{"id":184893,"date":"2024-05-09T14:09:08","date_gmt":"2024-05-09T06:09:08","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/184893.html"},"modified":"2024-05-09T14:09:12","modified_gmt":"2024-05-09T06:09:12","slug":"%e5%9c%a8%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e4%b8%ad%ef%bc%8c%e5%a6%82%e4%bd%95%e8%a1%a1%e9%87%8f%e8%b7%9d%e7%a6%bb","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/184893.html","title":{"rendered":"\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u5982\u4f55\u8861\u91cf\u8ddd\u79bb"},"content":{"rendered":"

\"\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u5982\u4f55\u8861\u91cf\u8ddd\u79bb\"<\/p>\n

\u8ddd\u79bb\u7684\u8861\u91cf\u6807\u51c6\u662f\u673a\u5668\u5b66\u4e60<\/a>\u7b97\u6cd5\u4e2d\u7684\u4e00\u4e2a\u57fa\u7840\u6982\u5ff5\uff0c\u7528\u6765\u8bc4\u4f30\u6837\u672c\u95f4\u7684\u5dee\u5f02\u6216\u8005\u76f8\u4f3c\u5ea6\u3002\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u5e38\u7528\u7684\u8ddd\u79bb\u8861\u91cf\u6807\u51c6\u5305\u62ec\u6b27\u6c0f\u8ddd\u79bb\u3001\u66fc\u54c8\u987f\u8ddd\u79bb\u3001\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb\u3001\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb\u3001\u6c49\u660e\u8ddd\u79bb\u3001\u4f59\u5f26\u76f8\u4f3c\u5ea6<\/strong>\u7b49\u3002\u5176\u4e2d\uff0c\u6b27\u6c0f\u8ddd\u79bb<\/strong>\u56e0\u5176\u51e0\u4f55\u610f\u4e49\u6e05\u6670\u3001\u8ba1\u7b97\u7b80\u4fbf\uff0c\u5728\u591a\u79cd\u7b97\u6cd5\u4e2d\u88ab\u5e7f\u6cdb\u5e94\u7528\uff0c\u5982K-\u5747\u503c\u805a\u7c7b\u548cK-\u6700\u8fd1\u90bb\u7b97\u6cd5\u3002<\/p>\n<\/p>\n

\u63a5\u4e0b\u6765\u5c06\u8be6\u7ec6\u63cf\u8ff0\u8fd9\u4e9b\u8ddd\u79bb\u8861\u91cf\u6807\u51c6\u7684\u5b9a\u4e49\u3001\u8ba1\u7b97\u65b9\u6cd5\u53ca\u5e94\u7528\u573a\u666f\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u6b27\u6c0f\u8ddd\u79bb<\/h3>\n<\/p>\n

\u6b27\u6c0f\u8ddd\u79bb\u662f\u6700\u76f4\u89c2\u7684\u8ddd\u79bb\u6d4b\u91cf\u65b9\u5f0f\uff0c\u5b83\u8868\u793a\u591a\u7ef4\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u70b9\u7684\u76f4\u7ebf\u8ddd\u79bb\u3002\u6570\u5b66\u4e0a\uff0c\u7ed9\u5b9a\u4e24\u70b9 ( P = (p_1, p_2, …, p_n) ) \u548c ( Q = (q_1, q_2, …, q_n) )\uff0c\u6b27\u6c0f\u8ddd\u79bb ( d ) \u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n

[ d(P,Q) = \\sqrt{(p_1 – q_1)^2 + (p_2 – q_2)^2 + … + (p_n – q_n)^2} ]<\/p>\n<\/p>\n

\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u6b27\u6c0f\u8ddd\u79bb\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u8861\u91cf\u6837\u672c\u4e4b\u95f4\u7684\u76f4\u63a5\u5dee\u5f02\uff0c\u5bf9\u4e8e\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6e\u7279\u5f81\u5177\u6709\u826f\u597d\u7684\u8861\u91cf\u6548\u679c\u3002\u4f46\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u5f53\u7279\u5f81\u7684\u91cf\u7eb2\u4e0d\u7edf\u4e00\u6216\u7279\u5f81\u7684\u5206\u5e03\u5dee\u5f02\u5f88\u5927\u65f6\uff0c\u76f4\u63a5\u4f7f\u7528\u6b27\u6c0f\u8ddd\u79bb\u53ef\u80fd\u4f1a\u5bfc\u81f4\u4e00\u4e9b\u7279\u5f81\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\u88ab\u653e\u5927\u6216\u7f29\u5c0f\uff0c\u56e0\u6b64\u5728\u4f7f\u7528\u524d\u5f80\u5f80\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u6807\u51c6\u5316\u5904\u7406\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u66fc\u54c8\u987f\u8ddd\u79bb<\/h3>\n<\/p>\n

\u53c8\u79f0\u4e3a\u57ce\u5e02\u8857\u533a\u8ddd\u79bb\uff0c\u5b83\u8ba1\u7b97\u7684\u662f\u5728\u6807\u51c6\u5750\u6807\u7cfb\u4e2d\u4e24\u70b9\u5728\u6807\u51c6\u5750\u6807\u7cfb\u8f74\u7ebf\u65b9\u5411\u4e0a\u7684\u7edd\u5bf9\u8f74\u8ddd\u603b\u548c\u3002\u7ed9\u5b9a\u4e24\u70b9 ( P ) \u548c ( Q ) \u7684\u5750\u6807\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb ( d ) \u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n<\/p>\n

[ d(P,Q) = |p_1 – q_1| + |p_2 – q_2| + … + |p_n – q_n| ]<\/p>\n<\/p>\n

\u66fc\u54c8\u987f\u8ddd\u79bb\u9002\u7528\u4e8e\u51e0\u4f55\u7279\u5f81\u4e3a\u201c\u7f51\u683c\u72b6\u201d\u6216\u201c\u66fc\u54c8\u987f\u5f0f\u201d\u5e03\u5c40\u7684\u6570\u636e\u96c6\u3002\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u5b83\u5e38\u5e38\u7528\u4e8e\u8ba1\u7b97\u7a00\u758f\u6570\u636e\u7684\u8ddd\u79bb\uff0c\u56e0\u4e3a\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7ecf\u5e38\u51fa\u73b0\u8bb8\u591a\u7684\u96f6\u5dee\u503c\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u53ef\u4ee5\u66f4\u597d\u5730\u53cd\u6620\u51fa\u975e\u96f6\u5143\u7d20\u7684\u5dee\u5f02\u3002<\/p>\n<\/p>\n

\u4e09\u3001\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb<\/h3>\n<\/p>\n

\u5b83\u57fa\u4e8e\u68cb\u76d8\u4e0a\u56fd\u738b\u79fb\u52a8\u7684\u6b65\u6570\u6765\u5b9a\u4e49\uff0c\u662f\u4e00\u79cd\u6781\u503c\u8ddd\u79bb\uff0c\u6307\u7684\u662f\u591a\u7ef4\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u70b9\u5bf9\u5e94\u5750\u6807\u5dee\u7684\u6700\u5927\u503c\u3002\u6570\u5b66\u4e0a\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<\/p>\n

[ d(P,Q) = \\max(|p_1 – q_1|, |p_2 – q_2|, …, |p_n – q_n|) ]<\/p>\n<\/p>\n

\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb\u5728\u5f88\u591a\u9700\u8981\u8bc4\u4f30\u6781\u7aef\u5dee\u5f02\u7684\u573a\u666f\u4e0b\u975e\u5e38\u6709\u7528\uff0c\u5982\u65e0\u7ebf\u7535\u6ce2\u8986\u76d6\u8303\u56f4\u4f30\u8ba1\u6216\u662f\u68cb\u76d8\u7c7b\u6e38\u620f\u7684AI<\/a>\u8ba1\u7b97\u4e2d\u3002<\/p>\n<\/p>\n

\u56db\u3001\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb<\/h3>\n<\/p>\n

\u8fd9\u662f\u4e00\u4e2a\u66f4\u4e00\u822c\u5316\u7684\u8ddd\u79bb\u5b9a\u4e49\u3002\u6b27\u6c0f\u8ddd\u79bb\u548c\u66fc\u54c8\u987f\u8ddd\u79bb\u90fd\u53ef\u4ee5\u770b\u4f5c\u662f\u5176\u7279\u4f8b\u3002\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb\u901a\u8fc7\u53c2\u6570 ( p ) \u6765\u5b9a\u4e49\u4e0d\u540c\u8ddd\u79bb\uff0c\u5e76\u53ef\u901a\u8fc7\u8be5\u53c2\u6570\u5728\u4e0d\u540c\u7684\u8ddd\u79bb\u5b9a\u4e49\u95f4\u8fdb\u884c\u8f6c\u6362\u3002\u7ed9\u5b9a\u53c2\u6570 ( p ) \u548c\u4e24\u70b9 ( P ) \u548c ( Q )\uff0c\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb ( d ) \u5b9a\u4e49\u4e3a\uff1a<\/p>\n<\/p>\n

[ d(P,Q) = (\\sum_{i=1}^{n} |p_i – q_i|^p)^{\\frac{1}{p}} ]<\/p>\n<\/p>\n

\u5f53 ( p=1 ) \u65f6\uff0c\u9000\u5316\u4e3a\u66fc\u54c8\u987f\u8ddd\u79bb\uff1b( p=2 ) \u65f6\uff0c\u5c31\u662f\u6b27\u6c0f\u8ddd\u79bb\uff1b\u5f53 ( p ) \u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u6210\u4e3a\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb\u3002<\/p>\n<\/p>\n

\u4e94\u3001\u6c49\u660e\u8ddd\u79bb<\/h3>\n<\/p>\n

\u6c49\u660e\u8ddd\u79bb\u7528\u6765\u8861\u91cf\u4e24\u4e2a\u7b49\u957f\u5b57\u7b26\u4e32\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u5b83\u662f\u4e24\u4e2a\u5b57\u7b26\u4e32\u5bf9\u5e94\u4f4d\u7f6e\u7684\u4e0d\u540c\u5b57\u7b26\u7684\u4e2a\u6570\u3002\u5728\u6570\u5b57\u901a\u4fe1\u548c\u4fe1\u606f\u7f16\u7801\u7406\u8bba\u4e2d\u5e94\u7528\u5e7f\u6cdb\uff0c\u540c\u6837\uff0c\u5728\u673a\u5668\u5b66\u4e60\u5c24\u5176\u662f\u5206\u7c7b\u95ee\u9898\u548c\u805a\u7c7b\u5206\u6790\u4e2d\u4e5f\u6709\u5176\u7528\u9014\u3002\u8ba1\u7b97\u516c\u5f0f\u7b80\u5355\u76f4\u89c2\uff0c\u5c31\u662f\u7edf\u8ba1\u4e24\u4e2a\u5b57\u7b26\u4e32\u4e2d\u4e0d\u540c\u4f4d\u7f6e\u7684\u5b57\u7b26\u6570\u76ee\u3002<\/p>\n<\/p>\n

[ d(P,Q) = \\sum_{i=1}^{n} I(p_i \\neq q_i) ]<\/p>\n<\/p>\n

\u5176\u4e2d ( I ) \u662f\u6307\u793a\u51fd\u6570\uff0c\u5f53 ( p_i \\neq q_i ) \u65f6\u53d6\u503c\u4e3a1\uff0c\u5426\u5219\u4e3a0\u3002<\/p>\n<\/p>\n

\u516d\u3001\u4f59\u5f26\u76f8\u4f3c\u5ea6<\/h3>\n<\/p>\n

\u4f3c\u5ea6\u7684\u6d4b\u91cf\u901a\u5e38\u4e0d\u662f\u7528\u8ddd\u79bb\u6765\u76f4\u63a5\u8861\u91cf\uff0c\u4f46\u5728\u5b9e\u8df5\u4e2d\uff0c\u53ef\u4ee5\u8fc2\u56de\u5730\u63ed\u793a\u6837\u672c\u95f4\u7684\u201c\u8ddd\u79bb\u201d\u3002\u4f59\u5f26\u76f8\u4f3c\u5ea6\u8861\u91cf\u7684\u662f\u4e24\u4e2a\u5411\u91cf\u5728\u65b9\u5411\u4e0a\u7684\u76f8\u4f3c\u7a0b\u5ea6\uff0c\u5176\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n

[ similarity = \\frac{P \\cdot Q}{|P| |Q|} = \\frac{\\sum_{i=1}^{n} p_i \\cdot q_i}{\\sqrt{\\sum_{i=1}^{n} p_i^2} \\cdot \\sqrt{\\sum_{i=1}^{n} q_i^2}} ]<\/p>\n<\/p>\n

\u4f59\u5f26\u76f8\u4f3c\u5ea6\u5728\u6587\u672c\u5206\u6790\u3001\u63a8\u8350\u7cfb\u7edf\u7b49\u9886\u57df\u5e94\u7528\u5e7f\u6cdb\u3002\u5f53\u8981\u8bc4\u4f30\u7684\u662f\u65b9\u5411\u7684\u76f8\u4f3c\u6027\u800c\u4e0d\u662f\u91cf\u7684\u5927\u5c0f\u65f6\uff0c\u4f59\u5f26\u76f8\u4f3c\u5ea6\u975e\u5e38\u6709\u6548\u3002<\/p>\n<\/p>\n

\u5728\u673a\u5668\u5b66\u4e60\u7684\u4e0d\u540c\u9886\u57df\u548c\u5e94\u7528\u4e2d\uff0c\u5408\u7406\u9009\u62e9\u548c\u5e94\u7528\u4e0a\u8ff0\u8ddd\u79bb\u8861\u91cf\u65b9\u6cd5\uff0c\u5bf9\u4e8e\u7b97\u6cd5\u7684\u6027\u80fd\u6709\u7740\u76f4\u63a5\u7684\u5f71\u54cd\u3002\u4e0d\u540c\u7684\u573a\u666f\u548c\u95ee\u9898\u7279\u5f81\u9700\u8981\u4e0d\u540c\u7684\u8ddd\u79bb\u8861\u91cf\u7b56\u7565\uff0c\u56e0\u6b64\u7406\u89e3\u8fd9\u4e9b\u8ddd\u79bb\u7684\u542b\u4e49\u53ca\u5176\u4f7f\u7528\u573a\u666f\u662f\u81f3\u5173\u91cd\u8981\u7684\u3002<\/p>\n<\/p>\n

\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

1. \u8ddd\u79bb\u662f\u5982\u4f55\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u8861\u91cf\u7684\uff1f<\/strong><\/p>\n

\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u8ddd\u79bb\u662f\u7528\u6765\u8861\u91cf\u6837\u672c\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u6216\u5dee\u5f02\u6027\u7684\u6307\u6807\u3002\u5e38\u7528\u7684\u8ddd\u79bb\u5ea6\u91cf\u65b9\u6cd5\u5305\u62ec\u6b27\u6c0f\u8ddd\u79bb\u3001\u66fc\u54c8\u987f\u8ddd\u79bb\u3001\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb\u7b49\u3002\u8fd9\u4e9b\u8ddd\u79bb\u5ea6\u91cf\u65b9\u6cd5\u80fd\u591f\u5728\u7279\u5f81\u7a7a\u95f4\u4e2d\u8ba1\u7b97\u6837\u672c\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u5e76\u5c06\u5176\u4f5c\u4e3a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u7684\u8f93\u5165\u3002<\/p>\n

2. \u6b27\u6c0f\u8ddd\u79bb\u548c\u66fc\u54c8\u987f\u8ddd\u79bb\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u6709\u4f55\u5e94\u7528\uff1f<\/strong><\/p>\n

\u6b27\u6c0f\u8ddd\u79bb\u548c\u66fc\u54c8\u987f\u8ddd\u79bb\u662f\u673a\u5668\u5b66\u4e60\u4e2d\u5e38\u7528\u7684\u8ddd\u79bb\u5ea6\u91cf\u65b9\u6cd5\u3002\u6b27\u6c0f\u8ddd\u79bb\u9002\u7528\u4e8e\u8fde\u7eed\u7279\u5f81\u7a7a\u95f4\uff0c\u8ba1\u7b97\u6837\u672c\u5728\u7279\u5f81\u7a7a\u95f4\u4e2d\u7684\u76f4\u7ebf\u8ddd\u79bb\uff1b\u66fc\u54c8\u987f\u8ddd\u79bb\u9002\u7528\u4e8e\u79bb\u6563\u7279\u5f81\u7a7a\u95f4\uff0c\u8ba1\u7b97\u6837\u672c\u5728\u7279\u5f81\u7a7a\u95f4\u4e2d\u7684\u57ce\u5e02\u8857\u533a\u8ddd\u79bb\u3002<\/p>\n

\u5728\u805a\u7c7b\u7b97\u6cd5\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u6b27\u6c0f\u8ddd\u79bb\u6216\u66fc\u54c8\u987f\u8ddd\u79bb\u6765\u8861\u91cf\u6837\u672c\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\uff0c\u4ece\u800c\u5c06\u76f8\u4f3c\u7684\u6837\u672c\u805a\u7c7b\u5728\u4e00\u8d77\u3002\u5728K\u8fd1\u90bb\u7b97\u6cd5\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u6b27\u6c0f\u8ddd\u79bb\u6216\u66fc\u54c8\u987f\u8ddd\u79bb\u6765\u5ea6\u91cf\u6d4b\u8bd5\u6837\u672c\u4e0e\u8bad\u7ec3\u6837\u672c\u4e4b\u95f4\u7684\u76f8\u4f3c\u7a0b\u5ea6\uff0c\u4ece\u800c\u627e\u5230\u8ddd\u79bb\u6d4b\u8bd5\u6837\u672c\u6700\u8fd1\u7684K\u4e2a\u90bb\u5c45\u3002<\/p>\n

3. \u9664\u4e86\u6b27\u6c0f\u8ddd\u79bb\u548c\u66fc\u54c8\u987f\u8ddd\u79bb\u5916\uff0c\u8fd8\u6709\u54ea\u4e9b\u8ddd\u79bb\u5ea6\u91cf\u65b9\u6cd5\u53ef\u4ee5\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u4f7f\u7528\uff1f<\/strong><\/p>\n

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