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class=\"size-large aligncenter\" src=\"http:\/\/zhangdi.dengxinbo.cn\/jieshi1.png\" width=\"300\" height=\"300\" \/><\/p>\n<p style=\"text-align: center\">\u56fe1\uff0c\u4f8b\u5b50\uff1a\u4e00\u4e2a\u4e8c\u7ef4\u76f4\u65b9\u56fe\u5bf9\u5e94\u7684\u4e8c\u7ef4\u6570\u7ec4<\/p>\n<\/blockquote>\n<p>\u8bf7\u770b\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u6765\u4e86\u89e3\u5982\u4f55\u505a\u53d8\u6362\u7684\u3002\u6709\u4e2a\u4e8c\u7ef4\u76f4\u65b9\u56fe\uff0c\u5305\u542b\u53d8\u91cfV<sub>0<\/sub>\uff08\u5bf9\u5e94\u56fe1\u7684X\u8f74\uff09\u548cV<sub>1<\/sub>\uff08\u5bf9\u5e94\u56fe1\u7684Y\u8f74\uff09\uff0c\u6bcf\u4e2a\u53d8\u91cf\u5404\u670915\u4e2abin\u3002\u53ef\u4ee5\u770b\u5230\u8fd9\u4e2a\u4e8c\u7ef4\u76f4\u65b9\u56fe\u4fdd\u5b58\u4e3a\u4e8c\u7ef4\u6570\u7ec4\u540e\uff0c\u5927\u591a\u6570\u6570\u636e\u9879\uff08\u65b9\u683c\uff09\u662f\u7a7a\u7684\uff08\u9891\u7387\u7b49\u4e8e0\uff09\u3002\u4e3a\u4e86\u964d\u4f4e\u6570\u636e\u5b58\u50a8\u5f00\u9500\uff0c\u6211\u4eec\u5148\u8ba1\u7b97V0\u53d8\u91cf\u7684bin\u7d22\u5f15bin[v<sub>0<\/sub>=0]\u5bf9\u5e94\u7684\u4e8c\u7ef4\u76f4\u65b9\u56fe\u6570\u636e\u9879\u4e4b\u548cA(v<sub>0<\/sub>=0)\u3002\u53c2\u4e0e\u8fd9\u4e2a\u8ba1\u7b97\u7684\u4e8c\u7ef4\u76f4\u65b9\u56fe\u6570\u636e\u9879\u5982\u4e0a\u56fe\u84dd\u6846\u6240\u793a\u3002\u7528\u516c\u5f0f\u8868\u8fbe\u5373A(v<sub>0<\/sub>=0) = \u2211f(v<sub>0<\/sub>=0\uff0cv1=i), i\u2208[0\uff0c14]\u3002\u5982\u679cA(v<sub>0<\/sub>=0) =0\uff0c\u5219\u4ece\u4e8c\u7ef4\u6570\u7ec4\u4e2d\u5220\u9664\u6240\u6709\u8fd9\u4e9b\u6570\u636e\u9879\u3002\u5426\u5219\uff0c\u6211\u4eec\u5411\u5b57\u5178\u4e2d\u63d2\u5165\u4e00\u4e2a\u65b0\u6761\u76ee\u3002\u4f9d\u6b21\u7c7b\u63a8\uff0c\u7b97\u5b8cV<sub>0<\/sub>\u53d8\u91cf\u7684\u5168\u90e8bin\u7d22\u5f15\u540e\uff0c\u518d\u7b97V<sub>1<\/sub>\u53d8\u91cf\u7684\u5168\u90e8bin\u7d22\u5f15\u3002\u6700\u7ec8\uff0c\u8f6c\u6362\u5b8c\u6210\u7684\u4e8c\u7ef4\u6570\u7ec4\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u53ea\u67095*5\u7684\u5927\u5c0f\uff0c\u662f\u539f\u59cb\u4e8c\u7ef4\u6570\u7ec4\u76841\/9\u3002<\/p>\n<blockquote><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large aligncenter\" src=\"http:\/\/zhangdi.dengxinbo.cn\/M0%20example.png\" width=\"129\" height=\"135\" \/><\/p>\n<p style=\"text-align: center\">\u56fe2\uff0c\u538b\u7f29\u540e\u7684\u4e8c\u7ef4\u6570\u7ec4<\/p>\n<\/blockquote>\n<p>4. \u5b57\u5178\u8868\u7684\u6784\u9020<\/p>\n<p>\u5728\u6570\u636e\u7a7a\u95f4\u8f6c\u6362\u4e4b\u540e\uff0c\u6211\u4eec\u5c06\u538b\u7f29\u540e\u7684\u591a\u7ef4\u6570\u7ec4\u8868\u793a\u4e3a\u7d22\u5f15\u548c\u9891\u7387\u5bf9\u7684\u96c6\u5408\uff0c\u5176\u4e2d\u6bcf\u4e2a\u952e\u503c\u5bf9\u5bf9\u5e94\u4e8e\u591a\u7ef4\u6570\u7ec4\u4e2d\u7684\u4e00\u4e2a\u975e\u7a7a\u6761\u76ee\u3002\u56fe2\u7684\u4f8b\u5b50\u5c31\u53ef\u4ee5\u8868\u793a\u6210\uff1a<\/p>\n<ul>\n<li>bin[v<sub>0<\/sub>=8, v<sub>1<\/sub> =1] : 7<\/li>\n<li>bin[v<sub>0<\/sub>=5, v<sub>1<\/sub> =4] : 6<\/li>\n<li>bin[v<sub>0<\/sub>=9, v<sub>1<\/sub>=4] : 3<\/li>\n<li>bin[v<sub>0<\/sub>=7,v<sub>1<\/sub>=6] : 6<\/li>\n<li>&#8230;&#8230;<\/li>\n<\/ul>\n<p>\u53ef\u4ee5\u770b\u51fa\u6b64\u96c6\u5408\u7684\u952e\u503c\u5bf9\u603b\u6570\u7b49\u4e8e\u591a\u7ef4\u6570\u7ec4\u4e2d\u975e0\u9879\u7684\u4e2a\u6570\u3002\u6b64\u96c6\u5408\u53ef\u4ee5\u65e0\u635f\u5730\u8f6c\u6362\u4e3a\u539f\u59cb\u7684\u591a\u7ef4\u6570\u7ec4\u3002\u8fd9\u4e2a\u96c6\u5408\u5c31\u662f\u6211\u4eec\u7684\u6570\u636e\u8f6c\u6362\u5b57\u5178\u8868\u3002<strong>\u6c42\u5b57\u5178\u8868\u7684\u8ba1\u7b97\u8fc7\u7a0b\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u8981\u5c06\u539f\u59cb\u7684\u591a\u7ef4\u6570\u7ec4\u4e2d\u975e\u96f6\u9879\u53d6\u51fa\uff0c\u7ec4\u6210\u5982\u56fe3\u4e0b\u6240\u793a\u7684\u952e\u503c\u5bf9\u5373\u53ef\u3002<\/strong><\/p>\n<blockquote><p><img loading=\"lazy\" decoding=\"async\" class=\"size-large aligncenter\" src=\"http:\/\/zhangdi.dengxinbo.cn\/histogram3.png\" width=\"135\" height=\"248\" \/><\/p>\n<p style=\"text-align: center\">\u56fe3\uff0c\u5b57\u5178\u8868\u4e2d\u7d22\u5f15\u7684\u8868\u793a\u65b9\u6cd5<\/p>\n<\/blockquote>\n<p>\u5728\u5b57\u5178\u8868\u4e2d\uff0c\u53ef\u4ee5\u628a\u6307\u793a\u591a\u4e2a\u53d8\u91cf\u7684\u7d22\u5f15\u7684\u6570\u503c\u653e\u5728\u4e00\u8d77\uff0c\u53ea\u8981\u6211\u4eec\u77e5\u9053\u90a3\u51e0\u4f4d\u8868\u793a\u7684\u662f\u54ea\u4e2a\u53d8\u91cf\u5c31\u884c\u3002\u8fd8\u662f\u4e4b\u524d\u7684\u4e8c\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684\u4f8b\u5b50\uff0c\u5176\u5b57\u5178\u8868\u5982\u56fe3\u4e0a\u6240\u793a\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u7d22\u5f15\u503c\u8f6c\u6362\u4e3a\u4e8c\u8fdb\u5236\uff0c\u5bf9\u5e94\u4e8e\u7b2c\u4e00\u4e2a\u53d8\u91cf\u7684\u4f4d\u88ab\u6d82\u6210\u7ea2\u8272\uff0c\u5bf9\u5e94\u4e8e\u7b2c\u4e8c\u4e2a\u53d8\u91cf\u7684\u4f4d\u88ab\u6d82\u6210\u7eff\u8272\uff0c\u5982\u56fe3\u4e0b\u534a\u90e8\u5206\u6240\u793a\u3002\u8fd9\u6837\u770b\u8d77\u6765\u66f4\u660e\u663e\uff0c\u4e5f\u66f4\u65b9\u4fbf\u8ba1\u7b97\uff1a\u6211\u4eec\u53ef\u4ee5\u64cd\u7eb5\u8fd9\u4e9b\u4f4d\u6765\u64cd\u4f5c\u4e0d\u540c\u53d8\u91cf\u7684bin\u7d22\u5f15\uff0c\u4ece\u800c\u8ba1\u7b97\u8fb9\u7f18\u5206\u5e03\uff0c\u6761\u4ef6\u5206\u5e03\u3002<\/p>\n<h2>\u00a0\u4e09\u3001\u57fa\u4e8e\u591a\u7ef4\u76f4\u65b9\u56fe\u538b\u7f29\u5b58\u50a8\u6cd5\u7684\u67e5\u8be2\u64cd\u4f5c<\/h2>\n<p>1. \u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684\u8fb9\u7f18\u5316\u8fd0\u7b97\uff08Histogram Marginalization\uff09<\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Marginal_distribution\"><b>\u8fb9\u7f18\u5206\u5e03<\/b>\uff08Marginal Distribution\uff09<\/a>\u6307\u5728<a href=\"https:\/\/baike.baidu.com\/item\/%E6%A6%82%E7%8E%87%E8%AE%BA\" target=\"_blank\" rel=\"noopener\">\u6982\u7387\u8bba<\/a>\u7684\u591a\u7ef4\u968f\u673a\u53d8\u91cf\u4e2d\uff0c\u53ea\u5305\u542b\u5176\u4e2d\u90e8\u5206\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\uff0c\u672c\u8d28\u4e00\u79cd\u964d\u7ef4\u64cd\u4f5c\u3002\u8003\u8651\u5230\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u76f8\u5f53\u4e8e\u591a\u4e2a\u53d8\u91cf\u7684\u8054\u5408\u5206\u5e03\u77e9\u9635\uff0c\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684\u8fb9\u7f18\u5316\u8fd0\u7b97\u5c31\u662f\u8ba1\u7b97\u5176\u90e8\u5206\u53d8\u91cf\u7684\u8fb9\u7f18\u5206\u5e03\uff0c\u4e5f\u5c31\u662f\u5305\u542b\u5176\u90e8\u5206\u53d8\u91cf\u7684\u5b50\u96c6\u3002\u4e3a\u4e86\u6784\u9020\u8fd9\u4e2a\u65b0\u7684\u76f4\u65b9\u56fe\uff0c\u6211\u4eec\u5c06\u9884\u5148\u5b58\u50a8\u7684\u591a\u53d8\u91cf\u67f1\u72b6\u56fe\u8fb9\u7f18\u5316\u5230\u7528\u6237\u6ca1\u6709\u9009\u62e9\u7684\u53d8\u91cf\u4e0a\u3002<\/p>\n<p>\u5047\u8bbe\u539f\u76f4\u65b9\u56fe\u6d89\u53ca\u56db\u4e2a\u53d8\u91cfA\u3001B\u3001C\u548cD\uff0c\u7528\u6237\u5bf9B\u548cD\u7684\u67f1\u72b6\u56fe\u611f\u5174\u8da3\uff0c\u60f3\u8ba1\u7b97\u53ea\u5305\u542bB\u548cD\u7684\u5b50\u76f4\u65b9\u56fe\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u53d8\u91cfA\u548cC\u4e0a\u7684\u591a\u53d8\u91cf\u76f4\u65b9\u56fe\u8fb9\u7f18\u5316\uff0c\u5373\uff1a<\/p>\n<p>P(B=b\uff0cD=d) = \u2211<sub>a<\/sub>\u2211<sub>c<\/sub> P(A=a\uff0cB=b\uff0cC=c\uff0cD=d)\u3002<\/p>\n<p>\u57fa\u4e8e\u4e0a\u6587\u63cf\u8ff0\u7684\u591a\u7ef4\u76f4\u65b9\u56fe\u538b\u7f29\u5b58\u50a8\u6cd5\uff0c\u5b57\u5178\u8868\u7d22\u5f15\u4e2d\u7684\u4e0d\u540c\u4f4d\u5bf9\u5e94\u4e8e\u4e0d\u540c\u53d8\u91cf\u7684bin\u7d22\u5f15\uff0c\u56e0\u6b64\u53ef\u4ee5\u4f7f\u7528\u6309\u4f4d\u4e0e\u8fd0\u7b97\uff0c\u7136\u540e\u4f7f\u7528\u9891\u7387\u548c\uff0c\u8f7b\u677e\u5730\u6267\u884c\u67f1\u72b6\u56fe\u8fb9\u7f18\u5316\u64cd\u4f5c\u3002\u4e0d\u9700\u8981\u5bf9\u7d22\u5f15\u8fdb\u884c\u89e3\u7801\u5c06\u8f6c\u6362\u540e\u7684bin\u7d22\u5f15\u6620\u5c04\u5230\u539f\u59cbbin\u7d22\u5f15\u3002<\/p>\n<blockquote><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large aligncenter\" src=\"http:\/\/zhangdi.dengxinbo.cn\/histogram4.png\" width=\"506\" height=\"212\" \/><\/p>\n<p style=\"text-align: center\">\u56fe4 \u6c42\u53ea\u5305\u542b\u53d8\u91cfB\u548cD\u7684\u5b50\u76f4\u65b9\u56fe<\/p>\n<\/blockquote>\n<p>\u5177\u4f53\u64cd\u4f5c\u8fc7\u7a0b\uff1a\u5305\u542b\u56db\u4e2a\u53d8\u91cfA\uff0cB\uff0cC\uff0cD\u7684\u591a\u7ef4\u76f4\u65b9\u56fe\u7684\u5b57\u5178\u8868\u5982\u56fe4(1)\u6240\u793a\u3002\u6bcf\u4e2a\u53d8\u91cf\u5bf9\u5e94\u4e24\u4f4d\u7684\u4e8c\u8fdb\u5236\u7d22\u5f15\u3002\u6211\u4eec\u8981\u6c42\u53ea\u5305\u542bB\u548cD\u7684\u5b50\u76f4\u65b9\u56fe\u3002\u53ef\u4ee5\u901a\u8fc7\u5c06\u7528\u6237\u672a\u9009\u62e9\u7684\u53d8\u91cf\u5bf9\u5e94\u7684\u4f4d\u8bbe\u7f6e\u4e3a0\uff0c\u7136\u540e\u6c42\u5177\u6709\u76f8\u540c\u7d22\u5f15\u7684\u9891\u7387\u4e4b\u548c\u6765\u5b8c\u6210\u8fb9\u7f18\u5316\u3002\u8fd9\u4e00\u6b65\u53ef\u4ee5\u7528\u8ba1\u7b97\u673a\u7684\u65b9\u6cd5\u6765\u505a\uff1a<\/p>\n<ul>\n<li>\u8bbe\u7f6e\u4e00\u4e2a\u63a9\u7801\uff0c\u8981\u53d6\u7684\u53d8\u91cfbit\u8bbe\u4e3a1\uff0c\u672a\u9009\u7684\u53d8\u91cfbit\u8bbe\u4e3a0\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u91ccABCD\u56db\u4e2a\u53d8\u91cf\u53d6B\u548cD\uff0c\u5219\u63a9\u7801\u4e3a00110011\uff0c\u5982\u56fe4(2)\u6240\u793a\uff1b<\/li>\n<li>\u7136\u540e\u8be5\u63a9\u7801\u4e0e\u5404\u4e2a\u53d8\u91cf\u7684\u7d22\u5f15bit\u4f4d\u6309\u4f4d\u4e0e\uff0c\u7ed3\u679c\u5982\u56fe4(3)\u6240\u793a\uff1b<\/li>\n<li>\u5c06\u56fe4(3)\u7684\u7ed3\u679c\uff0c\u5c06\u5176\u4e2d\u5177\u6709\u76f8\u540c\u7d22\u5f15bit\u4f4d\u5bf9\u5e94\u7684\u9891\u7387\u52a0\u8d77\u6765\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u8fb9\u7f18\u5206\u5e03\u7ed3\u679c\uff0c\u5982\u56fe4(4)\u6240\u793a\u3002<\/li>\n<\/ul>\n<p>2. \u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684bin\u5408\u5e76\u8fd0\u7b97\uff08Histogram Bin Merge\uff09<\/p>\n<p>\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684bin\u5408\u5e76\uff0c\u662f\u76f8\u90bb\u4ed3\u4f4d\u4e2d\u7684\u9891\u7387\u6cbf\u67d0\u4e9b\u7ef4\u5ea6\u8fdb\u884c\u7ec4\u5408\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u5177\u6709\u4e0d\u540c\u79bb\u6563\u5316\u6c34\u5e73\u7684\u76f4\u65b9\u56fe\u3002\u5f53\u67d0\u4e9b\u5206\u6790\u4efb\u52a1\u9700\u8981\u4e0d\u540c\u5206\u8fa8\u7387\u7684\u76f4\u65b9\u56fe\u65f6\uff08\u5206\u8fa8\u7387\u53ef\u4ee5\u76f4\u89c2\u5730\u7406\u89e3\u4e3abin\u7684\u5c3a\u5bf8\uff09\uff0c\u4f7f\u7528\u6b64\u64cd\u4f5c\u3002<\/p>\n<p>\u6211\u4eec\u5047\u8bbe\u9884\u5148\u8ba1\u7b97\u7684\u591a\u53d8\u91cf\u76f4\u65b9\u56fe\u662f\u4ee5\u6700\u9ad8\u5206\u8fa8\u7387\uff08\u6700\u5c0fbin\u7684\u5c3a\u5bf8\uff09\u5b9a\u4e49\u7684\u3002\u4e3a\u4e86\u65b9\u4fbf\u8d77\u89c1\uff0c\u5728\u6570\u636e\u7a7a\u95f4\u8f6c\u6362\u4e4b\u524d\uff0c\u6bcf\u4e2a\u53d8\u91cf\u7684bin\u4e2a\u6570\u8bbe\u7f6e\u4e3a2\u7684\u5e42\u3002\u5047\u8bbe\u5177\u67094\u4e2a\u53d8\u91cf\u7684\u9ad8\u5206\u8fa8\u7387\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u5728\u6570\u636e\u7a7a\u95f4\u8f6c\u6362\u524d\u7684bin\u6570\u4e3a2<sup>K1<\/sup>\u30012<sup>K2<\/sup>\u30012<sup>K3<\/sup>\u30012<sup>K4<\/sup>\uff0c\u5176\u4e2dK1=K2=K3=K4=4\uff0c\u4e5f\u5c31\u662fbin\u6570\u5747\u4e3a16\u3002\u8981\u6c42\u5bf9\u8fd9\u56db\u4e2a\u53d8\u91cf\u6309\u7167\u6bcf\u7ec4\u5305\u542b2<sup>1<\/sup>\u30012<sup>2<\/sup>\u30012<sup>1<\/sup>\u30012<sup>0<\/sup>\u4e2abin\u8fdb\u884cbin\u5408\u5e76\u3002\u6700\u7ec8\u8ba1\u7b97\u51fa\u65b0\u7684\u4f4e\u5206\u8fa8\u7387\u76f4\u65b9\u56fe\uff0c\u6bcf\u4e2a\u53d8\u91cf\u5e94\u5177\u67092<sup>K1-1<\/sup>=8\u30012<sup>K2-2<\/sup>=4\u30012<sup>K3-1<\/sup>=8\u30012<sup>Kn-0<\/sup>=16\u4e2abin\u3002<\/p>\n<blockquote><p><img decoding=\"async\" class=\"alignleft\" src=\"http:\/\/zhangdi.dengxinbo.cn\/histogram5.png\" \/><\/p>\n<p style=\"text-align: left\">\u56fe5\uff0c\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684bin\u5408\u5e76\u8fd0\u7b97\u4f8b\u5b50<\/p>\n<\/blockquote>\n<p>\u5bf9\u4e8e\u8fd9\u4e2a\u8981\u6c42\uff0c\u7528\u6237\u9700\u8981\u63d0\u4f9b\u4e00\u4e2a4\u7ef4\u5411\u91cf L={1,2,1,0}, \u4ee3\u8868\u6bcf\u4e2a\u7ef4\u5ea6\u4e0bbin\u5408\u5e76\u7684\u6307\u6807\u3002\u5177\u4f53\u7684bin\u5408\u5e76\u8ba1\u7b97\uff0c\u9700\u8981\u5148\u89e3\u7801bin\u7d22\u5f15\uff0c\u518d\u8fdb\u884c\u64cd\u4f5c\u3002\u5bf9\u4e8ebin\u5c3a\u5bf8\u4e0d\u53d8\u5316\u7684\u7ef4\u5ea6\uff0c\u4e5f\u5c31\u662fLi=0\u7684\u7ef4\u5ea6\uff0c\u5219\u4e0d\u9700\u8981\u89e3\u7801bin\u7d22\u5f15\u3002\u5728\u672c\u4f8b\u4e2d\u53ea\u6709A\uff0cB\uff0cC\u4e09\u4e2a\u5c3a\u5ea6\u9700\u8981\u89e3\u7801\uff0cD\u4e0d\u9700\u8981\u3002\u4f8b\u5b50\u76f4\u65b9\u56fe\u7684\u5b57\u5178\u8868\u5982\u56fe5(1)\u6240\u793a\u3002\u89e3\u7801bin\u7d22\u5f15\u540e\u7684\u7ed3\u679c\u5982\u56fe5(2)\u6240\u793a\u3002\u63a5\u4e0b\u6765\u7684\u64cd\u4f5c\u4e0e\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684\u8fb9\u7f18\u5316\u8fd0\u7b97\u4e00\u6837\uff0c\u53ea\u662f\u4f7f\u7528\u7684\u4f4d\u63a9\u7801\u4e0d\u540c\u3002\u4f4d\u63a9\u7801\u7684\u8ba1\u7b97\u65b9\u5f0f\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n<blockquote><p><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/zhangdi.dengxinbo.cn\/%E6%8E%A9%E7%A0%81%E7%9A%84%E8%AE%A1%E7%AE%97%E6%96%B9%E5%BC%8F.png\" \/><\/p>\n<p style=\"text-align: center\">\u56fe6\uff0c\u63a9\u7801\u7684\u8ba1\u7b97\u65b9\u5f0f<\/p>\n<\/blockquote>\n<p>\u5c06\u63a9\u7801\u4e0e\u89e3\u7801\u540e\u7684bin\u7d22\u5f15\u6309\u4f4d\u4e0e\uff0c\u7ed3\u679c\u5982\u56fe5(4)\u6240\u793a\u3002\u63a5\u4e0b\u6765\u5c06\u5177\u6709\u76f8\u540c\u7d22\u5f15\u7684\u9891\u7387\u52a0\u8d77\u6765\uff0c\u5f97\u5230\u6700\u7ec8\u7ed3\u679c\uff0c\u5982\u56fe5(5)\u6240\u793a\u3002<\/p>\n<p>3. \u6761\u4ef6\u76f4\u65b9\u56fe\u7684\u8fd0\u7b97\uff08Conditional Histogram\uff09<\/p>\n<p>\u8ba1\u7b97\u6761\u4ef6\u76f4\u65b9\u56fe\u5c31\u662f\u8ba1\u7b97<a href=\"https:\/\/blog.csdn.net\/thither_shore\/article\/details\/52192553\">\u6761\u4ef6\u5206\u5e03<\/a>\uff0c\u662f\u8ba1\u7b97\u6761\u4ef6\u71b5\u7684\u5173\u952e\u3002<\/p>\n<p>\u7ed9\u5b9an\u4e2a\u53d8\u91cf\u7684\u53d8\u91cf\u96c6V=V<sub>0<\/sub>\uff0cV<sub>1<\/sub>\uff0c\u2026\uff0cV<sub>n-1<\/sub>\uff0cV\u6709\u4e00\u4e2a\u5b50\u96c6U <span class=\"fontstyle0\">\u2282 <\/span><span class=\"fontstyle2\">V\uff0c<\/span>\u00a0\u548c\u53e6\u4e00\u4e2a\u5b50\u96c6W\u2208(V-U)\u3002\u6761\u4ef6\u76f4\u65b9\u56fe\u7684\u8fd0\u7b97\uff0c\u662f\u8ba1\u7b97W\u4e2d\u7684\u53d8\u91cf\u5728\u7279\u5b9a\u7684bin\u8303\u56f4\u4e0b\u5728U\u4e2d\u7684\u5206\u5e03\u3002\u5f53\u7528\u6237\u8981\u7814\u7a76\u4e00\u7ec4\u53d8\u91cfU\u548c\u53e6\u4e00\u7ec4\u53d8\u91cfW\u4e4b\u95f4\u7684\u5173\u7cfb\u5f0f\uff0c\u6761\u4ef6\u76f4\u65b9\u56fe\u662f\u6709\u7528\u7684\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97P(U|W)\u7684\u71b5\uff0c\u5b83\u8868\u793a\u5728\u7279\u5b9a\u503c\u7684\u8303\u56f4\u5185\uff0c\u7ed9\u5b9aW\u4e2d\u7684\u53d8\u91cf\uff0cU\u7684\u4e0d\u786e\u5b9a\u6027\u3002<\/p>\n<p>\u8ba1\u7b97\u6761\u4ef6\u67f1\u72b6\u56fe\u7684\u7b2c\u4e00\u6b65\u662f\u4e3aw\u4e2d\u7684\u53d8\u91cf\u9009\u62e9\u5c5e\u4e8e\u7279\u5b9abin\u8303\u56f4\u7684\u6240\u6709\u6761\u76ee\u3002\u5bf9\u4e8e\u6b64\u9009\u62e9\u6b65\u9aa4\uff0c\u6211\u4eec\u9700\u8981\u5bf9w\u4e2d\u7684\u53d8\u91cf\u8fdb\u884c\u89e3\u7801\uff0c\u4ee5\u83b7\u5f97\u5176\u539f\u59cbbin\u7d22\u5f15\u3002\u7136\u540e\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u9009\u5b9a\u7684\u6761\u76ee\uff0c\u4f7f\u7528\u4f4d\u63a9\u7801\u6267\u884c\u903b\u8f91\u4e0e\u64cd\u4f5c\uff0c\u4ee5\u5c06\u4e0eU\u4e2d\u7684\u53d8\u91cf\u4e0d\u5bf9\u5e94\u7684\u6240\u6709\u4f4d\u8bbe\u7f6e\u4e3a0\u3002\u901a\u8fc7\u5bf9\u5177\u6709\u76f8\u540c\u7d22\u5f15\u7684\u6761\u76ee\u7684\u9891\u7387\u6c42\u548c\u6765\u8ba1\u7b97\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n<p>\u4e5f\u662f\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u5177\u4f53\u7684\u4f8b\u5b50\uff1a\u6709\u4e00\u4e2a\u5177\u4f53\u76844\u7ef4\u76f4\u65b9\u56fe\uff0c\u5305\u542bA\uff0cB\uff0cC\uff0cD\uff0c\u56db\u4e2a\u53d8\u91cf\uff0c\u6bcf\u4e2a\u53d8\u91cf\u670916\u4e2abin\u3002\u5176\u5b57\u5178\u8868\u5982\u56fe7(1)\u6240\u793a\u3002\u5047\u8bbeU\u5305\u542b\u4e24\u4e2a\u53d8\u91cfB\u548cC\uff0cW\u5305\u542b\u4e24\u4e2a\u53d8\u91cfA\u548cD\u3002A\u7684\u6570\u503c\u8303\u56f4\u662f(min<sub>A<\/sub>, max<sub>A<\/sub>)\uff0cD\u7684\u6570\u503c\u8303\u56f4\u662f(min<sub>D<\/sub>, max<sub>D<\/sub>)\uff0c\u8fd9\u6761\u4ef6\u76f4\u65b9\u56fe\u7684\u67e5\u8be2\u64cd\u4f5c\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<p>P(bin(B)=b, bin(C)=c |\u00a0 min<sub>A<\/sub>\u00a0 <span class=\"fontstyle0\">\u2264 <\/span>bin(A) <span class=\"fontstyle0\">\u2264 max<sub>A<\/sub>\u00a0,\u00a0min<sub>D<\/sub>\u00a0 \u2264 bin(D) \u2264 max<sub>D<\/sub>\u00a0<\/span>) =\u00a0 \u2211<sub>a=minA<\/sub>\u2211<sub>d=minD<\/sub> P(bin(A)=a, bin(B)=b, bin(C)=c, bin(D)=d)<\/p>\n<blockquote><p><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/zhangdi.dengxinbo.cn\/histogram6.png\" \/><\/p>\n<p style=\"text-align: center\">\u56fe7\uff0c\u6761\u4ef6\u76f4\u65b9\u56fe\u7684\u8fd0\u7b97\u793a\u4f8b<\/p>\n<\/blockquote>\n<p>\u73b0\u5728\u8981\u6c42\u67e5\u8be2 <span class=\"fontstyle0\">P<\/span><span class=\"fontstyle1\">(<\/span><span class=\"fontstyle0\">A<\/span><span class=\"fontstyle2\">|<\/span><span class=\"fontstyle3\">11 <\/span><span class=\"fontstyle2\">\u2264 <\/span><span class=\"fontstyle0\">bin<\/span><span class=\"fontstyle1\">(<\/span><span class=\"fontstyle0\">C<\/span><span class=\"fontstyle1\">) <\/span><span class=\"fontstyle2\">\u2264 <\/span><span class=\"fontstyle3\">15<\/span><span class=\"fontstyle1\">)<\/span>\u00a0\u3002\u6211\u4eec\u9996\u5148\u5c06C\u7684bin\u7d22\u5f15\u89e3\u7801\uff0c\u83b7\u5f97\u539f\u59cb\u7684bin\u7d22\u5f15\uff0c\u7136\u540e\u9009\u5b9a<span class=\"fontstyle3\">11 <\/span><span class=\"fontstyle2\">\u2264 <\/span><span class=\"fontstyle0\">bin<\/span><span class=\"fontstyle1\">(<\/span><span class=\"fontstyle0\">C<\/span><span class=\"fontstyle1\">) <\/span><span class=\"fontstyle2\">\u2264 <\/span><span class=\"fontstyle3\">15\u8303\u56f4\u5185\u7684\u9891\u7387\uff0c\u5982\u56fe7(2)\u7eff\u8272\u90e8\u5206\u6240\u793a\u3002\u63a5\u4e0b\u6765\u8bbe\u7f6e\u63a9\u7801\uff0c\u63a9\u7801\u53ea\u6709\u8981\u67e5\u8be2\u7684A\u53d8\u91cf\u7d22\u5f15\u4f4d\u662f1\uff0c\u5176\u4ed6\u4e0d\u67e5\u8be2\u7684\u53d8\u91cf\u5bf9\u5e94\u7684\u7d22\u5f15\u4f4d\u90fd\u662f0\uff0c\u5982\u56fe7(3)\u6240\u793a\u3002\u63a5\u4e0b\u6765\u5c06\u56fe7(2)\u9009\u5b9a\u7684\u7eff\u8272\u9879\u4e0e\u63a9\u7801\u6309\u4f4d\u4e0e\uff0c\u5e76\u5c06\u76f8\u540cbin\u7d22\u5f15\u7684\u9891\u7387\u6c42\u548c\u3002\u7ed3\u679c\u5982\u56fe7(5)\u6240\u793a\u3002\u5728\u6570\u636e\u7a7a\u95f4\u8f6c\u6362\u5b8c\u6bd5\u540e\uff0c\u6bcf\u4e2a\u53d8\u91cf\u67094\u4e2abin\u3002<\/span><\/p>\n<p>\u65f6\u5e8f\u76f4\u65b9\u56fe(Time Histogram)<\/p>\n<p>\u5bf9\u4e8e\u65f6\u53d8\u591a\u53d8\u91cf\u6570\u636e\uff0c\u6211\u4eec\u5c06\u65f6\u95f4\u6b65\u6570\uff08time step\uff09\u89c6\u4e3a\u53e6\u4e00\u4e2a\u53d8\u91cf\uff0c\u5e76\u5c06bin\u6570\u8bbe\u7f6e\u4e3a\u65f6\u95f4\u6b65\u6570\u3002\u67e5\u8be2\u7684\u65f6\u5e8f\u76f4\u65b9\u56fe\u6709\u52a9\u4e8e\u663e\u793a\u6b64\u9009\u5b9a\u6570\u636e\u5757\u4e2d\u968f\u65f6\u95f4\u663e\u793a\u7684\u529f\u80fd\u3002\u65f6\u5e8f\u76f4\u65b9\u56fe\u67e5\u8be2\u4e0e\u76f4\u65b9\u56fe\u8fb9\u7f18\u5316\u67e5\u8be2\u7c7b\u4f3c\uff0c\u53ea\u662f\u53ef\u53d8\u65f6\u95f4\u6b65\u957f\u5fc5\u987b\u5305\u542b\u5728\u8fb9\u7f18\u53d8\u91cf\u4e2d\u3002\u5728\u67e5\u8be2\u8fc7\u7a0b\u4e2d\uff0c\u7528\u6237\u6307\u5b9a\u7528\u4e8e\u8ba1\u7b97\u65f6\u95f4\u67f1\u72b6\u56fe\u7684\u53d8\u91cf\u548c\u6570\u636e\u5757\u3002\u53d8\u91cf\u65f6\u95f4\u6b65\u5fc5\u987b\u5305\u542b\u5728\u8fd9\u4e9b\u9009\u5b9a\u53d8\u91cf\u4e2d\uff0c\u7136\u540e\u67e5\u8be2\u7684\u5176\u4f59\u90e8\u5206\u4e0e\u67f1\u72b6\u56fe\u8fb9\u7f18\u5316\u67e5\u8be2\u76f8\u540c\u3002<\/p>\n<h2>\u00a0\u56db\u3001\u603b\u7ed3<\/h2>\n<p>\u4ee5\u4e0a\u4ecb\u7ecd\u4e86\u4e00\u79cd\u591a\u53d8\u91cf\u8054\u5408\u76f4\u65b9\u56fe\u7684\u591a\u7ef4\u6570\u7ec4\u538b\u7f29\u5b58\u50a8\u6cd5\uff0c\u4ee5\u53ca\u4f7f\u7528\u8fd9\u79cd\u5b58\u50a8\u65b9\u6cd5\u5982\u4f55\u8fdb\u884c\u7684\u67e5\u8be2\u64cd\u4f5c\uff1a\u5305\u62ec\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684\u8fb9\u7f18\u5316\u8fd0\u7b97\uff0c\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684bin\u5408\u5e76\u8fd0\u7b97\uff0c\u6761\u4ef6\u76f4\u65b9\u56fe\u7684\u8fd0\u7b97\uff0c\u548c\u65f6\u5e8f\u76f4\u65b9\u56fe\u3002\u53ef\u4ee5\u770b\u5230\u6587\u4e2d\u6240\u793a\u7684\u538b\u7f29\u5b58\u50a8\u6cd5\uff0c\u4e0d\u4ec5\u53ef\u4ee5\u51cf\u5c0f\u7a7a\u95f4\u6d88\u8017\uff0c\u540c\u65f6\u4e5f\u652f\u6301\u591a\u79cd\u8fd0\u7b97\u3002<\/p>\n<p>\u56de\u987e\u4e00\u4e0b\u6211\u4eec\u7684\u5206\u6790\u8def\u5f84\uff1a<\/p>\n<ul>\n<li>\u5982\u4f55\u5728\u4e00\u4e2a\u591a\u7ef4\u6570\u636e\u96c6\u4e2d\u627e\u5230\u6700\u5177\u4ee3\u8868\u6027\u7684\u6570\u636e\u7ef4\u5ea6\uff1f<\/li>\n<li>\u53ef\u4ee5\u7528\u4fe1\u606f\u8bba\u65b9\u6cd5\uff0c\u9009\u62e9\u5177\u6709\u6700\u5927\u4fe1\u606f\u589e\u76ca\u7684\u6570\u636e\u7ef4\u5ea6\u3002<\/li>\n<li>\u5982\u4f55\u8ba1\u7b97\u4fe1\u606f\u589e\u76ca\uff1f\u9700\u8981\u8ba1\u7b97\u8054\u5408\u71b5\u548c\u6761\u4ef6\u71b5\u3002<\/li>\n<li>\u5982\u4f55\u8ba1\u7b97\u8054\u5408\u71b5\u548c\u6761\u4ef6\u71b5\uff1f\u9700\u8981\u8ba1\u7b97\u8054\u5408\u6982\u7387\u5206\u5e03\u3002<\/li>\n<li>\u5982\u4f55\u8ba1\u7b97\u8054\u5408\u6982\u7387\u5206\u5e03\uff1f\u53ef\u4ee5\u7528\u76f4\u65b9\u56fe\u505a\u62df\u5408\u3002<\/li>\n<li>\u591a\u53d8\u91cf\u8054\u5408\u76f4\u65b9\u56fe\u5982\u4f55\u8868\u793a\u548c\u8ba1\u7b97\uff1f\u53ef\u4ee5\u7528\u591a\u7ef4\u6570\u7ec4\u3002<\/li>\n<li>\u591a\u7ef4\u6570\u7ec4\u8868\u793a\u591a\u53d8\u91cf\u76f4\u65b9\u56fe\uff0c\u5176\u7a7a\u95f4\u6d88\u8017\u5448\u6307\u6570\u578b\u4e0a\u5347\uff0c\u4e0d\u4fbf\u4e8e\u5b58\u50a8\u548c\u8ba1\u7b97\uff0c\u600e\u4e48\u529e\uff1f\u53ef\u4ee5\u7528\u538b\u7f29\u7684\u4e8c\u7ef4\u6570\u7ec4\u5b58\u50a8\u6cd5\u3002<\/li>\n<li>\u6709\u4e86\u538b\u7f29\u7684\u4e8c\u7ef4\u6570\u7ec4\u5b58\u50a8\u6cd5\uff0c\u5982\u4f55\u8ba1\u7b97\u8054\u5408\u71b5\u548c\u6761\u4ef6\u71b5\uff1f\u4e0b\u4e00\u8282\u6211\u4eec\u5c31\u5177\u4f53\u8bb2\u8fd9\u4e2a\u3002<\/li>\n<\/ul>\n<p>\u53c2\u8003\u6587\u732e\uff1a<\/p>\n<p>Lu, K. and H.W. Shen. A compact multivariate histogram representation for query-driven visualization. 2015.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7ad9\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u89d2\u5ea6\uff0c\u591a\u7ef4\u8054\u5408\u76f4\u65b9\u56fe\u7684\u4e00<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[70,130],"class_list":["post-2019","post","type-post","status-publish","format-standard","hentry","category-data-visualization","tag-70","tag-130"],"_links":{"self":[{"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/posts\/2019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2019"}],"version-history":[{"count":0,"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/posts\/2019\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2019"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.divis.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}