{"id":64735,"date":"2021-05-24T09:00:30","date_gmt":"2021-05-24T08:00:30","guid":{"rendered":"https:\/\/datascientest.com\/?p=64735"},"modified":"2023-11-09T14:07:16","modified_gmt":"2023-11-09T14:07:16","slug":"comprendre-lalgorithme-t-sne-en-3-etapes","status":"publish","type":"post","link":"https:\/\/datascientest.com\/comprendre-lalgorithme-t-sne-en-3-etapes","title":{"rendered":"Comprendre l\u2019algorithme t-SNE en 3 \u00e9tapes"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"64735\" class=\"elementor elementor-64735\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-38e8a53 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"38e8a53\" 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-7c6caed\" data-id=\"7c6caed\" 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-7c0e8d2 elementor-widget elementor-widget-heading\" data-id=\"7c0e8d2\" 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\">Si vous vous \u00eates d\u00e9j\u00e0 int\u00e9ress\u00e9 aux m\u00e9thodes de r\u00e9duction de dimension, vous avez s\u00fbrement \u00e9tudi\u00e9 l'Analyse en Composantes Principales ou ACP. Dans cet article, nous allons nous int\u00e9resser \u00e0 l\u2019une des autres m\u00e9thodes de r\u00e9duction de dimension qui existe : t-SNE pour t-distributed Stochastic Neighbor Embedding. Cet algorithme propose une approche diff\u00e9rente de l\u2019ACP. <\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c709d5b elementor-widget elementor-widget-text-editor\" data-id=\"c709d5b\" 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<blockquote><p><span style=\"font-weight: 400;\">t-SNE est une technique de r\u00e9duction de dimension utilis\u00e9e en exploration de donn\u00e9es de grandes dimensions d\u00e9velopp\u00e9e en 2008 par Geoffrey Hinton et Laurens van der Maaten. Comme pour l\u2019ACP l\u2019objectif est de <\/span><b>d\u00e9terminer un espace de plus petite dimension tout en pr\u00e9servant les distances<\/b><span style=\"font-weight: 400;\"> entre les points.<\/span><\/p><\/blockquote>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-62a615c elementor-widget elementor-widget-heading\" data-id=\"62a615c\" 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\">t-SNE et ACP<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-77cbe16 elementor-widget elementor-widget-text-editor\" data-id=\"77cbe16\" 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\u2019<strong><a href=\"https:\/\/datascientest.com\/acp\">analyse en composantes<\/a><\/strong> principales est une m\u00e9thode largement utilis\u00e9e en r\u00e9duction de dimension qui cherche \u00e0 repr\u00e9senter les donn\u00e9es dans un hyperplan proche de sorte \u00e0<\/span><b> conserver au maximum la variance<\/b><span style=\"font-weight: 400;\"> du nuage de donn\u00e9es. <\/span><span style=\"font-weight: 400;\">En d\u2019autres termes, il s\u2019agit de repr\u00e9senter les donn\u00e9es dans un sous-espace de plus petite dimension maximisant l\u2019inertie totale du nuage projet\u00e9 dans cet espace.<\/span><span style=\"font-weight: 400;\"> Si vous voulez en savoir plus sur l&rsquo;ACP, regardez notre vid\u00e9o \u00e0 ce sujet\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-767a88e elementor-widget elementor-widget-video\" data-id=\"767a88e\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/ilWeGsudOGY&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.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-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{height:100%;width:100%;display:flex;border:none;background-color:#000}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-wrapper{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .elementor-open-inline .elementor-custom-embed-image-overlay{position:absolute;top:0;right:0;bottom:0;left:0;background-size:cover;background-position:50%}.elementor-widget-video .elementor-custom-embed-image-overlay{cursor:pointer;text-align:center}.elementor-widget-video .elementor-custom-embed-image-overlay:hover .elementor-custom-embed-play i{opacity:1}.elementor-widget-video .elementor-custom-embed-image-overlay img{display:block;width:100%;aspect-ratio:var(--video-aspect-ratio);-o-object-fit:cover;object-fit:cover;-o-object-position:center center;object-position:center center}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-custom-embed-image-overlay{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-custom-embed-image-overlay img{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .e-hosted-video .elementor-video{-o-object-fit:cover;object-fit:cover}.e-con-inner>.elementor-widget-video,.e-con>.elementor-widget-video{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-74b995a elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"74b995a\" 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\">Cliquez ici pour en savoir plus sur nos formations<\/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<div class=\"elementor-element elementor-element-0d1b516 elementor-widget elementor-widget-heading\" data-id=\"0d1b516\" 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 du t-SNE<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e500626 elementor-widget elementor-widget-text-editor\" data-id=\"e500626\" 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 t-SNE consiste \u00e0 cr\u00e9er une distribution de probabilit\u00e9 qui repr\u00e9sente les similarit\u00e9s entre voisins dans un espace en grande dimension et dans un espace de plus petite dimension. Par similarit\u00e9, nous allons chercher \u00e0 convertir les distances en probabilit\u00e9s. <strong>Il se d\u00e9coupe en 3 \u00e9tapes :<\/strong><\/span><\/p><ul><li><strong>\u00c9tape 1<\/strong><span style=\"font-weight: 400;\"><strong>\u00a0:<\/strong> Nous calculons les similarit\u00e9s des points dans l\u2019espace initial en grande dimension. Pour chaque point xi nous centrons une distribution gaussienne autour de ce point. Ensuite nous mesurons, pour chaque point xj (i diff\u00e9rent de j), la densit\u00e9 sous cette distribution gaussienne pr\u00e9c\u00e9demment d\u00e9finie. Enfin, nous normalisons pour chacun des points. Nous obtenons ainsi une liste de probabilit\u00e9s conditionnelles not\u00e9es\u00a0:<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6775a4a elementor-widget elementor-widget-image\" data-id=\"6775a4a\" 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=\"300\" height=\"59\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image2-300x59.png\" class=\"attachment-medium size-medium wp-image-64753\" alt=\"liste de probabilit\u00e9s conditionnelles not\u00e9es\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image2-300x59.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image2.png 409w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\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-7c9f304 elementor-widget elementor-widget-text-editor\" data-id=\"7c9f304\" 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\u2019\u00e9cart type se d\u00e9finit suivant une valeur appel\u00e9e <\/span><b>perplexit\u00e9<\/b><span style=\"font-weight: 400;\"> qui correspond au nombre de voisins autour de chaque point. Cette valeur est fix\u00e9e par l\u2019utilisateur \u00e0 l\u2019avance et permet d\u2019estimer l\u2019\u00e9cart type des distributions gaussiennes d\u00e9finies pour chaque point xi. Plus la perplexit\u00e9 est grande, plus la variance est grande.\u00a0<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\"><strong>Etape 2\u00a0:<\/strong> Nous avons besoin de cr\u00e9er un espace de plus petite dimension dans lequel nous allons repr\u00e9senter nos donn\u00e9es. \u00c9videmment au d\u00e9but nous ne connaissons pas les coordonn\u00e9es id\u00e9ales sur cet espace. Nous allons donc r\u00e9partir al\u00e9atoirement les points sur ce nouvel espace. Le reste est assez similaire \u00e0 l\u2019\u00e9tape 1, nous calculons les similarit\u00e9s des points dans l\u2019espace nouvellement cr\u00e9\u00e9, mais en utilisant une distribution<strong> t-Student<\/strong> et non pas Gaussienne. De la m\u00eame mani\u00e8re nous obtenons une liste de probabilit\u00e9s not\u00e9es\u00a0: <\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dfc2430 elementor-widget elementor-widget-image\" data-id=\"dfc2430\" 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=\"303\" height=\"86\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image1.png\" class=\"attachment-large size-large wp-image-64759\" alt=\"les similarit\u00e9s des points dans l\u2019espace nouvellement cr\u00e9\u00e9 mais en utilisant une distribution t-Student\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image1.png 303w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image1-300x85.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/>\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-3aec217 elementor-widget elementor-widget-text-editor\" data-id=\"3aec217\" 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 aria-level=\"1\"><span style=\"font-weight: 400;\"><strong>Etape 3\u00a0:<\/strong> Pour repr\u00e9senter fid\u00e8lement les points dans l\u2019espace de dimension plus petite nous aimerions, dans l\u2019id\u00e9al, que les mesures de similarit\u00e9 dans les deux espaces co\u00efncident. Nous avons donc besoin de comparer les similarit\u00e9s des points dans les deux espaces en utilisant la mesure <\/span><b>Kullback_Leibler (KL)<\/b><span style=\"font-weight: 400;\">. Nous cherchons ensuite \u00e0 la minimiser par descente de gradient pour obtenir les meilleurs yi possibles dans l\u2019espace de petite dimension. Cela revient \u00e0 minimiser l\u2019\u00e9cart entre les distributions de probabilit\u00e9s entre l\u2019espace d\u2019origine et l\u2019espace de plus petite dimension.\u00a0<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b738c1 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"9b738c1\" 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<div class=\"elementor-element elementor-element-c4ad0de elementor-widget elementor-widget-heading\" data-id=\"c4ad0de\" 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\">Comparaison des m\u00e9thodes ACP et t-SNE<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5847f52 elementor-widget elementor-widget-text-editor\" data-id=\"5847f52\" 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;\">Pour mieux saisir les diff\u00e9rences entre les deux m\u00e9thodes <strong>ACP et t-SNE<\/strong>, consid\u00e9rons le jeu de donn\u00e9es <strong>MNIST<\/strong>. Pour chacune des deux m\u00e9thodes, nous avons repr\u00e9sent\u00e9 les donn\u00e9es dans <strong>un espace \u00e0 deux dimensions. <\/strong><\/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-2a0aabe elementor-widget elementor-widget-image\" data-id=\"2a0aabe\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"685\" height=\"574\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image3.png\" class=\"attachment-large size-large wp-image-64761\" alt=\"le r\u00e9sultat obtenu avec une analyse en composantes principales\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image3.png 685w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image3-300x251.png 300w\" sizes=\"(max-width: 685px) 100vw, 685px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">R\u00e9duction de dimension avec la m\u00e9thode TSNE<\/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-5c4d450 elementor-widget elementor-widget-image\" data-id=\"5c4d450\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"686\" height=\"568\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image4.png\" class=\"attachment-large size-large wp-image-64760\" alt=\"r\u00e9sultat obtenu par r\u00e9duction de dimension avec la m\u00e9thode TSNE\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image4.png 686w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/image4-300x248.png 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">R\u00e9duction de dimension avec une ACP<\/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-68e6d60 elementor-widget elementor-widget-text-editor\" data-id=\"68e6d60\" 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;\">Sur la premi\u00e8re figure, nous avons le r\u00e9sultat obtenu par r\u00e9duction de dimension avec la <\/span><b>m\u00e9thode t-SNE<\/b><span style=\"font-weight: 400;\">. Sur la deuxi\u00e8me, nous avons le r\u00e9sultat obtenu avec une <\/span><b>analyse en composantes principales<\/b><span style=\"font-weight: 400;\">.\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-b7bacad elementor-widget elementor-widget-text-editor\" data-id=\"b7bacad\" 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;\">Il est clair que TSNE a r\u00e9ussi \u00e0 <\/span><b>regrouper les donn\u00e9es proches<\/b><span style=\"font-weight: 400;\"> et \u00e9loigner les donn\u00e9es dissemblables. Les points sont repr\u00e9sent\u00e9s en grappe, chacune des grappes correspondant \u00e0 un chiffre entre 1 et 6.\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-b9c2992 elementor-widget elementor-widget-text-editor\" data-id=\"b9c2992\" 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;\">Pour les r\u00e9sultats de l\u2019<\/span><b>ACP<\/b><span style=\"font-weight: 400;\"> la <\/span><b>s\u00e9paration des donn\u00e9es<\/b><span style=\"font-weight: 400;\"> dans l\u2019espace en 2 dimensions est <\/span><b>beaucoup moins nette<\/b><span style=\"font-weight: 400;\">. Nous pouvons voir, que pour certains chiffres comme 0 les points correspondants sont bien regroup\u00e9s entre eux. Cependant, pour d\u2019autres chiffres comme les points associ\u00e9s au chiffre 5 ils sont <\/span><b>r\u00e9partis de mani\u00e8re plus diffuse<\/b><span style=\"font-weight: 400;\">.\u00a0<\/span><span style=\"font-size: 15px; font-weight: 400;\">\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Si vous souhaitez vous former sur des sujets comme les techniques de r\u00e9duction de dimension, <a href=\"https:\/\/datascientest.com\/formations-data\">venez d\u00e9couvrir nos formations en format bootcamp ou bien continu\u00a0!<\/a><\/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-20df7b7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"20df7b7\" 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-321b6ae\" data-id=\"321b6ae\" 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-415060d elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"415060d\" 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\">En savoir plus sur nos formations<\/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<div class=\"elementor-element elementor-element-0de7193 elementor-widget elementor-widget-html\" data-id=\"0de7193\" 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\": \"t-SNE et ACP\u200b\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"L\u2019analyse en composantes principales est une m\u00e9thode largement utilis\u00e9e en r\u00e9duction de dimension qui cherche \u00e0 repr\u00e9senter les donn\u00e9es dans un hyperplan proche de sorte \u00e0 conserver au maximum la variance du nuage de donn\u00e9es. En d\u2019autres termes, il s\u2019agit de repr\u00e9senter les donn\u00e9es dans un sous-espace de plus petite dimension maximisant l\u2019inertie totale du nuage projet\u00e9 dans cet espace.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Le Principe du t-SNE\u200b\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"L\u2019algorithme t-SNE consiste \u00e0 cr\u00e9er une distribution de probabilit\u00e9 qui repr\u00e9sente les similarit\u00e9s entre voisins dans un espace en grande dimension et dans un espace de plus petite dimension. Par similarit\u00e9, nous allons chercher \u00e0 convertir les distances en probabilit\u00e9s. Il se d\u00e9coupe en 3 \u00e9tapes\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Comparaison des m\u00e9thodes ACP et t-SNE\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Pour mieux saisir les diff\u00e9rences entre les deux m\u00e9thodes ACP et t-SNE, consid\u00e9rons le jeu de donn\u00e9es MNIST. Pour chacune des deux m\u00e9thodes, nous avons repr\u00e9sent\u00e9 les donn\u00e9es dans un espace \u00e0 deux dimensions.\"\n    }\n  }]\n}\n<\/script>\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\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Si vous vous \u00eates d\u00e9j\u00e0 int\u00e9ress\u00e9 aux m\u00e9thodes de r\u00e9duction de dimension, vous avez s\u00fbrement \u00e9tudi\u00e9 l&rsquo;Analyse en Composantes Principales ou ACP. Dans cet article, nous allons nous int\u00e9resser \u00e0 l\u2019une des autres m\u00e9thodes de r\u00e9duction de dimension qui existe : t-SNE pour t-distributed Stochastic Neighbor Embedding. Cet algorithme propose une approche diff\u00e9rente de l\u2019ACP. [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":71520,"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>Comprendre l\u2019algorithme t-SNE en 3 \u00e9tapes<\/title>\n<meta name=\"description\" content=\"Si vous vous \u00eates d\u00e9j\u00e0 int\u00e9ress\u00e9 aux m\u00e9thodes de r\u00e9duction de dimension, vous avez s\u00fbrement \u00e9tudi\u00e9 l&#039;Analyse en Compostante Principales ou ACP. Dans cet article, nous allons nous int\u00e9resser \u00e0 l\u2019une des autres m\u00e9thodes de r\u00e9duction de dimension qui existe : t-SNE pour t-distributed Stochastic Neighbor Embedding. Cet algorithme propose une approche diff\u00e9rente de l\u2019ACP.\" \/>\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\/comprendre-lalgorithme-t-sne-en-3-etapes\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Comprendre l\u2019algorithme t-SNE en 3 \u00e9tapes\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/comprendre-lalgorithme-t-sne-en-3-etapes\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2021-05-24T08:00:30+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-09T14:07:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/04\/illu_tSNE_blog_2-05.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"562\" \/>\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=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/comprendre-lalgorithme-t-sne-en-3-etapes\",\"url\":\"https:\/\/datascientest.com\/comprendre-lalgorithme-t-sne-en-3-etapes\",\"name\":\"Comprendre l\u2019algorithme t-SNE en 3 \u00e9tapes\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2021-05-24T08:00:30+00:00\",\"dateModified\":\"2023-11-09T14:07:16+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\"},\"description\":\"Si vous vous \u00eates d\u00e9j\u00e0 int\u00e9ress\u00e9 aux m\u00e9thodes de r\u00e9duction de dimension, vous avez s\u00fbrement \u00e9tudi\u00e9 l'Analyse en Compostante Principales ou ACP. 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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. En collaboration \u00e9troite avec l'\u00e9quipe de d\u00e9veloppement, il adapte l'accompagnement acad\u00e9mique aux \u00e9volutions de l'\u00e9quipe data et \u00e0 l'internationalisation.\",\"sameAs\":[\"https:\/\/www.linkedin.com\/in\/raphaelkassel\/\",\"Data Science\"],\"url\":\"https:\/\/datascientest.com\/author\/raphaelkassel\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Comprendre l\u2019algorithme t-SNE en 3 \u00e9tapes","description":"Si vous vous \u00eates d\u00e9j\u00e0 int\u00e9ress\u00e9 aux m\u00e9thodes de r\u00e9duction de dimension, vous avez s\u00fbrement \u00e9tudi\u00e9 l'Analyse en Compostante Principales ou ACP. 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