002TPM\u662f\u901a\u8fc7\u5bf9\u7f51\u7edc\u7684\u90bb\u63a5\u77e9\u9635\u6309\u6bcf\u4e2a\u8282\u70b9\u7684\u5ea6\u8fdb\u884c\u5f52\u4e00\u5316\u5f97\u5230\u7684\u3002\u56fe(a)\u663e\u793a\u4e86\u4e00\u4e2a\u6709 100 \u4e2a\u8282\u70b9\u548c 5 \u4e2a\u533a\u5757\uff08\u793e\u533a\uff09\u7684\u793a\u4f8b\u7f51\u7edc\uff0c\u56fe(b)\u663e\u793a\u4e86\u5176\u5947\u5f02\u503c\u8c31\uff0c\u540c\u56fe\u4e2d\u8fd8\u663e\u793a\u4e86\u53e6\u5916\u4e24\u4e2a\u7531SBM\u751f\u6210\u7684\u7f51\u7edc\u8c31\uff0c\u5b83\u4eec\u7684\u5927\u5c0f\u548c\u5757\u6570\u76f8\u540c\uff0c\u4f46\u53c2\u6570\u4e0d\u540c\u3002\u56fe(c) \u662f\u5229\u7528\u57fa\u4e8eSVD\u7684\u7c97\u7c92\u5316\u65b9\u6cd5\u8fdb\u884c\u7f29\u51cf\u540e\u7684 (a) \u7f51\u7edc\u3002\u56fe(b)\u4e2d\uff0c\u5728\u4e0e\u533a\u5757\u6570\u76f8\u540c\u7684\u6a2a\u5750\u6807\u4e0a\u53ef\u4ee5\u89c2\u5bdf\u5230\u4e00\u4e2a\u660e\u663e\u7684\u5206\u754c\u70b9<\/span><\/span>(<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>0.3<\/span><\/span>,<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>=<\/span><\/span>5<\/span><\/span>)<\/span><\/span>\u3002\u53ef\u4ee5\u786e\u5b9a\uff0c\u5728\u8fd9\u4e2a\u7f51\u7edc\u6a21\u578b\u4e2d\u51fa\u73b0\u4e86\u6a21\u7cca\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u7a0b\u5ea6\u4e3a<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>(<\/span><\/span>0.3<\/span><\/span>)<\/span><\/span>=<\/span><\/span>0.56<\/span><\/span>\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n

4.5.3 \u5143\u80de\u81ea\u52a8\u673a<\/span><\/span><\/span><\/h3>\n

\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5173\u4e8e\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u7684\u5b9a\u4e49\u53ef\u5e94\u7528\u4e8e\u5143\u80de\u81ea\u52a8\u673a\uff0c\u4ee5\u53d1\u73b0\u5176\u5c40\u90e8\u6d8c\u73b0\u7ed3\u6784\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u91cc\u523b\u753b\u4e86\u5143\u80de\u81ea\u52a8\u673a\uff08\u7f16\u53f740\u7684\u57fa\u672c\u4e00\u7ef4\u5143\u80de\u81ea\u52a8\u673a\uff09\u5c40\u90e8TPM\u7684\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u3002(a)\u662f\u7b2c40\u53f7\u5143\u80de\u81ea\u52a8\u673a\u7684\u6f14\u5316\uff08\u89c4\u5219\u662f\uff1a000 \u2192 0, 001 \u2192 0, 010 \u2192 1, 011 \u2192 0, 100 \u2192 1, 101 \u2192 0, 110 \u2192 0, 111 \u2192 0\uff09\u3002\u5c40\u90e8TPM \u7531\u5305\u62ec\u6bcf\u4e2a\u5355\u5143\u53ca\u5176\u4e24\u4e2a\u76f8\u90bb\u5355\u5143\u7684\u5c40\u90e8\u7a97\u53e3\u83b7\u5f97\u3002\u56fe(b) \u663e\u793a\u4e86\u8fd9\u4e9b\u5c40\u90e8 TPM \u7684\u5947\u5f02\u503c\u7684\u53ef\u80fd\u9891\u8c31\uff0c\u5728\u8fd9\u4e9b\u9891\u8c31\u4e2d\u53ef\u80fd\u51fa\u73b0\u4e5f\u53ef\u80fd\u4e0d\u51fa\u73b0\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u3002\u56fe(c)\u7528\u7ea2\u70b9\u6807\u8bb0\u663e\u793a\u4e86\u6240\u6709\u5355\u5143\u548c\u65f6\u95f4\u6b65\u957f\u7684\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u5206\u5e03\uff08<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\uff09\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n


<\/span><\/span><\/h1>\n

\n
\n
\n
\n
\n

<\/span><\/section>\n

<\/span><\/section>\n
\n
<\/section>\n<\/section>\n<\/section>\n
\n

5. \u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u57fa\u4e8eSVD\u7684\u56e0\u679c\u6d8c\u73b0<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/span><\/p>\n

5.1 \u56e0\u679c\u6d8c\u73b0\u7684\u91cf\u5316\u6307\u6807<\/span><\/span><\/span><\/h2>\n

TPM\u77e9\u9635\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u4e0e\u5176\u5947\u5f02\u503c\u76f8\u5173\u3002\u540c\u6837\uff0c\u5728\u89c4\u5b9a<\/span><\/span>\u03f5<\/span><\/span>\u2265<\/span><\/span>0<\/span><\/span>\u4e4b\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u7b5b\u9009\u4e24\u4e2a\u534f\u65b9\u5dee\u77e9\u9635\u7684\u5947\u5f02\u503c\u6765\u8ba1\u7b97\u56e0\u679c\u6d8c\u73b0\uff0c\u5373<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span>\"image.png\"<\/span><\/sub>\u53d6\u5f97\u662f\u4e24\u4e2a\u77e9\u9635\u6709\u6548\u79e9\u7684\u6700\u5c0f\u503c\u3002<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>0<\/span><\/span>\u5c31\u662f\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\uff0c<\/span><\/span>\u03f5<\/span><\/span>><\/span><\/span>0<\/span><\/span>\u5c31\u662f\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/span><\/span><\/p>\n

\u548c\u79bb\u6563\u7684\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u6709\u6240\u4e0d\u540c\uff0c\u9ad8\u65af\u7cfb\u7edf\u56e0\u679c\u6d8c\u73b0\u73b0\u8c61\u7684\u672c\u8d28\u5728\u4e8e\u5176\u9ad8\u7ef4\u6761\u4ef6\u6982\u7387\u5b58\u5728\u5197\u4f59\u7684\u6b27\u5f0f\u7a7a\u95f4\u7ef4\u5ea6\uff0c\u8fd9\u4e9b\u7ef4\u5ea6\u4f1a\u9020\u6210\u4e0d\u53ef\u9006\u7684\u4ea7\u751f\uff0c\u7531\u4e24\u4e2a\u65b9\u5411\u7684\u534f\u65b9\u5dee\u77e9\u9635\u7684\u9006\u5bf9\u5e94\u7b49\u4e8e\u96f6\u6216\u63a5\u8fd1\u96f6\u5947\u5f02\u503c\u7684\u5947\u5f02\u5411\u91cf\u8868\u793a\u3002\u56e0\u679c\u6d8c\u73b0\u7684\u91cf\u5316\u672c\u8d28\u4e0a\uff0c\u662f\u901a\u8fc7\u6d4b\u91cf\u5f53\u8fd9\u4e9b\u5197\u4f59\u7ef4\u5ea6\u88ab\u6f5c\u5728\u7684\u6700\u4f73\u7c97\u7c92\u5ea6\u5316\u7b56\u7565\u53bb\u9664\u65f6\u7684\u5e73\u5747\u53ef\u9006\u6027\u6216\u968f\u673a\u6027\u7684\u6f5c\u5728\u6700\u4f18\u7ed3\u679c\u6765\u5b9e\u73b0\u7684\u3002<\/span><\/span><\/p>\n

5.1.1 \u4e0e\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u5b9a\u91cf\u5316\u7684\u5173\u7cfb<\/span><\/span><\/span><\/h3>\n

\u6839\u636e\u8fde\u7eed\u7cfb\u7edf\u57fa\u4e8e\u6709\u6548\u4fe1\u606f\u7684\u7684\u56e0\u679c\u6d8c\u73b0<\/span><\/span><\/p>\n

<\/section>\n

\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u6700\u4f18\u5316\u540e\u7684\u57fa\u4e8e\u7ef4\u5ea6\u5e73\u5747\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u548c\u57fa\u4e8eSVD\u7684\u56e0\u679c\u6d8c\u73b0\u5f7c\u6b64\u662f\u7b49\u4ef7\u7684\uff0c\u8fd9\u662f\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u57fa\u4e8eSVD\u7684\u56e0\u679c\u6d8c\u73b0\u548c\u57fa\u4e8eEI\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u8fd1\u4f3c\u7ebf\u6027\u5173\u7cfb\u4e3a\uff1a<\/span><\/span><\/p>\n

<\/section>\n

\u81f3\u6b64\uff0c\u4ece\u9ad8\u65af\u8fed\u4ee3\u7cfb\u7edf\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u6e05\u6670\u7684\u770b\u51fa\u53ef\u9006\u6027\u548c\u6709\u6548\u4fe1\u606f\u7684\u7ebf\u6027\u76f8\u5173\u6027\uff0c\u8bc1\u660e\u4e24\u8005\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u76f8\u4e92\u9a8c\u8bc1\u6216\u66ff\u6362\u3002<\/span><\/span><\/p>\n

5.2 \u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u57fa\u4e8eSVD\u7684\u7c97\u7c92\u5316\u7b56\u7565<\/span><\/span><\/span><\/h2>\n

\u5728\u5f97\u5230\u57fa\u4e8e\u5947\u5f02\u503c\u7684\u56e0\u679c\u6d8c\u73b0\u4e4b\u540e\uff0c\u548cTPM\u77e9\u9635\u7c7b\u4f3c\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u6839\u636e\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u548c\u6b63\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u7684\u5947\u5f02\u5411\u91cf\uff0c\u6307\u5b9a\u5728\u9ad8\u65af\u8fed\u4ee3\u7cfb\u7edf\u4e0a\u7684\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u5c06\u9ad8\u7ef4\u7684\u5411\u91cf\u6620\u5c04\u5230\u4f4e\u7ef4\u7a7a\u95f4\u3002\u8be5\u7c97\u7c92\u5316\u7b56\u7565\u4e3b\u8981\u64cd\u4f5c\u4f9d\u7136\u57fa\u4e8e\u5947\u5f02\u503c\u7684\u7b5b\u9009\uff0c\u4e3b\u8981\u6d41\u7a0b\u5982\u4e0b\u3002<\/span><\/span><\/span><\/p>\n

\u7b2c\u4e00\u6b65<\/span><\/span><\/span><\/h3>\n

\u5728\u5f97\u5230\u57fa\u4e8e\u5947\u5f02\u503c\u7684\u56e0\u679c\u6d8c\u73b0\u4e4b\u540e\uff0c\u548cTPM\u77e9\u9635\u7c7b\u4f3c\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u6839\u636e\u9006\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u548c\u6b63\u5411\u52a8\u529b\u5b66\u7684\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u7684\u5947\u5f02\u5411\u91cf\uff0c\u6307\u5b9a\u5728\u9ad8\u65af\u8fed\u4ee3\u7cfb\u7edf\u4e0a\u7684\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u5c06\u9ad8\u7ef4\u7684\u5411\u91cf\u6620\u5c04\u5230\u4f4e\u7ef4\u7a7a\u95f4\u3002\u57fa\u4e8eSVD\u7684\u7406\u8bba\uff0c<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u548c<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u90fd\u662f\u5bf9\u79f0\u77e9\u9635\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5f97\u5230SVD\u5206\u89e3<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u548c<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span>S<\/span><\/span>=<\/span><\/span>d<\/span><\/span>i<\/span><\/span>a<\/span><\/span>g<\/span><\/span>(<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>s<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u548c<\/span><\/span>K<\/span><\/span>=<\/span><\/span>d<\/span><\/span>i<\/span><\/span>a<\/span><\/span>g<\/span><\/span>(<\/span><\/span>\u03ba<\/span><\/span>i<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>\u03ba<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u5206\u522b\u662f\u5947\u5f02\u503c<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>\u2265<\/span><\/span>\u22ef<\/span><\/span>\u2265<\/span><\/span>s<\/span><\/span>n<\/span><\/span><\/sub>\u548c<\/span><\/span>\u03ba<\/span><\/span>1<\/span><\/span><\/sub>\u2265<\/span><\/span>\u22ef<\/span><\/span>\u2265<\/span><\/span>\u03ba<\/span><\/span>n<\/span><\/span><\/sub>\u7ec4\u6210\u7684\u5bf9\u89d2\u77e9\u9635\uff0c\u5947\u5f02\u5411\u91cf\u77e9\u9635<\/span><\/span>U<\/span><\/span>=<\/span><\/span>(<\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>u<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u548c<\/span><\/span>V<\/span><\/span>=<\/span><\/span>(<\/span><\/span>v<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>v<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u5206\u522b\u5305\u542b\u4e86\u4e24\u7ec4\u5947\u5f02\u503c\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\uff0c\u5b83\u4eec\u4e5f\u53ef\u4ee5\u88ab\u5206\u522b\u770b\u6210\u4e24\u4e2a\u751f\u6210\u7a7a\u95f4\u7684\u6b63\u4ea4\u57fa\u3002<\/span><\/span><\/span><\/p>\n

\u968f\u540e\u6211\u4eec\u6784\u9020\u65b0\u7684\u5947\u5f02\u503c<\/span><\/span>\"image.png\"<\/span><\/sub>\u5bf9\u89d2\u77e9\u9635\u4e0e\u5408\u5e76\u7684\u5947\u5f02\u5411\u91cf\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5176\u4e2d<\/span><\/span>\"image.png\"<\/span><\/sub>\u521a\u597d\u662f<\/span><\/span>\ud835\udc34<\/span><\/span>\ud835\udc47<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\ud835\udc34<\/span><\/span>\u548c<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u7684\u6240\u6709\u5947\u5f02\u503c\uff0c<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>\u2265<\/span><\/span>\u22ef<\/span><\/span>\u2265<\/span><\/span>s<\/span><\/span>n<\/span><\/span><\/sub>\u548c<\/span><\/span>\u03ba<\/span><\/span>1<\/span><\/span><\/sub>\u2265<\/span><\/span>\u22ef<\/span><\/span>\u2265<\/span><\/span>\u03ba<\/span><\/span>n<\/span><\/span><\/sub><\/span>\uff0c\u5171\u540c\u4ece\u5927\u5230\u5c0f\u6392\u5217\u540e\u4ea7\u751f\u7684\u65b0\u5947\u5f02\u503c\u8c31\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub>\u662f<\/span><\/span>U<\/span><\/span>=<\/span><\/span>(<\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>u<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u548c<\/span><\/span>V<\/span><\/span>=<\/span><\/span>(<\/span><\/span>v<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>v<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u4e2d\u4e0e<\/span><\/span>\"image.png\"<\/span><\/sub>\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\u3002<\/span><\/span><\/span><\/p>\n

\u6211\u4eec\u89c4\u5b9a\u9608\u503c<\/span><\/span>\u03f5<\/span><\/span>\uff0c\u5728\u7b2c\u4e00\u6b65\u4e2d\uff0c\u6211\u4eec\u89c4\u5b9a\u5927\u4e8e<\/span><\/span>\u03f5<\/span><\/span>\u7684<\/span><\/span>\"image.png\"<\/span><\/sub>\u6570\u91cf\u4e3a<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/sub><\/span>0<\/span><\/sub><\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5947\u5f02\u5411\u91cf\u77e9\u9635\u8fdb\u884c\u5206\u89e3\uff0c\u5f97\u5230<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2d<\/span><\/span>\"image.png\"<\/span><\/sub>\u8868\u793a\u6211\u4eec\u5e0c\u671b\u4fdd\u7559\u7684\u5947\u5f02\u503c\u5bf9\u5e94\u7684\u5947\u5f02\u5411\u91cf\u3002<\/span><\/span><\/span><\/p>\n

\u7b2c\u4e8c\u6b65<\/span><\/span><\/span><\/h3>\n

\u7531\u4e8e\u6211\u4eec\u5f97\u5230\u7684\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\u5c5e\u4e8e\u7a7a\u95f4<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u800c<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/sub><\/span>0<\/span><\/sub><\/span>\u4e0d\u4e00\u5b9a\u5c0f\u4e8en\uff1b\u540c\u65f6\uff0c\u7531\u4e8e<\/span><\/span>\"image.png\"<\/span><\/sub>\u4e2d\u7684\u5217\u5411\u91cf<\/span><\/span>\"image.png\"<\/span><\/sub>\u6e90\u4e8e<\/span><\/span>U<\/span><\/span>=<\/span><\/span>(<\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>u<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>,<\/span><\/span>V<\/span><\/span>=<\/span><\/span>(<\/span><\/span>v<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>v<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u4e24\u7ec4\u53ef\u4ee5\u5f20\u6210n\u7ef4\u7a7a\u95f4\u7684\u6b63\u4ea4\u57fa\uff0c\u65e0\u6cd5\u4fdd\u8bc1<\/span><\/span>\"image.png\"<\/span><\/sub>\u5f7c\u6b64\u4e4b\u95f4\u7684\u7ebf\u6027\u65e0\u5173\u548c\u6b63\u4ea4\u3002\u56e0\u6b64\u6211\u4eec\u65e0\u6cd5\u76f4\u63a5\u5229\u7528\u5176\u8f6c\u7f6e\u5bf9n\u7ef4\u5411\u91cf\u8fdb\u884c\u7c97\u7c92\u5316\uff0c\u56e0\u6b64\u8fd8\u9700\u8981\u7b2c\u4e8c\u6b65SVD\u5206\u89e3\uff0c\u6765\u5f97\u5230\u771f\u6b63\u7684\u6b63\u4ea4\u77e9\u9635\u3002\u6211\u4eec\u5229\u7528\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\u548c<\/span><\/span>S<\/span><\/span>~<\/span><\/span>\u8fdb\u884c\u7b2c\u4e8c\u6b65SVD\u5206\u89e3\uff0c\u5f97\u5230<\/span><\/span><\/span><\/p>\n

<\/section>\n

\"image.png\"<\/span><\/sub>\u5305\u542b\u77e9\u9635<\/span><\/span>\"image.png\"<\/span><\/sub>\u5bf9\u5e94\u7684\u5947\u5f02\u503c\uff0c\u7528\u540c\u6837\u7684\u65b9\u6cd5\u5f97\u5230\u5927\u4e8e<\/span><\/span>\u03f5<\/span><\/span>\u7684<\/span><\/span>\"image.png\"<\/span><\/sub>\u6570\u91cf\u4e3a<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u518d\u6b21\u5bf9\u5de6\u5947\u5f02\u5411\u91cf\u77e9\u9635\u8fdb\u884c\u5206\u89e3\u5f97\u5230<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u968f\u540e\u6211\u4eec\u4fbf\u53ef\u4ee5\u6839\u636e\u7b2c\u4e8c\u6b65\u5206\u89e3\u5f97\u5230\u7684\u5947\u5f02\u5411\u91cf\u76f4\u63a5\u751f\u6210\u7c97\u7c92\u5316\u53c2\u6570\u77e9\u9635\uff0c\u5373<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u8be5\u65b9\u6cd5\u53ef\u4ee5\u5168\u7a0b\u4f7f\u7528SVD\u5206\u89e3\u8fdb\u884c\uff0c\u4e0d\u4ec5\u7701\u53bb\u4e86\u7e41\u6742\u7684\u7b5b\u9009\u8fc7\u7a0b\uff0c\u800c\u4e14\u62e5\u6709\u66f4\u5e7f\u6cdb\u7684\u5e94\u7528\u8303\u56f4\u3002<\/span><\/span><\/span><\/p>\n

5.3 \u8fde\u7eed\u7cfb\u7edf\u5177\u4f53\u6848\u4f8b<\/span><\/span><\/span><\/h2>\n

5.3.1 \u589e\u957f\u6a21\u578b<\/span><\/span><\/span><\/h3>\n

\u5047\u8bbe\u4e00\u4e2a4\u7ef4\u7684\u5411\u91cf\uff0c\u524d\u4e24\u4e2a\u7ef4\u5ea6<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/sub>\u9075\u5faa\u589e\u957f\u7387\u4e3a0.2\u548c0.05\u7684\u9a6c\u5c14\u8428\u65af\u589e\u957f\u6a21\u578b\u3002\u540c\u65f6\u53e6\u5916\u4e24\u4e2a\u7ef4\u5ea6<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>\u76f4\u63a5\u590d\u5236\u4e86\u524d\u4e24\u4e2a\u7ef4\u5ea6\u7684\u72b6\u6001\u5982\u56fea\u6240\u793a\uff0c\u4ed6\u4eec\u548c\u524d\u4e24\u4e2a\u7ef4\u5ea6\u9ad8\u5ea6\u76f8\u5173\uff0c\u751a\u81f3\u53ef\u4ee5\u89c6\u4e3a\u5197\u4f59\u7684\u7ef4\u5ea6\uff0c\u6700\u7ec8\u751f\u6210\u6570\u636e\u5982\u56fed\u6240\u793a\uff0c\u5176\u4e2d<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>\u8868\u793a\u4e0d\u540c\u7ef4\u5ea6\u7684\u589e\u957f\u66f2\u7ebf\uff0c<\/span><\/span>y<\/span><\/span>1<\/span><\/span><\/sub>y<\/span><\/span>2<\/span><\/span><\/sub>\u8868\u793a\u7c97\u7c92\u5316\u540e\u7684\u5b8f\u89c2\u6001\u3002\u6211\u4eec\u8bbe\u5fae\u89c2\u6001<\/span><\/span>x<\/span><\/span>=<\/span><\/span>(<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>2<\/span><\/span>,<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>)<\/span><\/span>, \u6a21\u578b\u7684\u52a8\u529b\u5b66\u53ef\u4ee5\u5199\u6210<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u5176\u4e2d<\/span><\/span>\"image.png\"<\/span><\/sub>, <\/span><\/span>A<\/span><\/span>\u662f\u589e\u957f\u7387\u6784\u6210\u7684\u77e9\u9635\uff0c <\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/sup>=<\/span><\/span>0.1<\/span><\/span>\u662f\u5bf9\u89d2\u5316\u7684\u534f\u65b9\u5dee\u77e9\u9635, <\/span><\/span>a<\/span><\/span>0<\/span><\/span><\/sub>=<\/span><\/span>0<\/span><\/span>\u662f\u81ea\u7136\u53c2\u6570, \u5e76\u4e14<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u8be5\u77e9\u9635\u53ea\u6709\u4e24\u4e2a\u5947\u5f02\u503c\u77e9\u9635\u79e9<\/span><\/span>r<\/span><\/span>=<\/span><\/span>2<\/span><\/span><<\/span><\/span>4<\/span><\/span>\u3002\u7531\u4e8e\u6b63\u5411\u77e9\u9635\u662f\u5bf9\u89d2\u5355\u4f4d\u9635\u548c\u5e38\u6570\u6570\u4e58\u5f97\u5230\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u9006\u5411\u52a8\u529b\u5b66\u7684\u77e9\u9635\uff0c\u5982\u56feb\u6240\u793a\u3002\u5982\u56fec\u6240\u793a\uff0c\u6a2a\u8f74\u8868\u793a\u9006\u5411\u52a8\u529b\u5b66\u534f\u65b9\u5dee\u77e9\u9635\u7684\u5947\u5f02\u503c<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>\u2265<\/span><\/span>\u22ef<\/span><\/span>\u2265<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub>, \u7eb5\u8f74\u8868\u793a\u5947\u5f02\u503c\u5927\u5c0f, \u901a\u8fc7\u8ba1\u7b97\u6211\u4eec\u53ef\u4ee5\u5f97\u77e5\u6e05\u6670\u56e0\u679c\u6d8c\u73b0\u4e3a<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>(<\/span><\/span>0<\/span><\/span>)<\/span><\/span>=<\/span><\/span>0.4034<\/span><\/span>\uff0c\u9006\u5411\u52a8\u529b\u5b66\u534f\u65b9\u5dee\u77e9\u9635\u5982\u56feb\u6240\u793a\u3002<\/span><\/span><\/span><\/p>\n

\u540c\u65f6\u6211\u4eec\u53ef\u4ee5\u5bf9\u77e9\u9635A\u589e\u52a0\u4e00\u4e9b\u6270\u52a8\uff0c\u4f7f<\/span><\/span><\/p>\n

<\/section>\n

\u6b64\u65f6\u589e\u957f\u7387\u53c2\u6570\u77e9\u9635<\/span><\/span>A<\/span><\/span>\u548c<\/span><\/span>A<\/span><\/span>T<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>A<\/span><\/span>\uff08\u56fee\u6240\u793a\uff09\u90fd\u662f\u6ee1\u79e9\u77e9\u9635\uff0c\u4f46\u662f\u901a\u8fc7\u89c2\u5bdf\u56fef\u6240\u793a\u7684\u5947\u5f02\u503c\u8c31\uff0c\u6211\u4eec\u53ea\u80fd\u770b\u5230\u4e24\u4e2a\u8f83\u5927\u7684\u9006\u5411\u52a8\u529b\u5b66\u5947\u5f02\u503c<\/span><\/span>\uff0c<\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>\uff0c<\/span><\/span>s<\/span><\/span>2<\/span><\/span><\/sub>\uff0c\u6b64\u65f6\u6211\u4eec\u5c31\u9700\u8981\u5f15\u5165\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u3002\u6211\u4eec\u89c4\u5b9a\u9608\u503c<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>2<\/span><\/span>, \u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u53ef\u4ee5\u8ba1\u7b97\u5f97\u5230<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>(<\/span><\/span>\u03f5<\/span><\/span>)<\/span><\/span>=<\/span><\/span>0.4195<\/span><\/span>\u3002<\/span><\/span><\/span><\/p>\n

\u9488\u5bf9\u6e05\u6670\u548c\u6a21\u7cca\u56e0\u679c\u6d8c\u73b0\u7684\u60c5\u5f62\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5f97\u5230\u56feg\u548ch\u4e2d\u7684\u7c97\u7c92\u5316\u7b56\u7565\u53c2\u6570\u77e9\u9635\uff0c\u53ef\u4ee5\u770b\u5230A\u4e0d\u6ee1\u79e9\u7684\u65f6\u5019\uff0c\u7c97\u7c92\u5316\u7b56\u7565\u53ea\u4fdd\u7559\u4e86\u524d\u4e24\u4e2a\u7ef4\u5ea6\u7684\u4fe1\u606f\uff0c\u800cA\u6ee1\u79e9\u7684\u65f6\u5019\uff0c\u7c97\u7c92\u5316\u7b56\u7565\u5c06<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/sub>\u4fe1\u606f\u5408\u5e76\uff0c<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>\u4fe1\u606f\u5408\u5e76\uff0c\u8fbe\u5230\u964d\u7ef4\u7684\u6548\u679c\u3002\u5982\u56fed\u6240\u793a\uff0c\u5176\u4e2d<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>.<\/span><\/span>.<\/span><\/span>.<\/span><\/span>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>\u8868\u793a\u4e0d\u540c\u7ef4\u5ea6\u7684\u589e\u957f\u66f2\u7ebf\uff0c\u53ef\u89c1\u5b8f\u89c2\u6001\u8fd1\u4f3c\u4e8e\u4e8e\u5fae\u89c2\u6001<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/sub>\u548c<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>\u4e24\u7ec4\u53d8\u91cf\u5206\u522b\u6c42\u5e73\u5747\u5f97\u5230\u7684\u7ed3\u679c\u3002<\/span><\/span><\/span>
<\/span><\/p>\n

<\/span><\/p>\n

5.3.2 \u79bb\u6563\u5316\u5e03\u6717\u8fd0\u52a8<\/span><\/span><\/span><\/h3>\n

\u79bb\u6563\u5e03\u6717\u8fd0\u52a8\u662f\u79bb\u6563\u65f6\u95f4\u5185\u8fde\u7eed\u5e03\u6717\u8fd0\u52a8\u7684\u8fd1\u4f3c\uff0c\u5e38\u7528\u4e8e\u6570\u503c\u6a21\u62df\u548c\u968f\u673a\u8fc7\u7a0b\u5efa\u6a21\u3002\u65b9\u7a0b<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>+<\/span><\/sub><\/span><\/span>1<\/span><\/sub><\/span><\/span>=<\/span><\/span>A<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>+<\/span><\/span>\u03b5<\/span><\/span>t<\/span><\/span><\/sub>\u53ef\u4ee5\u88ab\u89c6\u4e3a\u5965\u6069\u65af\u5766-\u4e4c\u4f26\u8d1d\u514b\uff08OU\uff09\u8fc7\u7a0b\u7684\u79bb\u6563\u7248\u672c\u65b9\u6cd5\uff0c\u5982\u56fea\u6240\u793a\u3002\u5728\u8fd9\u4e2a\u6a21\u578b\u4e2d\uff0c<\/span><\/span>\u03bc<\/span><\/span>=<\/span><\/span>a<\/span><\/span>0<\/span><\/span><\/sub>+<\/span><\/span>A<\/span><\/span>x<\/span><\/span>t<\/span><\/span><\/sub>\u662f\u5f71\u54cd\u72b6\u6001\u6f14\u5316\u7684\u6f02\u79fb\u5411\u91cf\uff0c\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u8868\u793a\u6269\u6563\u7cfb\u6570\uff0c\u5b83\u51b3\u5b9a\u4e86<\/span><\/span>\u03b5<\/span><\/span>t<\/span><\/span>\u7ef4\u5ea6\u4e0a\u968f\u673a\u6ce2\u52a8\u7684\u5e45\u5ea6\u548c\u76f8\u5173\u6027\u3002<\/span><\/span><\/span><\/p>\n

\u5bf9<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u548c<\/span><\/span>A<\/span><\/span>T<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>A<\/span><\/span>\uff08\u5982\u56feb\u3001c\u6240\u793a\uff09\u8fdb\u884cSVD\u5206\u89e3\u4e4b\u540e\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u5947\u5f02\u5411\u91cf\u77e9\u9635<\/span><\/span>U<\/span><\/span>=<\/span><\/span>(<\/span><\/span>u<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>u<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u548c<\/span><\/span>V<\/span><\/span>=<\/span><\/span>(<\/span><\/span>v<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>v<\/span><\/span>n<\/span><\/span><\/sub>)<\/span><\/span>\u5176\u4e2d<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u5bf9\u89d2\u5316\u7684\u5947\u5f02\u503c\u77e9\u9635<\/span><\/span><\/span><\/p>\n

S<\/span><\/span>=<\/span><\/span>d<\/span><\/span>i<\/span><\/span>a<\/span><\/span>g<\/span><\/span>(<\/span><\/span>2<\/span><\/span>,<\/span><\/span>1.5<\/span><\/span>,<\/span><\/span>1.3<\/span><\/span>,<\/span><\/span>1.01<\/span><\/span>,<\/span><\/span>0.2<\/span><\/span>,<\/span><\/span>0.12<\/span><\/span>,<\/span><\/span>0.1<\/span><\/span>,<\/span><\/span>0.05<\/span><\/span>)<\/span><\/span>
<\/span><\/span><\/p>\n

K<\/span><\/span>=<\/span><\/span>d<\/span><\/span>i<\/span><\/span>a<\/span><\/span>g<\/span><\/span>(<\/span><\/span>1.6<\/span><\/span>,<\/span><\/span>1.25<\/span><\/span>,<\/span><\/span>1.1<\/span><\/span>,<\/span><\/span>1.05<\/span><\/span>,<\/span><\/span>0.5<\/span><\/span>,<\/span><\/span>0.4<\/span><\/span>,<\/span><\/span>0.25<\/span><\/span>,<\/span><\/span>0.1<\/span><\/span>)<\/span><\/span>.<\/span><\/span><\/span><\/p>\n

\u5728\u5f97\u5230\u56fed\u4e2d\u7684\u5947\u5f02\u503c\u8c31\u4e4b\u540e\uff0c\u89c4\u5b9a<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>0.6<\/span><\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>(<\/span><\/span>\u03f5<\/span><\/span>)<\/span><\/span>=<\/span><\/span>0.5167<\/span><\/span>\uff0c\u5176\u4e2d\u6709\u6548\u79e9<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>=<\/span><\/span>4<\/span><\/span>\uff0c <\/span><\/span>s<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>s<\/span><\/span>4<\/span><\/span><\/sub>\u548c<\/span><\/span>\u03ba<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>\u22ef<\/span><\/span>,<\/span><\/span>\u03ba<\/span><\/span>4<\/span><\/span><\/sub>\u9700\u8981\u88ab\u4fdd\u7559\u3002<\/span><\/span><\/span><\/p>\n

\u5f97\u5230\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\u548c<\/span><\/span>A<\/span><\/span>T<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>A<\/span><\/span>\u7684\u5947\u5f02\u503c\u8c31\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u5177\u4f53\u7684\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u5f97\u5230\u56fef\u4e2d\u7684\u77e9\u9635W\u3002\u901a\u8fc7\u7c97\u7c92\u5316\u7b56\u7565\u7684\u6c42\u89e3\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u5982\u56fef\u6240\u793a\u7684\u7c97\u7c92\u5316\u53c2\u6570\u77e9\u9635<\/span><\/span>W<\/span><\/span>\uff0c\u5176\u4fdd\u7559\u4e86<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>5<\/span><\/span><\/sub>\u56db\u4e2a\u7ef4\u5ea6\uff0c\u4ece\u56fee\u53ef\u770b\u51fa\u5728\u4f7f\u7528\u9ad8\u65af\u566a\u58f0\u8fed\u4ee3\u7cfb\u7edf\u57fa\u4e8eSVD\u7684\u7c97\u7c92\u5316\u7b56\u7565\u540e\u5f97\u5230\u7684\u56e0\u679c\u6d8c\u73b0\u6307\u6807<\/span><\/span>\"image.png\"<\/span><\/sub>\uff0c\u4f1a\u6bd4\u76f4\u63a5\u622a\u53d6<\/span><\/span>U<\/span><\/span>\u6216<\/span><\/span>V<\/span><\/span>\u5f97\u5230\u7684\u5bf9\u5e94\u56e0\u679c\u6d8c\u73b0\u5927\u5c0f<\/span><\/span>\"image.png\"<\/span><\/sub>\u7565\u66f4\u63a5\u8fd1\u7406\u8bba\u6700\u5927\u7684<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>(<\/span><\/span>\u03f5<\/span><\/span>)<\/span><\/span>\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n

5.3.3 SIR\u6a21\u578b<\/span><\/span><\/span><\/h3>\n

\u5728NIS+\u8bcd\u6761\u4e2d\u7684SIR\u6a21\u578b\u5728\u8fd9\u91cc\u4e5f\u53ef\u4ee5\u901a\u8fc7\u53ef\u9006\u6027\u4e0eSVD\u5206\u89e3\u8ba1\u7b97\u56e0\u679c\u6d8c\u73b0\u5e76\u7814\u7a76\u5176\u5e95\u5c42\u4ea7\u751f\u6d8c\u73b0\u7684\u673a\u7406\u3002\u73b0\u5b9e\u4e2d\u7684\u5927\u591a\u6570\u7cfb\u7edf\u90fd\u65e0\u6cd5\u83b7\u5f97\u7cbe\u786e\u7684\u52a8\u6001\u6a21\u578b\u6765\u8ba1\u7b97\u56e0\u679c\u6d8c\u73b0\u7684\u89e3\u6790\u89e3\u3002\u7136\u800c\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u89c2\u5bdf\u5230\u7684\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u6765\u83b7\u5f97\u8fd1\u4f3c\u52a8\u529b\u5b66\u3002\u6211\u4eec\u7528\u795e\u7ecf\u7f51\u7edc\uff08NN\uff09\u5728\u6613\u611f-\u611f\u67d3-\u6062\u590d\uff08SIR\uff09\u6a21\u578b\u751f\u6210\u7684\u8bad\u7ec3\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e0a\u4ea7\u751f\u56e0\u679c\u6d8c\u73b0\u73b0\u8c61\uff0c\u6a21\u578b\u6709\u4e24\u4e2a\u81ea\u7531\u5ea6\uff0c\u5982\u4e0b\u6240\u793a<\/span><\/span><\/p>\n

<\/section>\n

\u5176\u4e2dS\u8868\u793a\u6613\u611f\u6001\u6837\u672c\u7684\u6bd4\u4f8b\uff0cI\u8868\u793a\u611f\u67d3\u6001\u7684\u6bd4\u4f8b\uff0cR\u8868\u793a\u6062\u590d\u6001\u7684\u6bd4\u4f8b\uff0c\u4e09\u8005\u7684\u5173\u7cfb\u5982\u56fea\u6240\u793a\uff0c<\/span><\/span>\u03b2<\/span><\/span>\u548c<\/span><\/span>\u03b3<\/span><\/span>\u5206\u522b\u8868\u793aS\u4e0eI\u3001I\u4e0eR\u4e4b\u95f4\u7684\u8f6c\u5316\u7387\u3002\u6211\u4eec\u53ef\u4ee5\u91c7\u53d6\u548c\u589e\u957f\u6a21\u578b\u76f8\u540c\u7684\u6570\u636e\u5904\u7406\u65b9\u6cd5\uff0c<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>\u76f4\u63a5\u590d\u5236\u4e86\u524d\u4e24\u4e2a\u7ef4\u5ea6\u7684\u72b6\u6001\uff0c\u5f97\u5230<\/span><\/span>x<\/span><\/span>=<\/span><\/span>(<\/span><\/span>S<\/span><\/span>,<\/span><\/span>I<\/span><\/span>,<\/span><\/span>S<\/span><\/span>,<\/span><\/span>I<\/span><\/span>)<\/span><\/span>\uff0c\u4e4b\u540e\u6211\u4eec\u53ef\u4ee5\u5c06\u6a21\u578b\u79bb\u6563\u5316\uff0c\u5373<\/span><\/span><\/span><\/p>\n

<\/section>\n

\u7531\u6b64\u53ef\u4ee5\u5f97\u5230\u56feb\u4e2d\u7684\u751f\u6210\u6570\u636e\u3002\u4ece\u56fee\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c<\/span><\/span>A<\/span><\/span>T<\/span><\/span><\/sup>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>A<\/span><\/span>\uff08\u5982\u56fec\u6240\u793a\uff09\u6709\u4e24\u4e2a\u8f83\u5927\u7684\u5947\u5f02\u503c\uff0c\u5dee\u8ddd\u6bd4<\/span><\/span>\u03a3<\/span><\/span>\u2212<\/span><\/sup><\/span>1<\/span><\/sup><\/span>\uff08\u5982\u56fed\u6240\u793a\uff09\u66f4\u5927\uff0c<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>=<\/span><\/span>2<\/span><\/span>\uff0c\u56e0\u4e3a<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>5<\/span><\/span>\uff0c\u6b63\u9006\u5411\u7684\u534f\u65b9\u5dee\u77e9\u9635\u5982\u56fec\u548cd\u6240\u793a\u3002\u5728\u6a21\u578b\u8bad\u7ec3\u4e2d\uff0c\u5f53\u8bad\u7ec3\u5468\u671f\u4e3a50000\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u56e0\u679c\u6d8c\u73b0\u7684\u503c\u4e3a<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\uff08<\/span><\/span>\u03f5<\/span><\/span>\uff09<\/span><\/span>=<\/span><\/span>0.8685<\/span><\/span>\u3002<\/span><\/span><\/span><\/p>\n

\u56fef\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u56e0\u679c\u6d8c\u73b0<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u5e76\u4e0d\u662f\u6052\u7b49\u7684\uff0c\u800c\u662f\u4f1a\u968fS\u3001I\u7684\u4e0d\u540c\u53d1\u751f\u6539\u53d8\uff0c\u6211\u4eec\u5f97\u5230\u7684\u7ed3\u679c0.8685\u662f\u4e0d\u540c\u72b6\u6001\u7684<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u6c42\u5747\u503c\u540e\u5f97\u5230\u7684\u7ed3\u679c\uff1b\u89c2\u5bdf\u89c4\u5b9a<\/span><\/span>\u03f5<\/span><\/span>=<\/span><\/span>5<\/span><\/span>\u4e0b\u7684<\/span><\/span>r<\/span><\/span>\u03f5<\/span><\/span><\/sub>\u5747\u503c\uff08\u56feg\uff09\u4e5f\u53ef\u4ee5\u5f97\u5230\u76f8\u4f3c\u7684\u89c4\u5f8b\uff0c<\/span><\/span>\u0394<\/span><\/span>\u0393<\/span><\/span>\u03b1<\/span><\/span><\/sub>\u8f83\u5927\u7684\u5730\u65b9\uff0c\u6709\u6548\u79e9\u4f1a\u76f8\u7b49\u66f4\u63a5\u8fd12\u3002<\/span><\/span><\/span><\/p>\n

\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u56feh\u4e2d\u7684\u7c97\u7c92\u5316\u7b56\u7565\u53c2\u6570\u77e9\u9635\uff0c\u7c97\u7c92\u5316\u7b56\u7565\u5c06<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/sub>\u4fe1\u606f\u5408\u5e76\uff0c<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/sub>,<\/span><\/span>x<\/span><\/span>4<\/span><\/span><\/sub>\u4fe1\u606f\u5408\u5e76\uff0c\u8fbe\u5230\u964d\u7ef4\u7684\u6548\u679c\u3002<\/span><\/span><\/span><\/p>\n

<\/section>\n

<\/span><\/section>\n
\n
\n
\n

\u53c2\u8003\u6587\u732e<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

\n
\n
\n
\n


<\/span><\/p>\n

    <\/ol>\n


    <\/span><\/p>\n

      \n
    1. \n

       Hoel E P, Albantakis L, Tononi G. Quantifying causal emergence shows that macro can beat micro[J]. Proceedings of the National Academy of Sciences, 2013, 110(49): 19790-19795.<\/span><\/span><\/p>\n<\/li>\n

    2. \n

       Hoel E P. When the map is better than the territory[J]. Entropy, 2017, 19(5): 188.<\/span><\/span><\/p>\n<\/li>\n

    3. \n

       Rosas F E, Mediano P A, Jensen H J, et al. Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data[J]. PLoS computational biology, 2020, 16(12): e1008289.<\/span><\/span><\/p>\n<\/li>\n

    4. \n

       Barnett L, Seth AK. Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems. Physical Review E. 2023 Jul;108(1):014304.<\/span><\/span><\/p>\n<\/li>\n

    5. \n

       Mingzhe Yang, Zhipeng Wang, Kaiwei Liu, et al. Finding emergence in data by maximizing effective information. National Science Review, 2024, nwae279<\/span><\/span><\/p>\n<\/li>\n

    6. \n

       Zhang, J., Tao, R., Leong, K.H. et al. Dynamical reversibility and a new theory of causal emergence based on SVD. npj Complex 2, 3 (2025).<\/span><\/span><\/p>\n<\/li>\n

    7. \n

       Kaiwei Liu, Linli Pan, Zhipeng Wang, et al. SVD-based Causal Emergence for Gaussian Iterative Systems. arXiv:2502.08261, 2025.<\/span><\/span><\/p>\n<\/li>\n

    8. \n

       Schatten norm from Wikipedia. https:\/\/en.wikipedia.org\/wiki\/Schatten norm<\/span><\/span><\/p>\n<\/li>\n

    9. \n

       Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM review 52(3), 471\u2013501 (2010)<\/span><\/span><\/p>\n<\/li>\n

    10. \n

       Chi, Y., Lu, Y.M., Chen, Y.: Nonconvex optimization meets low-rank matrix factorization: An overview. IEEE Transactions on Signal Processing 67(20), 52395269 (2019)<\/span><\/span><\/p>\n<\/li>\n

    11. \n

       Cui, S., Wang, S., Zhuo, J., Li, L., Huang, Q., Tian, Q.: Towards discriminability and diversity: Batch nuclear-norm maximization under label insufficient situations. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp. 3941\u20133950 (2020)<\/span><\/span><\/p>\n<\/li>\n

    12. \n

       Fazel, M.: Matrix rank minimization with applications. PhD thesis, PhD thesis, Stanford University (2002)<\/span><\/span><\/p>\n<\/li>\n

    13. \n

       Hoel, E.P., Albantakis, L., Tononi, G.: Quantifying causal emergence shows that macro can beat micro. Proceedings of the National Academy of Sciences of the United States of America 110(49), 19790\u201319795 (2013) https:\/\/doi.org\/10.1073\/ pnas.1314922110<\/span><\/span><\/p>\n<\/li>\n

    14. \n

       Hoel, E.P.: When the map is better than the territory. Entropy 19(5) (2017) https:\/\/doi.org\/10.3390\/e19050188<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n


      <\/span><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

      \n
      \n

      (\u53c2\u8003\u6587\u732e\u53ef<\/span>\u4e0a\u4e0b\u6ed1\u52a8<\/span><\/strong>\u67e5\u770b)<\/span><\/p>\n<\/section>\n<\/section>\n


      <\/span><\/p>\n

      \u4f5c\u8005\u7b80\u4ecb<\/span><\/span><\/p>\n

      <\/section>\n
      <\/section>\n


      <\/span><\/p>\n

      \n

      \u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\uff0c\u4e00\u7ecf\u91c7\u7eb3\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01<\/span><\/p>\n<\/blockquote>\n


      <\/span><\/span><\/section>\n

      <\/span><\/section>\n
      \n
      \n
      \n
      \n

      \u52a0\u5165\u6211\u4eec<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


      <\/span><\/section>\n

      \u4eb2\u7231\u7684\u793e\u533a\u4f19\u4f34\u4e0e\u77e5\u8bc6\u63a2\u7d22\u8005\uff1a<\/span><\/span><\/strong><\/p>\n

      \u6211\u4eec\u8bda\u631a\u9080\u8bf7\u70ed\u7231\u77e5\u8bc6\u5206\u4eab\u7684\u60a8\uff0c\u52a0\u5165<\/span><\/span>\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u7f16\u5199\u5fd7\u613f\u56e2\u961f<\/span><\/span><\/strong>\uff01\u65e0\u8bba\u60a8\u662f\u9886\u57df\u4e13\u5bb6\uff0c\u8fd8\u662f\u5bf9\u7279\u5b9a\u4e3b\u9898\u5145\u6ee1\u70ed\u5ff1\u7684\u5b66\u4e60\u8005\uff0c\u8fd9\u91cc\u90fd\u6709\u60a8\u7684\u821e\u53f0\u3002\u901a\u8fc7\u7f16\u5199\u767e\u79d1\u8bcd\u6761\uff0c\u60a8\u5c06\u4e3a\u5168\u7403\u8bfb\u8005\u4f20\u9012\u6743\u5a01\u77e5\u8bc6\uff0c\u540c\u65f6\u83b7\u5f97<\/span><\/span>\u4e13\u5bb6\u6307\u5bfc<\/span><\/span><\/strong>\u4e0e<\/span><\/span>\u4e2a\u4eba\u80fd\u529b<\/span><\/span><\/strong>\u8dc3\u5347\u7684\u53cc\u91cd\u6210\u957f\u3002<\/span><\/span><\/p>\n


      <\/span><\/p>\n

      \ud83d\udcdd <\/span><\/span>\u5fd7\u613f\u8005\u804c\u8d23<\/span><\/span><\/strong><\/p>\n

      \u521b\u4f5c\u65b0\u8bcd\u6761\uff1a<\/span><\/span><\/strong>\u8986\u76d6\u590d\u6742\u7cfb\u7edf\u3001\u4eba\u5de5\u667a\u80fd\u7b49\u524d\u6cbf\u9886\u57df<\/span><\/span><\/p>\n

      \u8fed\u4ee3\u7ecf\u5178\u5185\u5bb9<\/span><\/span><\/strong>\uff1a\u66f4\u65b0\u73b0\u6709\u8bcd\u6761\uff0c\u5b88\u62a4\u77e5\u8bc6\u7684\u51c6\u786e\u6027\u4e0e\u65f6\u6548\u6027<\/span><\/span><\/p>\n

      \u8d28\u91cf\u5b88\u62a4\u8005<\/span><\/span><\/strong>\uff1a\u53c2\u4e0e\u5185\u5bb9\u6821\u5bf9\u5ba1\u6838\uff0c\u5171\u5efa\u7cbe\u54c1\u77e5\u8bc6\u5e93<\/span><\/span><\/p>\n


      <\/span><\/p>\n

      \ud83c\udf1f <\/span><\/span>\u6211\u4eec\u671f\u5f85\u60a8<\/span><\/span><\/strong><\/p>\n

      \u96c6\u667a\u8bfb\u4e66\u4f1a\u6210\u5458\uff08\u9700\u5b8c\u6210\u5171\u521b\u4efb\u52a1\u5e76\u83b7\u5f97\u9000\u8d39\u8d44\u683c\uff09<\/span><\/span><\/p>\n

      \u62e5\u6709\u6e05\u6670\u8868\u8fbe\u590d\u6742\u6982\u5ff5\u7684\u5199\u4f5c\u80fd\u529b<\/span><\/span><\/p>\n

      \u5bf9\u7279\u5b9a\u9886\u57df\u6709\u6df1\u5ea6\u7814\u7a76\u6216\u5f3a\u70c8\u5174\u8da3<\/span><\/span><\/p>\n

      \u5177\u5907\u4fe1\u606f\u68c0\u7d22\u4e0e\u6574\u5408\u7d20\u517b<\/span><\/span><\/p>\n

      \u6000\u63e3\u8d23\u4efb\u611f\u4e0e\u534f\u4f5c\u7cbe\u795e\uff0c\u613f\u4e3a\u77e5\u8bc6\u5171\u4eab\u8d4b\u80fd<\/span><\/span><\/p>\n


      <\/span><\/p>\n

      \ud83c\udf81 <\/span><\/span>\u60a8\u5c06\u6536\u83b7<\/span><\/span><\/strong><\/p>\n

      \u767e\u79d1\u79ef\u5206\uff08\u652f\u6301\u5151\u6362\u96c6\u667a\u4ff1\u4e50\u90e8\u5468\u8fb9\uff1a\u6587\u5316\u886b\u3001\u590d\u6742\u79d1\u5b66\u77e5\u8bc6\u5361\u7b49\uff09<\/span><\/span><\/p>\n

      \u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u6559\u6388\u4eb2\u81ea\u6307\u5bfc\u5199\u4f5c<\/span><\/span><\/p>\n

      \u79d1\u7814\u52a9\u7406\u664b\u5347\u901a\u9053\uff1a\u8868\u73b0\u4f18\u5f02\u8005\u53ef\u52a0\u5165\u5f20\u6c5f\u6559\u6388\u79d1\u7814\u56e2\u961f<\/span><\/span><\/p>\n

      \"\u56fe\u7247\"<\/section>\n
      <\/section>\n

      \u52a0\u5165\u5f20\u6c5f\u7ec4\u53d1\u8d77\u7684\u4efb\u4f55\u4e00\u671f\u8bfb\u4e66\u4f1a\u5e76\u5b8c\u6210\u5171\u521b\u4efb\u52a1\u5373\u53ef \u8ba9\u6211\u4eec\u4e00\u8d77\uff0c\u7528\u77e5\u8bc6\u8fde\u63a5\u4e16\u754c\uff01<\/span><\/span><\/p>\n


      <\/span>
      <\/span><\/section>\n
      \n
      \n
      \n
      \n

      \u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u516d\u5b63<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


      <\/span><\/section>\n

      \u5728\u9713\u8679\u706f\u7684\u95ea\u70c1\u3001\u8681\u7fa4\u7684\u7cbe\u5bc6\u534f\u4f5c\u3001\u4eba\u7c7b\u610f\u8bc6\u7684\u8bde\u751f\u4e2d\uff0c\u9690\u85cf\u7740\u5fae\u89c2\u4e0e\u5b8f\u89c2\u4e4b\u95f4\u6df1\u523b\u7684\u56e0\u679c\u5173\u8054\u2014\u2014\u8fd9\u4e9b\u770b\u4f3c\u7b80\u5355\u7684\u4e2a\u4f53\u884c\u4e3a\uff0c\u5982\u4f55\u8de8\u8d8a\u5c3a\u5ea6\uff0c\u6d8c\u73b0\u51fa\u4ee4\u4eba\u60ca\u53f9\u7684\u590d\u6742\u73b0\u8c61\uff1f\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u4e3a\u6211\u4eec\u63ed\u793a\u4e86\u7b54\u6848\uff1a\u590d\u6742\u7cfb\u7edf\u7684\u5b8f\u89c2\u7279\u5f81\u65e0\u6cd5\u901a\u8fc7\u5fae\u89c2\u5143\u7d20\u7684\u7b80\u5355\u53e0\u52a0\u89e3\u91ca\uff0c\u800c\u662f\u6e90\u4e8e\u591a\u5c3a\u5ea6\u52a8\u6001\u4ea4\u4e92\u4e2d\u6d8c\u73b0\u7684\u56e0\u679c\u7ed3\u6784\u3002\u4ece\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\u9a71\u52a8\u7684\u52a8\u6001\u53ef\u9006\u6027\u5206\u6790\uff0c\u5230\u56e0\u679c\u62bd\u8c61\u4e0e\u4fe1\u606f\u5206\u89e3\u7684\u91cf\u5316\u5de5\u5177\uff0c\u7814\u7a76\u8005\u4eec\u6b63\u9010\u6b65\u6784\u5efa\u8d77\u4e00\u5957\u8de8\u8d8a\u6570\u5b66\u3001\u7269\u7406\u4e0e\u4fe1\u606f\u79d1\u5b66\u7684\u7406\u8bba\u6846\u67b6\uff0c\u8bd5\u56fe\u89e3\u7801\u590d\u6742\u7cfb\u7edf\u7684\u201c\u6d8c\u73b0\u5bc6\u7801\u201d\u3002<\/span><\/span><\/p>\n


      <\/span><\/p>\n

      \u4e3a\u4e86\u7cfb\u7edf\u68b3\u7406\u56e0\u679c\u6d8c\u73b0\u6700\u65b0\u8fdb\u5c55\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u53d1\u8d77\u300c\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u7ec4\u7ec7\u5bf9\u672c\u8bdd\u9898\u611f\u5174\u8da3\u7684\u670b\u53cb\uff0c\u6df1\u5165\u7814\u8bfb\u76f8\u5173\u6587\u732e\uff0c\u6fc0\u53d1\u79d1\u7814\u7075\u611f\u3002<\/span><\/span><\/p>\n


      <\/span><\/p>\n

      \u8bfb\u4e66\u4f1a\u5c06\u4ece2025\u5e743\u670816\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u65e5\u65e99:00-11:00\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba110\u5468\u5de6\u53f3\u3002\u6bcf\u5468\u8fdb\u884c\u7ebf\u4e0a\u4f1a\u8bae\uff0c\u4e0e\u4e3b\u8bb2\u4eba\u7b49\u793e\u533a\u6210\u5458\u5f53\u9762\u4ea4\u6d41\uff0c\u4e4b\u540e\u53ef\u4ee5\u83b7\u5f97\u89c6\u9891\u56de\u653e\u6301\u7eed\u5b66\u4e60\u3002\u8bda\u631a\u9080\u8bf7\u9886\u57df\u5185\u7814\u7a76\u8005\u3001\u5bfb\u6c42\u8de8\u9886\u57df\u878d\u5408\u7684\u7814\u7a76\u8005\u52a0\u5165\uff0c\u5171\u540c\u63a2\u8ba8\u3002<\/span><\/span><\/p>\n


      <\/span><\/span><\/p>\n

      \"\u56fe\u7247\"<\/span><\/a><\/section>\n
      \n


      <\/span><\/span><\/p>\n

      \u8be6\u60c5\u8bf7\u89c1\uff1a\u56e0\u679c\u6d8c\u73b0\u7b2c\u516d\u5b63\u2014\u2014\u52a8\u529b\u5b66\u3001\u56e0\u679c\u62bd\u8c61\u4e0e\u4fe1\u606f\u5206\u89e3<\/a><\/span><\/span><\/p>\n<\/section>\n


      <\/span><\/p>\n

      \u63a8\u8350\u9605\u8bfb<\/span><\/span><\/strong><\/strong><\/strong><\/p>\n

      1. \u4ec0\u4e48\u6837\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u53ef\u4ee5\u88ab\u65e0\u635f\u5730\u7c97\u7c92\u5316\uff1f\uff5c\u96c6\u667a\u767e\u79d1<\/span><\/a><\/span><\/strong><\/section>\n
      2. \u57fa\u4e8e\u4fe1\u606f\u5206\u89e3\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff5c\u96c6\u667a\u767e\u79d1<\/span><\/a><\/span><\/strong>
      <\/span><\/strong><\/span><\/section>\n
      3. \u56e0\u679c\u6548\u5e94\u5ea6\u91cf\uff5c\u96c6\u667a\u767e\u79d1<\/span><\/a><\/span><\/strong>
      <\/span><\/strong><\/span><\/section>\n
      4. <\/span>\u6d8c\u73b0\u52a8\u529b\u5b66\u5982\u4f55\u7528\u6765\u5206\u6790\u590d\u6742\u7cfb\u7edf\uff1f | \u65b0\u8bfe\u4e0a\u7ebf<\/span><\/a><\/span><\/strong><\/span>
      <\/span><\/strong><\/strong><\/span><\/section>\n
      <\/strong>5. <\/span><\/strong>\u96c6\u667a\u5b66\u56ed\u7cbe\u54c1\u8bfe\u7a0b\u514d\u8d39\u5f00\u653e\uff0c\u89e3\u9501\u7cfb\u7edf\u79d1\u5b66\u4e0e AI \u65b0\u4e16\u754c<\/span><\/a><\/span><\/strong><\/section>\n

      6. \u9ad8\u8003\u5206\u6570\u53ea\u662f\u5f20\u5165\u573a\u5238\uff0c\u4f60\u7684\u79d1\u7814\u5192\u9669\u5728\u8fd9\u91cc\u542f\u822a\uff01<\/span><\/a><\/span><\/strong><\/p>\n

      7.<\/span><\/span><\/strong><\/strong><\/span> <\/span><\/span><\/strong><\/strong><\/span>\u7cfb\u7edf\u79d1\u5b66\u524d\u6cbf\u5341\u8bb2\uff1a\u7406\u89e3\u81ea\u7136\u3001\u751f\u547d\u4e0e\u793e\u4f1a\u7684\u590d\u6742\u6027<\/a><\/span><\/strong><\/strong><\/span><\/p>\n


      <\/span><\/strong><\/span><\/section>\n


      <\/span><\/p>\n

      \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c<\/span>\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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