{"id":3512,"date":"2022-08-05T09:00:19","date_gmt":"2022-08-05T00:00:19","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=3512"},"modified":"2022-08-05T09:00:19","modified_gmt":"2022-08-05T00:00:19","slug":"%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/","title":{"rendered":"\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3067\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306f\u3046\u307e\u304f\u3067\u304d\u308b\u306e\u304b\uff1f"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\" >\u6587\u732e\u60c5\u5831<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E6%A6%82%E8%A6%81\" >\u6982\u8981<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E4%BB%8A%E5%9B%9E%E7%B4%B9%E4%BB%8B%E3%81%99%E3%82%8B%E5%AE%9A%E5%BC%8F%E5%8C%96%E6%89%8B%E6%B3%95\" >\u4eca\u56de\u7d39\u4ecb\u3059\u308b\u5b9a\u5f0f\u5316\u624b\u6cd5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E5%BE%93%E6%9D%A5%E3%81%AE%E3%82%AF%E3%83%A9%E3%82%B9%E3%82%BF%E3%83%AA%E3%83%B3%E3%82%B0%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >\u5f93\u6765\u306e\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306e\u5b9a\u5f0f\u5316<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#One-hot_encoding%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >One-hot encoding\u306e\u5b9a\u5f0f\u5316<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E3%82%B9%E3%83%94%E3%83%B3%E5%A4%89%E6%95%B0%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E3%82%B3%E3%82%B9%E3%83%88%E9%96%A2%E6%95%B0%E3%81%AE%E6%9B%B8%E3%81%8D%E6%8F%9B%E3%81%88\" >\u30b9\u30d4\u30f3\u5909\u6570\u3092\u7528\u3044\u305f\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u66f8\u304d\u63db\u3048<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#Binary_clustering%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >Binary clustering\u306e\u5b9a\u5f0f\u5316<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E7%B5%90%E6%9E%9C\" >\u7d50\u679c<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#One-hot_encoding%E3%81%AE%E7%B5%90%E6%9E%9C\" >One-hot encoding\u306e\u7d50\u679c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#Binary_clustering_%E3%81%AE%E7%B5%90%E6%9E%9C\" >Binary clustering \u306e\u7d50\u679c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E7%B5%90%E8%AB%96\" >\u7d50\u8ad6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%83%a9%e3%82%b9%e3%82%bf%e3%83%aa%e3%83%b3%e3%82%b0\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30bf\u30a4\u30c8\u30eb\uff1aQuantum annealing for combinatorial clustering<br>\u8457\u8005\uff1aVaibhaw Kumar, Gideon Bass, Casey Tomlin, Joseph Dulny III<br>\u66f8\u8a8c\u60c5\u5831\uff1a<a href=\"https:\/\/arxiv.org\/abs\/1708.05753\">https:\/\/arxiv.org\/abs\/1708.05753<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3068\u306f\u3001\u6559\u5e2b\u7121\u3057\u5b66\u7fd2\u306e\u4e00\u3064\u3067\u3001\u985e\u4f3c\u3057\u305f\u7279\u5fb4\u3092\u6301\u3063\u305f\u30c7\u30fc\u30bf\u304c\u540c\u3058\u30b0\u30eb\u30fc\u30d7\u306b\u5c5e\u3059\u308b\u3088\u3046\u306b\u30b0\u30eb\u30fc\u30d7\u5206\u3051\u3059\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u4e3b\u306a\u624b\u6cd5\u306bk-means\u3084\u968e\u5c64\u578b\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306f\u5c40\u6240\u63a2\u7d22\u6cd5\u3067\u3042\u308b\u305f\u3081\u6700\u9069\u89e3\u306b\u5230\u9054\u3059\u308b\u4fdd\u8a3c\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u4e00\u65b9\u3067\u3001SA\u3084\u907a\u4f1d\u7684\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u3088\u3046\u306a\u5927\u57df\u7684\u306a\u63a2\u7d22\u624b\u6cd5\u3067\u306f\u5b9f\u884c\u6642\u9593\u304c\u9577\u304f\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002<br>\u305d\u3053\u3067\u3001\u672c\u8ad6\u6587\u3067\u306f\u9ad8\u901f\u306b\u5b9f\u884c\u53ef\u80fd\u306a\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3067\u8a08\u7b97\u53ef\u80fd\u306a\u5f62\u3067\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3092\u5b9a\u5f0f\u5316\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u305d\u306e\u6700\u9069\u5316\u3092\u5b9f\u884c\u3057\u5f97\u3089\u308c\u305f\u7d50\u679c\u3092k-means\u3068\u6bd4\u8f03\u3057\u3001\u63d0\u6848\u624b\u6cd5\u306e\u5229\u70b9\u3068\u6b20\u70b9\u306b\u3064\u3044\u3066\u8b70\u8ad6\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E4%BB%8A%E5%9B%9E%E7%B4%B9%E4%BB%8B%E3%81%99%E3%82%8B%E5%AE%9A%E5%BC%8F%E5%8C%96%E6%89%8B%E6%B3%95\"><\/span>\u4eca\u56de\u7d39\u4ecb\u3059\u308b\u5b9a\u5f0f\u5316\u624b\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001One-hot encoding\u3068Binary clustering\u306e2\u3064\u306e\u5b9a\u5f0f\u5316\u624b\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%BE%93%E6%9D%A5%E3%81%AE%E3%82%AF%E3%83%A9%E3%82%B9%E3%82%BF%E3%83%AA%E3%83%B3%E3%82%B0%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>\u5f93\u6765\u306e\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306f\u6b21\u306e\u30b3\u30b9\u30c8\u95a2\u6570$H$ \u306e\u6700\u5c0f\u5316\u3068\u3057\u3066\u8868\u73fe\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>H =<br>\\frac{1}{2} \\sum^K_{a=1} \\sum_{C(i)=C_a} \\sum_{C(j)=C_a} d(x_i,x_j) \\tag{1}<br>$$<\/p>\n\n\n\n<p>$x_i$\u306f\u5404\u30c7\u30fc\u30bf\u70b9\u3001$d(x_i,x_{j})$\u306f\u30c7\u30fc\u30bf\u70b9\u9593\u306e\u8ddd\u96e2\u3067\u3059\u3002\u307e\u305f\u3001$C(i)=C_a$\u306f$i$\u756a\u76ee\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u30af\u30e9\u30b9\u30bf\u30fc$C_a$\u306b\u5c5e\u3059\u308b\u3053\u3068\u3092\u8868\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u3053\u306e\u30b3\u30b9\u30c8\u95a2\u6570$H$\u306f\u540c\u3058\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u5c5e\u3059\u308b\u30c7\u30fc\u30bf\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u7dcf\u548c\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"One-hot_encoding%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span><span lang=\"EN-US\">One-hot encoding<\/span>\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001$N$\u500b\u306e\u30c7\u30fc\u30bf\u70b9$x_i(i=1 \\sim N)$\u3092$K$\u500b\u306e\u30af\u30e9\u30b9\u30bf\u30fc$C_a(a=1 \\sim K)$\u306b\u5272\u308a\u5f53\u3066\u308b\u3068\u3044\u3046\u554f\u984c\u3092\u8003\u3048\u307e\u3059\u3002<br>\u307e\u305a\u3001\u30c7\u30fc\u30bf\u70b9$x_i$\u304c\u30af\u30e9\u30b9\u30bf\u30fc$C_a$\u306b\u5c5e\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u8868\u73fe\u3059\u308b\u4e8c\u5024\u5909\u6570$q_{i,a}$\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>q_{i,a} =<br>\\begin{cases}<br>1 &amp; \\text{if \u30c7\u30fc\u30bf\u70b9x_i\u304c\u30af\u30e9\u30b9\u30bf\u30fcC_a\u306b\u5c5e\u3059\u308b} \\\\<br>0 &amp; \\text{otherwize}<br>\\end{cases}<br>\\tag{2}<br>$$<\/p>\n\n\n\n<p>\u3053\u306e\u8868\u73fe\u65b9\u6cd5\u3092One-hot encoding\u3068\u547c\u3073\u3001$q_{i,a}$\u306b\u3088\u308a\u30b3\u30b9\u30c8\u95a2\u6570$H$\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304d\u76f4\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>H&#8217; = \\frac{1}{2}\\sum^N_{i,j=1}d(x_i,x_j)\\sum^K_{a=1}q_{i,a}q_{j,a} \\tag{3}<br>$$<\/p>\n\n\n\n<p>\u3057\u304b\u3057\u3001\u3053\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u3092\u6700\u5c0f\u5316\u3059\u308b\u3068\u3059\u3079\u3066\u306e$q$\u304c0\u3001\u3059\u306a\u308f\u3061\u5168\u3066\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u3069\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u3082\u542b\u307e\u308c\u306a\u3044\u72b6\u614b\u304c\u6700\u9069\u89e3\u3068\u306a\u3063\u3066\u3057\u307e\u3044\u3001\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u304c\u5b9f\u73fe\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u5404\u30c7\u30fc\u30bf\u70b9\u304c\u305f\u30601\u3064\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u542b\u307e\u308c\u308b\u3088\u3046\u306b\u4ee5\u4e0b\u306e\u5236\u7d04$\\Phi_i$\u3092\u52a0\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\Phi_i = \\left(\\sum^K_{a=1}q_{i,a}-1\\right)^2 \\tag{4}<br>$$<\/p>\n\n\n\n<p>\u6700\u7d42\u7684\u306b\u3053\u306e\u554f\u984c\u306f\u4ee5\u4e0b\u306e\u30b3\u30b9\u30c8\u95a2\u6570$H$\u3067\u5b9a\u5f0f\u5316\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>H = H&#8217; + \\sum^N_{i=1}\\lambda_i \\Phi_i = \\frac{1}{2}\\sum^N_{i,j=1}d(x_i,x_j)\\sum^K_{a=1}q_{i,a}q_{j,a} + \\sum^N_{i=1}\\lambda_i\\left(\\sum^K_{a=1}q_{i,a}-1\\right)^2 \\tag{5}<br>$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001$\\lambda_i$\u306f\u5236\u7d04\u306e\u5f37\u3055\u3092\u6c7a\u3081\u308b\u4fc2\u6570\u3067\u3042\u308a\u3001\u5236\u7d04\u9055\u53cd\u3092\u8d77\u3053\u3055\u306a\u3044\u3088\u3046\u306b\u5341\u5206\u5927\u304d\u304f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5341\u5206\u306a\u5024\u3092\u8abf\u3079\u308b\u305f\u3081\u306b\u3001\u3042\u308b1\u3064\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u3069\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u3082\u5272\u308a\u5f53\u3066\u3089\u308c\u306a\u3044\u5834\u5408\u306b\u6700\u5927\u3067\u3069\u306e\u304f\u3089\u3044\u30b3\u30b9\u30c8\u95a2\u6570$H&#8217;$\u306e\u5024\u304c\u5c0f\u3055\u304f\u306a\u308b\u304b\u3092\u8003\u3048\u307e\u3059\u3002<br>\u3082\u3057\u3001\u5404\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u6700\u4f4e1\u3064\u306f\u30c7\u30fc\u30bf\u70b9\u304c\u5272\u308a\u5f53\u3066\u3089\u308c\u308b\u3068\u3059\u308b\u3068\u30011\u3064\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u542b\u307e\u308c\u308b\u30c7\u30fc\u30bf\u70b9\u306e\u500b\u6570\u306f\u6700\u5927\u3067$(N-K+1)$\u500b\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u6642\u3001\u3042\u308b1\u3064\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u3069\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u3082\u5272\u308a\u5f53\u3066\u3089\u308c\u306a\u304f\u306a\u308b\uff08\u5024\u304c0\u306b\u306a\u308b\uff09\u3068\u3001\u81ea\u8eab\u3092\u9664\u3044\u305f$(N-K)$\u500b\u306e\u30c7\u30fc\u30bf\u70b9\u3068\u306e\u9593\u306e\u8ddd\u96e2\u304c\u30b3\u30b9\u30c8\u95a2\u6570$H&#8217;$\u306b\u304a\u3044\u3066\u8db3\u3057\u5408\u308f\u3055\u308c\u306a\u304f\u306a\u308a\u307e\u3059\u3002\u56f31\u3067\u306f$N=6,K=3$\u306e\u30b1\u30fc\u30b9\u3092\u4f8b\u306b\u3053\u308c\u3092\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/05\/58461cd60a862029ee9607c6042493dd-e1654213427495.png\" alt=\"\" width=\"328\" height=\"329\"\/><figcaption>\u56f31: \u30b3\u30b9\u30c8\u95a2\u6570H\u304c\u6700\u3082\u6e1b\u5c11\u3059\u308b\u30b1\u30fc\u30b9\u306e\u4f8b<\/figcaption><\/figure><\/div>\n\n\n\n<p>\u30b3\u30b9\u30c8\u95a2\u6570$H&#8217;$\u304c\u6700\u3082\u6e1b\u5c11\u3059\u308b\u306e\u306f\u3001\u540c\u3058\u30af\u30e9\u30b9\u30bf\u30fc\u5185\u306e$(N-K)$\u500b\u306e\u70b9\u304c$x_i$\u304b\u3089$d$\u306e\u6700\u5927\u5024\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u5834\u5408\u3067\u3059\u3002\u3053\u308c\u3092\u6570\u5f0f\u3068\u3057\u3066\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\sum_{x_j \\in C_a}d(x_i,x_j) \\leq (N-K) \\cdot \\max_{x_j \\in C_a} d(x_i,x_j) \\tag{6}$$<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001\u3059\u3079\u3066\u306e$i$\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u3088\u3046\u306b$\\lambda_i = \\lambda$\u3068\u8a2d\u5b9a\u3059\u308b\u3068\u3001\u3042\u308b\u70b9\u3092\u3069\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u3082\u5272\u308a\u5f53\u3066\u306a\u3044\u4e8b\u306b\u3088\u308b\u30b3\u30b9\u30c8\u95a2\u6570$H&#8217;$\u306e\u6e1b\u5c11\u91cf\u304c\u5236\u7d04\u9055\u53cd\u306b\u3088\u308b$\\lambda\\Phi_i$\u306e\u5897\u52a0\u91cf\u3092\u4e0b\u56de\u308b\u305f\u3081\u3001\u5236\u7d04\u9055\u53cd\u3092\u9632\u3050\u4e8b\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\lambda \\geq (N-K) \\cdot \\max_{i,j} d(x_i,x_j) \\tag{7}$$<\/p>\n\n\n\n<p>\u5b9f\u8df5\u7684\u306b\u306f\u3001$d(x_i,x_j)$\u306e\u5024\u306f$ \\underset{i,j}{\\max} d(x_i,x_j)=1$\u3068\u306a\u308b\u3088\u3046\u6b63\u898f\u5316\u3055\u308c\u308b\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$ \\lambda = N-K \\tag{8}$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%B9%E3%83%94%E3%83%B3%E5%A4%89%E6%95%B0%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E3%82%B3%E3%82%B9%E3%83%88%E9%96%A2%E6%95%B0%E3%81%AE%E6%9B%B8%E3%81%8D%E6%8F%9B%E3%81%88\"><\/span>\u30b9\u30d4\u30f3\u5909\u6570\u3092\u7528\u3044\u305f\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u66f8\u304d\u63db\u3048<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u4e0a\u3067\u306e\u6570\u5024\u306e\u7cbe\u5ea6\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u305f\u3081\u306b\u3001\u30b3\u30b9\u30c8\u95a2\u6570 $H$\u3092\u30b9\u30d4\u30f3\u5909\u6570$s_{i,a}\\in\\{1,-1 \\}$ \u3067\u66f8\u304d\u63db\u3048\u307e\u3059\u3002$q_{i,a}$ \u3068$s_{i,a}$ \u306f$q_{i,a}=\\frac{1}{2}(s_{i,a}+1)$\u3068\u3044\u3046\u5bfe\u5fdc\u95a2\u4fc2\u306b\u3042\u308b\u305f\u3081\u3001\u30b3\u30b9\u30c8\u95a2\u6570 $H$ \u306f$s_{i,a}$\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304d\u76f4\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>H = \\frac{1}{2}\\sum^K_{a=1}\\sum^N_{i,j=1}d(x_i,x_j)\\frac{1}{2}(s_{i,a}+1)\\frac{1}{2}(s_{j,a}+1) + \\lambda \\sum^N_{i=1}\\left(\\sum^K_{a=1} \\left\\{\\frac{1}{2}(s_{i,a}+1)\\right\\}-1\\right)^2 \\tag{9}<br>$$<\/p>\n\n\n\n<p>\u30b3\u30b9\u30c8\u95a2\u6570 $H$\u3092\u5c55\u958b\u3057\u3066\u6700\u5c0f\u5316\u306b\u5f71\u97ff\u3057\u306a\u3044\u5b9a\u6570\u9805\u3092\u53d6\u308a\u9664\u304d\u3001\u5168\u4f53\u30924\u500d\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>H &amp;= \\frac{1}{2}\\sum^K_{a=1}\\sum_{(i,j)}d(x_i,x_j)s_{i,a}s_{j,a} + \\lambda \\sum^N_{i=1}\\sum_{(a,b)} s_{i,a}s_{i,b} \\\\ &amp;+ \\sum_{(i,j)}d(x_i,x_j)\\sum^K_{a=1}s_{i,a} + 2\\lambda(K-2)\\sum^N_{i=1}\\sum^K_{a=1}s_{i,a}<br>\\end{align} \\tag{10}<br>$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306e\u5236\u7d04\u306e\u4e0b\u3067\u4fc2\u6570 $\\lambda$\u306e\u6700\u5927\u5316\u3092\u8003\u3048\u307e\u3059\u3002 $K&gt;2$\u3067\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306e\u7cbe\u5ea6\u304c $n$ \u30d3\u30c3\u30c8\u3067\u3042\u308b\u5834\u5408\u3001 $\\lambda$\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u7b49\u5f0f\u304c\u6210\u7acb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>2 \\lambda(K-2) = 2^{n-1}-1 \\tag{11}<br>$$<\/p>\n\n\n\n<p>\u3053\u308c\u3068\u5f0f $(6)$\u3088\u308a\u3001\u30c7\u30fc\u30bf\u9593\u306e\u8ddd\u96e2 $d$\u306e\u5927\u304d\u3055\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u304c\u6210\u7acb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>|d| \\leq \\frac{2(2^{n-1}-1)}{(N-K)(K-2)} \\tag{12}<br>$$<\/p>\n\n\n\n<p>\u4e0a\u8a18\u306e\u4e0d\u7b49\u5f0f\u304b\u3089\u3001\u30c7\u30fc\u30bf\u306e\u500b\u6570$N$ \u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069 $d$\u306e\u6700\u5927\u5024\u304c\u5c0f\u3055\u304f\u306a\u308a\u3001\u6570\u5024\u306e\u7cbe\u5ea6\u304c\u60aa\u5316\u3059\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3053\u3046\u3044\u3063\u305f\u7406\u7531\u304b\u3089\u3001\u73fe\u4ee3\u306e$6$\u30d3\u30c3\u30c8\u306e\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3092\u30bd\u30eb\u30d0\u30fc\u306b\u7528\u3044\u308b\u5834\u5408\u306b\u306f\u3001\u30c7\u30fc\u30bf\u306e\u500b\u6570$N$ \u304c\u5c0f\u3055\u3044\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306e\u307f\u78ba\u5b9f\u306b\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binary_clustering%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span><span lang=\"EN-US\">Binary clustering<\/span>\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001 $N$ \u500b\u306e\u30c7\u30fc\u30bf\u70b9\u30922 \u500b\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u5272\u308a\u5f53\u3066\u308b\u3068\u3044\u3046\u554f\u984c\u3092\u8003\u3048\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u306b\u306f\u3001\u30b9\u30d4\u30f3\u5909\u6570\u3092\u7528\u3044\u3066\u30c7\u30fc\u30bf\u70b9\u304c\u30af\u30e9\u30b9\u30bf\u30fc1 \u306b\u5c5e\u3059\u308b\u3053\u3068\u3092$1$ \u3001\u5c5e\u3055\u306a\u3044\uff08\u30af\u30e9\u30b9\u30bf\u30fc2\u306b\u5c5e\u3059\u308b\uff09\u3053\u3068\u3092$-1$ \u3067\u8868\u73fe\u3059\u308b\u3053\u3068\u3067\u3001\u5168\u3066\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u5fc5\u305a\u3044\u305a\u308c\u304b\u4e00\u65b9\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u307e\u3059\u3002\u305d\u306e\u305f\u3081one-hot\u5236\u7d04\u3092\u7528\u3044\u306a\u3044\u4ee5\u4e0b\u306e\u30b3\u30b9\u30c8\u95a2\u6570$H$ \u3067\u5b9a\u5f0f\u5316\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>H = \\frac{1}{2} \\sum^N_{i,j=1}d(x_i,x_j)s_i s_j\\tag{13}<br>$$<\/p>\n\n\n\n<p>$d(x_i,x_j)$\u306e\u5024\u304c\u5927\u304d\u3044\u307b\u3069\u3001$s_i,s_j$\u306f\u7570\u306a\u308b\u5024\u3092\u53d6\u308d\u3046\u3068\u3059\u308b\u305f\u3081\u5225\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5b9a\u5f0f\u5316\u306b\u306f\u5236\u7d04\u304c\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\u3001\u6570\u5024\u306e\u7cbe\u5ea6\u306b\u3064\u3044\u3066\u5fc3\u914d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u3055\u3089\u306b\u3001$K=2$\u306e\u6642\u306eOne-hot encoding\u3068\u6bd4\u8f03\u3057\u3066\u4f7f\u7528\u3059\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u6570\u304c\u534a\u5206\u306b\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3067\u3001\u3053\u306e\u5b9a\u5f0f\u5316\u306f $K=2$\u306e\u5834\u5408\u306b\u3057\u304b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u3001\u3088\u308a\u591a\u304f\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u3078\u306e\u5272\u308a\u5f53\u3066\u3092\u6271\u3046\u306b\u306f\u3001\u5206\u5272\u3057\u305f\u5404\u30af\u30e9\u30b9\u30bf\u30fc\u3092\u518d\u5ea6\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306b\u3088\u308a\u5206\u5272\u3059\u308b\u968e\u5c64\u578b\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u7b49\u306e\u5229\u7528\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C\"><\/span>\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u3053\u3053\u307e\u3067\u3067\u63d0\u6848\u3057\u305f\u5b9a\u5f0f\u5316\u306b\u3088\u308b\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306e\u6027\u80fd\u3092\u3001\u65e2\u5b58\u624b\u6cd5\u3067\u3042\u308bk-means\u3068\u6bd4\u8f03\u3057\u307e\u3059\u3002\u63d0\u6848\u624b\u6cd5\u306e\u30bd\u30eb\u30d0\u30fc\u306b\u306f\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u3067\u5b9f\u884c\u53ef\u80fd\u306a\u554f\u984c\u30b5\u30a4\u30ba\u3067\u3042\u308c\u3070\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0(QA)\u30de\u30b7\u30f3\u3092\u3001\u554f\u984c\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u5834\u5408\u306fqbsolv\u3092\u5229\u7528\u3057\u307e\u3059\u3002qbsolv\u3068\u306f\u5143\u306e\u5927\u898f\u6a21\u306a\u554f\u984c\u3092\u5206\u5272\u3057\u3001\u30b5\u30a4\u30ba\u306e\u5c0f\u3055\u3044\u305d\u308c\u305e\u308c\u306e\u554f\u984c\u3092\u500b\u5225\u306b\u89e3\u304f\u30c4\u30fc\u30eb\u3067\u3059\u3002\u672c\u8ad6\u6587\u3067\u306f\u5206\u5272\u5f8c\u306e\u30bd\u30eb\u30d0\u30fc\u306b\u306f\u30bf\u30d6\u30fc\u30b5\u30fc\u30c1\u3068\u3044\u3046\u5c40\u6240\u63a2\u7d22\u6cd5\u3092\u7528\u3044\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"One-hot_encoding%E3%81%AE%E7%B5%90%E6%9E%9C\"><\/span><span lang=\"EN-US\">One-hot encoding<\/span>\u306e\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u307e\u305a\u3001$N=12,K=4$\u306e\u7d50\u679c\u3092\u56f3 2\u306b\u793a\u3057\u307e\u3059\u3002(a)~(c)\u306fk-means\u3001(d)\u306fOne-hot encoding\u306b\u3088\u308a\u5b9a\u5f0f\u5316\u3057QA\u30de\u30b7\u30f3\u3067\u89e3\u3044\u305f\u7d50\u679c\u3067\u3059\u3002k-means\u3067\u89e3\u304f\u969b\u3001\u30af\u30e9\u30b9\u30bf\u30fc\u306e\u4e2d\u5fc3\u306e\u3046\u3061\u3001\u4e00\u3064\u304c\u4e8c\u3064\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306e\u771f\u3093\u4e2d\u306b\u3001\u6b8b\u308a\u306e\u4e09\u3064\u304c\u4ed6\u306e\u4e8c\u3064\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306e\u8fd1\u304f\u306b\u521d\u671f\u5316\u3055\u308c\u3066\u3057\u307e\u3046\u3068\u6700\u9069\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u3044\u307e\u305b\u3093\u3002\u3053\u306e\u3088\u3046\u306a\u554f\u984c\u306f\u30c7\u30fc\u30bf\u70b9\u304c$2$\u6b21\u5143\u3088\u308a\u5927\u304d\u3044\u7a7a\u9593\u306b\u5c5e\u3059\u308b\u969b\u306b\u3088\u308a\u983b\u7e41\u306b\u8d77\u3053\u308a\u307e\u3059\u3002\u4e00\u65b9\u3001One-hot encoding\u3067\u5b9a\u5f0f\u5316\u3057QA\u30de\u30b7\u30f3\u3067\u89e3\u3044\u305f\u5834\u5408\u306b\u306f\u4f9d\u5b58\u3059\u308b\u521d\u671f\u5024\u304c\u5b58\u5728\u3057\u306a\u3044\u305f\u30811000\u30b5\u30f3\u30d7\u30eb\u5168\u3066\u3067\u6700\u9069\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/05\/MiConv.com__figure1.jpeg\" alt=\"\"\/><figcaption>\u56f32: $N=12,K=4$\u306e\u7d50\u679c\uff08(a)~(c)\u304ck-means\u3001(d)\u304cOne-hot encoding\u3002\u00d7\u5370\u306f\u30af\u30e9\u30b9\u30bf\u30fc\u306e\u4e2d\u5fc3\uff09(<a href=\"https:\/\/arxiv.org\/abs\/1708.05753\">https:\/\/arxiv.org\/abs\/1708.05753<\/a>)<\/figcaption><\/figure><\/div>\n\n\n\n<p>\u6b21\u306b\u3001\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u5834\u5408\u306e\u7d50\u679c\u3092\u56f33\u306b\u793a\u3057\u307e\u3059\u3002(a)\u304c $N=200$\u3001(b)\u304c $N=2000$\u3067\u3042\u308a\u3001\u3044\u305a\u308c\u3082$K =6$\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u7d50\u679c\u3092\u6bd4\u8f03\u3059\u308b\u6307\u6a19\u3068\u3057\u3066\u5404\u624b\u6cd5\u306b\u304a\u3051\u308bInertia\u3092\u88681\u306b\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002Inertia\u3068\u306f\u5168\u3066\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u3064\u3044\u3066\u5c5e\u3059\u308b\u30c7\u30fc\u30bf\u70b9\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306e\u4e2d\u5fc3\u304b\u3089\u306e\u8ddd\u96e2\u306e\u7dcf\u548c\u3092\u3068\u3063\u305f\u3082\u306e\u3067\u3042\u308a\u3001\u5c0f\u3055\u3044\u307b\u3069\u30af\u30e9\u30b9\u30bf\u30fc\u5185\u306e\u30c7\u30fc\u30bf\u70b9\u304c\u8fd1\u304f\u306b\u307e\u3068\u307e\u3063\u3066\u304a\u308a\u826f\u3044\u7d50\u679c\u3068\u306a\u308a\u307e\u3059\u3002\u306a\u304a\u3001k-means\u306b\u3064\u3044\u3066\u306f\u3001\u30af\u30e9\u30b9\u30bf\u30fc\u306e\u4e2d\u5fc3\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316\u3059\u308b\u5834\u5408\u3068\u3001\u4e2d\u5fc3\u3069\u3046\u3057\u304c\u96e2\u308c\u3066\u914d\u7f6e\u3055\u308c\u308b\u3088\u3046\u521d\u671f\u5316\u3092\u3059\u308bk-means++\u3092\u7528\u3044\u305f\u5834\u5408\u306e\u4e21\u65b9\u3067\u7d50\u679c\u3092\u51fa\u3057\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u300110\u901a\u308a\u306e\u521d\u671f\u5024\u306b\u5bfe\u3059\u308b\u7d50\u679c\u306e\u4e2d\u3067Inertia\u304c\u6700\u3082\u5c0f\u3055\u3044\u3082\u306e\u3092\u89e3\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u306b\u306f\u3001\u5168\u3066\u306e\u30b1\u30fc\u30b9\u3067One-hot encoding\u306fk-means\u3088\u308a\u3082\u660e\u3089\u304b\u306b\u52a3\u308b\u7d50\u679c\u3068\u306a\u308a\u307e\u3057\u305f\u3002\u3053\u306e\u7406\u7531\u306b\u3064\u3044\u3066\u3001One-hot encoding\u306f\u5b9a\u5f0f\u5316\u306e\u624b\u6cd5\u3067\u3042\u308a\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306e\u7d50\u679c\u306f\u7528\u3044\u305f\u30bd\u30eb\u30d0\u30fc\u306e\u6027\u80fd\u306b\u3082\u4f9d\u5b58\u3059\u308b\u4e8b\u304b\u3089\u3001\u30b5\u30a4\u30ba\u304c\u5927\u304d\u304f\u306a\u3063\u305f\u3053\u3068\u3067qbsolv\u306b\u3088\u308b\u6700\u9069\u5316\u304c\u5341\u5206\u306b\u884c\u3048\u306a\u304f\u306a\u3063\u305f\u306e\u3060\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/05\/MiConv.com__figure2.jpeg\" alt=\"\"\/><figcaption>\u56f33: \u30b5\u30a4\u30ba\u306e\u5927\u304d\u3044\u554f\u984c\u306b\u5bfe\u3059\u308b\u7d50\u679c\uff08(a)\u306fN=200\u3001(b)\u306fN=2000\u306e\u5834\u5408\u3002k-means\u306f\u30de\u30fc\u30ab\u30fc\u306e\u5f62\u3001One-hot encoding\u306f\u30de\u30fc\u30ab\u30fc\u306e\u8272\u304c\u30af\u30e9\u30b9\u30bf\u30fc\u306e\u5272\u308a\u5f53\u3066\u3092\u793a\u3057\u3066\u3044\u308b\u3002\uff09(<a href=\"https:\/\/arxiv.org\/abs\/1708.05753\">https:\/\/arxiv.org\/abs\/1708.05753<\/a>)<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image wp-block-image-table\"><figure class=\"aligncenter\"><figcaption>\u88681: k-means\u3068One-hot encoding\u306eInertia\u306e\u6bd4\u8f03(<a href=\"https:\/\/arxiv.org\/abs\/1708.05753\">https:\/\/arxiv.org\/abs\/1708.05753<\/a>)<\/figcaption><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/05\/table1-e1654210310744.png\" alt=\"\"><\/figure><\/div>\n\n\n\n<p>\u307e\u305f\u3001\u4e0a\u306e $N=200$\u306e\u554f\u984c\u306b\u304a\u3044\u3066\u3001qbsolv\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fcnum_repeat\u3092\u5909\u66f4\u3057\u305f\u969b\u306eInertia\u306e\u5024\u3092\u56f34\u306b\u793a\u3057\u307e\u3059\u3002num_repeat\u3068\u306fqbsolv\u306b\u3088\u308b\u554f\u984c\u306e\u5206\u5272\u3068\u6700\u9069\u5316\u306e\u8a66\u884c\u56de\u6570\u3092\u6c7a\u3081\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3067\u3059\u3002num_repeat\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066Inertia\u306e\u5024\u304c\u6e1b\u5c11\u3057\u3001k-means\u306e\u7d50\u679c\u306b\u8fd1\u3065\u3044\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u7d50\u679c\u304b\u3089\u3001\u30bd\u30eb\u30d0\u30fc\u3092\u6539\u826f\u3059\u308b\u3068One-hot encoding\u306b\u3088\u3063\u3066\u3088\u308a\u826f\u3044\u89e3\u304c\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308b\u3068\u4e88\u60f3\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/05\/MiConv.com__figure3.jpeg\" alt=\"\"\/><figcaption>\u56f34: num_repeat\u3092\u5909\u66f4\u3057\u305f\u969b\u306eInertia\u306e\u5024\uff08\u8d64\u306e\u5b9f\u7dda\u304cOne-hot encoding\u3001\u9752\u306e\u70b9\u7dda\u304ck-means\uff09(<a href=\"https:\/\/arxiv.org\/abs\/1708.05753\">https:\/\/arxiv.org\/abs\/1708.05753<\/a>)<\/figcaption><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binary_clustering_%E3%81%AE%E7%B5%90%E6%9E%9C\"><\/span>Binary clustering \u306e\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>$N\uff1d40$\u306e\u5834\u5408\u306f\u5b9f\u969b\u306e\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u3067\u3001 $N=1000,2000$\u306e\u5834\u5408\u306f\u3001qbsolv\u3067\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u307e\u3059\u3002\u56f3 5\u306f(a)\u304c $N=40$\u3001(b)\u304c $N\uff1d2000$\u306e\u554f\u984c\u3092\u89e3\u3044\u305f\u7d50\u679c\u3067\u3059\u3002\u307e\u305f\u3001\u5404\u624b\u6cd5\u306eInertia\u3092\u8868 2\u306b\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002Binary clustering\u306fOne-hot encoding\u3068\u306f\u7570\u306a\u308a\u3001\u30b5\u30a4\u30ba $N$\u306b\u3088\u3089\u305ak-means\u306e\u7d50\u679c\u3068\u6bd4\u3079\u308f\u305a\u304b\u306a\u9055\u3044\u3057\u304b\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/05\/MiConv.com__figure4.jpeg\" alt=\"\"\/><figcaption>\u56f35: Binary Clustering\u3068k-means\u306e\u6bd4\u8f03\uff08(a)\u306fN=40\u3001(b)\u306fN=2000\u306e\u5834\u5408\u3002k-means\u306f\u30de\u30fc\u30ab\u30fc\u306e\u5f62\u3001Binary Clustering\u306f\u30de\u30fc\u30ab\u30fc\u306e\u8272\u304c\u5272\u308a\u5f53\u3066\u3092\u793a\u3057\u3066\u3044\u308b\u3002\uff09(<a href=\"https:\/\/arxiv.org\/abs\/1708.05753\">https:\/\/arxiv.org\/abs\/1708.05753<\/a>)<\/figcaption><\/figure>\n\n\n\n<div class=\"wp-block-image wp-block-image-table\"><figure class=\"aligncenter\"><figcaption>\u88682: k-means\u3068Binary clustering\u306eInertia\u306e\u6bd4\u8f03(<a href=\"https:\/\/arxiv.org\/abs\/1708.05753\">https:\/\/arxiv.org\/abs\/1708.05753<\/a>)<\/figcaption><img decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/05\/table2-e1654210621836.png\" alt=\"\"><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E8%AB%96\"><\/span>\u7d50\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001One-hot encoding\u3068Binary clustering\u306e2\u3064\u306e\u624b\u6cd5\u3067\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3092\u5b9a\u5f0f\u5316\u3057\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3084qbsolv\u3067\u5b9f\u884c\u3057\u3066\u6027\u80fd\u3092\u8a55\u4fa1\u3057\u307e\u3057\u305f\u3002One-hot encoding\u3067\u306f\u30c7\u30fc\u30bf\u70b9\u304c\u591a\u3044\u5834\u5408\u306bk-means\u3088\u308a\u3082\u52a3\u308b\u7d50\u679c\u3068\u306a\u308a\u307e\u3057\u305f\u3002\u539f\u56e0\u3068\u3057\u3066\u306f\u3001\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u591a\u304f\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u5fc5\u8981\u3067\u3042\u308b\u3053\u3068\u3084\u3001\u5236\u7d04\u306e\u6570\u5024\u7cbe\u5ea6\u304c\u5341\u5206\u3067\u306a\u3044\u3053\u3068\u306a\u3069\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30bd\u30eb\u30d0\u30fc\u306e\u8cea\u304c\u5411\u4e0a\u3059\u308b\u3053\u3068\u3067\u3088\u3044\u89e3\u304c\u5f97\u3089\u308c\u308b\u3068\u4e88\u60f3\u3055\u308c\u307e\u3059\u3002\u5bfe\u3057\u3066Binary clustering\u3067\u306f\u30c7\u30fc\u30bf\u306e\u30b5\u30a4\u30ba\u306b\u3088\u3089\u305ak-means\u3068\u6bd4\u8f03\u3057\u3066\u3082\u3088\u3044\u7d50\u679c\u3068\u306a\u308a\u307e\u3057\u305f\u3002\u5236\u7d04\u304c\u306a\u304f\u3001\u4f7f\u7528\u3059\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u3082\u5c11\u306a\u3044\u4e8b\u304c\u305d\u306e\u7406\u7531\u3068\u3057\u3066\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Binary clustering\u3067\u306f\u30b5\u30a4\u30ba$N$ \u304c\u5927\u304d\u304f\u306a\u3063\u3066\u3082\u7d50\u679c\u304c\u60aa\u5316\u3057\u306a\u3044\u304c\u3001 $K=2$\u3068\u304b\u306a\u308a\u4f7f\u7528\u3067\u304d\u308b\u7bc4\u56f2\u304c\u9650\u3089\u308c\u3066\u3044\u307e\u3057\u305f\u3002 $K$\u304c3\u4ee5\u4e0a\u3067\u3082\u30e1\u30e2\u30ea\u3084\u6570\u5024\u7cbe\u5ea6\u3001\u89e3\u306e\u8cea\u306b\u554f\u984c\u304c\u306a\u3044\u3088\u3046\u306b\u62e1\u5f35\u304c\u3067\u304d\u306a\u3044\u304b\u8208\u5473\u304c\u3042\u308a\u307e\u3059\u3002\u4eca\u56de\u8aad\u3093\u3060\u8ad6\u6587\u306e\u5185\u5bb9\u3092\u3082\u3068\u306b\u5225\u306a\u5b9a\u5f0f\u5316\u3092\u8003\u3048\u3066\u307f\u305f\u3044\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\"><\/span>\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u6703\u7530\u88d5\u6a39<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3068\u306f\u3001\u6559\u5e2b\u7121\u3057\u5b66\u7fd2\u306e\u4e00\u3064\u3067\u3001\u985e\u4f3c\u3057\u305f\u7279\u5fb4\u3092\u6301\u3063\u305f\u30c7\u30fc\u30bf\u304c\u540c\u3058\u30b0\u30eb\u30fc\u30d7\u306b\u5c5e\u3059\u308b\u3088\u3046\u306b\u30b0\u30eb\u30fc\u30d7\u5206\u3051\u3059\u308b\u3053\u3068\u3092\u8a00\u3044\u307e\u3059\u3002\u4e3b\u306a\u624b\u6cd5\u306bk-means\u3084\u968e\u5c64\u578b\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306f\u5c40\u6240\u63a2\u7d22\u6cd5\u3067\u3042\u308b\u305f\u3081\u53b3\u5bc6\u89e3\u306b\u5230\u9054\u3059\u308b\u4fdd\u8a3c\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u4e00\u65b9\u3067\u3001SA\u3084\u907a\u4f1d\u7684\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u3088\u3046\u306a\u5927\u57df\u7684\u306a\u63a2\u7d22\u624b\u6cd5\u3067\u306f\u5b9f\u884c\u6642\u9593\u304c\u9577\u304f\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002<br \/>\n\u305d\u3053\u3067\u3001\u672c\u8ad6\u6587\u3067\u306f\u9ad8\u901f\u306b\u5b9f\u884c\u53ef\u80fd\u306a\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3067\u8a08\u7b97\u53ef\u80fd\u306a\u5f62\u3067\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3092\u5b9a\u5f0f\u5316\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u305d\u308c\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u305f\u7d50\u679c\u3092k-means\u3068\u6bd4\u8f03\u3057\u3001\u63d0\u6848\u624b\u6cd5\u306e\u5229\u70b9\u3068\u6b20\u70b9\u306b\u3064\u3044\u3066\u8b70\u8ad6\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[10,11,13,32,48,75,112,122],"class_list":["post-3512","post","type-post","status-publish","format-standard","hentry","category-review","tag-d-wave","tag-d-wave-2000q","tag-d-wave-advantage","tag-qbsolv","tag-48","tag-75","tag-112","tag-122"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3067\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306f\u3046\u307e\u304f\u3067\u304d\u308b\u306e\u304b\uff1f - T-QARD Harbor<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2022\/08\/05\/\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u306b\u3088\u308b\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3067\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306f\u3046\u307e\u304f\u3067\u304d\u308b\u306e\u304b\uff1f - T-QARD Harbor\" \/>\n<meta property=\"og:description\" content=\"\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3068\u306f\u3001\u6559\u5e2b\u7121\u3057\u5b66\u7fd2\u306e\u4e00\u3064\u3067\u3001\u985e\u4f3c\u3057\u305f\u7279\u5fb4\u3092\u6301\u3063\u305f\u30c7\u30fc\u30bf\u304c\u540c\u3058\u30b0\u30eb\u30fc\u30d7\u306b\u5c5e\u3059\u308b\u3088\u3046\u306b\u30b0\u30eb\u30fc\u30d7\u5206\u3051\u3059\u308b\u3053\u3068\u3092\u8a00\u3044\u307e\u3059\u3002\u4e3b\u306a\u624b\u6cd5\u306bk-means\u3084\u968e\u5c64\u578b\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306f\u5c40\u6240\u63a2\u7d22\u6cd5\u3067\u3042\u308b\u305f\u3081\u53b3\u5bc6\u89e3\u306b\u5230\u9054\u3059\u308b\u4fdd\u8a3c\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u4e00\u65b9\u3067\u3001SA\u3084\u907a\u4f1d\u7684\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u3088\u3046\u306a\u5927\u57df\u7684\u306a\u63a2\u7d22\u624b\u6cd5\u3067\u306f\u5b9f\u884c\u6642\u9593\u304c\u9577\u304f\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002 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