{"id":8393,"date":"2020-03-27T15:49:01","date_gmt":"2020-03-27T14:49:01","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=8393"},"modified":"2024-02-25T13:30:26","modified_gmt":"2024-02-25T12:30:26","slug":"criteres-de-qualite-internes","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/","title":{"rendered":"Criterios de calidad internos"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"8393\" class=\"elementor elementor-8393\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-28a9395 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"28a9395\" 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-3a62fc3\" data-id=\"3a62fc3\" 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-42d4b9f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"42d4b9f\" 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\/es\/particionamiento-de-datos\/\">\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\">Partici\u00f3n de datos<\/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-cdb7f09\" data-id=\"cdb7f09\" 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-2b7fc9d elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2b7fc9d\" 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\/es\/\">\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\">Pagina de inicio<\/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-e0b9fe2\" data-id=\"e0b9fe2\" 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-f5faf3c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f5faf3c\" 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:\/\/www.cs.swarthmore.edu\/~meeden\/cs63\/s16\/reading\/Clustering.pdf\" 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-41cb066 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"41cb066\" 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-7b4fa9a\" data-id=\"7b4fa9a\" 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-fdb584a elementor-widget elementor-widget-heading\" data-id=\"fdb584a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<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\">Contenido<\/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=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/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\/criterios-de-calidad-internos\/#Criteres-de-qualite-internes\" >Criterios de calidad internos<\/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\/criterios-de-calidad-internos\/#Liste\" >Lista<\/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\/criterios-de-calidad-internos\/#Comment-lire-les-mesures-de-qualite-interne\" >C\u00f3mo leer m\u00e9tricas de calidad interna<\/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\/criterios-de-calidad-internos\/#Somme-de-lerreur-quadratique\" >Suma del error cuadr\u00e1tico<\/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\/criterios-de-calidad-internos\/#Criteres-de-dispersion\" >Criterios de dispersi\u00f3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Uutilitaire-de-categorie\" >Utilidad de categor\u00eda<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Mesure-de-Coupe\" >Medici\u00f3n de corte<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Ball-Hall\" >sal\u00f3n de baile<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Banfeld-Raftery\" >Banfeld-Raftery<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Concordet\" >Concordeto<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Critere-C\" >Criterio C<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Calinski-Harabasz\" >Calinski-Harabasz<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Davies-Bouldin\" >Davies-Bouldin<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Det-Ratio\" >Relaci\u00f3n_detonaci\u00f3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Dunn\" >Dunn<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#GDImn\" >GDImn<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Baker-Hubert-Gamma\" >Baker-Hubert Gamma<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#G\" >G+<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Ksq-DetW\" >Ksq_DetW<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Log-Det-Ratio\" >Log_Det_Ratio<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Log-SS-Ratio\" >Log_SS_Ratio<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#McClain-Rao\" >McClain-Rao<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#PBM\" >PBM<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Point-Biserial\" >Punto-Biserial<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Ratkowsky-Lance\" >Lanza Ratkowsky<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Ray-Turi\" >Ray Turi<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Scott-Symons\" >Scott Simons<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#SD-Scat-et-SD-Dis\" >SD_Scat y SD_Dis<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#S-Dbw\" >S_Dbw<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Silhouette\" >Silueta<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Tau\" >Tau<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Trace-W\" >traza_W<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Trace-WiB\" >traza_WiB<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-34\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Wemmert-Gancarski\" >Wemmert-Gan\u00e7arski<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-35\" href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/criterios-de-calidad-internos\/#Xie-Beni\" >Xie-Beni<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Criteres-de-qualite-internes\"><\/span>Criterios de calidad internos<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-5949388a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5949388a\" 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-73abcf85\" data-id=\"73abcf85\" 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-5d1ad416 elementor-widget elementor-widget-text-editor\" data-id=\"5d1ad416\" 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<p><\/p>\n<p>Los criterios de calidad internos suelen medir la compacidad de los grupos utilizando una medida de similitud. Por lo general, mide la homogeneidad intragrupo, la separabilidad entre grupos o una combinaci\u00f3n de estas dos. No utiliza informaci\u00f3n externa junto con los datos en s\u00ed.&nbsp;<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"criterios de calidad internos\" width=\"97\" height=\"97\" title=\"\"><\/p>\n<p><\/p>\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-7b2fc8f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7b2fc8f\" 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-a2552c4\" data-id=\"a2552c4\" 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-8118be8 elementor-widget elementor-widget-heading\" data-id=\"8118be8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Liste\"><\/span>Lista<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-ecbaee7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ecbaee7\" 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-f938b08\" data-id=\"f938b08\" 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-78b43e0 elementor-widget elementor-widget-text-editor\" data-id=\"78b43e0\" 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<ul>\n<li>Suma del error cuadr\u00e1tico<\/li>\n<li>Criterios de dispersi\u00f3n<\/li>\n<li><span style=\"color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight ); font-size: 1.125rem;\">M\u00e9trica de utilidad de categor\u00eda<\/span><\/li>\n<li>Medidas de corte<\/li>\n<li>sal\u00f3n de baile<\/li>\n<li>Banfeld-Raftery<\/li>\n<li>Criterio de Condorcet<\/li>\n<li>Criterio C<\/li>\n<li>Calinski-Harabasz<\/li>\n<li>Davies-Bouldin<\/li>\n<li>Relaci\u00f3n_detonaci\u00f3n<\/li>\n<li>Dunn<\/li>\n<li>GDImn<\/li>\n<li>Gama<\/li>\n<li>G+<\/li>\n<li>Ksq_DetW<\/li>\n<li>Log_Det_Ratio<\/li>\n<li>Log_SS_Ratio<\/li>\n<li>McClain-Rao<\/li>\n<li>PBM<\/li>\n<li>punto biserial<\/li>\n<li>Lanza Ratkawsky<\/li>\n<li>Ray Turi<\/li>\n<li>Scott Simons<\/li>\n<li>SD_Scat<\/li>\n<li>SD_Dis<\/li>\n<li>S_Dbw<\/li>\n<li>Silueta<\/li>\n<li>Traza W<\/li>\n<li>rastreo WiB<\/li>\n<li>Wemmert-Gan\u00e7arski<\/li>\n<li>Xie-Beni<\/li>\n<\/ul>\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-e2152c2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e2152c2\" 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-f66ada4\" data-id=\"f66ada4\" 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-78c3f1f elementor-widget elementor-widget-heading\" data-id=\"78c3f1f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Comment-lire-les-mesures-de-qualite-interne\"><\/span>C\u00f3mo leer m\u00e9tricas de calidad interna<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-e186eca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e186eca\" 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-f3bf07b\" data-id=\"f3bf07b\" 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-327af23 elementor-widget elementor-widget-text-editor\" data-id=\"327af23\" 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<p>Para encontrar la mejor partici\u00f3n de los datos, generalmente ejecutamos una <a href=\"https:\/\/complex-systems-ai.com\/es\/algoritmico\/\">algoritmo<\/a> de <a href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/\">agrupamiento<\/a> con diferentes valores del n\u00famero esperado de clusters K: digamos que Km \u2264 K \u2264 KM. El algoritmo de agrupamiento aplicado podr\u00eda ser el agrupamiento jer\u00e1rquico ascendente (AHC) o el algoritmo k-means o cualquier otra t\u00e9cnica. Luego calculamos un \u00edndice de calidad QK para cada valor de K y seleccionamos la partici\u00f3n que condujo al &quot;mejor&quot; valor de QK.<\/p>\n<p>En esta secci\u00f3n se explica cu\u00e1l se considera el \u201cmejor\u201d valor para los diferentes \u00edndices de calidad.<\/p>\n<p>La tabla resume, para cada \u00edndice, qu\u00e9 regla se debe aplicar para determinar el mejor valor del \u00edndice. Por ejemplo, en el caso del \u00edndice Calinski-Harabasz, si el \u00edndice de calidad se ha calculado para diferentes particiones de los datos, la mejor partici\u00f3n es la correspondiente al mayor valor del \u00edndice.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-21108 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne1.png\" alt=\"calidad interna\" width=\"226\" height=\"525\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne1.png 226w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne1-129x300.png 129w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne1-5x12.png 5w\" sizes=\"(max-width: 226px) 100vw, 226px\" \/><\/p>\n<p>Las reglas de decisi\u00f3n llamadas max y min en la tabla significan seleccionar el valor de \u00edndice m\u00e1s grande o m\u00e1s peque\u00f1o, respectivamente. La regla de decisi\u00f3n denominada max diff significa que el mejor valor de K es el correspondiente a la mayor diferencia entre dos pendientes sucesivas. En un gr\u00e1fico que representa los valores del \u00edndice versus <a href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/calidad-sobre-numero-de-clusteres\/\">n\u00famero de grupos<\/a> seleccionado, esto corresponde a un codo.<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-21109 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne2.png\" alt=\"calidad interna\" width=\"417\" height=\"207\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne2.png 417w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne2-300x149.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Qualite_interne2-18x9.png 18w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p>\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-259f237 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"259f237\" 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-efb29a5\" data-id=\"efb29a5\" 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-8967d82 elementor-widget elementor-widget-heading\" data-id=\"8967d82\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Somme-de-lerreur-quadratique\"><\/span>Suma del error cuadr\u00e1tico\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-e16f51a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e16f51a\" 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-77f77c5\" data-id=\"77f77c5\" 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-e9b3d9f elementor-widget elementor-widget-text-editor\" data-id=\"e9b3d9f\" 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<p>Las m\u00e9tricas de calidad internas suelen medir la compacidad del cl\u00faster mediante una medida de similitud (como la Suma del error cuadr\u00e1tico). Por lo general, mide la homogeneidad dentro del grupo, la separabilidad entre grupos o una combinaci\u00f3n de estos dos. No utiliza informaci\u00f3n externa junto con los propios datos.<\/p>\n<p>La suma del error al cuadrado es la medida de criterio m\u00e1s simple y m\u00e1s utilizada para la agrupaci\u00f3n. Se calcula como:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Suma de error cuadr\u00e1tico Suma de error cuadr\u00e1tico\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval1.png\" alt=\"Suma del error cuadr\u00e1tico\" width=\"249\" height=\"73\" \/><\/figure>\n<p>donde C_k es el conjunto de instancias del cl\u00faster k; \u03bc_k es la media vectorial del grupo k. Los componentes de \u03bc_k se calculan como:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Suma de error cuadr\u00e1tico Suma de error cuadr\u00e1tico\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval2.png\" alt=\"Suma del error cuadr\u00e1tico\" width=\"184\" height=\"59\" \/><\/figure>\n<p>donde N_k = | C_k | es el n\u00famero de instancias que pertenecen al cl\u00faster k.<\/p>\n<p>Los m\u00e9todos de\u00a0<a href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/\">fraccionamiento<\/a>\u00a0que minimizan el criterio SSE a menudo se denominan particiones de varianza m\u00ednima, porque mediante una simple manipulaci\u00f3n algebraica el criterio SSE se puede escribir:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Suma de error cuadr\u00e1tico Suma de error cuadr\u00e1tico\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval3.png\" alt=\"Suma del error cuadr\u00e1tico\" width=\"320\" height=\"186\" \/><\/figure>\n<p>La funci\u00f3n de criterio SSE es adecuada para los casos en los que los cl\u00fasteres forman nubes compactas bien separadas entre s\u00ed.<\/p>\n<p>Se pueden generar criterios m\u00ednimos adicionales para SSE reemplazando el valor de S_k con expresiones como:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Suma de error cuadr\u00e1tico Suma de error cuadr\u00e1tico\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval4.png\" alt=\"Suma del error cuadr\u00e1tico\" width=\"238\" height=\"133\" \/><\/figure>\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-b91cd09 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b91cd09\" 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-5eb3547\" data-id=\"5eb3547\" 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-c705845 elementor-widget elementor-widget-heading\" data-id=\"c705845\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Criteres-de-dispersion\"><\/span>Criterios de dispersi\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-211bf88 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"211bf88\" 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-e63ecac\" data-id=\"e63ecac\" 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-a0c3525 elementor-widget elementor-widget-text-editor\" data-id=\"a0c3525\" 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<p>Las m\u00e9tricas de calidad interna generalmente miden la compacidad de los cl\u00fasteres utilizando una medida de similitud (como los criterios de dispersi\u00f3n: seguimiento, determinante, invariancia). Por lo general, mide la homogeneidad dentro del grupo, la separabilidad entre grupos o una combinaci\u00f3n de estos dos. No utiliza informaci\u00f3n externa junto con los propios datos.<\/p>\n<p>Los criterios de difusi\u00f3n escalar se derivan de las matrices de difusi\u00f3n, reflejando la difusi\u00f3n intra-cluster, la difusi\u00f3n entre-cluster y su suma: la matriz de difusi\u00f3n total. Para el grupo k-\u00e9simo, la matriz de difusi\u00f3n se puede calcular de la siguiente manera:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval5.png\" alt=\"Criterios de dispersi\u00f3n\" width=\"251\" height=\"62\" \/><\/figure>\n<p>La matriz de dispersi\u00f3n intra-conglomerados se calcula como la suma de la \u00faltima definici\u00f3n sobre todos los conglomerados W:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval6.png\" alt=\"Criterios de dispersi\u00f3n\" width=\"132\" height=\"68\" \/><\/figure>\n<p>La matriz de difusi\u00f3n entre conglomerados se puede calcular de la siguiente manera:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval7.png\" alt=\"Criterios de dispersi\u00f3n\" width=\"288\" height=\"75\" \/><\/figure>\n<p>donde \u03bc es el vector medio total y se define como:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval8.png\" alt=\"Criterios de dispersi\u00f3n\" width=\"160\" height=\"72\" \/><\/figure>\n<p>La matriz de difusi\u00f3n total debe calcularse de la siguiente manera:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval9.png\" alt=\"Criterios de dispersi\u00f3n\" width=\"287\" height=\"64\" \/><\/figure>\n<p>Se pueden derivar tres criterios escalares de S_W, S_B y S_T.<span id=\"La-trace\" class=\"ez-toc-section\"><\/span><\/p>\n<p>La traza es la suma de los elementos diagonales de una matriz. Minimizar el rastro de S_W es similar a minimizar\u00a0<a href=\"https:\/\/complex-systems-ai.com\/es\/partitionnement-de-donnees\/somme-de-lerreur-quadratique\/\">HSE<\/a>\u00a0y por lo tanto es de uso com\u00fan. Este criterio, que representa la dispersi\u00f3n intra-cluster, se calcula de la siguiente manera:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval10.png\" alt=\"Criterios de dispersi\u00f3n de trazas\" width=\"279\" height=\"71\" \/><\/figure>\n<p>Otro criterio, que se puede maximizar, es el criterio entre clusters:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval11.png\" alt=\"Criterios de dispersi\u00f3n de trazas\" width=\"227\" height=\"65\" \/><span id=\"Le-determinant\" class=\"ez-toc-section\"><\/span><\/figure>\n<p>El determinante de una matriz de dispersi\u00f3n mide aproximadamente el cuadrado del volumen de dispersi\u00f3n. Dado que S_B ser\u00e1 singular si el\u00a0<a href=\"https:\/\/complex-systems-ai.com\/es\/particionamiento-de-datos\/calidad-sobre-numero-de-clusteres\/\">n\u00famero de grupos<\/a>\u00a0es menor o igual que la dimensionalidad, o si mc es menor que la dimensionalidad, su determinante no es un criterio apropiado. Si asumimos que S_W no es singular, la funci\u00f3n del criterio determinante es:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval12.png\" alt=\"Criterios de dispersi\u00f3n decisivos\" width=\"180\" height=\"70\" \/><span id=\"Linvariance\" class=\"ez-toc-section\"><\/span><\/figure>\n<p>Los valores propios \u03bb_1, \u03bb_2,. . . , \u03bb_d de S_W * S_B son las invariantes lineales b\u00e1sicas de las matrices de difusi\u00f3n. Las particiones buenas son aquellas para las que los valores propios distintos de cero son grandes. Como resultado, se pueden derivar varios criterios, incluidos los valores propios. Tres de estos criterios son:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Criterios de Dispersi\u00f3n Criterios de Dispersi\u00f3n\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval13.png\" alt=\"Criterios de invariancia de dispersi\u00f3n\" width=\"262\" height=\"163\" \/><\/figure>\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-60f0862 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"60f0862\" 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-18fb3f5\" data-id=\"18fb3f5\" 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-d3630c2 elementor-widget elementor-widget-heading\" data-id=\"d3630c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Uutilitaire-de-categorie\"><\/span>Utilidad de categor\u00eda<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-39418bd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"39418bd\" 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-27f25a3\" data-id=\"27f25a3\" 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-f299b12 elementor-widget elementor-widget-text-editor\" data-id=\"f299b12\" 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<p>La utilidad de categor\u00eda se define como el aumento del n\u00famero esperado de valores de entidad que pueden predecirse correctamente dada una determinada agrupaci\u00f3n. Esta m\u00e9trica es \u00fatil para problemas que contienen un n\u00famero relativamente peque\u00f1o de caracter\u00edsticas nominales, cada una de las cuales tiene una cardinalidad peque\u00f1a.<\/p>\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-59aabb1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"59aabb1\" 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-c19d0d7\" data-id=\"c19d0d7\" 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-11082dc elementor-widget elementor-widget-heading\" data-id=\"11082dc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Mesure-de-Coupe\"><\/span>Medici\u00f3n de corte<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-ea23454 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ea23454\" 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-caedc2f\" data-id=\"caedc2f\" 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-09af387 elementor-widget elementor-widget-text-editor\" data-id=\"09af387\" 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<p>En algunos casos, es \u00fatil representar el problema de agrupamiento como un problema de corte m\u00ednimo. En tales casos, la calidad se mide como la relaci\u00f3n entre los pesos restantes y los pesos totales de corte. Si no hay restricciones sobre el tama\u00f1o de los cl\u00fasteres, es f\u00e1cil encontrar el valor \u00f3ptimo. Por lo tanto, se revisa la medici\u00f3n del min-cut para penalizar las estructuras desequilibradas.<\/p>\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-79822b2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"79822b2\" 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-12b2cd1\" data-id=\"12b2cd1\" 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-928e803 elementor-widget elementor-widget-heading\" data-id=\"928e803\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Ball-Hall\"><\/span>sal\u00f3n de baile<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-da5b85d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"da5b85d\" 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-093a76e\" data-id=\"093a76e\" 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-b3c6735 elementor-widget elementor-widget-text-editor\" data-id=\"b3c6735\" 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<p>La dispersi\u00f3n promedio de un grupo es el promedio de los cuadrados de las distancias de los puntos del grupo a su baricentro. El \u00edndice de Ball-Hall es el promedio, en todos los conglomerados, de su dispersi\u00f3n media:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21050\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/ball-hall.png\" alt=\"sal\u00f3n de baile\" width=\"239\" height=\"57\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/ball-hall.png 239w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/ball-hall-18x4.png 18w\" sizes=\"(max-width: 239px) 100vw, 239px\" \/><\/p>\n<p>En el caso particular donde todos los clusters tienen el mismo tama\u00f1o N\/K, esta suma se reduce a WGSS\/N.<\/p>\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-6c760ce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c760ce\" 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-6be47e5\" data-id=\"6be47e5\" 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-0568a1a elementor-widget elementor-widget-heading\" data-id=\"0568a1a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Banfeld-Raftery\"><\/span>Banfeld-Raftery <span class=\"ez-toc-section-end\"><\/span><\/h2>\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-f7c1874 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f7c1874\" 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-a3b1c40\" data-id=\"a3b1c40\" 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-218d47f elementor-widget elementor-widget-text-editor\" data-id=\"218d47f\" 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<p>Este \u00edndice es la suma ponderada de los logaritmos de las trazas de la matriz de varianza-covarianza de cada conglomerado.<\/p>\n<p>El \u00edndice se puede escribir de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21051\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Banfeld-Raftery.png\" alt=\"Banfeld-Raftery\" width=\"201\" height=\"52\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Banfeld-Raftery.png 201w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Banfeld-Raftery-18x5.png 18w\" sizes=\"(max-width: 201px) 100vw, 201px\" \/><\/p>\n<p>La cantidad Tr(WG{k})\/nk se puede interpretar como el promedio de los cuadrados de las distancias entre los puntos del cluster Ck y su baricentro G{k}. Si un grupo contiene un solo punto, esta traza es igual a 0 y el logaritmo no est\u00e1 definido.<\/p>\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-ac4d565 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ac4d565\" 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-9a9a7bd\" data-id=\"9a9a7bd\" 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-dceb6d5 elementor-widget elementor-widget-heading\" data-id=\"dceb6d5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Concordet\"><\/span>Concordeto<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-9592941 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9592941\" 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-6cefd17\" data-id=\"6cefd17\" 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-fcc9541 elementor-widget elementor-widget-text-editor\" data-id=\"fcc9541\" 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<p>Otro enfoque adecuado es aplicar la soluci\u00f3n de Condorcet al problema de agrupamiento. En este caso, el criterio se calcula de la siguiente manera:<\/p>\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\/eval14.png\" alt=\"criterios de calidad internos criterio de condorcet\" width=\"507\" height=\"86\" title=\"\"><\/figure>\n<p>donde s (x_j, x_k) y d (x_j, x_k) miden la similitud y la distancia de los vectores x_j y x_k.<\/p>\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-88e6ed3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"88e6ed3\" 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-ec991f1\" data-id=\"ec991f1\" 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-e8fa1f1 elementor-widget elementor-widget-heading\" data-id=\"e8fa1f1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Critere-C\"><\/span>Criterio C<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-97b904f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"97b904f\" 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-b809285\" data-id=\"b809285\" 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-50c8aee elementor-widget elementor-widget-text-editor\" data-id=\"50c8aee\" 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<p>El criterio C es una extensi\u00f3n del criterio de Condorcet y se define como (donde \u03b3 es un valor umbral):<\/p>\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\/eval15.png\" alt=\"criterio de calidad interno criterio C\" width=\"581\" height=\"91\" title=\"\"><\/figure>\n<p>Si consideramos las distancias NT entre pares de puntos como una serie de valores ordenados en orden ascendente, el \u00edndice C utiliza los valores NW m\u00e1s peque\u00f1os y los valores NW m\u00e1s grandes para calcular las sumas Smin y Smax: la suma S implica las distancias NW en esta secuencia que corresponden a pares presentes en un grupo (es decir, pares cuyos dos puntos est\u00e1n en el mismo grupo). Como m\u00e1ximo, las distancias 3NW se retienen efectivamente en el c\u00e1lculo de este \u00edndice.<\/p>\n<p>El criterio C se escribe entonces de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21052\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/C-index.png\" alt=\"\u00edndice C\" width=\"122\" height=\"40\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/C-index.png 122w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/C-index-18x6.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/C-index-120x40.png 120w\" sizes=\"(max-width: 122px) 100vw, 122px\" \/><\/p>\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-b8bad90 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b8bad90\" 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-2af6886\" data-id=\"2af6886\" 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-ef01086 elementor-widget elementor-widget-heading\" data-id=\"ef01086\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Calinski-Harabasz\"><\/span>Calinski-Harabasz<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-8daff3b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8daff3b\" 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-5004fac\" data-id=\"5004fac\" 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-e6dbf82 elementor-widget elementor-widget-text-editor\" data-id=\"e6dbf82\" 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<p>Rendimiento basado en\u00a0<a href=\"https:\/\/complex-systems-ai.com\/es\/partitionnement-de-donnees\/somme-de-lerreur-quadratique\/\">HSE<\/a>\u00a0media intra e inter-cluster (Tr):<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval20.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"291\" height=\"75\" \/><\/figure>\n<p>donde B_k es la matriz de\u00a0<a href=\"https:\/\/complex-systems-ai.com\/es\/partitionnement-de-donnees\/criteres-de-dispersion\/\">dispersi\u00f3n<\/a>\u00a0entre conglomerados y W_k es la matriz de dispersi\u00f3n intraconglomerado definida por:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval21.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"382\" height=\"177\" \/><\/figure>\n<p>con N el n\u00famero de puntos en nuestros datos, C_q el conjunto de puntos en el grupo q, c_q el centro del grupo q, c el centro de E, n_q el n\u00famero de puntos en el grupo q.<\/p>\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-efd8400 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"efd8400\" 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-c6235a4\" data-id=\"c6235a4\" 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-6687e37 elementor-widget elementor-widget-heading\" data-id=\"6687e37\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Davies-Bouldin\"><\/span>Davies-Bouldin<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-2a3e98d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2a3e98d\" 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-1dac4a2\" data-id=\"1dac4a2\" 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-cd6340a elementor-widget elementor-widget-text-editor\" data-id=\"cd6340a\" 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<p>Este \u00edndice trata a cada grupo individualmente y busca medir qu\u00e9 tan similar es al grupo m\u00e1s cercano. El \u00edndice DB se formula de la siguiente manera:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval25.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"263\" height=\"57\" \/><\/figure>\n<p>I (c_i) representa el promedio de las distancias entre los objetos que pertenecen al grupo C_i y su centro. Y I (c_i, c_j) representa la distancia entre los centros de los dos grupos C_i y C_j.<\/p>\n<p>Para cada conglomerado i de la partici\u00f3n, buscamos el conglomerado j que maximiza el \u00edndice descrito a continuaci\u00f3n:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval26.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"131\" height=\"45\" \/><\/figure>\n<p>Por lo tanto, la mejor partici\u00f3n es la que minimiza el promedio del valor calculado para cada cl\u00faster. En otras palabras, la mejor partici\u00f3n es la que minimiza la similitud entre los cl\u00fasteres.<\/p>\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-1f6a47b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1f6a47b\" 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-80b6592\" data-id=\"80b6592\" 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-7fcc0d5 elementor-widget elementor-widget-heading\" data-id=\"7fcc0d5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Det-Ratio\"><\/span>Relaci\u00f3n_detonaci\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-d2e7242 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d2e7242\" 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-5d23446\" data-id=\"5d23446\" 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-cdb4309 elementor-widget elementor-widget-text-editor\" data-id=\"cdb4309\" 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<p>El \u00edndice Det_Ratio se define as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21053\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Det_Ratio.png\" alt=\"Relaci\u00f3n_detonaci\u00f3n\" width=\"94\" height=\"42\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Det_Ratio.png 94w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Det_Ratio-18x8.png 18w\" sizes=\"(max-width: 94px) 100vw, 94px\" \/><\/p>\n<p>T denota la matriz de difusi\u00f3n total. Es la suma de las matrices BG y WG.<\/p>\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-f315920 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f315920\" 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-c5f63e3\" data-id=\"c5f63e3\" 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-f7391f8 elementor-widget elementor-widget-heading\" data-id=\"f7391f8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Dunn\"><\/span>Dunn<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-afe7606 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"afe7606\" 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-fb8dfe7\" data-id=\"fb8dfe7\" 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-c101781 elementor-widget elementor-widget-text-editor\" data-id=\"c101781\" 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<p>El \u00edndice de Dunn es otra m\u00e9trica de validaci\u00f3n de cl\u00faster interna que se puede calcular de la siguiente manera:<\/p>\n<ol>\n<li>Para cada grupo, calcule la distancia entre cada uno de los objetos del grupo y los objetos de los otros grupos<\/li>\n<li>Utilice el m\u00ednimo de esta distancia por par como separaci\u00f3n entre grupos (separaci\u00f3n m\u00ednima)<\/li>\n<li>Para cada grupo, calcule la distancia entre los objetos del mismo grupo.<\/li>\n<li>Use la distancia m\u00e1xima intra-cluster (es decir, el di\u00e1metro m\u00e1ximo) como compacidad intra-cluster<\/li>\n<li>Calcule el \u00edndice de Dunn (D) de la siguiente manera:<\/li>\n<\/ol>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval27.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"188\" height=\"53\" \/><\/figure>\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-d182825 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d182825\" 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-64fbf91\" data-id=\"64fbf91\" 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-78a30d7 elementor-widget elementor-widget-heading\" data-id=\"78a30d7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"GDImn\"><\/span>GDImn<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-086b7e3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"086b7e3\" 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-45dd064\" data-id=\"45dd064\" 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-2966835 elementor-widget elementor-widget-text-editor\" data-id=\"2966835\" 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<p>El \u00cdndice Generalizado de Dunn (GDI) da un valor basado en el \u201cbuen comportamiento\u201d de los conglomerados y sus miembros, medido en funci\u00f3n de las distancias entre los conglomerados y dentro de los conglomerados.<\/p>\n<p>Denotemos con la letra \u03b4 una medida de la distancia entre grupos y con \u0394 una medida de la distancia dentro de los grupos (que tambi\u00e9n se llama di\u00e1metro del grupo). El \u00edndice GDI, relativo a estas distancias, se define de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21061\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI1.png\" alt=\"GDI\" width=\"155\" height=\"40\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI1.png 155w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI1-150x40.png 150w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI1-18x5.png 18w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><\/p>\n<p>Con k y k&#039; entre 1 y K.<\/p>\n<p>Se han sugerido seis definiciones diferentes de \u03b4 (denotadas \u03b41 a \u03b46) y tres definiciones de \u0394 (denotadas \u03941 a \u03943). Esto conduce a 18 \u00edndices diferentes denominados Cuv: aqu\u00ed u es un n\u00famero entero que designa la distancia entre los grupos (1 \u2264 u \u2264 6) yv un n\u00famero entero que designa la distancia dentro de los grupos (1 \u2264 v \u2264 3). Las definiciones de las distancias \u0394 dentro del grupo son:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21062\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI2.png\" alt=\"GDI\" width=\"294\" height=\"144\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI2.png 294w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI2-18x9.png 18w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><\/p>\n<p>Aqu\u00ed d es la distancia euclidiana. El factor 2 en la definici\u00f3n de \u03943 permite interpretar el valor como un di\u00e1metro en lugar de un radio. Las definiciones de las distancias entre conglomerados \u03b4 son:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21063 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI3.png\" alt=\"GDI\" width=\"453\" height=\"250\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI3.png 453w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI3-300x166.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/GDI3-18x10.png 18w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Las primeras cuatro distancias (\u03b41 a \u03b44) aparecen en los algoritmos de agrupamiento ascendente y se denominan enlace \u00fanico, enlace completo, enlace promedio y enlace centroide, respectivamente. La medida \u03b45 es el promedio ponderado (con los pesos nk y nk\u2032) de las distancias promedio entre los puntos de los clusters Ck y Ck\u2032 y su respectivo baricentro. La medida \u03b46 es la distancia de Hausdorff DH.<\/p>\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-0fb66c7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0fb66c7\" 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-a9a8f9b\" data-id=\"a9a8f9b\" 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-ab35f1f elementor-widget elementor-widget-heading\" data-id=\"ab35f1f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Baker-Hubert-Gamma\"><\/span>Baker-Hubert Gamma <span class=\"ez-toc-section-end\"><\/span><\/h2>\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-c0e8be7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c0e8be7\" 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-ea3d5c8\" data-id=\"ea3d5c8\" 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-23ddf12 elementor-widget elementor-widget-text-editor\" data-id=\"23ddf12\" 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<p>El \u00edndice Baker-Hubert Gamma es una adaptaci\u00f3n, en el marco del clustering, del \u00edndice \u0393 de <a href=\"https:\/\/complex-systems-ai.com\/es\/correlacion-y-regresiones\/\">correlaci\u00f3n<\/a> entre dos vectores de datos A y B del mismo tama\u00f1o.<\/p>\n<p>Generalmente, para dos \u00edndices i y j tales que ai &lt; aj, decimos que los dos vectores son concordantes si bi &lt; bj, es decir si los valores se clasifican en el mismo orden en los dos vectores. Calculamos el n\u00famero s+ de pares concordantes {i, j} y el n\u00famero s\u2212 de pares discordantes. Tenga en cuenta que las desigualdades son estrictas, lo que significa que se eliminan los v\u00ednculos. En este contexto, el \u00edndice \u0393 se define cl\u00e1sicamente de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21059\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Gamma1.png\" alt=\"Gama\" width=\"120\" height=\"39\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Gamma1.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Gamma1-18x6.png 18w\" sizes=\"(max-width: 120px) 100vw, 120px\" \/><\/p>\n<p>El valor est\u00e1 entre -1 y 1.<\/p>\n<p>En el contexto de una partici\u00f3n, el primer vector A se elige como el conjunto de distancias dij entre pares de puntos {Mi,Mj} (con i &lt; j). El segundo vector B es un vector binario: en este vector, la coordenada correspondiente a un par {Mi,Mj} vale 0 si los dos puntos est\u00e1n en el mismo grupo y 1 en caso contrario. Estos dos vectores tienen una longitud NT = N(N \u2212 1)\/2.<\/p>\n<p>El n\u00famero s+ representa el n\u00famero de veces que una distancia entre dos puntos que pertenecen al mismo grupo (es decir, una pareja para la cual el valor del vector B es 0) es estrictamente menor que la distancia entre dos puntos n que no pertenecen al mismo grupo. grupo (es decir, una pareja para la cual el valor del vector B es 1).<\/p>\n<p>El n\u00famero s\u2212 representa el n\u00famero de veces que ocurre la situaci\u00f3n contraria, es decir que una distancia entre dos puntos pertenecientes al mismo cluster (valor 0 en B) es estrictamente mayor que una distancia entre dos puntos que no pertenecen al mismo grupo. (valor 1 en B). No se tendr\u00e1n en cuenta los casos en los que exista empate (empate o ex-aequos).<\/p>\n<p>Hay distancias NB entre conglomerados y, para cada una de ellas, comparamos con las distancias intra-conglomerados NW: finalmente realizamos comparaciones NB \u00d7 NW. Podemos escribir los n\u00fameros s+ y s\u2212 de la siguiente forma:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21060 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Gamma2.png\" alt=\"Gama\" width=\"395\" height=\"178\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Gamma2.png 395w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Gamma2-300x135.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Gamma2-18x8.png 18w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\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-2863f02 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2863f02\" 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-0b9bd11\" data-id=\"0b9bd11\" 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-0ed4003 elementor-widget elementor-widget-heading\" data-id=\"0ed4003\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"G\"><\/span>G+<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-de18e53 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de18e53\" 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-11dc790\" data-id=\"11dc790\" 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-c3009fb elementor-widget elementor-widget-text-editor\" data-id=\"c3009fb\" 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<p>Utilizando las mismas notaciones que para el \u00edndice \u0393 de Baker-Hubert, el \u00edndice G+ se define de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21064\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/G.png\" alt=\"G+\" width=\"238\" height=\"42\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/G.png 238w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/G-18x3.png 18w\" sizes=\"(max-width: 238px) 100vw, 238px\" \/><\/p>\n<p>Es la proporci\u00f3n de pares discordantes entre todos los pares de puntos distintos.<\/p>\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-ac3fd45 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ac3fd45\" 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-4bec7cd\" data-id=\"4bec7cd\" 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-25032a7 elementor-widget elementor-widget-heading\" data-id=\"25032a7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Ksq-DetW\"><\/span>Ksq_DetW<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-9e96afc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9e96afc\" 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-3b7c85f\" data-id=\"3b7c85f\" 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-1034b2d elementor-widget elementor-widget-text-editor\" data-id=\"1034b2d\" 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<p>Como su nombre indica, su f\u00f3rmula es K\u00b2|WG|.<\/p>\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-bc96c18 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bc96c18\" 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-c242462\" data-id=\"c242462\" 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-e73a419 elementor-widget elementor-widget-heading\" data-id=\"e73a419\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Log-Det-Ratio\"><\/span>Log_Det_Ratio<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-fe9cff0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fe9cff0\" 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-a962b59\" data-id=\"a962b59\" 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-96ea979 elementor-widget elementor-widget-text-editor\" data-id=\"96ea979\" 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<p>El \u00edndice Log_Det_Ratio se define as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21065\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Log_Det_Ratio.png\" alt=\"Log_Det_Ratio\" width=\"161\" height=\"39\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Log_Det_Ratio.png 161w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Log_Det_Ratio-18x4.png 18w\" sizes=\"(max-width: 161px) 100vw, 161px\" \/><\/p>\n<p>donde T es la matriz de difusi\u00f3n y WG. Esta es una variante logar\u00edtmica del \u00edndice Det_Ratio.<\/p>\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-58e0e89 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"58e0e89\" 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-1753697\" data-id=\"1753697\" 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-b117979 elementor-widget elementor-widget-heading\" data-id=\"b117979\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Log-SS-Ratio\"><\/span>Log_SS_Ratio<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-4746e87 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4746e87\" 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-0623ff1\" data-id=\"0623ff1\" 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-d9458bd elementor-widget elementor-widget-text-editor\" data-id=\"d9458bd\" 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<p>El \u00edndice Log_SS_Ratio se define as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21066\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Log_SS_Ratio.png\" alt=\"Log_SS_Ratio\" width=\"128\" height=\"41\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Log_SS_Ratio.png 128w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Log_SS_Ratio-18x6.png 18w\" sizes=\"(max-width: 128px) 100vw, 128px\" \/><\/p>\n<p>donde BGSS y WGSS son las trazas de las matrices BG y WG respectivamente.<\/p>\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-670bef1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"670bef1\" 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-5e7e0e4\" data-id=\"5e7e0e4\" 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-02e59b8 elementor-widget elementor-widget-heading\" data-id=\"02e59b8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"McClain-Rao\"><\/span>McClain-Rao<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-356350c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"356350c\" 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-5c4b167\" data-id=\"5c4b167\" 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-e96f30f elementor-widget elementor-widget-text-editor\" data-id=\"e96f30f\" 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<p>En cuanto al \u00edndice C, sea SW la suma de las distancias dentro del grupo:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21067 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao1.png\" alt=\"McClain-Rao\" width=\"325\" height=\"60\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao1.png 325w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao1-300x55.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao1-18x3.png 18w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/p>\n<p>Recuerde que el n\u00famero total de distancias entre pares de puntos que pertenecen al mismo grupo es NW. Denotaremos SB la suma de las distancias entre grupos:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21068 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao2.png\" alt=\"McClain-Rao\" width=\"351\" height=\"56\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao2.png 351w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao2-300x48.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao2-18x3.png 18w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/p>\n<p>El n\u00famero total de distancias entre pares de puntos que no pertenecen al mismo grupo es NB = N(N \u2212 1)\/2 \u2212 NW. El \u00edndice de McClain-Rao se define como el cociente entre las distancias medias dentro de un conglomerado y entre conglomerados:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21069\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao3.png\" alt=\"McClain-Rao\" width=\"169\" height=\"37\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao3.png 169w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/McClain-Rao3-18x4.png 18w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><\/p>\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-196a0a7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"196a0a7\" 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-541f1ef\" data-id=\"541f1ef\" 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-65335bd elementor-widget elementor-widget-heading\" data-id=\"65335bd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"PBM\"><\/span>PBM<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-7557679 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7557679\" 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-29c5270\" data-id=\"29c5270\" 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-00ab12b elementor-widget elementor-widget-text-editor\" data-id=\"00ab12b\" 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<p>El \u00edndice PBM (acr\u00f3nimo formado por las iniciales de los nombres de sus autores, Pakhira, Bandyopadhyay y Maulik) se calcula a partir de las distancias entre los puntos y sus baricentros y de las distancias entre los propios baricentros.<\/p>\n<p>Denotemos por DB la mayor distancia entre dos baricentros del c\u00famulo:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21070\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM.png\" alt=\"PBM\" width=\"191\" height=\"50\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM.png 191w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM-18x5.png 18w\" sizes=\"(max-width: 191px) 100vw, 191px\" \/><\/p>\n<p>Por otro lado, denotamos EW la suma de las distancias de los puntos de cada grupo a su baricentro y ET la suma de las distancias de todos los puntos al baricentro G de todos los datos:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21071\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM2.png\" alt=\"PBM\" width=\"216\" height=\"108\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM2.png 216w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM2-18x9.png 18w\" sizes=\"(max-width: 216px) 100vw, 216px\" \/><\/p>\n<p>El \u00edndice PBM se define as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21072\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM3.png\" alt=\"PBM\" width=\"172\" height=\"45\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM3.png 172w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/PBM3-18x5.png 18w\" sizes=\"(max-width: 172px) 100vw, 172px\" \/><\/p>\n<p>ET es una constante que no depende de la partici\u00f3n ni del n\u00famero de cl\u00fasteres.<\/p>\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-f6e7e33 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f6e7e33\" 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-3388b20\" data-id=\"3388b20\" 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-ca94ff7 elementor-widget elementor-widget-heading\" data-id=\"ca94ff7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Point-Biserial\"><\/span>Punto-Biserial<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-75ab1c8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"75ab1c8\" 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-899c1c5\" data-id=\"899c1c5\" 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-a6818be elementor-widget elementor-widget-text-editor\" data-id=\"a6818be\" 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<p>En t\u00e9rminos generales, en estad\u00edstica, el coeficiente biserial puntual es una medida de correlaci\u00f3n entre una variable continua A y una variable binaria B (es decir, una variable cuyos valores son 0 o 1). A y B son conjuntos de la misma longitud n.<\/p>\n<p>Los valores de A se dividen en dos grupos A0 y A1 dependiendo de si el valor correspondiente en B es 0 o 1. Sean MA0 y MA1 los promedios en A0 y A1, y nA0 y nA1 el n\u00famero de elementos de cada grupo. . El coeficiente de correlaci\u00f3n punto-biserial se define como la cantidad:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21076\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial1.png\" alt=\"punto-biserial\" width=\"249\" height=\"50\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial1.png 249w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial1-18x4.png 18w\" sizes=\"(max-width: 249px) 100vw, 249px\" \/><\/p>\n<p>donde sn es la desviaci\u00f3n est\u00e1ndar de A.<\/p>\n<p>En el contexto de una comparaci\u00f3n entre diferentes agrupaciones, el t\u00e9rmino sn se puede omitir porque no depende de las particiones sino s\u00f3lo del conjunto de datos completo.<\/p>\n<p>Como en el caso del \u00edndice \u0393, adaptamos esta definici\u00f3n eligiendo A como el conjunto de NT distancias entre pares de puntos Mi y Mj. El valor correspondiente en B es 1 si los dos puntos est\u00e1n en el mismo grupo y 0 en caso contrario:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21077\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial2.png\" alt=\"punto-biserial\" width=\"198\" height=\"79\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial2.png 198w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial2-18x7.png 18w\" sizes=\"(max-width: 198px) 100vw, 198px\" \/><\/p>\n<p>MA1 es el promedio de todas las distancias dentro del grupo y MA0 es el promedio de todas las distancias entre grupos. Por tanto, la definici\u00f3n del \u00edndice biserial puntual es:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21078 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial3.png\" alt=\"punto-biserial\" width=\"350\" height=\"42\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial3.png 350w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial3-300x36.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/point-biserial3-18x2.png 18w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\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-b22f56d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b22f56d\" 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-6e5b837\" data-id=\"6e5b837\" 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-231339d elementor-widget elementor-widget-heading\" data-id=\"231339d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Ratkowsky-Lance\"><\/span>Lanza Ratkowsky<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-3895b7e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3895b7e\" 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-2e7289f\" data-id=\"2e7289f\" 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-1e73917 elementor-widget elementor-widget-text-editor\" data-id=\"1e73917\" 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<p>Calculamos el promedio \u00afR de los cocientes entre BGSS y TSS para cada dimensi\u00f3n de los datos, es decir para cada columna de la matriz A. Nota:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21079\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ratkowsky-Lance1.png\" alt=\"Lanza Ratkowsky\" width=\"251\" height=\"181\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ratkowsky-Lance1.png 251w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ratkowsky-Lance1-18x12.png 18w\" sizes=\"(max-width: 251px) 100vw, 251px\" \/><\/p>\n<p>BGSSj es de hecho el j-\u00e9simo t\u00e9rmino diagonal de la matriz BG. El \u00edndice Ratkowsky-Lance (\u00afc\/\u221aK) se define de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21080\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ratkowsky-Lance2.png\" alt=\"Lanza Ratkowsky\" width=\"115\" height=\"45\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ratkowsky-Lance2.png 115w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ratkowsky-Lance2-18x7.png 18w\" sizes=\"(max-width: 115px) 100vw, 115px\" \/><\/p>\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-9218dd5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9218dd5\" 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-f50f3fc\" data-id=\"f50f3fc\" 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-a137a00 elementor-widget elementor-widget-heading\" data-id=\"a137a00\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Ray-Turi\"><\/span>Ray Turi<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-54dd638 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"54dd638\" 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-e8526db\" data-id=\"e8526db\" 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-89edfad elementor-widget elementor-widget-text-editor\" data-id=\"89edfad\" 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<p>El \u00edndice de Ray-Turi se define como un cociente:<\/p>\n<p>\u2013 el numerador es la media de los cuadrados de las distancias de todos los puntos con respecto al baricentro del c\u00famulo al que pertenecen:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21082 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi1.png\" alt=\"Ray Turi\" width=\"418\" height=\"65\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi1.png 418w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi1-300x47.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi1-18x3.png 18w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>\u2013 el denominador es el m\u00ednimo de los cuadrados de las distancias \u0394kk\u2032 entre todos los baricentros del cluster:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21083 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi2.png\" alt=\"Ray Turi\" width=\"389\" height=\"40\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi2.png 389w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi2-300x31.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi2-18x2.png 18w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Por tanto, el \u00edndice de Ray-Turi se puede escribir de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21084\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi3.png\" alt=\"Ray Turi\" width=\"112\" height=\"51\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi3.png 112w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Ray-Turi3-18x8.png 18w\" sizes=\"(max-width: 112px) 100vw, 112px\" \/><\/p>\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-733ac7d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"733ac7d\" 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-0ecab9d\" data-id=\"0ecab9d\" 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-238db92 elementor-widget elementor-widget-heading\" data-id=\"238db92\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Scott-Symons\"><\/span>Scott Simons<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-fb3045d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fb3045d\" 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-2217bdd\" data-id=\"2217bdd\" 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-75cdf6b elementor-widget elementor-widget-text-editor\" data-id=\"75cdf6b\" 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<p>Este \u00edndice es la suma ponderada de los logaritmos de los determinantes de la matriz de varianza-covarianza de cada conglomerado. Esto se puede escribir de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21085\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Scott-Symons.png\" alt=\"Scott Simons\" width=\"193\" height=\"52\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Scott-Symons.png 193w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Scott-Symons-18x5.png 18w\" sizes=\"(max-width: 193px) 100vw, 193px\" \/><\/p>\n<p>Los determinantes de las matrices WG{k} son mayores o iguales a 0 porque estas matrices son semidefinidas positivas. Si alguno de ellos es 0, el \u00edndice no est\u00e1 definido.<\/p>\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-b578942 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b578942\" 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-47e1f41\" data-id=\"47e1f41\" 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-06ccfbe elementor-widget elementor-widget-heading\" data-id=\"06ccfbe\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"SD-Scat-et-SD-Dis\"><\/span>SD_Scat y SD_Dis<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-e29c493 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e29c493\" 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-1659231\" data-id=\"1659231\" 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-a72a87d elementor-widget elementor-widget-text-editor\" data-id=\"a72a87d\" 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<p>Definimos dos cantidades S y D llamadas respectivamente difusi\u00f3n media de conglomerados y separaci\u00f3n total entre conglomerados.<\/p>\n<p>La difusi\u00f3n promedio de los grupos, denominada S, se define de la siguiente manera. Considere el vector de varianzas para cada variable en el conjunto de datos. Es un vector V de tama\u00f1o p definido por:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21086\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD1.png\" alt=\"Dakota del Sur\" width=\"186\" height=\"30\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD1.png 186w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD1-18x3.png 18w\" sizes=\"(max-width: 186px) 100vw, 186px\" \/><\/p>\n<p>De manera similar, definimos vectores de varianza V{k} para cada grupo Ck:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21087\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD2.png\" alt=\"Dakota del Sur\" width=\"240\" height=\"40\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD2.png 240w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD2-18x3.png 18w\" sizes=\"(max-width: 240px) 100vw, 240px\" \/><\/p>\n<p>La cantidad S es la media de las normas de los vectores V{k} dividida por la norma del vector V:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21088\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD3.png\" alt=\"Dakota del Sur\" width=\"137\" height=\"75\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD3.png 137w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD3-18x10.png 18w\" sizes=\"(max-width: 137px) 100vw, 137px\" \/><\/p>\n<p>Por otro lado, la separaci\u00f3n total entre conglomerados, denotada como D, se define de la siguiente manera. Denotaremos Dmax y Dmin respectivamente como la distancia m\u00e1s grande y m\u00e1s peque\u00f1a entre los baricentros de los grupos:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21089\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD4.png\" alt=\"Dakota del Sur\" width=\"261\" height=\"185\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD4.png 261w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD4-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD4-120x85.png 120w\" sizes=\"(max-width: 261px) 100vw, 261px\" \/><\/p>\n<p>El \u00edndice SD finalmente se define as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21090\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD5.png\" alt=\"Dakota del Sur\" width=\"84\" height=\"19\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD5.png 84w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/SD5-18x4.png 18w\" sizes=\"(max-width: 84px) 100vw, 84px\" \/><\/p>\n<p>donde \u03b1 es un peso igual al valor de D obtenido para la partici\u00f3n con mayor n\u00famero de clusters. Para comparar varias particiones de los datos, primero es necesario calcular el valor de D correspondiente al mayor n\u00famero de conglomerados para encontrar el valor del coeficiente \u03b1 y luego calcular los dem\u00e1s \u00edndices a partir de este coeficiente.<\/p>\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-482bd2f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"482bd2f\" 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-d4ab056\" data-id=\"d4ab056\" 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-a86cb8b elementor-widget elementor-widget-heading\" data-id=\"a86cb8b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"S-Dbw\"><\/span>S_Dbw<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-a9a0234 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a9a0234\" 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-adeb914\" data-id=\"adeb914\" 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-36c2356 elementor-widget elementor-widget-text-editor\" data-id=\"36c2356\" 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<p>Este \u00edndice se basa en la noci\u00f3n de densidad de puntos pertenecientes a dos conglomerados. Primero definimos un valor l\u00edmite \u03c3 igual a la ra\u00edz cuadrada de la suma de las normas de los vectores de varianza V{k} dividida por el n\u00famero de clusters:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21091\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw1.png\" alt=\"S_Dbw\" width=\"156\" height=\"65\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw1.png 156w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw1-18x8.png 18w\" sizes=\"(max-width: 156px) 100vw, 156px\" \/><\/p>\n<p>La densidad \u03b3kk\u2032 para un punto dado, en relaci\u00f3n con dos grupos Ck y Ck\u2032, es igual al n\u00famero de puntos en estos dos grupos cuya distancia desde este punto es menor que \u03c3. Geom\u00e9tricamente, esto equivale a considerar la bola de radio \u03c3 centrada en un punto dado y contar el n\u00famero de puntos de Ck \u222a Ck\u2032 ubicados en esta bola.<\/p>\n<p>Para cada par de conglomerados, eval\u00faemos las densidades de los baricentros G{k} y G{k\u2032} de los conglomerados y de su punto medio Hkk\u2032. Formamos el cociente Rkk&#039; entre la densidad en el medio y la mayor densidad en los dos baricentros:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-21092 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw2.png\" alt=\"S_Dbw\" width=\"270\" height=\"51\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw2.png 270w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw2-18x3.png 18w\" sizes=\"(max-width: 270px) 100vw, 270px\" \/><\/p>\n<p>Por otro lado, definimos una densidad entre conglomerados G como el promedio de los cocientes Rkk\u2032:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21093\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw3.png\" alt=\"S_Dbw\" width=\"173\" height=\"50\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw3.png 173w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw3-18x5.png 18w\" sizes=\"(max-width: 173px) 100vw, 173px\" \/><\/p>\n<p>El \u00edndice S-Dbw se define como la suma de la dispersi\u00f3n promedio en los conglomerados S y la densidad entre conglomerados G:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21094\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw4.png\" alt=\"S_Dbw\" width=\"71\" height=\"15\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw4.png 71w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/S_Dbw4-18x4.png 18w\" sizes=\"(max-width: 71px) 100vw, 71px\" \/><\/p>\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-c2b7719 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c2b7719\" 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-aaadc71\" data-id=\"aaadc71\" 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-eb345d9 elementor-widget elementor-widget-heading\" data-id=\"eb345d9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Silhouette\"><\/span>Silueta<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-71115ac elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"71115ac\" 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-a49fcc5\" data-id=\"a49fcc5\" 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-6c0e6f7 elementor-widget elementor-widget-text-editor\" data-id=\"6c0e6f7\" 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<p>Valida el rendimiento basado en distancias intra e inter-cl\u00faster:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval22.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"217\" height=\"73\" \/><\/figure>\n<p>con a (i) la disimilitud promedio con los otros datos del conglomerado yb (i) la disimilitud m\u00e1s d\u00e9bil con cualquier conglomerado no miembro para cada x_i y centro del conglomerado y:<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval23.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"350\" height=\"167\" \/><\/figure>\n<p>El coeficiente de silueta var\u00eda entre -1 (peor clasificaci\u00f3n) y 1 (mejor clasificaci\u00f3n). A menudo se calcula el promedio general de Silhouette.<\/p>\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette Calinski-Harabasz\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/eval24.png\" alt=\"Calinski-Harabasz, Davies-Bouldin, Dunn y Silhouette\" width=\"638\" height=\"300\" \/><\/figure>\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-03af559 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"03af559\" 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-c972bcd\" data-id=\"c972bcd\" 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-ed97439 elementor-widget elementor-widget-heading\" data-id=\"ed97439\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Tau\"><\/span>Tau<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-62a2c12 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"62a2c12\" 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-06cb92f\" data-id=\"06cb92f\" 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-b9dabc0 elementor-widget elementor-widget-text-editor\" data-id=\"b9dabc0\" 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<p>Utilizando las mismas notaciones que para el \u00edndice Gamma, el \u00edndice \u03c4 de Kendall entre dos vectores de datos de longitud NT se define cl\u00e1sicamente en estad\u00edstica como la cantidad:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21095\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau1.png\" alt=\"Tau\" width=\"132\" height=\"61\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau1.png 132w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau1-18x8.png 18w\" sizes=\"(max-width: 132px) 100vw, 132px\" \/><\/p>\n<p>Los n\u00fameros s+ y s\u2212 no cuentan los enlaces, por lo que si una distancia entre grupos y una distancia dentro de un grupo son iguales, no ingresan en el numerador. Para tener en cuenta las igualdades modificamos el denominador y definimos el \u00edndice corregido \u03c4c as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21096\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau2.png\" alt=\"Tau\" width=\"178\" height=\"48\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau2.png 178w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau2-18x5.png 18w\" sizes=\"(max-width: 178px) 100vw, 178px\" \/><\/p>\n<p>con<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21097\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau3.png\" alt=\"Tau\" width=\"173\" height=\"136\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau3.png 173w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau3-15x12.png 15w\" sizes=\"(max-width: 173px) 100vw, 173px\" \/><\/p>\n<p>donde ti es el n\u00famero de valores en el i-\u00e9simo grupo de enlaces para el vector A y uj es el n\u00famero de valores en el j-\u00e9simo grupo de enlaces para el vector B. Aqu\u00ed el vector B consta solo de valores 0 y 1 (correspondientes respectivamente a los pares inter-cluster e intra-cluster) y as\u00ed tenemos:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21098\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau4.png\" alt=\"Tau\" width=\"267\" height=\"26\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau4.png 267w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau4-18x2.png 18w\" sizes=\"(max-width: 267px) 100vw, 267px\" \/><\/p>\n<p>Un c\u00e1lculo simple muestra que \u03bd0 \u2212 \u03bd2 = NBNW. Si asumimos razonablemente que el vector A contiene pocos valores id\u00e9nticos, podemos estimar que \u03bd2 es insignificante en comparaci\u00f3n con \u03bd0. Esto justifica la siguiente definici\u00f3n del \u00edndice de agrupamiento Tau:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21099\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau5.png\" alt=\"Tau\" width=\"211\" height=\"73\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau5.png 211w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Tau5-18x6.png 18w\" sizes=\"(max-width: 211px) 100vw, 211px\" \/><\/p>\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-2a87e5e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2a87e5e\" 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-c78aba0\" data-id=\"c78aba0\" 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-6b07908 elementor-widget elementor-widget-heading\" data-id=\"6b07908\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Trace-W\"><\/span>traza_W<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-af26b9f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"af26b9f\" 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-16906d0\" data-id=\"16906d0\" 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-ceb1398 elementor-widget elementor-widget-text-editor\" data-id=\"ceb1398\" 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<p>El \u00edndice Trace_W se define as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21100\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Trace_W.png\" alt=\"traza_W\" width=\"157\" height=\"18\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Trace_W.png 157w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Trace_W-150x18.png 150w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Trace_W-18x2.png 18w\" sizes=\"(max-width: 157px) 100vw, 157px\" \/><\/p>\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-45a60ed elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"45a60ed\" 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-defb9ad\" data-id=\"defb9ad\" 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-9645602 elementor-widget elementor-widget-heading\" data-id=\"9645602\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Trace-WiB\"><\/span>traza_WiB<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-61a417f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"61a417f\" 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-e986e70\" data-id=\"e986e70\" 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-fdf042e elementor-widget elementor-widget-text-editor\" data-id=\"fdf042e\" 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<p>El \u00edndice Trace_WiB se define as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21101\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Trace_WiB.png\" alt=\"traza_WiB\" width=\"139\" height=\"22\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Trace_WiB.png 139w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Trace_WiB-18x3.png 18w\" sizes=\"(max-width: 139px) 100vw, 139px\" \/><\/p>\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-d20c853 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d20c853\" 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-b209e29\" data-id=\"b209e29\" 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-b242fa9 elementor-widget elementor-widget-heading\" data-id=\"b242fa9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Wemmert-Gancarski\"><\/span>Wemmert-Gan\u00e7arski<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-26f43b6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"26f43b6\" 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-24107a4\" data-id=\"24107a4\" 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-a9a35b6 elementor-widget elementor-widget-text-editor\" data-id=\"a9a35b6\" 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<p>El \u00edndice de Wemmert-Gan\u00e7arski se construye a partir de los cocientes de distancias entre los puntos y los baricentros de todos los conglomerados.<\/p>\n<p>Para un punto M perteneciente al grupo Ck, formamos el cociente R(M) entre la distancia de este punto al baricentro del grupo al que pertenece y la distancia m\u00e1s peque\u00f1a desde este punto a los baricentros de todos los dem\u00e1s grupos:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21102\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski1.png\" alt=\"Wemmert-Gan\u00e7arski\" width=\"199\" height=\"60\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski1.png 199w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski1-18x5.png 18w\" sizes=\"(max-width: 199px) 100vw, 199px\" \/><\/p>\n<p>Luego promediamos estos cocientes en cada grupo. Si este promedio es mayor que 1 lo ignoramos, en caso contrario tomamos su complemento a 1. Espec\u00edficamente definamos:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21103\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski2.png\" alt=\"Wemmert-Gan\u00e7arski\" width=\"234\" height=\"45\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski2.png 234w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski2-18x3.png 18w\" sizes=\"(max-width: 234px) 100vw, 234px\" \/><\/p>\n<p>El \u00edndice de Wemmert-Gan\u00e7arski se define como el promedio ponderado, para todos los grupos, de las cantidades Jk as\u00ed:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21104\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski3.png\" alt=\"Wemmert-Gan\u00e7arski\" width=\"111\" height=\"51\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski3.png 111w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski3-18x8.png 18w\" sizes=\"(max-width: 111px) 100vw, 111px\" \/><\/p>\n<p>Que se puede reescribir como:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21105\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski4.png\" alt=\"Wemmert-Gan\u00e7arski\" width=\"257\" height=\"64\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski4.png 257w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Wemmert-Gancarski4-18x4.png 18w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/p>\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-d61bcbb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d61bcbb\" 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-2af5b65\" data-id=\"2af5b65\" 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-31b2660 elementor-widget elementor-widget-heading\" data-id=\"31b2660\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Xie-Beni\"><\/span>Xie-Beni<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-33bef5d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"33bef5d\" 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-2ad1fbe\" data-id=\"2ad1fbe\" 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-89cb38a elementor-widget elementor-widget-text-editor\" data-id=\"89cb38a\" 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<p>El \u00edndice Xie-Beni es un \u00edndice de agrupaci\u00f3n difusa, pero tambi\u00e9n se aplica a la agrupaci\u00f3n aguda.<\/p>\n<p>Se define como el cociente entre el error cuadr\u00e1tico medio y el m\u00ednimo de las distancias cuadr\u00e1ticas m\u00ednimas entre los puntos de los conglomerados. El error cuadr\u00e1tico medio, en el caso del clustering neto, es simplemente la cantidad 1\/N*WGSS, es decir, el promedio de los cuadrados de las distancias de todos los puntos con respecto al baricentro del cluster al que pertenecen.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21106\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Xie-Beni1.png\" alt=\"Xie-Beni\" width=\"207\" height=\"49\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Xie-Beni1.png 207w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Xie-Beni1-18x4.png 18w\" sizes=\"(max-width: 207px) 100vw, 207px\" \/><\/p>\n<p>y el \u00edndice Xie-Beni se puede escribir de la siguiente manera:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-21107\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Xie-Beni2.png\" alt=\"Xie-Beni\" width=\"161\" height=\"51\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Xie-Beni2.png 161w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/Xie-Beni2-18x6.png 18w\" sizes=\"(max-width: 161px) 100vw, 161px\" \/><\/p>\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>Inicio Wiki de partici\u00f3n de datos Criterios de calidad internos Los criterios de calidad internos generalmente miden la compacidad de los cl\u00fasteres utilizando una m\u00e9trica... <\/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-8393","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/8393","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=8393"}],"version-history":[{"count":15,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/8393\/revisions"}],"predecessor-version":[{"id":21112,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/8393\/revisions\/21112"}],"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=8393"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}