{"id":2078,"date":"2020-05-15T14:56:04","date_gmt":"2020-05-15T14:56:04","guid":{"rendered":"https:\/\/datascientest.com\/?p=2078"},"modified":"2023-11-09T14:14:39","modified_gmt":"2023-11-09T14:14:39","slug":"algorithme-des-k-means","status":"publish","type":"post","link":"https:\/\/datascientest.com\/algorithme-des-k-means","title":{"rendered":"K-means : Focus sur cet algorithme de Clustering &amp; Machine Learning"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2078\" class=\"elementor elementor-2078\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-83bdb14 e-flex e-con-boxed e-con\" data-id=\"83bdb14\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6f2d49e elementor-widget elementor-widget-heading\" data-id=\"6f2d49e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Le clustering est une discipline particuli\u00e8re du Machine Learning ayant pour objectif de s\u00e9parer vos donn\u00e9es en groupes homog\u00e8nes ayant des caract\u00e9ristiques communes. C\u2019est un domaine tr\u00e8s appr\u00e9ci\u00e9 en marketing, par exemple, o\u00f9 l\u2019on cherche souvent \u00e0 segmenter les bases clients pour d\u00e9tecter des comportements particuliers.\u00a0L\u2019algorithme des K-moyennes (K-means) est un algorithme non supervis\u00e9 tr\u00e8s connu en mati\u00e8re de Clustering.\u00a0<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-96bb793 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"96bb793\" data-element_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-5632ead\" data-id=\"5632ead\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7d11ce8 elementor-widget elementor-widget-text-editor\" data-id=\"7d11ce8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><span style=\"font-weight: normal;\">Dans cet article nous allons d\u00e9tailler son fonctionnement et les moyens utiles pour l\u2019optimiser.\u00a0<\/span><\/p><p><span style=\"font-weight: normal;\">Cet algorithme a \u00e9t\u00e9 con\u00e7u en 1957 au sein des Laboratoires Bell par Stuart P.Lloyd comme technique de modulation par impulsion et codage(MIC) . Il n\u2019a \u00e9t\u00e9 pr\u00e9sent\u00e9 au grand publique qu\u2019en 1982. En 1965 Edward W.Forgy avait d\u00e9j\u00e0 publi\u00e9 un algorithme quasiment similaire c\u2019est pourquoi le K-means est souvent nomm\u00e9 algorithme de Lloyd-Forgy.\u00a0<\/span><\/p><p><span style=\"font-weight: normal;\">Les champs d\u2019application sont divers : segmentation client, analyse de donn\u00e9e, segmenter une image, apprentissage semi-supervis\u00e9\u2026.<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-929e246 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"929e246\" data-element_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-a1fe6da\" data-id=\"a1fe6da\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8886804 elementor-widget elementor-widget-heading\" data-id=\"8886804\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Le Principe de l'algorithme des k-means <\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-30be98c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"30be98c\" data-element_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-6859462\" data-id=\"6859462\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4b0ef24 elementor-widget elementor-widget-text-editor\" data-id=\"4b0ef24\" data-element_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<p><span style=\"font-weight: normal;\">\u00c9tant donn\u00e9s des points et un entier k, l&rsquo;algorithme vise \u00e0 diviser les points en k groupes, appel\u00e9s clusters, homog\u00e8nes et compacts. Regardons l\u2019exemple ci-dessous :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-7008b3f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7008b3f\" data-element_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-50 elementor-inner-column elementor-element elementor-element-4127eba\" data-id=\"4127eba\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e652dc2 elementor-widget elementor-widget-image\" data-id=\"e652dc2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"377\" height=\"368\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans1.png\" class=\"attachment-large size-large wp-image-2670\" alt=\"kmeans\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans1.png 377w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans1-300x293.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/>\t\t\t\t\t\t\t\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-50 elementor-inner-column elementor-element elementor-element-a72f911\" data-id=\"a72f911\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-193ed58 elementor-widget elementor-widget-image\" data-id=\"193ed58\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"377\" height=\"368\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-2.png\" class=\"attachment-large size-large wp-image-2671\" alt=\"machine learning\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-2.png 377w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-2-300x293.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\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-468e132 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"468e132\" data-element_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-f20d958\" data-id=\"f20d958\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6c62017 elementor-widget elementor-widget-text-editor\" data-id=\"6c62017\" data-element_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<p><span style=\"font-weight: normal;\">Sur ce jeu de donn\u00e9es en 2D il appara\u00eet clair que l\u2019on peut le diviser en 3 groupes.<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t<div class=\"elementor-element elementor-element-d02d8c0 e-flex e-con-boxed e-con\" data-id=\"d02d8c0\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d34ca41 elementor-widget elementor-widget-heading\" data-id=\"d34ca41\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Concr\u00e8tement comment s\u2019y prend-on ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a23335e elementor-widget elementor-widget-text-editor\" data-id=\"a23335e\" data-element_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<p><span style=\"font-weight: normal;\">L\u2019id\u00e9e est assez simple et intuitive. La premi\u00e8re \u00e9tape consiste \u00e0 d\u00e9finir 3 centro\u00efdes al\u00e9atoirement auxquels on associe 3 \u00e9tiquettes par exemple 0,1,2. Ensuite nous allons pour chaque point <strong>r<\/strong><\/span><strong>egarder leur distance aux 3 centro\u00efdes<\/strong> <span style=\"font-weight: normal;\">et nous associons le point au centro\u00efde le plus proche et l\u2019\u00e9tiquette correspondante. Cela revient \u00e0 <\/span><strong>\u00e9tiqueter nos donn\u00e9es<\/strong><span style=\"font-weight: normal;\">.<br \/><\/span><\/p><p><span style=\"font-weight: normal;\">Enfin on recalcule 3 nouveaux centro\u00efdes qui seront les centres de gravit\u00e9 de chaque nuage de points labellis\u00e9s. On r\u00e9p\u00e8te ces \u00e9tapes jusqu\u2019\u00e0 ce que les nouveaux centro\u00efdes ne bougent plus des pr\u00e9c\u00e9dents. Le r\u00e9sultat final se trouve sur la figure de droite.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-208e804 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"208e804\" data-element_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-0adf5f9\" data-id=\"0adf5f9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-19774ce elementor-widget elementor-widget-heading\" data-id=\"19774ce\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Notion de distance et initialisation<\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-19bfb85 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"19bfb85\" data-element_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-199daea\" data-id=\"199daea\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d86a552 elementor-widget elementor-widget-text-editor\" data-id=\"d86a552\" data-element_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<p><span style=\"font-weight: normal;\">Vous l\u2019aurez compris dans cet algorithme deux points sont cl\u00e9 : <\/span>Quelle est la m\u00e9trique utilis\u00e9e pour \u00e9valuer la distance entre les points et les centro\u00efdes ? Quel est le nombre de clusters \u00e0 choisir ?<\/p><p><span style=\"font-weight: normal;\">Dans l\u2019algorithme des k-moyennes g\u00e9n\u00e9ralement on utilise la <\/span>distance euclidienne<span style=\"font-weight: normal;\">, soient p = (p1,\u2026.,pn) et q = (q1,\u2026.,qn)<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ab17e5d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ab17e5d\" data-element_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-1f0abcd\" data-id=\"1f0abcd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f054890 elementor-widget elementor-widget-image\" data-id=\"f054890\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"766\" height=\"77\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans3.png\" class=\"attachment-large size-large wp-image-2672\" alt=\"machine learning\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans3.png 766w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans3-300x30.png 300w\" sizes=\"(max-width: 766px) 100vw, 766px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2293bf4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2293bf4\" data-element_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-2ee10b0\" data-id=\"2ee10b0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-59928b0 elementor-widget elementor-widget-text-editor\" data-id=\"59928b0\" data-element_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<p><span style=\"font-weight: normal;\">Elle permet d\u2019\u00e9valuer la distance entre chaque point et les centro\u00efdes. Pour chaque point on calcule la distance euclidienne entre ce point et chacun des centro\u00efdes puis on l\u2019associe au centro\u00efde le plus proche c\u2019est-\u00e0-dire celui avec la plus petite distance.<br \/><\/span><\/p><p><span style=\"font-weight: normal;\">Dans l\u2019exemple pr\u00e9c\u00e9dent il \u00e9tait ais\u00e9 de trouver le nombre id\u00e9al de clusters simplement en visualisant graphiquement. G\u00e9n\u00e9ralement les jeux de donn\u00e9es ont plus de deux dimensions et il est donc <\/span>difficile de visualiser le nuage de points et d\u2019identifier rapidement le nombre de clusters optimal<span style=\"font-weight: normal;\">. Supposons dans l\u2019exemple pr\u00e9c\u00e9dent que nous n\u2019avons pas visualiser les donn\u00e9es avant et d\u00e9cidons de tester diff\u00e9rentes fois avec un nombre de clusters initiaux diff\u00e9rents. Voici les r\u00e9sultats obtenus :<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c6455a7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c6455a7\" data-element_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-d14bf75\" data-id=\"d14bf75\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-59c2dac elementor-widget elementor-widget-image\" data-id=\"59c2dac\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"268\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans4.png\" class=\"attachment-large size-large wp-image-2673\" alt=\"kmeans4\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans4.png 943w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans4-300x101.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans4-768x257.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2295316 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2295316\" data-element_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-7b4f71f\" data-id=\"7b4f71f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7aea976 elementor-widget elementor-widget-text-editor\" data-id=\"7aea976\" data-element_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<p><span style=\"font-weight: normal;\">Le partitionnement est inexact car le nombre de clusters initiaux est bien sup\u00e9rieur au nombre id\u00e9al en l\u2019occurrence 3. Il existe des m\u00e9thodes pour <\/span><strong>d\u00e9terminer le nombre de clusters id\u00e9al<\/strong><span style=\"font-weight: normal;\">. La plus connu est la <\/span><strong>m\u00e9thode du coude<\/strong><span style=\"font-weight: normal;\">. Elle s\u2019appuie sur la <\/span>notion d\u2019inertie<span style=\"font-weight: normal;\">. On d\u00e9finit cette derni\u00e8re comme ceci : la somme des distances euclidiennes entre chaque point et son centro\u00efde associ\u00e9. Evidemment <\/span>plus on fixe un nombre initial de clusters \u00e9lev\u00e9s et plus on r\u00e9duit l\u2019inertie : les points ont plus de chance d\u2019\u00eatre \u00e0 c\u00f4t\u00e9 d\u2019un centro\u00efde. <span style=\"font-weight: normal;\">Regardons ce que cela donne sur notre exemple : <\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6e312f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6e312f6\" data-element_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-698f8a4\" data-id=\"698f8a4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-42e7d34 elementor-widget elementor-widget-image\" data-id=\"42e7d34\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"739\" height=\"333\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans5.png\" class=\"attachment-large size-large wp-image-2674\" alt=\"clustering\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans5.png 739w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans5-300x135.png 300w\" sizes=\"(max-width: 739px) 100vw, 739px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-dc8a01f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dc8a01f\" data-element_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-5326143\" data-id=\"5326143\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3fb53ab elementor-widget elementor-widget-text-editor\" data-id=\"3fb53ab\" data-element_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<p><span style=\"font-weight: normal;\">On remarque que l\u2019inertie stagne \u00e0 partir de 3 clusters. Cette m\u00e9thode est concluante. On peut la coupler avec <strong>une <\/strong><\/span><strong>approche plus pr\u00e9cise mais qui requiert plus de temps de calcul : le coefficient de silhouette<\/strong><span style=\"font-weight: normal;\">. Il se d\u00e9finit comme suit : <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f5d9dc elementor-widget elementor-widget-image\" data-id=\"6f5d9dc\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"127\" height=\"56\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/formule-kmeans.png\" class=\"attachment-large size-large wp-image-2676\" alt=\"formule kmeans\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-958c30d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"958c30d\" data-element_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-b7dc336\" data-id=\"b7dc336\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-506e785 elementor-widget elementor-widget-text-editor\" data-id=\"506e785\" data-element_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<ul><li><p>a<span style=\"font-weight: normal;\"> la moyenne des distances aux autres observations du m\u00eame cluster (cad la <\/span>moyenne intra-cluster<span style=\"font-weight: normal;\">). <\/span><\/p><\/li><\/ul><ul><li><p>b<span style=\"font-weight: normal;\"> la <\/span>distance moyenne au cluster le plus proche<span style=\"font-weight: normal;\">. <\/span><\/p><\/li><\/ul><p><span style=\"font-weight: normal;\">Ce coefficient peut varier entre -1 et +1. Un coefficient proche de +1 signifie que l\u2019observation est situ\u00e9e bien \u00e0 l\u2019int\u00e9rieur de son propre cluster, tandis qu\u2019un coefficient proche de 0 signifie qu\u2019elle se situe pr\u00e8s d\u2019une fronti\u00e8re ; enfin, un coefficient proche de -1 signifie que l\u2019observation est associ\u00e9e au mauvais cluster.\u00a0<\/span><\/p><p><span style=\"font-weight: normal;\">Comme pour l\u2019inertie il est judicieux d\u2019afficher l\u2019\u00e9volution du coefficient en fonction du nombre de clusters comme ci-dessous : <\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-37e99bd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"37e99bd\" data-element_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-54a16ae\" data-id=\"54a16ae\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1ca0d19 elementor-widget elementor-widget-image\" data-id=\"1ca0d19\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"627\" height=\"306\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans6.png\" class=\"attachment-large size-large wp-image-2679\" alt=\"cluster\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans6.png 627w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans6-300x146.png 300w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e26775f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e26775f\" data-element_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-dc3eb89\" data-id=\"dc3eb89\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-52d26fa elementor-widget elementor-widget-text-editor\" data-id=\"52d26fa\" data-element_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<p><span style=\"font-weight: normal;\">Cette m\u00e9thode permet \u00e9galement de d\u00e9celer le nombre de clusters id\u00e9al c\u2019est-\u00e0-dire 3.<br \/><\/span><\/p><p><span style=\"font-weight: normal;\">Il est \u00e9galement primordial en plus de ces deux m\u00e9thodes de faire une analyse pouss\u00e9e des clusters cr\u00e9\u00e9s. J\u2019entends par l\u00e0 <strong>une <\/strong><\/span><strong>analyse descriptive pr\u00e9cise et approfondie pour d\u00e9terminer les caract\u00e9ristiques communes de chaque cluster<\/strong><span style=\"font-weight: normal;\">. Cela vous permettra de comprendre les profils types de chaque cluster.<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7e93203 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7e93203\" data-element_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-1b7f782\" data-id=\"1b7f782\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3f7aea9 elementor-widget elementor-widget-heading\" data-id=\"3f7aea9\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Et maintenant la pratique en python<\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8c929c2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8c929c2\" data-element_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-0f4f6db\" data-id=\"0f4f6db\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3b80299 elementor-widget elementor-widget-text-editor\" data-id=\"3b80299\" data-element_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<p><span style=\"font-weight: 400;\">L\u2019entra\u00eenement d\u2019un algorithme des K-moyennes est facilit\u00e9 avec la librairie\u00a0<\/span><a href=\"https:\/\/scikit-learn.org\/stable\/\" target=\"_blank\" rel=\"noopener\">Scikit-Learn<\/a><span style=\"font-weight: 400;\">. Notre jeu de donn\u00e9es qui a servi d\u2019exemples se cr\u00e9e facilement avec la fonctionalit\u00e9 make_blobs de Scikit-Learn. Voici comment l\u2019impl\u00e9menter en code\u00a0: <\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-37f8bb9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"37f8bb9\" data-element_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-124ae29\" data-id=\"124ae29\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a181145 elementor-widget elementor-widget-image\" data-id=\"a181145\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"215\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans7.png\" class=\"attachment-large size-large wp-image-2680\" alt=\"clustering\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans7.png 943w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans7-300x81.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans7-768x207.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8e36f59 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8e36f59\" data-element_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-3df65fd\" data-id=\"3df65fd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4e7cd2f elementor-widget elementor-widget-text-editor\" data-id=\"4e7cd2f\" data-element_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<p><span style=\"font-weight: normal;\">Maintenant que nous avons notre jeu de donn\u00e9es on peut passer \u00e0 l\u2019impl\u00e9mentation d\u2019un K-means. Nous allons utiliser la librairie Scikit-Learn et visualiser le r\u00e9sultat : <\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4c9cae7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4c9cae7\" data-element_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-90cdff3\" data-id=\"90cdff3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-10222c7 elementor-widget elementor-widget-image\" data-id=\"10222c7\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"635\" height=\"383\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans8.png\" class=\"attachment-large size-large wp-image-2683\" alt=\"clustering\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans8.png 635w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans8-300x181.png 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-268344d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"268344d\" data-element_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-6da6fe0\" data-id=\"6da6fe0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c5baac5 elementor-widget elementor-widget-text-editor\" data-id=\"c5baac5\" data-element_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<p><span style=\"font-weight: normal;\">L\u2019attribut n_clusters de la classe KMeans de Scikit-Learn permet de fixer le nombre de centro\u00efdes que l\u2019on souhaite. Par cons\u00e9quent elle d\u00e9finit aussi le nombre de centro\u00efdes initiaux. Cette classe utilise par d\u00e9faut non pas une m\u00e9thode d\u2019initialisation al\u00e9atoire mais une m\u00e9thode d\u00e9velopp\u00e9e en 2007 par David Arthur et Sergei Vassilvitskii d\u00e9nomm\u00e9e <\/span><strong>K-MEANS ++<\/strong><span style=\"font-weight: normal;\">. Elle consiste \u00e0 <\/span><strong>s\u00e9lectionner des centro\u00efdes distincts les uns des autres ce qui limite les risques de convergence vers une solution non-optimale<\/strong><span style=\"font-weight: normal;\">. La distance par d\u00e9faut utilis\u00e9e est bien \u00e9videmment la distance euclidienne d\u00e9finie plus haut. <\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c7c159a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c7c159a\" data-element_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-5c54478\" data-id=\"5c54478\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7272c2b elementor-widget elementor-widget-heading\" data-id=\"7272c2b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Les limites de l\u2019algorithme des k-means<\/h3>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a4ecbbb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a4ecbbb\" data-element_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-7bd6f8d\" data-id=\"7bd6f8d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ac165c9 elementor-widget elementor-widget-text-editor\" data-id=\"ac165c9\" data-element_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<p><span style=\"font-weight: normal;\">Comme nous l\u2019avons vu l\u2019algorithme n\u00e9cessite en amont de <\/span><strong>d\u00e9finir le nombre de partitions<\/strong><span style=\"font-weight: normal;\">. Cela demande d\u2019en avoir une id\u00e9e pr\u00e9cise et m\u00eame si nous avons vu deux m\u00e9thodes compl\u00e9mentaires pour optimiser sur certains jeux de donn\u00e9es elles ne sont pas infaillibles.\u00a0<\/span><\/p><p><span style=\"font-weight: normal;\">En effet les jeux de donn\u00e9es avec des formes elliptiques par exemple poseront probl\u00e8me. Dans l\u2019exemple ci-dessous on voit clairement deux groupes s\u2019apparentant \u00e0 deux ellipses. La figure de droite montre le r\u00e9sultat apr\u00e8s utilisation de l\u2019algorithme des k-moyennes. Il est clair que celui-ci n\u2019a pas r\u00e9ussi \u00e0 identifier nos deux ellipses.<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bca31a1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bca31a1\" data-element_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-8f64690\" data-id=\"8f64690\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1296839 elementor-widget elementor-widget-image\" data-id=\"1296839\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"252\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-9.png\" class=\"attachment-large size-large wp-image-2685\" alt=\"kmeans\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-9.png 943w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-9-300x94.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-9-768x242.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bd0cb99 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bd0cb99\" data-element_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-c6ef310\" data-id=\"c6ef310\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5a1e338 elementor-widget elementor-widget-text-editor\" data-id=\"5a1e338\" data-element_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<p><span style=\"font-weight: normal;\">L&rsquo;utilisation d\u2019un algorithme de clustering tel que l\u2019algorithme des k-means n\u2019est pas ais\u00e9e suivant les donn\u00e9es dont vous disposez. Il faudra souvent les retravailler.\u00a0<\/span><\/p>\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\t\t<\/div>\n\t\t<\/section>\n\t\t<div class=\"elementor-element elementor-element-81a375e e-flex e-con-boxed e-con\" data-id=\"81a375e\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6fde1ba elementor-widget elementor-widget-text-editor\" data-id=\"6fde1ba\" data-element_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<p><span style=\"font-weight: normal;\">Chez Datascientest nous vous apprenons \u00e0 ma\u00eetriser les principaux algorithmes de clustering ainsi qu\u2019\u00e0 les interpr\u00e9ter sur des jeux de donn\u00e9es.\u00a0<\/span><\/p><p><span style=\"font-weight: normal;\">N\u2019h\u00e9sitez pas \u00e0 explorer\u00a0<\/span><a href=\"https:\/\/datascientest.com\/#formations\" target=\"_blank\" rel=\"noopener\">nos offres de formations<\/a><span style=\"font-weight: normal;\">\u00a0 et \u00e0\u00a0<\/span><a href=\"https:\/\/datascientest.com\/postuler\" target=\"_blank\" rel=\"noopener\">postuler \u00e0 l&rsquo;une d&rsquo;entre elles<\/a><span style=\"font-weight: normal;\">\u00a0pour d\u00e9couvrir le clustering mais \u00e9galement de nombreux autres domaines du Machine Learning.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Le clustering est une discipline particuli\u00e8re du Machine Learning ayant pour objectif de s\u00e9parer vos donn\u00e9es en groupes homog\u00e8nes ayant des caract\u00e9ristiques communes. C\u2019est un domaine tr\u00e8s appr\u00e9ci\u00e9 en marketing, par exemple, o\u00f9 l\u2019on cherche souvent \u00e0 segmenter les bases clients pour d\u00e9tecter des comportements particuliers.&nbsp;L\u2019algorithme des K-moyennes (K-means) est un algorithme non supervis\u00e9 tr\u00e8s [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":207945,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>K-means : Focus sur cet algorithme de Clustering &amp; Machine Learning<\/title>\n<meta name=\"description\" content=\"L\u2019algorithme des K-moyennes (K-means) est un algorithme de non supervis\u00e9 tr\u00e8s connu en mati\u00e8re de Clustering, discipline du Machine Learning.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/algorithme-des-k-means\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"K-means : Focus sur cet algorithme de Clustering &amp; Machine Learning\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/algorithme-des-k-means\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2020-05-15T14:56:04+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-09T14:14:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/05\/kmeans-2-1.png\" \/>\n\t<meta property=\"og:image:width\" content=\"377\" \/>\n\t<meta property=\"og:image:height\" content=\"368\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Raphael Kassel\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raphael Kassel\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/algorithme-des-k-means\",\"url\":\"https:\/\/datascientest.com\/algorithme-des-k-means\",\"name\":\"K-means : Focus sur cet algorithme de Clustering &amp; Machine Learning\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2020-05-15T14:56:04+00:00\",\"dateModified\":\"2023-11-09T14:14:39+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\"},\"description\":\"L\u2019algorithme des K-moyennes (K-means) est un algorithme de non supervis\u00e9 tr\u00e8s connu en mati\u00e8re de Clustering, discipline du Machine Learning.\",\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/datascientest.com\/algorithme-des-k-means\"]}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/datascientest.com\/#website\",\"url\":\"https:\/\/datascientest.com\/\",\"name\":\"Formation Data Science | DataScientest.com\",\"description\":\"Leader de la formation en Data Science\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/datascientest.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\",\"name\":\"Raphael Kassel\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg\",\"contentUrl\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg\",\"caption\":\"Raphael Kassel\"},\"description\":\"Raphael Kassel est le Head of Data Programs chez DataScientest. Il supervise une \u00e9quipe Data, impl\u00e9mente de nouveaux parcours comme \\\"Chef de projet IA\\\" et \\\"Data Product Manager\\\", et contribue \u00e0 la modernisation des op\u00e9rations du groupe. 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