{"id":1368,"date":"2019-06-25T18:42:34","date_gmt":"2019-06-25T16:42:34","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=1368"},"modified":"2021-10-26T16:57:52","modified_gmt":"2021-10-26T14:57:52","slug":"les-k-plus-proches-voisins","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2019\/06\/25\/les-k-plus-proches-voisins\/","title":{"rendered":"Les k plus proches voisins"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Dans le programme de NSI, on abord l&rsquo;algorithme des <em>k<\/em> plus proches voisins. Je vais tenter de vous expliquer avec un sch\u00e9ma ce que cela signifie que de trouver de tels voisins.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Prenons l&rsquo;exemple de points dans un rep\u00e8re orthonorm\u00e9 dans le carr\u00e9 [0;10]x[0;10] : ils sont soit bleus, soit rouges. On dit que \u00ab\u00a0bleu\u00a0\u00bb et \u00ab\u00a0rouge\u00a0\u00bb sont les <em>classes<\/em> des points.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si on met au hasard un point dans ce m\u00eame carr\u00e9, on peur se demander de quels points est-il le plus proche, ce qui donnera sa classe \u00e9ventuelle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">J&rsquo;ai fait un programme en Python qui:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>choisit au hasard 10 points rouges et 10 points bleus et qui les affichent;<\/li><li>choisit un point vert au hasard;<\/li><li>qui d\u00e9termine la distance entre le point vert et chacun des autres points;<\/li><li>qui d\u00e9termine enfin la classe \u00e9ventuelle du point vert et qui affiche les distances prises en compte.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">On obtient par exemple :<\/p>\n\n\n\n<figure class=\"wp-block-gallery columns-3 is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\"><ul class=\"blocks-gallery-grid\"><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-3.png\" alt=\"\" data-id=\"1369\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1369\" class=\"wp-image-1369\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-3.png 640w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-3-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-3-600x450.png 600w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-4.png\" alt=\"\" data-id=\"1370\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1370\" class=\"wp-image-1370\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-4.png 640w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-4-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-4-600x450.png 600w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-5.png\" alt=\"\" data-id=\"1371\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1371\" class=\"wp-image-1371\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-5.png 640w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-5-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-5-600x450.png 600w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-6.png\" alt=\"\" data-id=\"1372\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1372\" class=\"wp-image-1372\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-6.png 640w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-6-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-6-600x450.png 600w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-7.png\" alt=\"\" data-id=\"1373\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1373\" class=\"wp-image-1373\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-7.png 640w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-7-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-7-600x450.png 600w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure><\/li><\/ul><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pour t\u00e9l\u00e9charger le programme Python, c&rsquo;est ci-dessous pour les abonn\u00e9\u00b7e\u00b7s:<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter um_article\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k_voisins.zip\">k_voisins<\/a><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k_voisins.zip\" class=\"wp-block-file__button\" download>T\u00e9l\u00e9charger<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Dans le programme de NSI, on abord l&rsquo;algorithme des k plus proches voisins. Je vais tenter de vous expliquer avec un sch\u00e9ma ce que cela signifie que de trouver de tels voisins. Prenons l&rsquo;exemple de points dans un rep\u00e8re orthonorm\u00e9 dans le carr\u00e9 [0;10]x[0;10] : ils sont soit bleus, soit [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,5],"tags":[122],"class_list":["post-1368","post","type-post","status-publish","format-standard","hentry","category-enseignement","category-python","tag-nsi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Les k plus proches voisins - Mathweb.fr<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.mathweb.fr\/euclide\/2019\/06\/25\/les-k-plus-proches-voisins\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les k plus proches voisins - Mathweb.fr\" \/>\n<meta property=\"og:description\" content=\"Dans le programme de NSI, on abord l&rsquo;algorithme des k plus proches voisins. Je vais tenter de vous expliquer avec un sch\u00e9ma ce que cela signifie que de trouver de tels voisins. Prenons l&rsquo;exemple de points dans un rep\u00e8re orthonorm\u00e9 dans le carr\u00e9 [0;10]x[0;10] : ils sont soit bleus, soit [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.mathweb.fr\/euclide\/2019\/06\/25\/les-k-plus-proches-voisins\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathweb.fr\" \/>\n<meta property=\"article:published_time\" content=\"2019-06-25T16:42:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-26T14:57:52+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/06\/k-voisins-3.png\" \/>\n<meta name=\"author\" content=\"St\u00e9phane Pasquet\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"St\u00e9phane Pasquet\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/2019\\\/06\\\/25\\\/les-k-plus-proches-voisins\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/2019\\\/06\\\/25\\\/les-k-plus-proches-voisins\\\/\"},\"author\":{\"name\":\"St\u00e9phane Pasquet\",\"@id\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/#\\\/schema\\\/person\\\/e4d3bb07968238378f0d5052a70dcd69\"},\"headline\":\"Les k plus proches voisins\",\"datePublished\":\"2019-06-25T16:42:34+00:00\",\"dateModified\":\"2021-10-26T14:57:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/2019\\\/06\\\/25\\\/les-k-plus-proches-voisins\\\/\"},\"wordCount\":181,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/#\\\/schema\\\/person\\\/e4d3bb07968238378f0d5052a70dcd69\"},\"image\":{\"@id\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/2019\\\/06\\\/25\\\/les-k-plus-proches-voisins\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/wp-content\\\/uploads\\\/2019\\\/06\\\/k-voisins-3.png\",\"keywords\":[\"nsi\"],\"articleSection\":[\"Enseignement\",\"Python\"],\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/2019\\\/06\\\/25\\\/les-k-plus-proches-voisins\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/2019\\\/06\\\/25\\\/les-k-plus-proches-voisins\\\/\",\"url\":\"https:\\\/\\\/www.mathweb.fr\\\/euclide\\\/2019\\\/06\\\/25\\\/les-k-plus-proches-voisins\\\/\",\"name\":\"Les k plus proches voisins - 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