{"id":31526,"date":"2021-01-22T09:59:48","date_gmt":"2021-01-22T08:59:48","guid":{"rendered":"https:\/\/datascientest.com\/?p=31526"},"modified":"2023-11-09T14:10:16","modified_gmt":"2023-11-09T14:10:16","slug":"svm-machine-learning","status":"publish","type":"post","link":"https:\/\/datascientest.com\/svm-machine-learning","title":{"rendered":"SVM, quoi, comment, pourquoi ? Part.2"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"31526\" class=\"elementor elementor-31526\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9d030ad e-flex e-con-boxed e-con\" data-id=\"9d030ad\" 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-679abed elementor-widget elementor-widget-heading\" data-id=\"679abed\" 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\">Bienvenue dans la seconde partie de ce dossier d\u00e9di\u00e9 au Support Vector Machine.\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<div class=\"elementor-element elementor-element-4d995b7 e-flex e-con-boxed e-con\" data-id=\"4d995b7\" 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-93e0640 elementor-widget elementor-widget-text-editor\" data-id=\"93e0640\" 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: 400;\"><a href=\"https:\/\/datascientest.com\/svm\">Dans l\u2019article pr\u00e9c\u00e9dent<\/a>, nous avions d\u00e9taill\u00e9 le fonctionnement et les principaux d\u00e9fauts des Maximal Margin Classifier.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Notre objectif maintenant est d\u2019autoriser notre algorithme \u00e0 r\u00e9aliser un certain nombre <\/span><b>d\u2019erreurs<\/b><span style=\"font-weight: 400;\"> lors du choix de la droite de s\u00e9paration.<\/span><span style=\"font-weight: 400;\"> On parle alors de \u00ab\u00a0<\/span><b>soft margin\u00a0\u00bb<\/b><span style=\"font-weight: 400;\">, que l\u2019on pourrait traduire par \u00ab\u00a0marge souple\u00a0\u00bb. Nous allons maintenant d\u00e9tailler le fonctionnement de l\u2019algorithme <\/span><b>Soft Margin Classifiers, <\/b><span style=\"font-weight: 400;\">\u00e0 mi chemin entre le <\/span><b>Support Vector Machine<\/b><span style=\"font-weight: 400;\"> et le <\/span><b>Maximal Margin Classifier.<\/b><\/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-11a4a6b e-flex e-con-boxed e-con\" data-id=\"11a4a6b\" 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-1e5dd34 elementor-widget elementor-widget-heading\" data-id=\"1e5dd34\" 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\">Soft Margin Classifiers<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1b8e06d elementor-widget elementor-widget-text-editor\" data-id=\"1b8e06d\" 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;\">Dans le pr\u00e9c\u00e9dent article, nous avions d\u00e9fini\u00a0 ce qu\u2019\u00e9tait la <\/span><b>marge, <\/b><span style=\"font-weight: 400;\">c&rsquo;est-\u00e0 -dire <\/span><span style=\"font-weight: 400;\">la distance qui s\u00e9pare une droite de l\u2019observation la plus proche.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Dans cette deuxi\u00e8me partie, nous utiliserons aussi le terme de <\/span><b>marge<\/b><span style=\"font-weight: 400;\"> mais il d\u00e9signera cette fois <\/span><b>l\u2019ensemble des points plus proches de la droite que l\u2019observation la plus proche. <\/b><\/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-23c3c87 elementor-widget elementor-widget-image\" data-id=\"23c3c87\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0.png\" class=\"attachment-full size-full wp-image-31874\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\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-fba3143 elementor-widget elementor-widget-text-editor\" data-id=\"fba3143\" 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;\">Ici par exemple, la marge est l\u2019aire en <\/span><b>rose <\/b><span style=\"font-weight: 400;\">sur le graphique. Il s\u2019agit en fait de <\/span><b>l\u2019espace qui s\u00e9pare les 2 droites ext\u00e9rieures.\u00a0<\/b><\/p><p><span style=\"font-weight: 400;\">Pour rendre notre algorithme plus flexible, nous allons utiliser un <\/span><b>seuil<\/b><span style=\"font-weight: 400;\">, qui correspond au nombre d\u2019observations que nous tol\u00e9rerons \u00e0<\/span><b> l\u2019int\u00e9rieur de la marge<\/b><span style=\"font-weight: 400;\">. On cherche ensuite \u00e0 d\u00e9terminer, comme pr\u00e9c\u00e9demment, la droite de s\u00e9paration qui maximise la marge. Mais on ne se soucie plus d\u00e9sormais des observations qui se trouvent \u00e0 l&rsquo;int\u00e9rieur de la marge. Cela nous permet d\u2019obtenir une certaine <\/span><b>insensibilit\u00e9 aux valeurs extr\u00eames.<\/b><\/p><p><span style=\"font-weight: 400;\">Voici ce que l\u2019on obtient dans l\u2019exemple pr\u00e9c\u00e9dent avec des valeurs de seuil diff\u00e9rentes : <\/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-306b052 e-flex e-con-boxed e-con\" data-id=\"306b052\" 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<div class=\"elementor-element elementor-element-0d013b8 e-con-full e-flex e-con\" data-id=\"0d013b8\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c67e93f elementor-widget elementor-widget-image\" data-id=\"c67e93f\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/1.png\" class=\"attachment-large size-large wp-image-31876\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/1.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/1-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Aucune observation dans la marge\t<\/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>\n\t\t<div class=\"elementor-element elementor-element-06dc027 e-con-full e-flex e-con\" data-id=\"06dc027\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-39c3ed8 elementor-widget elementor-widget-image\" data-id=\"39c3ed8\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/2.png\" class=\"attachment-large size-large wp-image-31877\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/2.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/2-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">1 observation dans la marge <\/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>\n\t\t<div class=\"elementor-element elementor-element-10e9143 e-con-full e-flex e-con\" data-id=\"10e9143\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5f90036 elementor-widget elementor-widget-image\" data-id=\"5f90036\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/3.png\" class=\"attachment-large size-large wp-image-31881\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/3.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/3-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">2 observations dans la marge<\/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>\n\t\t<div class=\"elementor-element elementor-element-2a18e27 e-con-full e-flex e-con\" data-id=\"2a18e27\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2571862 elementor-widget elementor-widget-image\" data-id=\"2571862\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/4.png\" class=\"attachment-large size-large wp-image-31883\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/4.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/4-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">3 observations dans la marge<\/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>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d7ec93b e-flex e-con-boxed e-con\" data-id=\"d7ec93b\" 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-5d0e5d9 elementor-widget elementor-widget-text-editor\" data-id=\"5d0e5d9\" 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><span style=\"font-weight: 400;\">Comme on pouvait s\u2019y attendre, le fait d\u2019augmenter le seuil augmente la marge.<\/span><\/p><\/blockquote><p><span style=\"font-weight: 400;\"> N\u00e9anmoins, ceci ne veut pas dire pour autant que la classification est meilleure. On utilise alors la <\/span><b>validation crois\u00e9e<\/b><span style=\"font-weight: 400;\"> pour choisir le meilleur seuil possible.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Si vous n\u2019avez jamais entendu parl\u00e9 de validation crois\u00e9e (ou cross validation), <a href=\"https:\/\/datascientest.com\/glossary\/validation-croisee-cross-validation\" target=\"_blank\" rel=\"noopener\">en voici une d\u00e9finition rapide<\/a>.<\/span><\/p><p><span style=\"font-weight: 400;\">En r\u00e9alit\u00e9, lorsque l\u2019on augmente le seuil, on diminue la variance mais on augmente le biais. Dans le jargon, on dit que plus le seuil est \u00e9lev\u00e9, plus le risque d\u2019<\/span><b>overfitting<\/b><span style=\"font-weight: 400;\"> est faible.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Remarque : Les observations qui se trouvent \u00e0 l&rsquo;int\u00e9rieur et aux fronti\u00e8res de la marge sont appel\u00e9es vecteurs supports (ou Support Vectors), et l\u2019algorithme Soft Margin Classifiers s\u2019appelle aussi <\/span><b>Support Vectors Classifier<\/b><span style=\"font-weight: 400;\">.<\/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-e4f95c6 e-flex e-con-boxed e-con\" data-id=\"e4f95c6\" 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-54e859a elementor-widget elementor-widget-heading\" data-id=\"54e859a\" 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\">Support Vector Machine<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f5f08d3 elementor-widget elementor-widget-text-editor\" data-id=\"f5f08d3\" 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; color: #000000;\">Nous avons trouv\u00e9 une solution au premier probl\u00e8me, mais pas au second. Ainsi, l\u2019algorithme Support Vector Classifier ne fonctionne toujours pas dans le cas suivant :<\/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-f58ab4d elementor-widget elementor-widget-image\" data-id=\"f58ab4d\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-1.png\" class=\"attachment-full size-full wp-image-31890\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-1.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/pasted-image-0-1-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\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-e9b0ae7 elementor-widget elementor-widget-text-editor\" data-id=\"e9b0ae7\" 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;\">En fait, lorsque l\u2019algorithme ne fonctionne pas, on dit que les donn\u00e9es ne sont pas <\/span><b>lin\u00e9airement s\u00e9parables<\/b><span style=\"font-weight: 400;\">, et il existe des outils math\u00e9matiques pour d\u00e9terminer si un jeu de donn\u00e9es est, ou n\u2019est pas lin\u00e9airement s\u00e9parable.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Lorsque l\u2019on fait face \u00e0 un jeu de donn\u00e9es, on utilise donc ces outils.<\/span><span style=\"font-weight: 400;\"> Si le jeu de donn\u00e9es est lin\u00e9airement s\u00e9parable, pas besoin d\u2019aller chercher tr\u00e8s loin, on applique <strong>Soft Margin Classifier<\/strong>. Les choses se corsent en revanche lorsque le jeu de donn\u00e9es n\u2019est pas lin\u00e9airement s\u00e9parable.<\/span><\/p><p><span style=\"font-weight: 400;\">Pour simplifier la visualisation, nous allons changer le jeu de donn\u00e9es, et prendre cette fois des observations de <\/span><b>dimension 1<\/b><span style=\"font-weight: 400;\">, c&rsquo;est-\u00e0-dire sur un droite (et pas un plan). <\/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-0b98efe elementor-widget elementor-widget-image\" data-id=\"0b98efe\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/aaaaa.png\" class=\"attachment-full size-full wp-image-31891\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/aaaaa.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/aaaaa-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\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-f59dc25 elementor-widget elementor-widget-text-editor\" data-id=\"f59dc25\" 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;\">Inutile de vous expliquer pourquoi aucune droite ne peut s\u00e9parer les \u00ab\u00a0+\u00a0\u00bb et les \u00ab\u00a0&#8211;\u00a0\u00bb dans cette configuration particuli\u00e8re.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">L\u2019id\u00e9e du <\/span><b>Support Vector Machine <\/b><span style=\"font-weight: 400;\">est de projeter les donn\u00e9es dans un espace de plus grande dimensions, pour les rendre s\u00e9parables.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Reprenons notre exemple en dimension 1. Nous allons <\/span><b>projeter les donn\u00e9es<\/b><span style=\"font-weight: 400;\"> dans un espace de dimension 2. Pour ce faire, nous aurons besoin de ce que nous appelons une <\/span><b>fonction noyau <\/b><span style=\"font-weight: 400;\">(ou kernel function). Cette derni\u00e8re va servir d\u2019interm\u00e9diaire entre les deux espaces.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Prenons par exemple comme fonction noyau la fonction cube (f(x) = x^3). Voici comment appliquer la fonction noyau sur le jeu de donn\u00e9es pour le projeter dans un espace de dimension 2 :<\/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-356f860 e-flex e-con-boxed e-con\" data-id=\"356f860\" 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<div class=\"elementor-element elementor-element-e94e047 e-con-full e-flex e-con\" data-id=\"e94e047\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7b2e56e elementor-widget elementor-widget-image\" data-id=\"7b2e56e\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/bbbbb.png\" class=\"attachment-large size-large wp-image-31923\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/bbbbb.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/bbbbb-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\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>\n\t\t<div class=\"elementor-element elementor-element-3a4b73c e-con-full e-flex e-con\" data-id=\"3a4b73c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a93448a elementor-view-default elementor-position-top elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"a93448a\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<link rel=\"stylesheet\" href=\"https:\/\/datascientest.com\/wp-content\/uploads\/elementor\/css\/custom-widget-icon-box.min.css?ver=1730971578\">\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h3 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d218a20 e-con-full e-flex e-con\" data-id=\"d218a20\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e33477e elementor-widget elementor-widget-image\" data-id=\"e33477e\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/cccc.png\" class=\"attachment-large size-large wp-image-31924\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/cccc.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/cccc-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\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>\n\t\t<div class=\"elementor-element elementor-element-81c866d e-con-full e-flex e-con\" data-id=\"81c866d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fe0fb0f elementor-view-default elementor-position-top elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"fe0fb0f\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-grip-lines\" viewBox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M496 288H16c-8.8 0-16 7.2-16 16v32c0 8.8 7.2 16 16 16h480c8.8 0 16-7.2 16-16v-32c0-8.8-7.2-16-16-16zm0-128H16c-8.8 0-16 7.2-16 16v32c0 8.8 7.2 16 16 16h480c8.8 0 16-7.2 16-16v-32c0-8.8-7.2-16-16-16z\"><\/path><\/svg>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h3 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0b1198b e-con-full e-flex e-con\" data-id=\"0b1198b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2c85099 elementor-widget elementor-widget-image\" data-id=\"2c85099\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/dddd.png\" class=\"attachment-large size-large wp-image-31933\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/dddd.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/dddd-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\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>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0cdc2fd e-flex e-con-boxed e-con\" data-id=\"0cdc2fd\" 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-6a836f0 elementor-widget elementor-widget-text-editor\" data-id=\"6a836f0\" 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;\">Autrement dit, si l\u2019on note f la fonction noyau, pour chaque observation x, on place un point de coordonn\u00e9es (x, f(x)) dans le plan.<\/span><\/p><p><span style=\"font-weight: 400;\">Le jeu de donn\u00e9es projet\u00e9 est maintenant s\u00e9parable comme le montre l\u2019image suivante. On peut utiliser l\u2019algorithme <\/span><b>Soft Margin Classifiers <\/b><span style=\"font-weight: 400;\">dont on a explicit\u00e9 le fonctionnement pr\u00e9c\u00e9demment pour calculer la meilleure droite de s\u00e9paration et le tour est jou\u00e9.<\/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-f74a419 elementor-widget elementor-widget-image\" data-id=\"f74a419\" 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=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/e.png\" class=\"attachment-full size-full wp-image-31934\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/e.png 349w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/01\/e-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\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-4c9dfbb elementor-widget elementor-widget-text-editor\" data-id=\"4c9dfbb\" 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;\">Nous venons de d\u00e9tailler le fonctionnement des <\/span><b>Support Vector Machine<\/b><span style=\"font-weight: 400;\">. Et m\u00eame si nous avons volontairement pass\u00e9 certains d\u00e9tails sous silence (notamment concernant le choix de la fonction noyau), vous avez d\u00e9sormais une vue d\u2019ensemble sur le sujet.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">Les algorithmes de SVM peuvent \u00eatre adapt\u00e9s \u00e0 des probl\u00e8mes de classification portant sur plus de 2 classes, et \u00e0 des probl\u00e8mes de r\u00e9gression. Il s\u2019agit donc d\u2019une m\u00e9thode<\/span><b> simple et rapide<\/b><span style=\"font-weight: 400;\"> \u00e0 mettre en \u0153uvre sur tout type de <a href=\"https:\/\/datascientest.com\/datasets-top-5-des-sites-ou-trouver-des-jeux-de-donnees-de-qualite\">datasets<\/a>, ce qui explique certainement son succ\u00e8s. L\u00e0 o\u00f9 un r\u00e9seau de neurones demande un travail en amont pour d\u00e9terminer la bonne structure et les bons param\u00e8tres \u00e0 utiliser, les SVM obtiennent de bons r\u00e9sultats m\u00eame sans pr\u00e9paration. Si vous souhaitez en apprendre plus sur le <a href=\"https:\/\/datascientest.com\/machine-learning-tout-savoir\">Machine Learning<\/a>, je vous invite \u00e0 <strong>regarder cet autre article<\/strong> <strong>qui d\u00e9taille le fonctionnement des algorithmes de Boosting<\/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-a1f5dd4 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"a1f5dd4\" 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\/algorithmes-de-boosting-adaboost-gradient-boosting-xgboost\">\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\">Lire l'article<\/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\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Bienvenue dans la seconde partie de ce dossier d\u00e9di\u00e9 au Support Vector Machine.&nbsp; Dans l\u2019article pr\u00e9c\u00e9dent, nous avions d\u00e9taill\u00e9 le fonctionnement et les principaux d\u00e9fauts des Maximal Margin Classifier.&nbsp; Notre objectif maintenant est d\u2019autoriser notre algorithme \u00e0 r\u00e9aliser un certain nombre d\u2019erreurs lors du choix de la droite de s\u00e9paration. On parle alors de \u00ab\u00a0soft [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":26183,"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>SVM Machine Learning : D\u00e9tail du fonctionnement de l&#039;algorithme<\/title>\n<meta name=\"description\" content=\"SVM Machine Learning: Connaissez vous l&#039;algorithme de ML SVM (support vector machine) ? Dans cet article, nous d\u00e9taillons son fonctionnement .\" \/>\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\/svm-machine-learning\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"SVM, quoi, comment, pourquoi ? 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