{"id":14554,"date":"2023-03-05T19:35:36","date_gmt":"2023-03-05T11:35:36","guid":{"rendered":"http:\/\/139.9.1.231\/?p=14554"},"modified":"2024-08-12T15:24:10","modified_gmt":"2024-08-12T07:24:10","slug":"vector-quantization-vqvae","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2023\/03\/05\/vector-quantization-vqvae\/","title":{"rendered":"Vector Quantization \u77e2\u91cf\u91cf\u5316 [VQVAE]"},"content":{"rendered":"\n<p class=\"has-text-align-center has-light-pink-background-color has-background\"><strong><em><a href=\"http:\/\/www.mqasem.net\/vectorquantization\/vq.html\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/www.mqasem.net\/vectorquantization\/vq.html<\/a><\/em><\/strong><\/p>\n\n\n\n<p>      <strong>VQ<\/strong>, \u5373<strong>Vector Quantization<\/strong>\uff0c\u77e2\u91cf\u91cf\u5316\uff0c\u5728\u591a\u4e2a\u573a\u666f\u4e0b\u4f7f\u7528\uff0c\u5982\u56fe\u50cf\u538b\u7f29\uff0c\u58f0\u97f3\u538b\u7f29\uff0c\u8bed\u97f3\u8bc6\u522b\u7b49\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center has-bright-blue-background-color has-background\"><strong><em>Github: <a href=\"https:\/\/github.com\/lucidrains\/vector-quantize-pytorch\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/github.com\/lucidrains\/vector-quantize-pytorch<\/a><\/em><\/strong><\/p>\n\n\n\n<p>       \u77e2\u91cf\u91cf\u5316\u65b9\u6cd5\uff0c\u5373Vector Quantization\uff0c\u5176\u5177\u4f53\u5b9a\u4e49\u4e3a\uff1a\u5c06\u4e00\u4e2a\u5411\u91cf\u7a7a\u95f4\u4e2d\u7684\u70b9\u7528\u5176\u4e2d\u7684\u4e00\u4e2a\u6709\u9650\u5b50\u96c6\u6765\u8fdb\u884c\u7f16\u7801\u7684\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p class=\"has-light-gray-background-color has-background\"><strong>\u4ec0\u4e48\u662fVQ?<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-1024x471.png\" alt=\"\" class=\"wp-image-14568\" width=\"570\" height=\"262\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-1024x471.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-300x138.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-768x353.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image.png 1028w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/figure><\/div>\n\n\n\n<p>        \u4f5c\u4e3a\u793a\u4f8b\uff0c\u6211\u4eec\u5728\u4e0d\u5931\u4e00\u822c\u6027\u7684\u60c5\u51b5\u4e0b\u91c7\u7528\u4e8c\u7ef4\u60c5\u51b5\u4e0b\u7684\u5411\u91cf\u3002 \u56fe 1 \u663e\u793a\u4e86\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e9b\u5411\u91cf\u3002 \u4e0e\u6bcf\u4e2a\u5411\u91cf\u7c07\u76f8\u5173\u8054\u7684\u662f\u4e00\u4e2a\u4ee3\u8868\u6027\u4ee3\u7801\u5b57\u3002 \u6bcf\u4e2a\u4ee3\u7801\u5b57\u90fd\u4f4d\u4e8e\u5176\u81ea\u5df1\u7684 Voronoi \u533a\u57df\u4e2d\u3002 \u4e3a\u4e86\u8bf4\u660e\uff0c\u8fd9\u4e9b\u533a\u57df\u5728\u56fe 1 \u4e2d\u7528\u5047\u60f3\u7ebf\u5206\u9694\u3002 \u7ed9\u5b9a\u4e00\u4e2a\u8f93\u5165\u5411\u91cf\uff0c\u88ab\u9009\u62e9\u6765\u8868\u793a\u5b83\u7684\u4ee3\u7801\u5b57\u662f\u5728\u540c\u4e00\u4e2a Voronoi \u533a\u57df\u4e2d\u7684\u7801\u5b57\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" src=\"https:\/\/pic3.zhimg.com\/v2-651e8c5460e76c76106696f7c90d12a2_r.jpg\" alt=\"\" width=\"404\" height=\"309\"\/><\/figure><\/div>\n\n\n\n<p>\u76f8\u4e92\u6b27\u51e0\u91cc\u5fb7\u8ddd\u79bb\u6700\u8fd1\u7684\u70b9\u4ee3\u8868\u4e3a\u7801\u5b57<\/p>\n\n\n\n<p>\u6b27\u51e0\u91cc\u5fb7\u8ddd\u79bb\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-1.png\" alt=\"\" class=\"wp-image-14574\" width=\"325\" height=\"97\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-1.png 505w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-1-300x90.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-light-gray-background-color has-background\"><strong>VQ\u5982\u4f55\u5728\u538b\u7f29\u4e2d\u5de5\u4f5c\uff1f<\/strong><\/p>\n\n\n\n<p>       Vevtor quantizer\u7531\u4e24\u4e2a\u64cd\u4f5c\u7ec4\u6210\u3002 \u7b2c\u4e00\u4e2a\u662f\u7f16\u7801\u5668\uff0c\u7b2c\u4e8c\u4e2a\u662f\u89e3\u7801\u5668\u3002 \u7f16\u7801\u5668\u91c7\u7528\u8f93\u5165\u5411\u91cf\u5e76\u8f93\u51fa\u63d0\u4f9b\u6700\u4f4e\u5931\u771f\u7684\u7801\u5b57\u7d22\u5f15\u3002 \u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u901a\u8fc7\u8bc4\u4f30\u8f93\u5165\u5411\u91cf\u4e0e\u7801\u672c\u4e2d\u6bcf\u4e2a\u7801\u5b57\u4e4b\u95f4\u7684\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\uff0c\u53ef\u4ee5\u627e\u5230\u6700\u4f4e\u5931\u771f\u3002 \u4e00\u65e6\u627e\u5230\u6700\u63a5\u8fd1\u7684\u7801\u5b57\uff0c\u8be5\u7801\u5b57\u7684\u7d22\u5f15\u5c31\u4f1a\u901a\u8fc7\u901a\u9053\u53d1\u9001\uff08\u8be5\u901a\u9053\u53ef\u4ee5\u662f\u8ba1\u7b97\u673a\u5b58\u50a8\u3001\u901a\u4fe1\u901a\u9053\u7b49\uff09\u3002 \u5f53\u7f16\u7801\u5668\u63a5\u6536\u5230\u4ee3\u7801\u5b57\u7684\u7d22\u5f15\u65f6\uff0c\u5b83\u7528\u76f8\u5173\u7684\u4ee3\u7801\u5b57\u66ff\u6362\u7d22\u5f15\u3002&nbsp;<\/p>\n\n\n\n<p>   \u5728\u77e2\u91cf\u91cf\u5316\u7f16\u7801\u4e2d\uff0c\u5173\u952e\u662f\u7801\u672c\u7684\u5efa\u7acb\u548c\u7801\u5b57\u641c\u7d22\u7b97\u6cd5\uff0c\u5982\u679c\u60f3\u5bf9\u77e2\u91cf\u91cf\u5316\u6709\u4e2a\u6574\u4f53\u7684\u6982\u89c8\uff0c\u5f3a\u70c8\u63a8\u8350\u300aHandbook of Image and Video Processing\u300b\u4e00\u4e66\u4e2dFundamentals of Vector Quantization\u7ae0\u8282\u3002\u4e0b\u9762\u5bf9\u77e2\u91cf\u91cf\u5316\u4e2d\u4e24\u7c7b\u5178\u578b\u7684\u65b9\u6cd5\u591a\u9636\u6bb5\u77e2\u91cf\u91cf\u5316\u3001\u4e58\u79ef\u91cf\u5316\u4ee5\u53ca\u4e58\u79ef\u91cf\u5316\u7684\u6539\u8fdb\u505a\u7b80\u5355\u4ecb\u7ecd\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"932\" height=\"559\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-2.png\" alt=\"\" class=\"wp-image-14579\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-2.png 932w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-2-300x180.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-2-768x461.png 768w\" sizes=\"(max-width: 932px) 100vw, 932px\" \/><\/figure>\n\n\n\n<p class=\"has-light-gray-background-color has-background\"><strong>codebook\u5982\u4f55\u8bbe\u8ba1\uff1f<\/strong><\/p>\n\n\n\n<p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u8ba8\u8bba\u4e86 VQ \u7684\u5de5\u4f5c\u65b9\u5f0f\uff0c\u4f46\u6211\u4eec\u8fd8\u6ca1\u6709\u8ba8\u8bba\u5982\u4f55\u751f\u6210\u7801\u672c\u3002 \u4ec0\u4e48\u7801\u5b57\u6700\u80fd\u4ee3\u8868\u4e00\u7ec4\u7ed9\u5b9a\u7684\u8f93\u5165\u5411\u91cf\uff1f \u5e94\u8be5\u9009\u591a\u5c11\uff1f<\/p>\n\n\n\n<p>\u4e0d\u5e78\u7684\u662f\uff0c\u8bbe\u8ba1\u4e00\u4e2a\u6700\u80fd\u4ee3\u8868\u8f93\u5165\u5411\u91cf\u96c6\u7684\u5bc6\u7801\u672c\u662f NP \u96be\u7684\u3002 \u8fd9\u610f\u5473\u7740\u5b83\u9700\u8981\u5728\u7a7a\u95f4\u4e2d\u7a77\u5c3d\u641c\u7d22\u6700\u4f73\u53ef\u80fd\u7684\u7801\u5b57\uff0c\u5e76\u4e14\u968f\u7740\u7801\u5b57\u6570\u91cf\u7684\u589e\u52a0\uff0c\u641c\u7d22\u5448\u6307\u6570\u589e\u957f\uff08\u5982\u679c\u4f60\u80fd\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u627e\u5230\u6700\u4f73\u89e3\u51b3\u65b9\u6848\uff0c\u4f60\u7684\u540d\u5b57\u5c06\u6c38\u8fdc\u8f7d\u5165\u53f2\u518c\uff09\u3002 \u56e0\u6b64\uff0c\u6211\u4eec\u6c42\u52a9\u4e8e\u6b21\u4f18\u7801\u672c\u8bbe\u8ba1\u65b9\u6848\uff0c\u7b2c\u4e00\u4e2a\u60f3\u5230\u7684\u662f\u6700\u7b80\u5355\u7684\u3002 \u5b83\u4ee5 Linde-Buzo-Gray \u7684\u540d\u5b57\u547d\u540d\u4e3a LBG\uff0cLinde-Buzo-Gray \u662f\u8fd9\u4e2a\u60f3\u6cd5\u7684\u4f5c\u8005\u3002 \u8be5\u7b97\u6cd5\u7c7b\u4f3c\u4e8ek-means\u7b97\u6cd5\u3002<\/p>\n\n\n\n<p>\u7b97\u6cd5\u5982\u4e0b\uff0c<\/p>\n\n\n\n<ol><li>\u786e\u5b9a\u7801\u5b57\u6570 N \u6216\u7801\u672c\u7684\u5927\u5c0f\u3002<\/li><\/ol>\n\n\n\n<p>2. \u968f\u673a\u9009\u62e9N\u4e2a\u7801\u5b57\uff0c\u5c06\u5176\u4f5c\u4e3a\u521d\u59cb\u7801\u672c\u3002 \u53ef\u4ee5\u4ece\u4e00\u7ec4\u8f93\u5165\u5411\u91cf\u4e2d\u968f\u673a\u9009\u62e9\u521d\u59cb\u7801\u5b57\u3002<\/p>\n\n\n\n<p>3. \u4f7f\u7528\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u5ea6\u91cf\u5c06\u6bcf\u4e2a\u7801\u5b57\u5468\u56f4\u7684\u5411\u91cf\u805a\u7c7b\u3002 \u8fd9\u662f\u901a\u8fc7\u83b7\u53d6\u6bcf\u4e2a\u8f93\u5165\u5411\u91cf\u5e76\u627e\u5230\u5b83\u4e0e\u6bcf\u4e2a\u7801\u5b57\u4e4b\u95f4\u7684\u6b27\u51e0\u91cc\u5fb7\u8ddd\u79bb\u6765\u5b8c\u6210\u7684\u3002 \u8f93\u5165\u5411\u91cf\u5c5e\u4e8e\u4ea7\u751f\u6700\u5c0f\u8ddd\u79bb\u7684\u7801\u5b57\u7c07\u3002<\/p>\n\n\n\n<p>4. \u8ba1\u7b97\u65b0\u7684\u7801\u5b57\u96c6\u3002 \u8fd9\u662f\u901a\u8fc7\u83b7\u53d6\u6bcf\u4e2a\u96c6\u7fa4\u7684\u5e73\u5747\u503c\u6765\u5b8c\u6210\u7684\u3002 \u6dfb\u52a0\u6bcf\u4e2a\u5411\u91cf\u7684\u5206\u91cf\u5e76\u9664\u4ee5\u7fa4\u96c6\u4e2d\u7684\u5411\u91cf\u6570\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-3.png\" alt=\"\" class=\"wp-image-14581\" width=\"160\" height=\"42\"\/><\/figure><\/div>\n\n\n\n<p>\u91cd\u590d2\u548c3\u76f4\u5230\u6240\u6709\u7801\u5b57\u4e0d\u518d\u53d8\u5316\u6216\u8005\u53d8\u5316\u5f88\u5c0f\u4e3a\u6b62\u3002<\/p>\n\n\n\n<p>\u8be5\u7b97\u6cd5\u662f\u8fc4\u4eca\u4e3a\u6b62\u6700\u53d7\u6b22\u8fce\u7684\uff0c\u8fd9\u662f\u7531\u4e8e\u5b83\u7684\u7b80\u5355\u6027\u3002 \u867d\u7136\u5b83\u662f\u5c40\u90e8\u6700\u4f18\u7684\uff0c\u4f46\u901f\u5ea6\u5f88\u6162\u3002 \u5b83\u6162\u7684\u539f\u56e0\u662f\u56e0\u4e3a\u5bf9\u4e8e\u6bcf\u6b21\u8fed\u4ee3\uff0c\u786e\u5b9a\u6bcf\u4e2a\u805a\u7c7b\u9700\u8981\u5c06\u6bcf\u4e2a\u8f93\u5165\u5411\u91cf\u4e0e\u7801\u672c\u4e2d\u7684\u6240\u6709\u7801\u5b57\u8fdb\u884c\u6bd4\u8f83\u3002<\/p>\n\n\n\n<h3 class=\"has-light-blue-background-color has-background\">\u5178\u578b\u7684\u65b9\u6cd5:<\/h3>\n\n\n\n<p>        \u4e0b\u9762\u5bf9\u77e2\u91cf\u91cf\u5316\u4e2d\u4e24\u7c7b\u5178\u578b\u7684\u65b9\u6cd5\u591a\u9636\u6bb5\u77e2\u91cf\u91cf\u5316\u3001\u4e58\u79ef\u91cf\u5316\u4ee5\u53ca\u4e58\u79ef\u91cf\u5316\u7684\u6539\u8fdb\u505a\u7b80\u5355\u4ecb\u7ecd\u3002<\/p>\n\n\n\n<h4 class=\"has-light-gray-background-color has-background\" id=\"\u591a\u9636\u6bb5\u77e2\u91cf\u91cf\u5316\">1\u3001\u591a\u9636\u6bb5\u77e2\u91cf\u91cf\u5316\uff1a<\/h4>\n\n\n\n<p>         \u591a\u9636\u6bb5\u77e2\u91cf\u91cf\u5316\uff08Multi-Stage Vector Quantization\uff0cMSVQ\uff09\u4e5f\u79f0\u4e3a\u6b8b\u5dee\u77e2\u91cf\u91cf\u5316\uff08Residual Vector Quantization, RVQ\uff09\uff0c\u5b83\u662f\u4e00\u79cd\u601d\u60f3\uff0c\u5373\u5c06\u7f16\u7801\u4efb\u52a1\u5206\u89e3\u4e3a\u4e00\u7cfb\u5217\u7ea7\u8054\u8fc7\u7a0b\u3002\u7ea7\u8054\u8fc7\u7a0b\u53ef\u4ee5\u7528\u4e0b\u56fe\u76f4\u89c2\u7684\u5c55\u793a\u51fa\u6765\uff1a<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-4.png\" alt=\"\" class=\"wp-image-14587\" width=\"414\" height=\"261\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-4.png 784w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-4-300x189.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-4-768x485.png 768w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/figure><\/div>\n\n\n\n<p>        \u5982\u4e0a\u56fe\u6240\u793a\uff0c\u5bf9\u4e8e\u5f85\u91cf\u5316\u7684\u5411\u91cfx\uff0c\u7ecf\u8fc7\u4e00\u7ea7\u91cf\u5316\u5668quantizer1\u540e\uff0c\u5f97\u5230\u7684\u91cf\u5316\u6b8b\u5dee\u4e3ar1 = x &#8211; C1b1\uff0c\u5176\u4e2dC1\u4e3a\u4e00\u7ea7\u91cf\u5316\u5668\u7684\u7801\u672c\uff0cb1\u4e3ax\u7ecf\u8fc7\u4e00\u7ea7\u91cf\u5316\u5668quantizer1\u540e\u7684\u8868\u793a\u7ed3\u679c\uff0c\u5c06\u4e00\u7ea7\u91cf\u5316\u8bef\u5deer1\u4f5c\u4e3a\u4e8c\u7ea7\u91cf\u5316\u5668\u7684\u8f93\u5165\uff0c\u540e\u9762\u8fc7\u7a0b\u4e0e\u6b64\u7c7b\u4f3c\u3002\u901a\u8fc7\u8fd9\u79cd\u7ea7\u8054\u91cf\u5316\u7684\u91cf\u5316\u65b9\u5f0f\uff0c\u5f53\u6784\u5efa\u7684\u91cf\u5316\u5668\u4e3a\u65e0\u7a77\u4e2a\u65f6\uff0cx\u53ef\u4ee5\u88ab\u8fd9\u65e0\u7a77\u4e2a\u7801\u672c\u7cbe\u786e\u8868\u793a\u3002\u4e0a\u56fe\u53f3\u4fa7\u5b50\u56fe\u6bd4\u8f83\u76f4\u89c2\u7684\u63cf\u7ed8\u4e86x\u88ab\u591a\u4e2a\u7801\u672c\u9010\u6b65\u8fd1\u4f3c\u7684\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p>      \u4e0a\u8ff0 C1\u3001C2\u3001\u2026\u3001Ci\u3001\u2026 \u8fd9\u4e9b\u7801\u672c\u5728\u6784\u5efa\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u91c7\u7528KMeans\u7b49\u65b9\u5f0f\u5f97\u5230\u5404\u4e2a\u91cf\u5316\u5668\u7684\u7801\u672c\u3002\u4ee5\u4e0a\u9762\u6784\u5efa\u76844\u4e2a\u7ea7\u8054\u7684\u7801\u672c\u4e3a\u4f8b\uff0c\u5f53\u5f97\u5230\u7801\u672cC1\u3001C2\u3001C3\u3001C4\u540e\uff0cx\u91cf\u5316\u7684\u7ed3\u679c\u5373\u53ef\u7528[b1, b2, b3, b4]\u8868\u793a\u3002\u5bf9\u4e8exq\u67e5\u8be2\u5411\u91cf\u4e0ex\u8ddd\u79bb\u7684\u8ba1\u7b97\uff0c\u5728\u8ba1\u7b97xq\u4e0e C1\u3001C2\u3001\u2026\u3001Ci\u3001\u2026 \u4e4b\u95f4\u7684\u5185\u79ef\u8ddd\u79bb\u8868\u540e\uff0c\u53ef\u4ee5\u901a\u8fc7\u67e5\u8868\u7684\u65b9\u5f0f\uff0c\u83b7\u53d6\u5230\u975e\u5bf9\u79f0\u8ddd\u79bb\u3002<\/p>\n\n\n\n<p>     \u8fd9\u79cd\u591a\u9636\u6bb5\u7ea7\u8054\u7684\u77e2\u91cf\u91cf\u5316\u65b9\u5f0f\uff0c\u76f8\u6bd4\u5355\u9636\u6bb5\u4e00\u6b21\u6027\u91cf\u5316\uff0c\u6781\u5927\u7684\u964d\u4f4e\u4e86\u7801\u672c\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u6d88\u8017\u7684\u8ba1\u7b97\u8d44\u6e90\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c4\u4e2a\u9636\u6bb5\u7684MSVQ\uff0c\u6bcf\u9636\u6bb5\u7528KMeans\u53ea\u9700\u6784\u5efa\u6784\u5efa256\u5927\u5c0f\u7684\u7801\u672c\uff0c\u5219\u5bf9\u7a7a\u95f4\u5206\u5272\u6784\u5efa\u7684cell\u6570\u76ee\u4e3a256<em>256<\/em>256256\uff0c\u6548\u7387\u662f\u5f88\u9ad8\u7684\uff0c\u4f46\u662f\u5982\u679c\u91c7\u7528\u5355\u9636\u6bb5\u4e00\u6b21\u6027\u91cf\u5316\u6784\u5efa4294967296\u5927\u5c0f\u7684\u7801\u672c\uff0c\u8fd9\u4e2a\u7801\u672c\u6839\u672c\u6ca1\u6cd5\u7528KMeans\u805a\u51fa\u6765\u3002\u6b64\u5916\u5728\u8ba1\u7b97\u8ddd\u79bb\u7684\u65f6\u5019\uff0c\u91c7\u75284\u9636\u6bb5\u7684MSVQ\u65b9\u5f0f\uff0c\u53ea\u9700\u8ba1\u7b974256\u6b21\u8ddd\u79bb\u7684\u8ba1\u7b97\u6784\u6210\u8ddd\u79bb\u8868\uff0c\u7136\u540e\u91c7\u7528\u67e5\u8868\u65b9\u5f0f\u8ba1\u7b97\u8ddd\u79bb\uff0c\u800c\u5355\u9636\u6bb5\u4e00\u6b21\u6027\u91cf\u5316\u9700\u8981\u8ba1\u7b974294967296\u6b21\u7684\u8ddd\u79bb\u8ba1\u7b97\u3002MSVQ\u7684\u8fdb\u4e00\u6b65\u52a0\u901f\u7248\u672c\u662f\u5012\u6392MSVQ\uff0c\u5c06\u4e00\u7ea7\u7801\u672c\u89c6\u4e3a\u5012\u6392\u94fe\uff0c\u4ece\u800c\u6784\u5efa\u5012\u6392\u7ed3\u6784\uff0c\u6784\u5efaMSVQ\u5012\u6392\u7ed3\u6784\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u5c06MSVQ\u7c7b\u6bd4\u6210\u201c\u6df1\u5ea6\u52a0\u6df1\u201d\u7684\u8fc7\u7a0b\uff0c\u4e0b\u9762\u4ecb\u7ecd\u7684\u975e\u5e38\u7ecf\u5178\u7684\u4e58\u79ef\u91cf\u5316\u65b9\u6cd5\uff0c\u53ef\u4ee5\u4e3a\u201c\u5bbd\u5ea6\u52a0\u5bbd\u201d\u7684\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<h4 class=\"has-light-gray-background-color has-background\" id=\"\u4e58\u79ef\u91cf\u5316\">2\u3001\u4e58\u79ef\u91cf\u5316\uff1a<\/h4>\n\n\n\n<p>       \u4e58\u79ef\u91cf\u5316(Product Quantization\uff0cPQ)\u662fHerve Jegou\u57282011\u5e74\u63d0\u51fa\u7684\u4e00\u79cd\u975e\u5e38\u7ecf\u5178\u5b9e\u7528\u7684\u77e2\u91cf\u91cf\u5316\u7d22\u5f15\u65b9\u6cd5\uff0c\u5728\u5de5\u4e1a\u754c\u5411\u91cf\u7d22\u5f15\u4e2d\u5df2\u5f97\u5230\u5e7f\u6cdb\u7684\u5f15\u7528\uff0c\u5e76\u4f5c\u4e3a\u4e3b\u8981\u7684\u5411\u91cf\u7d22\u5f15\u65b9\u6cd5\uff0c\u5728Fasis\u6709\u975e\u5e38\u9ad8\u6548\u7684\u5b9e\u73b0\u3002\u4e58\u79ef\u91cf\u5316\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5206\u6bb5\uff08\u5212\u5206\u5b50\u7a7a\u95f4\uff09\u548c\u805a\u7c7b\uff0c\u6216\u8005\u8bf4\u5177\u4f53\u5e94\u7528\u5230ANN\u8fd1\u4f3c\u6700\u8fd1\u90bb\u641c\u7d22\u4e0a\uff0cKMeans\u662fPQ\u4e58\u79ef\u91cf\u5316\u5b50\u7a7a\u95f4\u6570\u76ee\u4e3a1\u7684\u7279\u4f8b\u3002PQ\u4e58\u79ef\u91cf\u5316\u751f\u6210\u7801\u672c\u548c\u91cf\u5316\u7684\u8fc7\u7a0b\u53ef\u4ee5\u7528\u5982\u4e0b\u56fe\u793a\u6765\u8bf4\u660e\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"432\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-5-1024x432.png\" alt=\"\" class=\"wp-image-14599\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-5-1024x432.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-5-300x127.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-5-768x324.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-5.png 1124w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>      \u5728\u8bad\u7ec3\u9636\u6bb5\uff0c\u9488\u5bf9N\u4e2a\u8bad\u7ec3\u6837\u672c\uff0c\u5047\u8bbe\u6837\u672c\u7ef4\u5ea6\u4e3a128\u7ef4\uff0c\u6211\u4eec\u5c06\u5176\u5207\u5206\u4e3a4\u4e2a\u5b50\u7a7a\u95f4\uff0c\u5219\u6bcf\u4e00\u4e2a\u5b50\u7a7a\u95f4\u7684\u7ef4\u5ea6\u4e3a32\u7ef4\uff0c\u7136\u540e\u6211\u4eec\u5728\u6bcf\u4e00\u4e2a\u5b50\u7a7a\u95f4\u4e2d\uff0c\u5bf9\u5b50\u5411\u91cf\u91c7\u7528K-Means\u5bf9\u5176\u8fdb\u884c\u805a\u7c7b(\u56fe\u4e2d\u793a\u610f\u805a\u6210256\u7c7b)\uff0c\u8fd9\u6837\u6bcf\u4e00\u4e2a\u5b50\u7a7a\u95f4\u90fd\u80fd\u5f97\u5230\u4e00\u4e2a\u7801\u672c\u3002\u8fd9\u6837\u8bad\u7ec3\u6837\u672c\u7684\u6bcf\u4e2a\u5b50\u6bb5\uff0c\u90fd\u53ef\u4ee5\u7528\u5b50\u7a7a\u95f4\u7684\u805a\u7c7b\u4e2d\u5fc3\u6765\u8fd1\u4f3c\uff0c\u5bf9\u5e94\u7684\u7f16\u7801\u5373\u4e3a\u7c7b\u4e2d\u5fc3\u7684ID\u3002\u5982\u56fe\u6240\u793a\uff0c\u901a\u8fc7\u8fd9\u6837\u4e00\u79cd\u7f16\u7801\u65b9\u5f0f\uff0c\u8bad\u7ec3\u6837\u672c\u4ec5\u4f7f\u7528\u7684\u5f88\u77ed\u7684\u4e00\u4e2a\u7f16\u7801\u5f97\u4ee5\u8868\u793a\uff0c\u4ece\u800c\u8fbe\u5230\u91cf\u5316\u7684\u76ee\u7684\u3002\u5bf9\u4e8e\u5f85\u7f16\u7801\u7684\u6837\u672c\uff0c\u5c06\u5b83\u8fdb\u884c\u76f8\u540c\u7684\u5207\u5206\uff0c\u7136\u540e\u5728\u5404\u4e2a\u5b50\u7a7a\u95f4\u91cc\u9010\u4e00\u627e\u5230\u8ddd\u79bb\u5b83\u4eec\u6700\u8fd1\u7684\u7c7b\u4e2d\u5fc3\uff0c\u7136\u540e\u7528\u7c7b\u4e2d\u5fc3\u7684id\u6765\u8868\u793a\u5b83\u4eec\uff0c\u5373\u5b8c\u6210\u4e86\u5f85\u7f16\u7801\u6837\u672c\u7684\u7f16\u7801\u3002<\/p>\n\n\n\n<p>      \u6b63\u5982\u524d\u9762\u6240\u8bf4\u7684\uff0c\u5728\u77e2\u91cf\u91cf\u5316\u7f16\u7801\u4e2d\uff0c\u5173\u952e\u662f\u7801\u672c\u7684\u5efa\u7acb\u548c\u7801\u5b57\u7684\u641c\u7d22\u7b97\u6cd5\uff0c\u5728\u4e0a\u9762\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u5efa\u7acb\u7684\u7801\u672c\u4ee5\u53ca\u91cf\u5316\u7f16\u7801\u7684\u65b9\u5f0f\u3002\u5269\u4e0b\u7684\u91cd\u70b9\u5c31\u662f\u67e5\u8be2\u6837\u672c\u4e0edataset\u4e2d\u7684\u6837\u672c\u8ddd\u79bb\u5982\u4f55\u8ba1\u7b97\u7684\u95ee\u9898\u4e86\u3002<\/p>\n\n\n\n<p>    \u5728\u67e5\u8be2\u9636\u6bb5\uff0cPQ\u540c\u6837\u5728\u8ba1\u7b97\u67e5\u8be2\u6837\u672c\u4e0edataset\u4e2d\u5404\u4e2a\u6837\u672c\u7684\u8ddd\u79bb\uff0c\u53ea\u4e0d\u8fc7\u8fd9\u79cd\u8ddd\u79bb\u7684\u8ba1\u7b97\u8f6c\u5316\u4e3a\u95f4\u63a5\u8fd1\u4f3c\u7684\u65b9\u6cd5\u800c\u83b7\u5f97\u3002PQ\u4e58\u79ef\u91cf\u5316\u65b9\u6cd5\u5728\u8ba1\u7b97\u8ddd\u79bb\u7684\u65f6\u5019\uff0c\u6709\u4e24\u79cd\u8ddd\u79bb\u8ba1\u7b97\u65b9\u5f0f\uff0c\u4e00\u79cd\u662f\u5bf9\u79f0\u8ddd\u79bb\uff0c\u53e6\u5916\u4e00\u79cd\u662f\u975e\u5bf9\u79f0\u8ddd\u79bb\u3002\u975e\u5bf9\u79f0\u8ddd\u79bb\u7684\u635f\u5931\u5c0f(\u4e5f\u5c31\u662f\u66f4\u63a5\u8fd1\u771f\u5b9e\u8ddd\u79bb)\uff0c\u5b9e\u9645\u4e2d\u4e5f\u7ecf\u5e38\u91c7\u7528\u8fd9\u79cd\u8ddd\u79bb\u8ba1\u7b97\u65b9\u5f0f\u3002\u4e0b\u9762\u8fc7\u7a0b\u793a\u610f\u7684\u662f\u67e5\u8be2\u6837\u672c\u6765\u5230\u65f6\uff0c\u4ee5\u975e\u5bf9\u79f0\u8ddd\u79bb\u7684\u65b9\u5f0f(\u7ea2\u6846\u6807\u8bc6\u51fa\u6765\u7684\u90e8\u5206)\u8ba1\u7b97\u5230dataset\u6837\u672c\u95f4\u7684\u8ba1\u7b97\u793a\u610f\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img src=\"blob:http:\/\/139.9.1.231\/a8b50680-03bf-485f-9c2c-b3cefaa0b4b5\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u5177\u4f53\u5730\uff0c\u67e5\u8be2\u5411\u91cf\u6765\u5230\u65f6\uff0c\u6309\u8bad\u7ec3\u6837\u672c\u751f\u6210\u7801\u672c\u7684\u8fc7\u7a0b\uff0c\u5c06\u5176\u540c\u6837\u5206\u6210\u76f8\u540c\u7684\u5b50\u6bb5\uff0c\u7136\u540e\u5728\u6bcf\u4e2a\u5b50\u7a7a\u95f4\u4e2d\uff0c\u8ba1\u7b97\u5b50\u6bb5\u5230\u8be5\u5b50\u7a7a\u95f4\u4e2d\u6240\u6709\u805a\u7c7b\u4e2d\u5fc3\u5f97\u8ddd\u79bb\uff0c\u5982\u56fe\u4e2d\u6240\u793a\uff0c\u53ef\u4ee5\u5f97\u52304*256\u4e2a\u8ddd\u79bb\uff0c\u8fd9\u91cc\u4e3a\u4fbf\u4e8e\u540e\u9762\u7684\u7406\u89e3\u8bf4\u660e\uff0c\u53ef\u4ee5\u628a\u8fd9\u4e9b\u7b97\u597d\u7684\u8ddd\u79bb\u79f0\u4f5c\u8ddd\u79bb\u8868\u3002\u5728\u8ba1\u7b97\u5e93\u4e2d\u67d0\u4e2a\u6837\u672c\u5230\u67e5\u8be2\u5411\u91cf\u7684\u8ddd\u79bb\u65f6\uff0c\u6bd4\u5982\u7f16\u7801\u4e3a(124, 56, 132, 222)\u8fd9\u4e2a\u6837\u672c\u5230\u67e5\u8be2\u5411\u91cf\u7684\u8ddd\u79bb\u65f6\uff0c\u6211\u4eec\u5206\u522b\u5230\u8ddd\u79bb\u8868\u4e2d\u53d6\u5404\u4e2a\u5b50\u6bb5\u5bf9\u5e94\u7684\u8ddd\u79bb\u5373\u53ef\uff0c\u6bd4\u5982\u7f16\u7801\u4e3a124\u8fd9\u4e2a\u5b50\u6bb5\uff0c\u5728\u7b2c1\u4e2a\u7b97\u51fa\u7684256\u4e2a\u8ddd\u79bb\u91cc\u9762\u628a\u7f16\u53f7\u4e3a124\u7684\u90a3\u4e2a\u8ddd\u79bb\u53d6\u51fa\u6765\u5c31\u53ef\uff0c\u6240\u6709\u5b50\u6bb5\u5bf9\u5e94\u7684\u8ddd\u79bb\u53d6\u51fa\u6765\u540e\uff0c\u5c06\u8fd9\u4e9b\u5b50\u6bb5\u7684\u8ddd\u79bb\u6c42\u548c\u76f8\u52a0\uff0c\u5373\u5f97\u5230\u8be5\u6837\u672c\u5230\u67e5\u8be2\u6837\u672c\u95f4\u7684\u975e\u5bf9\u79f0\u8ddd\u79bb\u3002\u6240\u6709\u8ddd\u79bb\u7b97\u597d\u540e\uff0c\u6392\u5e8f\u540e\u5373\u5f97\u5230\u6211\u4eec\u6700\u7ec8\u60f3\u8981\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u4ece\u4e0a\u9762\u8fd9\u4e2a\u8fc7\u7a0b\u53ef\u4ee5\u5f88\u6e05\u695a\u5730\u770b\u51faPQ\u4e58\u79ef\u91cf\u5316\u80fd\u591f\u52a0\u901f\u7d22\u5f15\u7684\u539f\u7406\uff1a\u5373\u5c06\u5168\u6837\u672c\u7684\u8ddd\u79bb\u8ba1\u7b97\uff0c\u8f6c\u5316\u4e3a\u5230\u5b50\u7a7a\u95f4\u7c7b\u4e2d\u5fc3\u7684\u8ddd\u79bb\u8ba1\u7b97\u3002\u6bd4\u5982\u4e0a\u9762\u6240\u4e3e\u7684\u4f8b\u5b50\uff0c\u539f\u672cbrute-force search\u7684\u65b9\u5f0f\u8ba1\u7b97\u8ddd\u79bb\u7684\u6b21\u6570\u968f\u6837\u672c\u6570\u76eeN\u6210\u7ebf\u6027\u589e\u957f\uff0c\u4f46\u662f\u7ecf\u8fc7PQ\u7f16\u7801\u540e\uff0c\u5bf9\u4e8e\u8017\u65f6\u7684\u8ddd\u79bb\u8ba1\u7b97\uff0c\u53ea\u8981\u8ba1\u7b974*256\u6b21\uff0c\u51e0\u4e4e\u53ef\u4ee5\u5ffd\u7565\u6b64\u65f6\u95f4\u7684\u6d88\u8017\u3002\u53e6\u5916\uff0c\u4ece\u4e0a\u56fe\u4e5f\u53ef\u4ee5\u770b\u51fa\uff0c\u5bf9\u7279\u5f81\u8fdb\u884c\u7f16\u7801\u540e\uff0c\u53ef\u4ee5\u7528\u4e00\u4e2a\u76f8\u5bf9\u6bd4\u8f83\u77ed\u7684\u7f16\u7801\u6765\u8868\u793a\u6837\u672c\uff0c\u81ea\u7136\u5bf9\u4e8e\u5185\u5b58\u7684\u6d88\u8017\u8981\u5927\u5927\u5c0f\u4e8ebrute-force search\u7684\u65b9\u5f0f\u3002<\/p>\n\n\n\n<p>\u5728\u67d0\u4e9b\u7279\u6b8a\u7684\u573a\u5408\uff0c\u6211\u4eec\u603b\u662f\u5e0c\u671b\u83b7\u5f97\u7cbe\u786e\u7684\u8ddd\u79bb\uff0c\u800c\u4e0d\u662f\u8fd1\u4f3c\u7684\u8ddd\u79bb\uff0c\u5e76\u4e14\u6211\u4eec\u603b\u662f\u559c\u6b22\u83b7\u53d6\u5411\u91cf\u95f4\u7684\u4f59\u5f26\u76f8\u4f3c\u5ea6\uff08\u4f59\u5f26\u76f8\u4f3c\u5ea6\u8ddd\u79bb\u8303\u56f4\u5728[-1,1]\u4e4b\u95f4\uff0c\u4fbf\u4e8e\u8bbe\u7f6e\u56fa\u5b9a\u7684\u9608\u503c\uff09\uff0c\u9488\u5bf9\u8fd9\u79cd\u573a\u666f\uff0c\u53ef\u4ee5\u9488\u5bf9PQ\u4e58\u79ef\u91cf\u5316\u5f97\u5230\u7684\u524dtop@K\u505a\u4e00\u4e2abrute-force search\u7684\u6392\u5e8f\u3002<\/p>\n\n\n\n<h4 class=\"has-light-gray-background-color has-background\" id=\"\u5012\u6392\u4e58\u79ef\u91cf\u5316\">3\u3001\u5012\u6392\u4e58\u79ef\u91cf\u5316<\/h4>\n\n\n\n<p>\u5012\u6392PQ\u4e58\u79ef\u91cf\u5316(IVFPQ)\u662fPQ\u4e58\u79ef\u91cf\u5316\u7684\u66f4\u8fdb\u4e00\u6b65\u52a0\u901f\u7248\u3002\u5176\u52a0\u901f\u7684\u672c\u8d28\u9003\u4e0d\u5f00\u5728\u6700\u524d\u9762\u5f3a\u8c03\u7684\u662f\u52a0\u901f\u539f\u7406\uff1a<strong>brute-force\u641c\u7d22\u7684\u65b9\u5f0f\u662f\u5728\u5168\u7a7a\u95f4\u8fdb\u884c\u641c\u7d22\uff0c\u4e3a\u4e86\u52a0\u5feb\u67e5\u627e\u7684\u901f\u5ea6\uff0c\u51e0\u4e4e\u6240\u6709\u7684ANN\u65b9\u6cd5\u90fd\u662f\u901a\u8fc7\u5bf9\u5168\u7a7a\u95f4\u5206\u5272\uff0c\u5c06\u5176\u5206\u5272\u6210\u5f88\u591a\u5c0f\u7684\u5b50\u7a7a\u95f4\uff0c\u5728\u641c\u7d22\u7684\u65f6\u5019\uff0c\u901a\u8fc7\u67d0\u79cd\u65b9\u5f0f\uff0c\u5feb\u901f\u9501\u5b9a\u5728\u67d0\u4e00\uff08\u51e0\uff09\u5b50\u7a7a\u95f4\uff0c\u7136\u540e\u5728\u8be5\uff08\u51e0\u4e2a\uff09\u5b50\u7a7a\u95f4\u91cc\u505a\u904d\u5386<\/strong>\u3002\u5728\u4e0a\u4e00\u5c0f\u8282\u53ef\u4ee5\u770b\u51fa\uff0cPQ\u4e58\u79ef\u91cf\u5316\u8ba1\u7b97\u8ddd\u79bb\u7684\u65f6\u5019\uff0c\u8ddd\u79bb\u867d\u7136\u5df2\u7ecf\u9884\u5148\u7b97\u597d\u4e86\uff0c\u4f46\u662f\u5bf9\u4e8e\u6bcf\u4e2a\u6837\u672c\u5230\u67e5\u8be2\u6837\u672c\u7684\u8ddd\u79bb\uff0c\u8fd8\u662f\u5f97\u8001\u8001\u5b9e\u5b9e\u6328\u4e2a\u53bb\u6c42\u548c\u76f8\u52a0\u8ba1\u7b97\u8ddd\u79bb\u3002\u4f46\u662f\uff0c\u5b9e\u9645\u4e0a\u6211\u4eec\u611f\u5174\u8da3\u7684\u662f\u90a3\u4e9b\u8ddf\u67e5\u8be2\u6837\u672c\u76f8\u8fd1\u7684\u6837\u672c\uff08\u59d1\u4e14\u79f0\u8fd9\u6837\u7684\u533a\u57df\u4e3a\u611f\u5174\u8da3\u533a\u57df\uff09\uff0c\u4e5f\u5c31\u662f\u8bf4\u8001\u8001\u5b9e\u5b9e\u6328\u4e2a\u76f8\u52a0\u5176\u5b9e\u505a\u4e86\u5f88\u591a\u7684\u65e0\u7528\u529f\uff0c\u5982\u679c\u80fd\u591f\u901a\u8fc7\u67d0\u79cd\u624b\u6bb5\u5feb\u901f\u5c06\u5168\u5c40\u904d\u5386\u9501\u5b9a\u4e3a\u611f\u5174\u8da3\u533a\u57df\uff0c\u5219\u53ef\u4ee5\u820d\u53bb\u4e0d\u5fc5\u8981\u7684\u5168\u5c40\u8ba1\u7b97\u4ee5\u53ca\u6392\u5e8f\u3002\u5012\u6392PQ\u4e58\u79ef\u91cf\u5316\u7684\u201d\u5012\u6392\u201c\uff0c\u6b63\u662f\u8fd9\u6837\u4e00\u79cd\u601d\u60f3\u7684\u4f53\u73b0\uff0c\u5728\u5177\u4f53\u5b9e\u65bd\u624b\u6bb5\u4e0a\uff0c\u91c7\u7528\u7684\u662f\u901a\u8fc7\u805a\u7c7b\u7684\u65b9\u5f0f\u5b9e\u73b0\u611f\u5174\u8da3\u533a\u57df\u7684\u5feb\u901f\u5b9a\u4f4d\uff0c\u5728\u5012\u6392PQ\u4e58\u79ef\u91cf\u5316\u4e2d\uff0c\u805a\u7c7b\u53ef\u4ee5\u8bf4\u5e94\u7528\u5f97\u6dcb\u6f13\u5c3d\u81f4\u3002<\/p>\n\n\n\n<p>\u5012\u6392PQ\u4e58\u79ef\u91cf\u5316\u6574\u4e2a\u8fc7\u7a0b\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"596\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-7-1024x596.png\" alt=\"\" class=\"wp-image-14607\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-7-1024x596.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-7-300x175.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-7-768x447.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-7.png 1163w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u5728PQ\u4e58\u79ef\u91cf\u5316\u4e4b\u524d\uff0c\u589e\u52a0\u4e86\u4e00\u4e2a\u7c97\u91cf\u5316\u8fc7\u7a0b\u3002\u5177\u4f53\u5730\uff0c\u5148\u5bf9N\u4e2a\u8bad\u7ec3\u6837\u672c\u91c7\u7528KMeans\u8fdb\u884c\u805a\u7c7b\uff0c\u8fd9\u91cc\u805a\u7c7b\u7684\u6570\u76ee\u4e00\u822c\u8bbe\u7f6e\u5f97\u4e0d\u5e94\u8fc7\u5927\uff0c\u4e00\u822c\u8bbe\u7f6e\u4e3a1024\u5dee\u4e0d\u591a\uff0c\u8fd9\u79cd\u53ef\u4ee5\u4ee5\u6bd4\u8f83\u5feb\u7684\u901f\u5ea6\u5b8c\u6210\u805a\u7c7b\u8fc7\u7a0b\u3002\u5f97\u5230\u4e86\u805a\u7c7b\u4e2d\u5fc3\u540e\uff0c\u9488\u5bf9\u6bcf\u4e00\u4e2a\u6837\u672cx_i\uff0c\u627e\u5230\u5176\u8ddd\u79bb\u6700\u8fd1\u7684\u7c7b\u4e2d\u5fc3c_i\u540e\uff0c\u4e24\u8005\u76f8\u51cf\u5f97\u5230\u6837\u672cx_i\u7684\u6b8b\u5dee\u5411\u91cf(x_i-c_i)\uff0c\u540e\u9762\u5269\u4e0b\u7684\u8fc7\u7a0b\uff0c\u5c31\u662f\u9488\u5bf9(x_i-c_i)\u7684PQ\u4e58\u79ef\u91cf\u5316\u8fc7\u7a0b\uff0c\u6b64\u8fc7\u7a0b\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n\n\n\n<p>\u5728\u67e5\u8be2\u7684\u65f6\u5019\uff0c\u901a\u8fc7\u76f8\u540c\u7684\u7c97\u91cf\u5316\uff0c\u53ef\u4ee5\u5feb\u901f\u5b9a\u4f4d\u5230\u67e5\u8be2\u5411\u91cf\u5c5e\u4e8e\u54ea\u4e2ac_i\uff08\u5373\u5728\u54ea\u4e00\u4e2a\u611f\u5174\u8da3\u533a\u57df\uff09\uff0c\u7136\u540e\u5728\u8be5\u611f\u5174\u8da3\u533a\u57df\u6309\u4e0a\u9762\u6240\u8ff0\u7684PQ\u4e58\u79ef\u91cf\u5316\u8ddd\u79bb\u8ba1\u7b97\u65b9\u5f0f\u8ba1\u7b97\u8ddd\u79bb\u3002<\/p>\n\n\n\n<h4 class=\"has-light-gray-background-color has-background\" id=\"\u6700\u4f18\u4e58\u79ef\u91cf\u5316\">4\u3001\u6700\u4f18\u4e58\u79ef\u91cf\u5316<\/h4>\n\n\n\n<p>    \u6700\u4f18\u4e58\u79ef\u91cf\u5316\uff08Optimal Product Quantization, OPQ\uff09\u662fPQ\u7684\u4e00\u79cd\u6539\u8fdb\u7248\u672c\u3002\u5176\u6539\u8fdb\u4f53\u73b0\u5728\uff0c\u81f4\u529b\u4e8e\u5728\u5b50\u7a7a\u95f4\u5206\u5272\u65f6\uff0c\u5bf9\u5404\u5b50\u7a7a\u95f4\u7684\u65b9\u5dee\u8fdb\u884c\u5747\u8861\u3002\u5728\u5177\u4f53\u5b9e\u73b0\u7684\u65f6\u5019\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06Optimal\u7684\u8fc7\u7a0b\u5b9e\u73b0\u4e3a\u4e00\u4e2a\u7ec4\u4ef6\u3002<\/p>\n\n\n\n<p>   \u901a\u5e38\uff0c\u7528\u4e8e\u68c0\u7d22\u7684\u539f\u59cb\u7279\u5f81\u7ef4\u5ea6\u8f83\u9ad8\uff0c\u6240\u4ee5\u5b9e\u9645\u5728\u4f7f\u7528PQ\u7b49\u65b9\u6cd5\u6784\u5efa\u7d22\u5f15\u7684\u65f6\u5019\uff0c\u5e38\u4f1a\u5bf9\u9ad8\u7ef4\u7684\u7279\u5f81\u4f7f\u7528PCA\u7b49\u964d\u7ef4\u65b9\u6cd5\u5bf9\u7279\u5f81\u5148\u505a\u964d\u7ef4\u5904\u7406\uff0c\u8fd9\u6837\u964d\u7ef4\u9884\u5904\u7406\uff0c\u53ef\u4ee5\u8fbe\u5230\u4e24\u4e2a\u76ee\u7684\uff1a\u4e00\u662f\u964d\u4f4e\u7279\u5f81\u7ef4\u5ea6\uff1b\u4e8c\u662f\u5728\u5bf9\u5411\u91cf\u8fdb\u884c\u5b50\u6bb5\u5207\u5206\u7684\u65f6\u5019\u8981\u6c42\u7279\u5f81\u5404\u4e2a\u7ef4\u5ea6\u662f\u4e0d\u76f8\u5173\u7684\uff0c\u505a\u5b8cPCA\u4e4b\u540e\uff0c\u53ef\u4ee5\u4e00\u5b9a\u7a0b\u5ea6\u7f13\u89e3\u8fd9\u4e2a\u95ee\u9898\u3002\u4f46\u662f\u8fd9\u4e48\u505a\u4e86\u540e\uff0c\u5728\u5207\u5206\u5b50\u6bb5\u7684\u65f6\u5019\uff0c\u91c7\u7528\u987a\u5e8f\u5207\u5206\u5b50\u6bb5\u4ecd\u7136\u5b58\u5728\u4e00\u5b9a\u7684\u95ee\u9898\uff0c\u8fd9\u4e2a\u95ee\u9898\u53ef\u4ee5\u501f\u7528ITQ\u4e2d\u7684\u4e00\u4e2a\u4e8c\u7ef4\u5e73\u9762\u7684\u4f8b\u5b50\u52a0\u4ee5\u8bf4\u660e\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"416\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-8-1024x416.png\" alt=\"\" class=\"wp-image-14609\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-8-1024x416.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-8-300x122.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-8-768x312.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2023\/03\/image-8.png 1110w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>     \u5982\u4e0a\u9762a\u56fe\u6240\u793a\uff0c\u5bf9\u4e8ePCA\u964d\u7ef4\u540e\u7684\u4e8c\u7ef4\u7a7a\u95f4\uff0c\u5047\u8bbe\u5728\u505aPQ\u7684\u65f6\u5019\uff0c\u5c06\u5b50\u6bb5\u6570\u76ee\u8bbe\u7f6e\u4e3a2\u6bb5\uff0c\u5373\u5207\u5206\u6210x\u548cy\u4e24\u4e2a\u5b50\u5411\u91cf\uff0c\u7136\u540e\u5206\u522b\u5728x\u548cy\u4e0a\u505a\u805a\u7c7b\uff08\u5047\u8bbe\u805a\u7c7b\u4e2d\u5fc3\u8bbe\u7f6e\u4e3a2\uff09\u3002\u5bf9a\u56fe\u548cc\u56fe\u805a\u7c7b\u7684\u7ed3\u679c\u8fdb\u884c\u6bd4\u8f83\uff0c\u53ef\u4ee5\u660e\u663e\u7684\u53d1\u73b0\uff0ca\u56fe\u5728y\u65b9\u5411\u4e0a\u805a\u7c7b\u7684\u6548\u679c\u660e\u663e\u5dee\u4e8ec\u56fe\uff0c\u800cPQ\u53c8\u662f\u91c7\u7528\u805a\u7c7b\u4e2d\u5fc3\u6765\u8fd1\u4f3c\u539f\u59cb\u5411\u91cf\uff08\u8fd9\u91cc\u6307\u964d\u7ef4\u540e\u7684\u5411\u91cf\uff09\uff0c\u4e5f\u5c31\u662fc\u56fe\u662f\u6211\u4eec\u9700\u8981\u7684\u7ed3\u679c\u3002\u8fd9\u4e2a\u95ee\u9898\u53ef\u4ee5\u8f6c\u5316\u4e3a\u6570\u636e\u65b9\u5dee\u6765\u63cf\u8ff0\uff1a\u5728\u505aPQ\u7f16\u7801\u65f6\uff0c\u5bf9\u4e8e\u5207\u5206\u7684\u5404\u4e2a\u5b50\u7a7a\u95f4\uff0c\u6211\u4eec\u5e94\u5c3d\u53ef\u80fd\u4f7f\u5f97\u5404\u4e2a\u5b50\u7a7a\u95f4\u7684\u65b9\u5dee\u6bd4\u8f83\u63a5\u8fd1\uff0c\u6700\u7406\u60f3\u7684\u60c5\u51b5\u662f\u5404\u4e2a\u5b50\u7a7a\u95f4\u7684\u65b9\u5dee\u90fd\u76f8\u7b49\u3002\u4e0a\u56fea\u56fe\u4e2d\uff0cx\u548cy\u5404\u4e2a\u65b9\u5411\u7684\u65b9\u5dee\u660e\u663e\u662f\u5dee\u5f97\u6bd4\u8f83\u5927\u7684\uff0c\u800c\u5bf9\u4e8ec\u56fe\uff0cx\u548cy\u65b9\u5411\u5404\u4e2a\u65b9\u5411\u7684\u65b9\u5dee\u5dee\u4e0d\u591a\u662f\u6bd4\u8f83\u63a5\u8fd1\u7684\u3002<\/p>\n\n\n\n<p>     \u4e3a\u4e86\u5728\u5207\u5206\u5b50\u6bb5\u7684\u65f6\u5019\uff0c\u4f7f\u5f97\u5404\u4e2a\u5b50\u7a7a\u95f4\u7684\u65b9\u5dee\u5c3d\u53ef\u80fd\u7684\u4e00\u81f4\uff0cHerve Jegou\u5728<a href=\"https:\/\/lear.inrialpes.fr\/pubs\/2010\/JDSP10\/jegou_compactimagerepresentation.pdf\">Aggregating local descriptors into a compact image representation<\/a>\u4e2d\u63d0\u51fa\u4f7f\u7528\u4e00\u4e2a\u6b63\u4ea4\u77e9\u9635\u6765\u5bf9PCA\u964d\u7ef4\u540e\u7684\u6570\u636e\u518d\u505a\u4e00\u6b21\u53d8\u6362\uff0c\u4f7f\u5f97\u5404\u4e2a\u5b50\u7a7a\u95f4\u7684\u65b9\u5dee\u5c3d\u53ef\u80fd\u7684\u4e00\u81f4\u3002\u5176\u5bf9\u5e94\u7684\u5f85\u4f18\u5316\u76ee\u6807\u51fd\u6570\u89c1\u8bba\u6587\u7684\u7b2c5\u9875\uff0c\u7531\u4e8e\u4f18\u5316\u8be5\u76ee\u6807\u51fd\u6570\u6781\u5176\u56f0\u96be\uff0cHerve Jegou\u4f7f\u7528\u4e86Householder\u77e9\u9635\u6765\u5f97\u5230\u8be5\u6b63\u4ea4\u77e9\u9635\uff0c\u4f46\u662f\u5f97\u5230\u7684\u8be5\u6b63\u4ea4\u77e9\u9635\u5e76\u4e0d\u80fd\u5f88\u597d\u7684\u5747\u8861\u5b50\u7a7a\u95f4\u7684\u65b9\u5dee\u3002<\/p>\n\n\n\n<p>    OPQ\u81f4\u529b\u4e8e\u89e3\u51b3\u7684\u95ee\u9898\u6b63\u662f\u5bf9\u5404\u4e2a\u5b50\u7a7a\u95f4\u65b9\u5dee\u7684\u5747\u8861\u3002\u5177\u4f53\u5230\u65b9\u6cd5\u4e0a\uff0cOPQ\u501f\u9274\u4e86ITQ\u7684\u601d\u60f3\uff0c\u5728\u805a\u7c7b\u7684\u65f6\u5019\u5bf9\u805a\u7c7b\u4e2d\u5fc3\u5bfb\u627e\u5bf9\u5e94\u7684\u6700\u4f18\u65cb\u8f6c\u77e9\u9635\uff0c\u4f7f\u5f97\u6240\u6709\u5b50\u7a7a\u95f4\u4e2d\u5404\u4e2a\u6570\u636e\u70b9\u5230\u5bf9\u5e94\u5b50\u7a7a\u95f4\u7684\u7c7b\u4e2d\u5fc3\u7684L2\u635f\u5931\u7684\u6c42\u548c\u6700\u5c0f\u3002OPQ\u5728\u5177\u4f53\u6c42\u89e3\u7684\u65f6\u5019\uff0c\u5206\u4e3a\u975e\u53c2\u6c42\u89e3\u65b9\u6cd5\u548c\u5e26\u53c2\u6c42\u89e3\u65b9\u6cd5\uff0c\u5177\u4f53\u4e3a\uff1a<\/p>\n\n\n\n<ul><li>\u975e\u53c2\u6c42\u89e3\u65b9\u6cd5\u3002\u8ddfITQ\u7684\u6c42\u89e3\u8fc7\u7a0b\u4e00\u6837\u3002<\/li><li>\u5e26\u53c2\u6c42\u89e3\u65b9\u6cd5\u3002\u5e26\u53c2\u6c42\u89e3\u65b9\u6cd5\u5047\u8bbe\u6570\u636e\u670d\u4ece\u9ad8\u65af\u5206\u5e03\uff0c\u5728\u6b64\u6761\u4ef6\u4e0b\uff0c\u6700\u7ec8\u53ef\u4ee5\u5c06\u6c42\u89e3\u8fc7\u7a0b\u7b80\u5316\u4e3a\u6570\u636e\u7ecf\u8fc7PCA\u5206\u89e3\u540e\uff0c\u7279\u5f81\u503c\u5982\u4f55\u5206\u7ec4\u7684\u95ee\u9898\u3002\u5728\u5b9e\u9645\u4e2d\uff0c\u8be5\u89e3\u6cd5\u66f4\u5177\u5907\u9ad8\u5b9e\u7528\u6027\u3002<\/li><\/ul>\n\n\n\n<p>      \u4ece\u4e0a\u9762\u53ef\u4ee5\u770b\u5230\uff0c\u5012\u6392\u4e58\u79ef\u91cf\u5316IVFPQ\u53ef\u4ee5\u89c6\u4e3a1\u9636\u6bb5\u7684MSVQ\u548cPQ\u7684\u7ed3\u5408\u7248\u672c\uff0c\u800cOPQ\u662fPQ\u5bf9\u5b50\u7a7a\u95f4\u65b9\u5dee\u5747\u8861\u7684\u6539\u8fdb\u3002\u57fa\u4e8e\u8fd9\u6837\u4e00\u79cd\u666e\u9002\u6027\u7684\u89c6\u89d2\uff0c<strong>\u53ef\u4ee5\u6784\u5efa\u4e00\u79cd\u77e2\u91cf\u91cf\u5316\u6846\u67b6\uff0cMSVQ\u3001PQ\u3001OPQ\u4e2d\u7684O\uff0c\u90fd\u662f\u8be5\u77e2\u91cf\u91cf\u5316\u6846\u67b6\u4e2d\u7684\u57fa\u7840\u7ec4\u4ef6<\/strong>\uff0c\u901a\u8fc7\u8fd9\u4e9b\u7ec4\u4ef6\u7684\u7ec4\u5408\uff0c\u6211\u4eec\u53ef\u4ee5\u654f\u6377\u7684\u5f97\u5230\u4e0a\u9762\u4ecb\u7ecd\u65b9\u6cd5\u7684\u5404\u79cd\u5b9e\u73b0\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>http:\/\/www.mqasem.net\/vectorquantization\/vq.html VQ, \u5373V &hellip; <a href=\"http:\/\/139.9.1.231\/index.php\/2023\/03\/05\/vector-quantization-vqvae\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Vector Quantization \u77e2\u91cf\u91cf\u5316 [VQVAE]<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[11,4,34],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/14554"}],"collection":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/comments?post=14554"}],"version-history":[{"count":52,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/14554\/revisions"}],"predecessor-version":[{"id":17116,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/14554\/revisions\/17116"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=14554"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=14554"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=14554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}