{"id":8426,"date":"2020-03-27T18:07:52","date_gmt":"2020-03-27T17:07:52","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=8426"},"modified":"2022-12-03T23:04:49","modified_gmt":"2022-12-03T22:04:49","slug":"statistique-de-hopkins","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/hopkins-statistic\/","title":{"rendered":"Hopkins statistic"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"8426\" class=\"elementor elementor-8426\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-799a593 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"799a593\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f66f0fc\" data-id=\"f66f0fc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-231c140 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"231c140\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/data-partitioning\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Data partitioning<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column 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class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-30f38ae2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"30f38ae2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7aef9ad0\" data-id=\"7aef9ad0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-470a1fb5 elementor-widget elementor-widget-text-editor\" data-id=\"470a1fb5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">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 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class=\"wp-block-paragraph\">Before grouping together a dataset, we can test if there really are clusters. We need to test the hypothesis of the existence of patterns in the data against a uniformly distributed dataset (homogeneous distribution).<\/p>\n\n<p class=\"wp-block-paragraph\">The Hopkins statistic is calculated as follows:<\/p>\n\n<ol class=\"wp-block-list\">\n<li>Sample n points (p_i) from the dataset (D) uniformly and calculate the distance to their nearest neighbor (d (p_i))<\/li>\n<li>Generate n points (q_i) evenly distributed in the space of the dataset and calculate their distance to the nearest neighbors in D (d (q_i))<\/li>\n<li>Calculate the quotient H:<\/li>\n<\/ol>\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval18.png\" alt=\"Hopkins statistic\" width=\"245\" height=\"57\" title=\"\"><\/figure>\n\n<p class=\"wp-block-paragraph\">If the data is evenly distributed, the value of H will be approximately 0.5.<\/p>\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval19.png\" alt=\"Hopkins statistic\" width=\"524\" height=\"336\" title=\"\"><\/figure>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Data Partitioning Hopkins Stats Wiki Home Page Before clustering a dataset, we can test if there really are clusters. We \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":8271,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-8426","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=8426"}],"version-history":[{"count":6,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8426\/revisions"}],"predecessor-version":[{"id":19004,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8426\/revisions\/19004"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/8271"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=8426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}