{"id":176925,"date":"2022-09-27T09:38:32","date_gmt":"2022-09-27T09:38:32","guid":{"rendered":"https:\/\/datascientest.com\/?p=176925"},"modified":"2023-11-09T14:03:37","modified_gmt":"2023-11-09T14:03:37","slug":"spectral-clustering","status":"publish","type":"post","link":"https:\/\/datascientest.com\/spectral-clustering","title":{"rendered":"Spectral Clustering : d\u00e9finition, fonctionnement, utilisation"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"176925\" class=\"elementor elementor-176925\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c3c3d83 e-flex e-con-boxed e-con\" data-id=\"c3c3d83\" 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-5a5cdfe elementor-widget elementor-widget-text-editor\" data-id=\"5a5cdfe\" 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<h2>\u00ab\u00a0Data drives all we do\u00a0\u00bb, le slogan de Cambridge Analytica se v\u00e9rifie en permanence: les donn\u00e9es influencent et structurent nos choix, en tant que consommateurs, citoyens, politiques, entrepreneurs\u2026<\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-851d34f elementor-widget elementor-widget-text-editor\" data-id=\"851d34f\" 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;\">Ces donn\u00e9es sont une manne d\u2019informations d\u00e9cisionnelles. \u00c0 petite \u00e9chelle, c\u2019est relativement simple. Mais les experts de la data ont besoin d\u2019outils performants pour traiter et trier <strong>l\u2019ensemble des informations \u00e0 une \u00e9chelle macro<\/strong> (comme au niveau de la population fran\u00e7aise). Le spectral clustering est justement l\u2019un de ces outils.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Alors, qu\u2019est-ce que concr\u00e8tement le spectral clustering et quelle est son utilit\u00e9? Quels sont les avantages et les limites de ce mod\u00e8le ?<\/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<div class=\"elementor-element elementor-element-50f5440 e-flex e-con-boxed e-con\" data-id=\"50f5440\" 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-ce56ef6 elementor-widget elementor-widget-heading\" data-id=\"ce56ef6\" 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><h3 class=\"elementor-heading-title elementor-size-default\">Qu\u2019est-ce que le spectral clustering ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-629b0f3 elementor-widget elementor-widget-heading\" data-id=\"629b0f3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">D\u00e9finition<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9431b1f elementor-widget elementor-widget-text-editor\" data-id=\"9431b1f\" 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>Le spectral clustering est l\u2019un des composants du <a href=\"https:\/\/datascientest.com\/machine-learning-tout-savoir\">machine learning<\/a> et de l\u2019<a href=\"https:\/\/datascientest.com\/intelligence-artificielle-definition\">intelligence artificielle<\/a>.<\/p><p>Il s\u2019agit d\u2019un algorithme de partitionnement des donn\u00e9es reposant sur la th\u00e9orie spectrale des graphes et l&rsquo;alg\u00e8bre lin\u00e9aire.<\/p><p>L\u2019id\u00e9e est de segmenter un graphe en plusieurs petits groupes ayant des valeurs similaires ou proches.<\/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-3fc9157 elementor-widget elementor-widget-heading\" data-id=\"3fc9157\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">La diff\u00e9rence entre clustering et classification<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f02d651 elementor-widget elementor-widget-text-editor\" data-id=\"f02d651\" 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>La classification implique de regrouper les donn\u00e9es en fonction d\u2019une classe ou d\u2019un groupe d\u00e9fini \u00e0 l\u2019avance.<\/p><p>\u00c0 l\u2019inverse, avec le clustering, l\u2019algorithme ne conna\u00eet pas les classes avant de faire le regroupement. On parle alors de <a href=\"https:\/\/datascientest.com\/apprentissage-non-supervise\">technique d\u2019apprentissage non supervis\u00e9<\/a>.<\/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-2fbde72 elementor-widget elementor-widget-heading\" data-id=\"2fbde72\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les diff\u00e9rents types de partitionnement de donn\u00e9es<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5d7d60c elementor-widget elementor-widget-text-editor\" data-id=\"5d7d60c\" 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>Il existe plusieurs types de partitionnement des donn\u00e9es qui diff\u00e8rent au niveau de leur fonctionnement et de leur objectif. \u00c0 ce titre, il convient de distinguer le spectral clustering :<\/p><ul><li><a href=\"https:\/\/datascientest.com\/algorithme-des-k-means\">Le K-means<\/a> : il s\u2019agit d\u2019\u00e9tablir une moyenne de r\u00e9f\u00e9rence parmi un jeu de donn\u00e9es. L\u2019id\u00e9e est alors de d\u00e9finir un profil type qui pourra toucher le plus grand nombre. \u00c0 l\u2019inverse, le partitionnement de donn\u00e9es spectral a pour objectif de cr\u00e9er diff\u00e9rents groupes ayant un maximum de points communs.<\/li><li><a href=\"https:\/\/datascientest.com\/machine-learning-clustering-dbscan\">Le DBSCAN<\/a> : cet algorithme se base sur la distance et la densit\u00e9 des clusters pour effectuer des sous-groupes. De son c\u00f4t\u00e9, le spectral clustering se base sur la similarit\u00e9 des donn\u00e9es.<\/li><\/ul>\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<div class=\"elementor-element elementor-element-fdfbce5 e-flex e-con-boxed e-con\" data-id=\"fdfbce5\" 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-8aa5cf8 elementor-widget elementor-widget-heading\" data-id=\"8aa5cf8\" 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\">\u00c0 quoi sert le spectral clustering ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9388267 elementor-widget elementor-widget-heading\" data-id=\"9388267\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Qui utilise le spectral clustering ?<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d0c890d elementor-widget elementor-widget-text-editor\" data-id=\"d0c890d\" 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;\">Le spectral clustering est particuli\u00e8rement utilis\u00e9 par les <\/span><b>professionnels du marketing<\/b><span style=\"font-weight: 400;\"> pour comprendre le comportement des utilisateurs ou de la cible.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Mais attention, cet algorithme exige des comp\u00e9tences sp\u00e9cifiques. \u00c0 ce titre, ce sont les data analysts, data scientists et autres experts en analyse de donn\u00e9es qui ont vocation \u00e0 l\u2019utiliser.\u00a0<\/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-8e0a173 elementor-widget elementor-widget-heading\" data-id=\"8e0a173\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Dans quels domaines est utilis\u00e9 le spectral clustering ?<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-df881a9 elementor-widget elementor-widget-text-editor\" data-id=\"df881a9\" 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;\">Le partitionnement spectral permettant de traiter des donn\u00e9es \u00e0 grande \u00e9chelle, cette m\u00e9thode est souvent <\/span><b>utilis\u00e9e \u00e0 des fins marketing.<\/b><span style=\"font-weight: 400;\"> Les entreprises utilisent alors cet algorithme pour <\/span><b>segmenter leurs cibles<\/b><span style=\"font-weight: 400;\"> en fonction de leurs attentes, leurs besoins, leur profil, leur niveau de maturit\u00e9, etc.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">En outre, le spectral clustering peut aussi \u00eatre utilis\u00e9<\/span><b> en politique<\/b><span style=\"font-weight: 400;\">, en particulier en p\u00e9riode d\u2019\u00e9lection. En s\u00e9parant la masse d\u2019\u00e9lecteurs en petits groupes, les candidats peuvent communiquer avec chacun d\u2019entre eux de mani\u00e8re plus personnalis\u00e9e. <\/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<div class=\"elementor-element elementor-element-1b392d2 e-flex e-con-boxed e-con\" data-id=\"1b392d2\" 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-327c2d3 elementor-widget elementor-widget-heading\" data-id=\"327c2d3\" 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\">Comment fonctionne l\u2019algorithme spectral clustering ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-71c9ff6 elementor-widget elementor-widget-text-editor\" data-id=\"71c9ff6\" 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\u2019algorithme du clustering spectral se r\u00e9alise en plusieurs \u00e9tapes :\u00a0<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">La construction d\u2019un graphe \u00e0 travers la matrice par affinit\u00e9 (ou matrice par similarit\u00e9, matrice adjacente) ;\u00a0<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">La segmentation des points de donn\u00e9es dans des espaces dimensionnels plus petits ;<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">L\u2019utilisation des valeurs propres et vecteurs propres pour d\u00e9finir les sous-graphes.\u00a0<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Pour mieux comprendre son fonctionnement, nous vous expliquons les trois notions essentielles du spectral clustering.\u00a0<\/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-7d89a69 elementor-widget elementor-widget-heading\" data-id=\"7d89a69\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les graphiques<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bbd48d5 elementor-widget elementor-widget-image\" data-id=\"bbd48d5\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/www.techiedelight.com\/wp-content\/uploads\/undirected-graph.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Graphe non-orient\u00e9 <\/br> Source : techiedelight.com<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-031c0f8 elementor-widget elementor-widget-text-editor\" data-id=\"031c0f8\" 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;\">Les graphes sont <\/span><b>un ensemble de n\u0153uds reli\u00e9s par un ensemble d&rsquo;ar\u00eates. <\/b><span style=\"font-weight: 400;\">Ces n\u0153uds et ces ar\u00eates peuvent \u00eatre li\u00e9s entre eux ou non.<\/span><\/p><p><span style=\"font-weight: 400;\">Mais dans tous les cas, les graphes permettent de repr\u00e9senter de nombreux types de donn\u00e9es.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Pour le spectral clustering, il faut partir d\u2019un graphe ; soit de voisinage, soit des plus proches voisins (KNN), soit totalement connect\u00e9.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Ensuite, celui-ci est traduit sous forme de matrice. Plus pr\u00e9cis\u00e9ment, la matrice adjacente. <\/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-72fa43c elementor-widget elementor-widget-heading\" data-id=\"72fa43c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les matrices<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d080e7d elementor-widget elementor-widget-text-editor\" data-id=\"d080e7d\" 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><b>La matrice adjacente<\/b><span style=\"font-weight: 400;\"> (A) synth\u00e9tise les relations entre tous les points de donn\u00e9es du graphe.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Par exemple :\u00a0<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Les donn\u00e9es qui interagissent\u00a0 = 1<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Les donn\u00e9es qui n\u2019interagissent pas = 0<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">La matrice peut alors ressembler au tableau ci-dessous :\u00a0<\/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-4f253ea elementor-widget elementor-widget-html\" data-id=\"4f253ea\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<table class=\"tftable\" border=\"1\">\r\n<tr><td>1<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr>\r\n<tr><td>0<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr>\r\n<tr><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr>\r\n<tr><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr>\r\n<\/table>\r\n\r\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b560a40 elementor-widget elementor-widget-text-editor\" data-id=\"b560a40\" 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;\">Ensuite, c\u2019est <\/span><b>la matrice de degr\u00e9<\/b><span style=\"font-weight: 400;\"> (D) qui intervient. En se fondant sur la matrice A, elle calcule la somme des liens (horizontaux et verticaux). Sur la base de l\u2019exemple pr\u00e9c\u00e9dent, voici le r\u00e9sultat : <\/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-1dc6165 elementor-widget elementor-widget-html\" data-id=\"1dc6165\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<table class=\"tftable\" border=\"1\">\r\n<tr><td>0<\/td><td>0<\/td><td>0<\/td><td>2<\/td><\/tr>\r\n<tr><td>0<\/td><td>3<\/td><td>0<\/td><td>0<\/td><\/tr>\r\n<tr><td>0<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr>\r\n<tr><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><\/tr>\r\n<\/table>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f3f4148 elementor-widget elementor-widget-text-editor\" data-id=\"f3f4148\" 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;\">Enfin,<\/span><b> la matrice Laplacienne<\/b><span style=\"font-weight: 400;\"> (L) correspond \u00e0 la matrice de degr\u00e9 moins la matrice adjacente, soit L=D-A. <\/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-35e6056 elementor-widget elementor-widget-html\" data-id=\"35e6056\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<table class=\"tftable\" border=\"1\">\r\n<tr><td>-1<\/td><td>0<\/td><td>0<\/td><td>-1<\/td><\/tr>\r\n<tr><td>0<\/td><td>2<\/td><td>-1<\/td><td>-1<\/td><\/tr>\r\n<tr><td>0<\/td><td>-1<\/td><td>1<\/td><td>0<\/td><\/tr>\r\n<tr><td>1<\/td><td>-1<\/td><td>0<\/td><td>0<\/td><\/tr>\r\n<\/table>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e0c42e8 elementor-widget elementor-widget-text-editor\" data-id=\"e0c42e8\" 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;\">Cette matrice est ensuite repr\u00e9sent\u00e9e visuellement sous la forme d\u2019un graphe, que l\u2019on appelle : graphe Laplacian.\u00a0<\/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-dc0ba52 elementor-widget elementor-widget-heading\" data-id=\"dc0ba52\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les vecteurs<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-554ba55 elementor-widget elementor-widget-text-editor\" data-id=\"554ba55\" 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;\">La repr\u00e9sentation visuelle du graphe Laplacian (A) implique de<\/span><b> conna\u00eetre les valeurs propres (eigenvalues= \u03bb) et les vecteurs propres (eigenvectors=x).\u00a0<\/b><\/p><p><span style=\"font-weight: 400;\">Soit\u00a0 Ax = \u03bbx<\/span><\/p><p><span style=\"font-weight: 400;\">Il est possible de trouver les eigenvalues et les eigenvectors d&rsquo;une matrice <\/span><b>en utilisant numpy sur Python.\u00a0<\/b><\/p><p><span style=\"font-weight: 400;\">L\u2019utilisation de ces matrices et vecteurs permet ensuite de regrouper plusieurs sous-graphes en fonction de leurs similarit\u00e9s. L&rsquo;une des m\u00e9thodes les plus courantes pour le Spectral Clustering sera alors d&rsquo;appliquer un algorithme plus classique de Clustering tel que la m\u00e9thode des Kmeans\u00a0 sur les vecteurs propres de cette matrice. Cette m\u00e9thode peut \u00eatre directement impl\u00e9ment\u00e9e \u00e0 l&rsquo;aide du module Spectral Clustering de la biblioth\u00e8que Sklearn. Quant aux valeurs propres, elles permettront de d\u00e9terminer le nombre de clusters optimaux pour le partitionnement de vos donn\u00e9es.<\/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-3cebecb elementor-widget elementor-widget-text-editor\" data-id=\"3cebecb\" 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<blockquote><p style=\"text-align: left;\"><span style=\"text-decoration: underline;\"><span style=\"font-weight: 400;\">Bon \u00e0 savoir<\/span><\/span><span style=\"font-weight: 400;\"> : le nombre de sous-graphes (clusters) d\u00e9pend de l\u2019objectif et du degr\u00e9 de ciblage d\u00e9sir\u00e9. D\u2019un point de vue macro, il est pr\u00e9f\u00e9rable d\u2019avoir un nombre de clusters restreint pour une meilleure vision d\u2019ensemble. Mais d\u2019un point de vue micro, il est tout aussi int\u00e9ressant d\u2019aller dans le d\u00e9tail avec un maximum de sous-groupes. <\/span><\/p><\/blockquote>\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<div class=\"elementor-element elementor-element-4d2473b e-flex e-con-boxed e-con\" data-id=\"4d2473b\" 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-fb65605 elementor-widget elementor-widget-heading\" data-id=\"fb65605\" 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\">Pourquoi utiliser le partitionnement spectral ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c13d8d7 elementor-widget elementor-widget-text-editor\" data-id=\"c13d8d7\" 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\u2019utilisation du partitionnement spectral est absolument indispensable pour <\/span><b>comprendre sa cible et s\u2019adresser \u00e0 elle de mani\u00e8re personnalis\u00e9e.\u00a0<\/b><\/p><p><span style=\"font-weight: 400;\">Prenons l\u2019exemple de personnes abonn\u00e9es \u00e0 une marque de v\u00eatements (c\u2019est la base de notre matrice adjacente). Ce n\u2019est pas parce qu\u2019elles pr\u00e9sentent toutes une m\u00eame affinit\u00e9, qu\u2019elles ont toutes le m\u00eame profil.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Parmi les abonn\u00e9s, on peut retrouver :\u00a0<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Des clients fid\u00e8les ;\u00a0<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Des prospects qui h\u00e9sitent ;\u00a0<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Des stylistes qui recherchent des sources d\u2019inspiration ;\u00a0<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Des professionnels du marketing qui effectuent une veille ; <\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Etc.\u00a0<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Le spectral clustering permet alors de segmenter les donn\u00e9es en petits sous-groupes de plus petites dimensions.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Pour les entreprises, conna\u00eetre chaque sous-groupe permet d\u2019adapter sa communication et son offre. Il s\u2019agit de<\/span><b> s\u2019adresser aux bonnes personnes, au bon moment et de la bonne mani\u00e8re,<\/b><span style=\"font-weight: 400;\"> afin de multiplier ses chances de convertir.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Et comme vu pr\u00e9c\u00e9demment, les politiciens peuvent aussi utiliser cet algorithme pour convaincre leurs \u00e9lecteurs.\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\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-129d80a e-flex e-con-boxed e-con\" data-id=\"129d80a\" 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-b584064 elementor-widget elementor-widget-heading\" data-id=\"b584064\" 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\">Quels sont les avantages et inconv\u00e9nients du spectral clustering ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bad459c elementor-widget elementor-widget-image\" data-id=\"bad459c\" 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=\"640\" height=\"354\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/09\/200528094346386326.png\" class=\"attachment-large size-large wp-image-176928\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/09\/200528094346386326.png 640w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/09\/200528094346386326-300x166.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/>\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<div class=\"elementor-element elementor-element-d133678 elementor-widget elementor-widget-text-editor\" data-id=\"d133678\" 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\u2019avantage incontestable du spectral clustering est sa capacit\u00e9 \u00e0<\/span><b> classer un ensemble de donn\u00e9es non convexes entre elles.\u00a0<\/b><\/p><p><span style=\"font-weight: 400;\">Cependant, il s\u2019agit d\u2019une <\/span><b>notion complexe <\/b><span style=\"font-weight: 400;\">qui n\u00e9cessite de bien comprendre son fonctionnement, mais aussi, et surtout, de ma\u00eetriser l\u2019alg\u00e8bre lin\u00e9aire et la th\u00e9orie spectrale des graphes.<\/span><\/p><p><span style=\"font-weight: 400;\">Cela dit, l\u2019outil numpy sur Python permet de faire les calculs afin de simplifier le travail des analystes.\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\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ca776ab e-flex e-con-boxed e-con\" data-id=\"ca776ab\" 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-1cd1a35 elementor-widget elementor-widget-heading\" data-id=\"1cd1a35\" 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\">Comment se former au spectral clustering ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f33d72 elementor-widget elementor-widget-text-editor\" data-id=\"1f33d72\" 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>Le spectral clustering \u00e9tant particuli\u00e8rement complexe, il est primordial de bien se former pour comprendre son fonctionnement.<br \/>\u00c0 ce titre, une <a href=\"https:\/\/datascientest.com\/formations-data\">formation d\u2019excellence en data science<\/a> vous permettra de ma\u00eetriser les outils n\u00e9cessaires \u00e0 la mise en place de cet algorithme.<\/p><p>Vous pourrez ensuite utiliser ces comp\u00e9tences dans les entreprises ou dans les institutions publiques pour les aider \u00e0 am\u00e9liorer leur communication, leurs offres et leurs performances.<\/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<div class=\"elementor-element elementor-element-cb89043 e-flex e-con-boxed e-con\" data-id=\"cb89043\" 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-915991e elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"915991e\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formations-data\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9couvrir nos formations en Data Science<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\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<div class=\"elementor-element elementor-element-1ce6568 e-flex e-con-boxed e-con\" data-id=\"1ce6568\" 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-de33744 elementor-widget elementor-widget-html\" data-id=\"de33744\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Qu\u2019est-ce que le spectral clustering ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Le spectral clustering est l\u2019un des composants du machine learning et de l\u2019intelligence artificielle. Il s\u2019agit d\u2019un algorithme de partitionnement des donn\u00e9es reposant sur la th\u00e9orie spectrale des graphes et l'alg\u00e8bre lin\u00e9aire. L\u2019id\u00e9e est de segmenter un graphe en plusieurs petits groupes ayant des valeurs similaires ou proches.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"\u00c0 quoi sert le spectral clustering ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Le spectral clustering est particuli\u00e8rement utilis\u00e9 par les professionnels du marketing pour comprendre le comportement des utilisateurs ou de la cible.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Pourquoi utiliser le partitionnement spectral ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"L\u2019utilisation du partitionnement spectral est absolument indispensable pour comprendre sa cible et s\u2019adresser \u00e0 elle de mani\u00e8re personnalis\u00e9e.\"\n    }\n  }]\n}\n<\/script>\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>\u00ab\u00a0Data drives all we do\u00a0\u00bb, le slogan de Cambridge Analytica se v\u00e9rifie en permanence: les donn\u00e9es influencent et structurent nos choix, en tant que consommateurs, citoyens, politiques, entrepreneurs\u2026 Ces donn\u00e9es sont une manne d\u2019informations d\u00e9cisionnelles. \u00c0 petite \u00e9chelle, c\u2019est relativement simple. Mais les experts de la data ont besoin d\u2019outils performants pour traiter et trier [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":176927,"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>Spectral Clustering : d\u00e9finition, fonctionnement, utilisation<\/title>\n<meta name=\"description\" content=\"Le spectral clustering est l\u2019un des composants du machine learning et de l\u2019intelligence artificielle. 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