{"id":8345,"date":"2020-03-27T14:19:27","date_gmt":"2020-03-27T13:19:27","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=8345"},"modified":"2022-12-03T23:04:45","modified_gmt":"2022-12-03T22:04:45","slug":"fonction-de-similarite","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/funcion-de-similitud\/","title":{"rendered":"Funci\u00f3n de similitud"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"8345\" class=\"elementor elementor-8345\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e34103a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e34103a\" 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-6345be2\" data-id=\"6345be2\" 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-b6c627a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b6c627a\" 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\/partitionnement-de-donnees\/\">\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\">Partitionnement de donn\u00e9es<\/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 elementor-col-33 elementor-top-column elementor-element elementor-element-248bea8\" data-id=\"248bea8\" 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-cdac318 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"cdac318\" 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\/\">\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\">Page d'accueil<\/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 elementor-col-33 elementor-top-column elementor-element elementor-element-75c91e0\" data-id=\"75c91e0\" 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-64164fb elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"64164fb\" 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:\/\/en.wikipedia.org\/wiki\/Similarity_measure\" target=\"_blank\" rel=\"noopener\">\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\">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-44637194 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"44637194\" 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-2903e39e\" data-id=\"2903e39e\" 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-712a54c0 elementor-widget elementor-widget-text-editor\" data-id=\"712a54c0\" 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_82_2 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\">Contenus<\/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=\"Alternar tabla de contenidos\"><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:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/funcion-de-similitud\/#Fonction-de-similarite\" >Fonction de similarit\u00e9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/funcion-de-similitud\/#Mesure-du-cosinus\" >Mesure du cosinus<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/funcion-de-similitud\/#Mesure-de-correlation-de-Pearson\" >Mesure de corr\u00e9lation de Pearson<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/funcion-de-similitud\/#Mesure-de-Jaccard-etendue\" >Mesure de Jaccard \u00e9tendue<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/funcion-de-similitud\/#Mesure-du-coefficient-de-Dice\" >Mesure du coefficient de Dice<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Fonction-de-similarite\"><\/span>Fonction de similarit\u00e9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Un concept alternatif \u00e0 celui de la distance est la fonction de similarit\u00e9 (mesure du cosinus, mesure de <a href=\"https:\/\/complex-systems-ai.com\/es\/correlacion-y-regresiones\/\">corr\u00e9lation<\/a> de Pearson, Mesure de Jaccard \u00e9tendue, mesure du coefficient de Dice) s(x_i, x_j) qui compare les deux vecteurs x_i et x_j. Cette fonction doit \u00eatre sym\u00e9trique (\u00e0 savoir s(x_i, x_j) = s(x_j, x_i)) et avoir une grande valeur lorsque x_i et x_j sont en quelque sorte \u00absimilaires\u00bb et constituent la plus grande valeur pour des vecteurs identiques.<\/p>\n\n<p>Une fonction de similitude o\u00f9 la plage cible est [0,1] est appel\u00e9e fonction de similitude dichotomique. En fait, les m\u00e9thodes de calcul de \u00abdistances\u00bb dans le cas des <a href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/medidas-de-distancia-para-atributos-binarios\/\">attributs binaires<\/a> et nominaux peuvent \u00eatre consid\u00e9r\u00e9es comme des fonctions de similitude plut\u00f4t que comme des distances.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mesure-du-cosinus\"><\/span>Mesure du cosinus<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>Lorsque l&rsquo;angle entre les deux vecteurs est une mesure significative de leur similitude, le produit int\u00e9rieur normalis\u00e9 peut \u00eatre une mesure de similitude appropri\u00e9e:<\/p>\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\/mesure11.png\" alt=\"Fonction de similarit\u00e9 mesure du cosinus\" width=\"197\" height=\"65\" title=\"\"><\/figure>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mesure-de-correlation-de-Pearson\"><\/span>Mesure de corr\u00e9lation de Pearson<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>La corr\u00e9lation de Pearson normalis\u00e9e est d\u00e9finie comme (avec x\u0304 la valeur caract\u00e9ristique moyenne de x sur toutes les dimensions):<\/p>\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\/mesure12.png\" alt=\"Fonction de similarit\u00e9 mesure de corr\u00e9lation de Pearson\" width=\"262\" height=\"58\" title=\"\"><\/figure>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mesure-de-Jaccard-etendue\"><\/span>Mesure de Jaccard \u00e9tendue<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>La mesure de Jaccard \u00e9tendue a \u00e9t\u00e9 pr\u00e9sent\u00e9e par Strehl et Ghosh en 2000 et elle est d\u00e9finie comme:<\/p>\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\/mesure13.png\" alt=\"Fonction de similarit\u00e9 mesure de Jaccard \u00e9tendue\" width=\"286\" height=\"66\" title=\"\"><\/figure>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mesure-du-coefficient-de-Dice\"><\/span>Mesure du coefficient de Dice<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>La mesure du coefficient de Dice est similaire \u00e0 la mesure de Jaccard \u00e9tendue et elle est d\u00e9finie comme suit:<\/p>\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/mesure14.png\" alt=\"Fonction de similarit\u00e9 mesure du coefficient de DIce\" width=\"219\" height=\"68\" 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>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Particionamiento de datos P\u00e1gina de inicio de Wiki Funci\u00f3n de similitud Un concepto alternativo al de distancia es la funci\u00f3n de similitud (medida coseno, \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-8345","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/8345","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=8345"}],"version-history":[{"count":8,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/8345\/revisions"}],"predecessor-version":[{"id":18983,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/8345\/revisions\/18983"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/8271"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=8345"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}