{"id":666,"date":"2023-11-06T17:23:53","date_gmt":"2023-11-06T09:23:53","guid":{"rendered":"https:\/\/www.wennroy.com\/?p=666"},"modified":"2023-11-07T14:59:01","modified_gmt":"2023-11-07T06:59:01","slug":"hdbscan","status":"publish","type":"post","link":"https:\/\/wennroy.com\/index.php\/2023\/11\/06\/hdbscan\/","title":{"rendered":"HDBSCAN"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Ref:<\/strong> <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A Youtube Video<\/p>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/dGsxd67IFiU?si=anHb70NE6411_Inj\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen=\"\"><\/iframe>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/pberba.github.io\/stats\/2020\/01\/17\/hdbscan\/\">A github io blog<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Clustering<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u822c\u6211\u4eec\u7684cluster\u5206\u4e3aCentroid based cluster \u548c Density Based Cluster\u3002\u4f46John\u66f4\u63a8\u8350\u662f\u5c06cluster\u5206\u4e3a Flat Cluster\u548cHierarchical Cluster\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Flat<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Hierarchical<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Centroid \/ Parametric<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">K-manes<br>GMM<\/td><td class=\"has-text-align-center\" data-align=\"center\">Ward Complete-linkage<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Density \/ Non-Parametric<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">DBSCAN<br>Mean Shift<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>HDBSCAN<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Hierarchical Density Based Clustering<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u822c\u6709\u4e09\u4e2a\u95ee\u9898\u6211\u4eec\u9700\u8981\u89e3\u51b3\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u5982\u4f55\u53bb\u4f30\u8ba1pdf<\/li><li>\u5982\u4f55\u53bb\u5207\u4e00\u4e2a\u6d77\u5e73\u9762(how to determine the level set)<\/li><li>Computational complexity<\/li><\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u9996\u5148\u662f\u5982\u4f55\u53bb\u4f30\u8ba1pdf<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Locally approxiate the density. \u5c31\u5982\u540cDBSCAN\u505a\u7684\u4e00\u6837\u3002\u6211\u4eec\u4e00\u822c\u5bfb\u627e\u7684\u662f\u540c\u65f6\u56ca\u62ecmin_pts\u4e2a\u70b9\u7684\u6700\u5c0f\u7684\u534a\u5f84\uff0c\u6765\u4f5c\u4e3a\u4e00\u4e2alocal density\u7684\u5feb\u901f\u4f30\u8ba1\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5176\u6b21\u662f\u5982\u4f55\u5207\u4e00\u4e2a\u6d77\u5e73\u9762<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\u6211\u4eec\u6765\u770b\u4e00\u5f20\u56fe\uff0c\u5982\u679c\u6211\u4eec\u662fpure euclidean distance\u7684\u60c5\u51b5\u65f6\uff0c\u6211\u4eec\u5728\u4e00\u7ef4\u6570\u636e\u4e0a\u53ea\u9700\u8981\u50cfhierarchical cluster\u4e00\u6837\u753b\u51fa\u4ee5\u4e0b\u7684\u8fd9\u5f20\u56fe\u5c31\u597d\u4e86\uff0c\u7136\u540e\u7eb5\u5207\u4e00\u5200\u5c31\u80fd\u591f\u786e\u5b9a\u6211\u4eec\u8981\u5206\u7684cluster\u6570\u91cf\u3002\u4f4e\u4e8e\u67d0\u4e2a\u5bc6\u5ea6\u7684\u70b9\u90fd\u5c06\u89c6\u4e3a\u566a\u58f0\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"851\" height=\"617\" src=\"https:\/\/www.wennroy.com\/wp-content\/uploads\/2023\/11\/image.png\" alt=\"\" class=\"wp-image-668\" srcset=\"https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image.png 851w, https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image-768x557.png 768w, https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image-281x204.png 281w, https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image-414x300.png 414w, https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image-413x300.png 413w\" sizes=\"auto, (max-width: 851px) 100vw, 851px\" \/><figcaption>\u4e00\u7ef4\u6570\u636e\u4e0a\u7684hierarchical plot<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u662f\uff0c\u6211\u4eec\u5f80\u5f80\u8fd8\u9700\u8981\u5176\u4ed6\u7684\u6761\u4ef6\uff0c\u4f8b\u5982\u6211\u4eec\u8981\u4e00\u4e2acluster\u8fd8\u8981\u8db3\u591f\u7684dense\u3002\u56e0\u6b64\uff0c\u63d0\u51fa\u4e86\u4e00\u4e2a\u65b0\u7684\u8ddd\u79bb\u8ba1\u7b97\u65b9\u6cd5(Mutual Reachability Distance)\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$d_{\\text{mreach}}(X_i, X_j) = \\left\\lbrace\\begin{align}\\max\\{\\kappa(X_i), \\kappa(X_j), d(X_i, X_j)\\}\\quad &amp;X_i\\not=X_j\\\\0 \\quad&amp;X_i = X_j\\end{align}\\right.$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff0c$\\kappa(X_i)$ \u662f\u5bf9\u4e8e$X_i$\u8fd9\u4e2a\u70b9\u6700\u8fd1\u7684$k$\u4e2a\u70b9\u7684\u8ddd\u79bb\u3002\u8fd9\u6837\u5b9a\u4e49\u7684\u8ddd\u79bb\uff0c\u6709\u5229\u4e8e\u5c06\u539f\u672c\u5c31\u5f88\u7a00\u758f\u7684point\u8d4b\u4e88\u6bd4\u8f83\u5927\u7684\u8ddd\u79bb\uff0c\u8ba9\u4ed6\u4e0d\u5bb9\u6613\u88ab\u7eb3\u5165\u5230\u4e00\u4e2acluster\u4e2d\u95f4\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Computational cost<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u65f6\u95f4\u590d\u6742\u5ea6\u662f$O(n^2)$\u3002\u5b9e\u9645\u4e0a\uff0c\u6700\u82b1\u65f6\u95f4\u7684\u90e8\u5206\u662fSingle linkage computation, which can be reduced to minimal spanning tree computation\u3002\u76f4\u89c9\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u7c7b\u4f3c\u4e8eprim&#8217;s algorithm\u53bb\u8ba1\u7b97\u6700\u5c0f\u751f\u6210\u6811\uff0c\u4f46\u6211\u4eec\u5b9e\u9645\u4e0a\u6709$n^2$\u6761\u8fb9\uff0c\u662f\u4e2a\u5b8c\u6574\u7684\u56fe\uff0c\u5bf9\u4e8eprim&#8217;s algorithm\u6765\u8bf4\uff0c\u5e76\u4e0d\u662f\u4e00\u4e2a\u6709\u6548\u4e14\u5feb\u901f\u7684\u60c5\u51b5\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528Boruvka&#8217;s algorithm\u6765\u8ba1\u7b97\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u7ec8\u7684\u9009\u62e9\uff1a<strong>Dual Tree Boruvka for Euclidean Minimum Spanning Trees<\/strong>. Reduced to $n\\log(n)$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u4e14Mutual Reachability Distance\u540c\u6837\u9002\u7528\u4e8e\u8fd9\u6837\u7684\u8ba1\u7b97\uff0c\u56e0\u4e3a\u552f\u4e00requirement for this algorithm to work\u53ea\u662ftriangle inequality holding\uff0c\u4ed6\u4eec\u901a\u8fc7\u4e00\u4e9b\u6280\u5de7\u548c\u4fee\u6539\uff0c\u6700\u7ec8\u8bbe\u8ba1\u51fa\u4e86\u6539\u8fdb\u7248\u7684\u8ba1\u7b97\u65b9\u6cd5\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5173\u4e8e\u4e0e\u5176\u4ed6cluster method\u7684\u5bf9\u6bd4<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"838\" height=\"631\" src=\"https:\/\/www.wennroy.com\/wp-content\/uploads\/2023\/11\/image-1.png\" alt=\"\" class=\"wp-image-680\" srcset=\"https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image-1.png 838w, https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image-1-768x578.png 768w, https:\/\/wennroy.com\/wp-content\/uploads\/2023\/11\/image-1-281x212.png 281w\" sizes=\"auto, (max-width: 838px) 100vw, 838px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Ref: A Youtube Video A gi &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","footnotes":""},"categories":[63,41,46],"tags":[64,65,66],"class_list":["post-666","post","type-post","status-publish","format-standard","hentry","category-cluster","category-python","category-statistics","tag-cluster","tag-hdbscan","tag-statistics"],"_links":{"self":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts\/666","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/comments?post=666"}],"version-history":[{"count":14,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts\/666\/revisions"}],"predecessor-version":[{"id":683,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts\/666\/revisions\/683"}],"wp:attachment":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/media?parent=666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/categories?post=666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/tags?post=666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}