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tables","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Ftraitement-tables","0.snt-2nde\u002Fsd-donnees-structurees\u002F4.traitement-tables",{"title":115,"path":116,"stem":117},"Le cloud","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fcloud","0.snt-2nde\u002Fsd-donnees-structurees\u002F5.cloud",{"title":119,"path":120,"stem":121,"children":122},"Localisation, cartographie et mobilité","\u002Fsnt-2nde\u002Fse-localisation-cartographie","0.snt-2nde\u002Fse-localisation-cartographie\u002F0.index",[123,124,128,132,136,140],{"title":119,"path":120,"stem":121},{"title":125,"path":126,"stem":127},"GPS et Galileo — se situer grâce aux satellites","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fgps-galileo","0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo",{"title":129,"path":130,"stem":131},"Décoder une trame NMEA","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Ftrame-nmea","0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea",{"title":133,"path":134,"stem":135},"Cartes numériques — GeoPortail et OpenStreetMap","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fcartes-numeriques","0.snt-2nde\u002Fse-localisation-cartographie\u002F3.cartes-numeriques",{"title":137,"path":138,"stem":139},"Itinéraires et graphes","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fitineraires-graphes","0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes",{"title":141,"path":142,"stem":143},"Confidentialité de la position","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fconfidentialite-position","0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position",{"title":145,"path":146,"stem":147,"children":148},"Informatique embarquée et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee","0.snt-2nde\u002Fsf-info-embarquee\u002F0.index",[149,150,154,158],{"title":145,"path":146,"stem":147},{"title":151,"path":152,"stem":153},"Systèmes informatiques embarqués","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fsystemes-embarques","0.snt-2nde\u002Fsf-info-embarquee\u002F1.systemes-embarques",{"title":155,"path":156,"stem":157},"Capteurs et actionneurs","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fcapteurs-actionneurs","0.snt-2nde\u002Fsf-info-embarquee\u002F2.capteurs-actionneurs",{"title":159,"path":160,"stem":161},"IHM et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fihm-objet-connecte","0.snt-2nde\u002Fsf-info-embarquee\u002F3.ihm-objet-connecte",{"title":163,"path":164,"stem":165,"children":166},"Photographie numérique","\u002Fsnt-2nde\u002Fsg-photo-numerique","0.snt-2nde\u002Fsg-photo-numerique\u002F0.index",[167,168,172,176,180],{"title":163,"path":164,"stem":165},{"title":169,"path":170,"stem":171},"Photosites, pixels et résolution","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fpixels-resolution","0.snt-2nde\u002Fsg-photo-numerique\u002F1.pixels-resolution",{"title":173,"path":174,"stem":175},"Les algorithmes de l'appareil photo","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Falgorithmes-photo","0.snt-2nde\u002Fsg-photo-numerique\u002F2.algorithmes-photo",{"title":177,"path":178,"stem":179},"Les métadonnées EXIF","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fmetadonnees-exif","0.snt-2nde\u002Fsg-photo-numerique\u002F3.metadonnees-exif",{"title":181,"path":182,"stem":183},"Traiter une image en Python","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Ftraitement-rgb","0.snt-2nde\u002Fsg-photo-numerique\u002F4.traitement-rgb",{"title":185,"path":186,"stem":187,"children":188},"Notions transversales de programmation","\u002Fsnt-2nde\u002Fsh-prog-notions","0.snt-2nde\u002Fsh-prog-notions\u002F0.index",[189,190,194,198,202],{"title":185,"path":186,"stem":187},{"title":191,"path":192,"stem":193},"Séquences d'instructions et variables","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fsequences-affectations","0.snt-2nde\u002Fsh-prog-notions\u002F1.sequences-affectations",{"title":195,"path":196,"stem":197},"Instructions conditionnelles","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fconditionnelles","0.snt-2nde\u002Fsh-prog-notions\u002F2.conditionnelles",{"title":199,"path":200,"stem":201},"Boucles bornées et non bornées","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fboucles","0.snt-2nde\u002Fsh-prog-notions\u002F3.boucles",{"title":203,"path":204,"stem":205},"Définitions et appels de fonctions","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Ffonctions","0.snt-2nde\u002Fsh-prog-notions\u002F4.fonctions",{"title":207,"path":208,"stem":209,"children":210},"Démo des widgets MDC","\u002Fsnt-2nde\u002Fzz-demo-widgets","0.snt-2nde\u002Fzz-demo-widgets\u002F0.index",[211,212,216,220],{"title":207,"path":208,"stem":209},{"title":213,"path":214,"stem":215},"Démo statique — callouts, code, BO, illustration","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fstatique","0.snt-2nde\u002Fzz-demo-widgets\u002F1.statique",{"title":217,"path":218,"stem":219},"Démo interactive — self-eval et python-snippet","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Finteractif","0.snt-2nde\u002Fzz-demo-widgets\u002F2.interactif",{"title":221,"path":222,"stem":223},"Démo · 14 widgets de manipulation NSI","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fwidgets-manipulation","0.snt-2nde\u002Fzz-demo-widgets\u002F3.widgets-manipulation",{"title":225,"path":226,"stem":227,"children":228},"NSI — Première","\u002Fnsi-1ere","1.nsi-1ere\u002F0.index",[229,230,234,256,282,304,328,354,380,410],{"title":225,"path":226,"stem":227},{"title":231,"path":232,"stem":233},"Relecture pédagogique — 8 chapitres NSI 1ère (PA → PH)","\u002Fnsi-1ere\u002Freview","1.nsi-1ere\u002FREVIEW",{"title":235,"path":236,"stem":237,"children":238},"Histoire de l'informatique","\u002Fnsi-1ere\u002Fpa-histoire-info","1.nsi-1ere\u002Fpa-histoire-info\u002F0.index",[239,240,244,248,252],{"title":235,"path":236,"stem":237},{"title":241,"path":242,"stem":243},"De la préantiquité aux machines à calculer","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fpreantiquite-aux-machines","1.nsi-1ere\u002Fpa-histoire-info\u002F1.preantiquite-aux-machines",{"title":245,"path":246,"stem":247},"La machine universelle (1930-1950)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fmachine-universelle","1.nsi-1ere\u002Fpa-histoire-info\u002F2.machine-universelle",{"title":249,"path":250,"stem":251},"Les ordinateurs modernes (1947-1990)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fordinateurs-modernes","1.nsi-1ere\u002Fpa-histoire-info\u002F3.ordinateurs-modernes",{"title":253,"path":254,"stem":255},"Réseaux, Web et IA (1969 à aujourd'hui)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Freseaux-et-web","1.nsi-1ere\u002Fpa-histoire-info\u002F4.reseaux-et-web",{"title":257,"path":258,"stem":259,"children":260},"Représentation des données — types et valeurs","\u002Fnsi-1ere\u002Fpb-types-valeurs","1.nsi-1ere\u002Fpb-types-valeurs\u002F0.index",[261,262,266,270,274,278],{"title":257,"path":258,"stem":259},{"title":263,"path":264,"stem":265},"Bases de numération et entiers positifs","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbases-entiers-positifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs",{"title":267,"path":268,"stem":269},"Entiers relatifs et complément à deux","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fentiers-relatifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F2.entiers-relatifs",{"title":271,"path":272,"stem":273},"Nombres flottants et virgule 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compréhension","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fcomprehension","1.nsi-1ere\u002Fpc-types-construits\u002F2.comprehension",{"title":297,"path":298,"stem":299},"Tuples et p-uplets nommés","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftuples","1.nsi-1ere\u002Fpc-types-construits\u002F3.tuples",{"title":301,"path":302,"stem":303},"Dictionnaires","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fdictionnaires","1.nsi-1ere\u002Fpc-types-construits\u002F4.dictionnaires",{"title":305,"path":306,"stem":307,"children":308},"Traitement de données en tables","\u002Fnsi-1ere\u002Fpd-tables-donnees","1.nsi-1ere\u002Fpd-tables-donnees\u002F0.index",[309,310,314,318,322],{"title":305,"path":306,"stem":307},{"title":311,"path":312,"stem":313},"Tables et CSV","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftables-csv","1.nsi-1ere\u002Fpd-tables-donnees\u002F1.tables-csv",{"title":315,"path":316,"stem":317},"Recherche et filtrage","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Frecherche","1.nsi-1ere\u002Fpd-tables-donnees\u002F2.recherche",{"title":319,"path":320,"stem":321},"Trier une table","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftri","1.nsi-1ere\u002Fpd-tables-donnees\u002F3.tri",{"title":323,"path":324,"stem":325,"children":326},"Fusion et indexation","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ffusion-indexation","1.nsi-1ere\u002Fpd-tables-donnees\u002F4.fusion-indexation",[327],{"title":323,"path":324,"stem":325},{"title":329,"path":330,"stem":331,"children":332},"IHM sur le Web","\u002Fnsi-1ere\u002Fpe-ihm-web","1.nsi-1ere\u002Fpe-ihm-web\u002F0.index",[333,334,338,342,346,350],{"title":329,"path":330,"stem":331},{"title":335,"path":336,"stem":337},"HTML et CSS — rappel de structure","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fhtml-css-bases","1.nsi-1ere\u002Fpe-ihm-web\u002F1.html-css-bases",{"title":339,"path":340,"stem":341},"Formulaires HTML","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fformulaires","1.nsi-1ere\u002Fpe-ihm-web\u002F2.formulaires",{"title":343,"path":344,"stem":345},"Événements JavaScript","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fevenements-js","1.nsi-1ere\u002Fpe-ihm-web\u002F3.evenements-js",{"title":347,"path":348,"stem":349},"Manipulation du DOM","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fdom-interaction","1.nsi-1ere\u002Fpe-ihm-web\u002F4.dom-interaction",{"title":351,"path":352,"stem":353},"Client, serveur et HTTP","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fclient-serveur-http","1.nsi-1ere\u002Fpe-ihm-web\u002F5.client-serveur-http",{"title":355,"path":356,"stem":357,"children":358},"Architectures matérielles et systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os","1.nsi-1ere\u002Fpf-archi-os\u002F0.index",[359,360,364,368,372,376],{"title":355,"path":356,"stem":357},{"title":361,"path":362,"stem":363},"Le modèle de von Neumann","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fvon-neumann","1.nsi-1ere\u002Fpf-archi-os\u002F1.von-neumann",{"title":365,"path":366,"stem":367},"Périphériques et interface homme-machine","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fperipheriques-ihm","1.nsi-1ere\u002Fpf-archi-os\u002F2.peripheriques-ihm",{"title":369,"path":370,"stem":371},"Les systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fsystemes-exploitation","1.nsi-1ere\u002Fpf-archi-os\u002F3.systemes-exploitation",{"title":373,"path":374,"stem":375},"Linux et le shell","\u002Fnsi-1ere\u002Fpf-archi-os\u002Flinux-shell","1.nsi-1ere\u002Fpf-archi-os\u002F4.linux-shell",{"title":377,"path":378,"stem":379},"Réseaux et protocoles","\u002Fnsi-1ere\u002Fpf-archi-os\u002Freseaux","1.nsi-1ere\u002Fpf-archi-os\u002F5.reseaux",{"title":381,"path":382,"stem":383,"children":384},"Langages et programmation","\u002Fnsi-1ere\u002Fpg-langages-prog","1.nsi-1ere\u002Fpg-langages-prog\u002F0.index",[385,386,390,394,398,402,406],{"title":381,"path":382,"stem":383},{"title":387,"path":388,"stem":389},"Diversité et unité des langages de programmation","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fdiversite-langages","1.nsi-1ere\u002Fpg-langages-prog\u002F1.diversite-langages",{"title":391,"path":392,"stem":393},"Constructions élémentaires","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fconstructions-elementaires","1.nsi-1ere\u002Fpg-langages-prog\u002F2.constructions-elementaires",{"title":395,"path":396,"stem":397},"Fonctions","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Ffonctions","1.nsi-1ere\u002Fpg-langages-prog\u002F3.fonctions",{"title":399,"path":400,"stem":401},"Spécification d'une fonction","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fspecification","1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification",{"title":403,"path":404,"stem":405},"Mise au point des programmes","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fmise-au-point","1.nsi-1ere\u002Fpg-langages-prog\u002F5.mise-au-point",{"title":407,"path":408,"stem":409},"Utilisation de bibliothèques","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fbibliotheques","1.nsi-1ere\u002Fpg-langages-prog\u002F6.bibliotheques",{"title":411,"path":412,"stem":413,"children":414},"Algorithmique","\u002Fnsi-1ere\u002Fph-algorithmique","1.nsi-1ere\u002Fph-algorithmique\u002F0.index",[415,416,420,424,428,432,436],{"title":411,"path":412,"stem":413},{"title":417,"path":418,"stem":419},"Parcours séquentiel d'un tableau","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fparcours-sequentiel","1.nsi-1ere\u002Fph-algorithmique\u002F1.parcours-sequentiel",{"title":421,"path":422,"stem":423},"Bases de la complexité","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fcomplexite-bases","1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases",{"title":425,"path":426,"stem":427},"Tris par sélection et par insertion","\u002Fnsi-1ere\u002Fph-algorithmique\u002Ftris","1.nsi-1ere\u002Fph-algorithmique\u002F3.tris",{"title":429,"path":430,"stem":431},"Recherche dichotomique","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fdichotomie","1.nsi-1ere\u002Fph-algorithmique\u002F4.dichotomie",{"title":433,"path":434,"stem":435},"Algorithmes gloutons","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fgloutons","1.nsi-1ere\u002Fph-algorithmique\u002F5.gloutons",{"title":437,"path":438,"stem":439},"Les k plus proches voisins (k-NN)","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fknn","1.nsi-1ere\u002Fph-algorithmique\u002F6.knn",{"title":441,"path":442,"stem":443,"children":444},"NSI — Terminale","\u002Fnsi-tale","2.nsi-tale\u002F0.index",[445,446,450,476,498,536,560],{"title":441,"path":442,"stem":443},{"title":447,"path":448,"stem":449},"Review pédagogique — chapitres NSI Terminale (TA, TB, TC, TD, TE)","\u002Fnsi-tale\u002Freview","2.nsi-tale\u002FREVIEW",{"title":451,"path":452,"stem":453,"children":454},"Structures de données","\u002Fnsi-tale\u002Fta-structures-donnees","2.nsi-tale\u002Fta-structures-donnees\u002F0.index",[455,456,460,464,468,472],{"title":451,"path":452,"stem":453},{"title":457,"path":458,"stem":459},"Objet, classe, interface","\u002Fnsi-tale\u002Fta-structures-donnees\u002Finterface-implementation","2.nsi-tale\u002Fta-structures-donnees\u002F1.interface-implementation",{"title":461,"path":462,"stem":463},"Implémenter une structure — l'exemple de la file FIFO","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fimplementer-une-structure","2.nsi-tale\u002Fta-structures-donnees\u002F2.implementer-une-structure",{"title":465,"path":466,"stem":467},"Listes, piles, files, dictionnaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Flistes-piles-files-dict","2.nsi-tale\u002Fta-structures-donnees\u002F3.listes-piles-files-dict",{"title":469,"path":470,"stem":471},"Arbres binaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires","2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires",{"title":473,"path":474,"stem":475},"Graphes","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fgraphes","2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes",{"title":477,"path":478,"stem":479,"children":480},"Bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees","2.nsi-tale\u002Ftb-bases-de-donnees\u002F0.index",[481,482,486,490,494],{"title":477,"path":478,"stem":479},{"title":483,"path":484,"stem":485},"Le modèle relationnel","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fmodele-relationnel","2.nsi-tale\u002Ftb-bases-de-donnees\u002F1.modele-relationnel",{"title":487,"path":488,"stem":489},"Bases de données relationnelles et anomalies de schéma","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fbase-relationnelle","2.nsi-tale\u002Ftb-bases-de-donnees\u002F2.base-relationnelle",{"title":491,"path":492,"stem":493},"Le langage SQL","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsql","2.nsi-tale\u002Ftb-bases-de-donnees\u002F3.sql",{"title":495,"path":496,"stem":497},"Les systèmes de gestion de bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsgbd","2.nsi-tale\u002Ftb-bases-de-donnees\u002F4.sgbd",{"title":499,"path":500,"stem":501,"children":502},"Architectures matérielles, systèmes d'exploitation et réseaux","\u002Fnsi-tale\u002Ftc-archi-os-reseaux","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F0.index",[503,504,508,512,516,520,524,528,532],{"title":499,"path":500,"stem":501},{"title":505,"path":506,"stem":507},"Le système sur puce (SoC)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fsysteme-sur-puce","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F1.systeme-sur-puce",{"title":509,"path":510,"stem":511},"Processus et ordonnancement par l'OS","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprocessus-os","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F2.processus-os",{"title":513,"path":514,"stem":515},"L'interblocage (deadlock)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Finterblocage","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F3.interblocage",{"title":517,"path":518,"stem":519},"Principes du routage","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Froutage-principes","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F4.routage-principes",{"title":521,"path":522,"stem":523},"Protocoles de routage RIP et OSPF","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprotocoles-rip-ospf","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F5.protocoles-rip-ospf",{"title":525,"path":526,"stem":527},"Chiffrement symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-symetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F6.chiffrement-symetrique",{"title":529,"path":530,"stem":531},"Chiffrement asymétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-asymetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique",{"title":533,"path":534,"stem":535},"HTTPS — l'échange de clé symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fhttps-tls","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F8.https-tls",{"title":381,"path":537,"stem":538,"children":539},"\u002Fnsi-tale\u002Ftd-langages-prog","2.nsi-tale\u002Ftd-langages-prog\u002F0.index",[540,541,544,548,552,556],{"title":381,"path":537,"stem":538},{"title":403,"path":542,"stem":543},"\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmise-au-point","2.nsi-tale\u002Ftd-langages-prog\u002F1.mise-au-point",{"title":545,"path":546,"stem":547},"Modularité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmodularite","2.nsi-tale\u002Ftd-langages-prog\u002F2.modularite",{"title":549,"path":550,"stem":551},"Récursivité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Frecursivite","2.nsi-tale\u002Ftd-langages-prog\u002F3.recursivite",{"title":553,"path":554,"stem":555},"Paradigmes de programmation","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fparadigmes","2.nsi-tale\u002Ftd-langages-prog\u002F4.paradigmes",{"title":557,"path":558,"stem":559},"Programme comme donnée — calculabilité et indécidabilité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fprogramme-comme-donnee","2.nsi-tale\u002Ftd-langages-prog\u002F5.programme-comme-donnee",{"title":411,"path":561,"stem":562,"children":563},"\u002Fnsi-tale\u002Fte-algorithmique","2.nsi-tale\u002Fte-algorithmique\u002F0.index",[564,565,569,573,577,581],{"title":411,"path":561,"stem":562},{"title":566,"path":567,"stem":568},"Algorithmes sur les arbres binaires","\u002Fnsi-tale\u002Fte-algorithmique\u002Farbres-binaires-algos","2.nsi-tale\u002Fte-algorithmique\u002F1.arbres-binaires-algos",{"title":570,"path":571,"stem":572},"Parcours de graphes — DFS, BFS, cycles, chemins","\u002Fnsi-tale\u002Fte-algorithmique\u002Fgraphes-parcours","2.nsi-tale\u002Fte-algorithmique\u002F2.graphes-parcours",{"title":574,"path":575,"stem":576},"Diviser pour régner","\u002Fnsi-tale\u002Fte-algorithmique\u002Fdiviser-pour-regner","2.nsi-tale\u002Fte-algorithmique\u002F3.diviser-pour-regner",{"title":578,"path":579,"stem":580},"Programmation dynamique","\u002Fnsi-tale\u002Fte-algorithmique\u002Fprogrammation-dynamique","2.nsi-tale\u002Fte-algorithmique\u002F4.programmation-dynamique",{"title":582,"path":583,"stem":584},"Recherche textuelle — l'algorithme de Boyer-Moore","\u002Fnsi-tale\u002Fte-algorithmique\u002Frecherche-textuelle","2.nsi-tale\u002Fte-algorithmique\u002F5.recherche-textuelle",{"id":586,"title":437,"bo":587,"body":589,"description":4085,"eval":4086,"extension":4087,"labo":4086,"meta":4088,"navigation":1841,"path":438,"quizzes":4089,"readingTime":1827,"seo":4096,"stem":439,"tp":4086,"__hash__":4097},"cours\u002F1.nsi-1ere\u002Fph-algorithmique\u002F6.knn.md",[588],"PH01",{"type":590,"value":591,"toc":4073},"minimark",[592,597,627,630,634,648,654,762,800,804,814,881,1020,1363,1811,1814,1961,2371,2375,2429,2827,3167,3199,3231,3366,3520,3543,3547,3565,3593,3597,3604,3836,3903,3921,3925,4058,4062,4069],[593,594,596],"h2",{"id":595},"introduction","Introduction",[598,599,600,601,605,606,609,610,613,614,618,619,622,623,626],"p",{},"Les cours précédents portaient sur des algorithmes ",[602,603,604],"strong",{},"déterministes"," (qui\nproduisent toujours la même sortie pour une même entrée) : on sait\nexactement ce qu'ils calculent, et on peut prouver leur correction.\nCe dernier cours change de registre — il introduit un ",[602,607,608],{},"algorithme\nd'apprentissage",", le ",[602,611,612],{},"k plus proches voisins"," (ou ",[615,616,617],"em",{},"k-Nearest Neighbors",",\nk-NN). On lui fournit des exemples déjà étiquetés, et il classe un nouvel\nexemple ",[602,620,621],{},"par ressemblance"," aux exemples connus. C'est un avant-goût de\nl'",[602,624,625],{},"apprentissage automatique"," que vous approfondirez en Terminale et au-delà.",[628,629],"bo-ref",{"code":588},[593,631,633],{"id":632},"le-cœur-du-concept","Le cœur du concept",[598,635,636,639,640,643,644,647],{},[602,637,638],{},"Problème"," : on vous donne un ensemble de points dans un plan, chacun\nétiqueté avec une ",[602,641,642],{},"classe"," (par exemple « chat » ou « chien », ou\n« iris setosa » \u002F « iris versicolor »). On vous présente un ",[602,645,646],{},"nouveau point","\nsans étiquette. Quelle classe lui attribuer ?",[598,649,650,653],{},[602,651,652],{},"Idée du k-NN"," :",[655,656,657,669,723,759],"ol",{},[658,659,660,661,664,665,668],"li",{},"Calculer la ",[602,662,663],{},"distance"," entre le nouveau point et ",[602,666,667],{},"chaque"," point\nétiqueté.",[658,670,671,672,722],{},"Sélectionner les ",[602,673,674,721],{},[675,676,679,701],"span",{"className":677},[678],"katex",[675,680,683],{"className":681},[682],"katex-mathml",[684,685,687],"math",{"xmlns":686},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[688,689,690,697],"semantics",{},[691,692,693],"mrow",{},[694,695,696],"mi",{},"k",[698,699,696],"annotation",{"encoding":700},"application\u002Fx-tex",[675,702,706],{"className":703,"ariaHidden":705},[704],"katex-html","true",[675,707,710,715],{"className":708},[709],"base",[675,711],{"className":712,"style":714},[713],"strut","height:0.6944em;",[675,716,696],{"className":717,"style":720},[718,719],"mord","mathnormal","margin-right:0.0315em;"," plus proches",".",[658,724,725,726,729,730,758],{},"Regarder leur ",[602,727,728],{},"classe majoritaire"," parmi ces ",[675,731,733,746],{"className":732},[678],[675,734,736],{"className":735},[682],[684,737,738],{"xmlns":686},[688,739,740,744],{},[691,741,742],{},[694,743,696],{},[698,745,696],{"encoding":700},[675,747,749],{"className":748,"ariaHidden":705},[704],[675,750,752,755],{"className":751},[709],[675,753],{"className":754,"style":714},[713],[675,756,696],{"className":757,"style":720},[718,719]," voisins.",[658,760,761],{},"Attribuer cette classe au nouveau point.",[763,764,765],"tip",{},[598,766,767,770,771,799],{},[602,768,769],{},"Analogie"," : si vos ",[675,772,774,787],{"className":773},[678],[675,775,777],{"className":776},[682],[684,778,779],{"xmlns":686},[688,780,781,785],{},[691,782,783],{},[694,784,696],{},[698,786,696],{"encoding":700},[675,788,790],{"className":789,"ariaHidden":705},[704],[675,791,793,796],{"className":792},[709],[675,794],{"className":795,"style":714},[713],[675,797,696],{"className":798,"style":720},[718,719]," voisins de palier sont tous fans d'opéra, il est\nprobable que vous le soyez aussi. Le k-NN parie sur cette « contagion\nlocale » des étiquettes.",[593,801,803],{"id":802},"la-distance-euclidienne","La distance euclidienne",[598,805,806,807,809,810,813],{},"Pour mesurer à quel point deux points sont proches, on utilise une\n",[602,808,663],{},". La plus classique est la ",[602,811,812],{},"distance euclidienne"," — celle de\nla règle, en ligne droite.",[598,815,816,819,820,850,851,880],{},[602,817,818],{},"En 1D",", c'est tout simplement l'écart entre deux nombres : pour deux\npoints ",[675,821,823,837],{"className":822},[678],[675,824,826],{"className":825},[682],[684,827,828],{"xmlns":686},[688,829,830,835],{},[691,831,832],{},[694,833,834],{},"a",[698,836,834],{"encoding":700},[675,838,840],{"className":839,"ariaHidden":705},[704],[675,841,843,847],{"className":842},[709],[675,844],{"className":845,"style":846},[713],"height:0.4306em;",[675,848,834],{"className":849},[718,719]," et ",[675,852,854,868],{"className":853},[678],[675,855,857],{"className":856},[682],[684,858,859],{"xmlns":686},[688,860,861,866],{},[691,862,863],{},[694,864,865],{},"b",[698,867,865],{"encoding":700},[675,869,871],{"className":870,"ariaHidden":705},[704],[675,872,874,877],{"className":873},[709],[675,875],{"className":876,"style":714},[713],[675,878,865],{"className":879},[718,719]," sur une droite,",[675,882,885],{"className":883},[884],"katex-display",[675,886,888,937],{"className":887},[678],[675,889,891],{"className":890},[682],[684,892,894],{"xmlns":686,"display":893},"block",[688,895,896,934],{},[691,897,898,901,906,908,911,913,916,919,923,925,928,930,932],{},[694,899,900],{},"d",[902,903,905],"mo",{"stretchy":904},"false","(",[694,907,834],{},[902,909,910],{"separator":705},",",[694,912,865],{},[902,914,915],{"stretchy":904},")",[902,917,918],{},"=",[694,920,922],{"mathvariant":921},"normal","∣",[694,924,834],{},[902,926,927],{},"−",[694,929,865],{},[694,931,922],{"mathvariant":921},[694,933,722],{"mathvariant":921},[698,935,936],{"encoding":700},"d(a, b) = |a - b|.",[675,938,940,984,1007],{"className":939,"ariaHidden":705},[704],[675,941,943,947,950,954,957,961,966,969,973,977,981],{"className":942},[709],[675,944],{"className":945,"style":946},[713],"height:1em;vertical-align:-0.25em;",[675,948,900],{"className":949},[718,719],[675,951,905],{"className":952},[953],"mopen",[675,955,834],{"className":956},[718,719],[675,958,910],{"className":959},[960],"mpunct",[675,962],{"className":963,"style":965},[964],"mspace","margin-right:0.1667em;",[675,967,865],{"className":968},[718,719],[675,970,915],{"className":971},[972],"mclose",[675,974],{"className":975,"style":976},[964],"margin-right:0.2778em;",[675,978,918],{"className":979},[980],"mrel",[675,982],{"className":983,"style":976},[964],[675,985,987,990,993,996,1000,1004],{"className":986},[709],[675,988],{"className":989,"style":946},[713],[675,991,922],{"className":992},[718],[675,994,834],{"className":995},[718,719],[675,997],{"className":998,"style":999},[964],"margin-right:0.2222em;",[675,1001,927],{"className":1002},[1003],"mbin",[675,1005],{"className":1006,"style":999},[964],[675,1008,1010,1013,1016],{"className":1009},[709],[675,1011],{"className":1012,"style":946},[713],[675,1014,865],{"className":1015},[718,719],[675,1017,1019],{"className":1018},[718],"∣.",[598,1021,1022,1025,1026,850,1205,653],{},[602,1023,1024],{},"En 2D",", on applique le théorème de Pythagore au triangle rectangle formé\npar les deux points. Pour deux points ",[675,1027,1029,1067],{"className":1028},[678],[675,1030,1032],{"className":1031},[682],[684,1033,1034],{"xmlns":686},[688,1035,1036,1064],{},[691,1037,1038,1041,1043,1045,1053,1055,1062],{},[694,1039,1040],{},"A",[902,1042,918],{},[902,1044,905],{"stretchy":904},[1046,1047,1048,1051],"msub",{},[694,1049,1050],{},"x",[694,1052,1040],{},[902,1054,910],{"separator":705},[1046,1056,1057,1060],{},[694,1058,1059],{},"y",[694,1061,1040],{},[902,1063,915],{"stretchy":904},[698,1065,1066],{"encoding":700},"A = (x_A, y_A)",[675,1068,1070,1089],{"className":1069,"ariaHidden":705},[704],[675,1071,1073,1077,1080,1083,1086],{"className":1072},[709],[675,1074],{"className":1075,"style":1076},[713],"height:0.6833em;",[675,1078,1040],{"className":1079},[718,719],[675,1081],{"className":1082,"style":976},[964],[675,1084,918],{"className":1085},[980],[675,1087],{"className":1088,"style":976},[964],[675,1090,1092,1095,1098,1154,1157,1160,1202],{"className":1091},[709],[675,1093],{"className":1094,"style":946},[713],[675,1096,905],{"className":1097},[953],[675,1099,1101,1104],{"className":1100},[718],[675,1102,1050],{"className":1103},[718,719],[675,1105,1108],{"className":1106},[1107],"msupsub",[675,1109,1113,1145],{"className":1110},[1111,1112],"vlist-t","vlist-t2",[675,1114,1117,1140],{"className":1115},[1116],"vlist-r",[675,1118,1122],{"className":1119,"style":1121},[1120],"vlist","height:0.3283em;",[675,1123,1125,1130],{"style":1124},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[675,1126],{"className":1127,"style":1129},[1128],"pstrut","height:2.7em;",[675,1131,1137],{"className":1132},[1133,1134,1135,1136],"sizing","reset-size6","size3","mtight",[675,1138,1040],{"className":1139},[718,719,1136],[675,1141,1144],{"className":1142},[1143],"vlist-s","​",[675,1146,1148],{"className":1147},[1116],[675,1149,1152],{"className":1150,"style":1151},[1120],"height:0.15em;",[675,1153],{},[675,1155,910],{"className":1156},[960],[675,1158],{"className":1159,"style":965},[964],[675,1161,1163,1167],{"className":1162},[718],[675,1164,1059],{"className":1165,"style":1166},[718,719],"margin-right:0.0359em;",[675,1168,1170],{"className":1169},[1107],[675,1171,1173,1194],{"className":1172},[1111,1112],[675,1174,1176,1191],{"className":1175},[1116],[675,1177,1179],{"className":1178,"style":1121},[1120],[675,1180,1182,1185],{"style":1181},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[675,1183],{"className":1184,"style":1129},[1128],[675,1186,1188],{"className":1187},[1133,1134,1135,1136],[675,1189,1040],{"className":1190},[718,719,1136],[675,1192,1144],{"className":1193},[1143],[675,1195,1197],{"className":1196},[1116],[675,1198,1200],{"className":1199,"style":1151},[1120],[675,1201],{},[675,1203,915],{"className":1204},[972],[675,1206,1208,1243],{"className":1207},[678],[675,1209,1211],{"className":1210},[682],[684,1212,1213],{"xmlns":686},[688,1214,1215,1240],{},[691,1216,1217,1220,1222,1224,1230,1232,1238],{},[694,1218,1219],{},"B",[902,1221,918],{},[902,1223,905],{"stretchy":904},[1046,1225,1226,1228],{},[694,1227,1050],{},[694,1229,1219],{},[902,1231,910],{"separator":705},[1046,1233,1234,1236],{},[694,1235,1059],{},[694,1237,1219],{},[902,1239,915],{"stretchy":904},[698,1241,1242],{"encoding":700},"B = (x_B, y_B)",[675,1244,1246,1265],{"className":1245,"ariaHidden":705},[704],[675,1247,1249,1252,1256,1259,1262],{"className":1248},[709],[675,1250],{"className":1251,"style":1076},[713],[675,1253,1219],{"className":1254,"style":1255},[718,719],"margin-right:0.0502em;",[675,1257],{"className":1258,"style":976},[964],[675,1260,918],{"className":1261},[980],[675,1263],{"className":1264,"style":976},[964],[675,1266,1268,1271,1274,1314,1317,1320,1360],{"className":1267},[709],[675,1269],{"className":1270,"style":946},[713],[675,1272,905],{"className":1273},[953],[675,1275,1277,1280],{"className":1276},[718],[675,1278,1050],{"className":1279},[718,719],[675,1281,1283],{"className":1282},[1107],[675,1284,1286,1306],{"className":1285},[1111,1112],[675,1287,1289,1303],{"className":1288},[1116],[675,1290,1292],{"className":1291,"style":1121},[1120],[675,1293,1294,1297],{"style":1124},[675,1295],{"className":1296,"style":1129},[1128],[675,1298,1300],{"className":1299},[1133,1134,1135,1136],[675,1301,1219],{"className":1302,"style":1255},[718,719,1136],[675,1304,1144],{"className":1305},[1143],[675,1307,1309],{"className":1308},[1116],[675,1310,1312],{"className":1311,"style":1151},[1120],[675,1313],{},[675,1315,910],{"className":1316},[960],[675,1318],{"className":1319,"style":965},[964],[675,1321,1323,1326],{"className":1322},[718],[675,1324,1059],{"className":1325,"style":1166},[718,719],[675,1327,1329],{"className":1328},[1107],[675,1330,1332,1352],{"className":1331},[1111,1112],[675,1333,1335,1349],{"className":1334},[1116],[675,1336,1338],{"className":1337,"style":1121},[1120],[675,1339,1340,1343],{"style":1181},[675,1341],{"className":1342,"style":1129},[1128],[675,1344,1346],{"className":1345},[1133,1134,1135,1136],[675,1347,1219],{"className":1348,"style":1255},[718,719,1136],[675,1350,1144],{"className":1351},[1143],[675,1353,1355],{"className":1354},[1116],[675,1356,1358],{"className":1357,"style":1151},[1120],[675,1359],{},[675,1361,915],{"className":1362},[972],[675,1364,1366],{"className":1365},[884],[675,1367,1369,1450],{"className":1368},[678],[675,1370,1372],{"className":1371},[682],[684,1373,1374],{"xmlns":686,"display":893},[688,1375,1376,1447],{},[691,1377,1378,1380,1382,1384,1386,1388,1390,1392],{},[694,1379,900],{},[902,1381,905],{"stretchy":904},[694,1383,1040],{},[902,1385,910],{"separator":705},[694,1387,1219],{},[902,1389,915],{"stretchy":904},[902,1391,918],{},[1393,1394,1395],"msqrt",{},[691,1396,1397,1399,1405,1407,1413,1422,1425,1427,1433,1435,1441],{},[902,1398,905],{"stretchy":904},[1046,1400,1401,1403],{},[694,1402,1050],{},[694,1404,1040],{},[902,1406,927],{},[1046,1408,1409,1411],{},[694,1410,1050],{},[694,1412,1219],{},[1414,1415,1416,1418],"msup",{},[902,1417,915],{"stretchy":904},[1419,1420,1421],"mn",{},"2",[902,1423,1424],{},"+",[902,1426,905],{"stretchy":904},[1046,1428,1429,1431],{},[694,1430,1059],{},[694,1432,1040],{},[902,1434,927],{},[1046,1436,1437,1439],{},[694,1438,1059],{},[694,1440,1219],{},[1414,1442,1443,1445],{},[902,1444,915],{"stretchy":904},[1419,1446,1421],{},[698,1448,1449],{"encoding":700},"d(A, B) = \\sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}",[675,1451,1453,1489],{"className":1452,"ariaHidden":705},[704],[675,1454,1456,1459,1462,1465,1468,1471,1474,1477,1480,1483,1486],{"className":1455},[709],[675,1457],{"className":1458,"style":946},[713],[675,1460,900],{"className":1461},[718,719],[675,1463,905],{"className":1464},[953],[675,1466,1040],{"className":1467},[718,719],[675,1469,910],{"className":1470},[960],[675,1472],{"className":1473,"style":965},[964],[675,1475,1219],{"className":1476,"style":1255},[718,719],[675,1478,915],{"className":1479},[972],[675,1481],{"className":1482,"style":976},[964],[675,1484,918],{"className":1485},[980],[675,1487],{"className":1488,"style":976},[964],[675,1490,1492,1496],{"className":1491},[709],[675,1493],{"className":1494,"style":1495},[713],"height:1.24em;vertical-align:-0.2561em;",[675,1497,1500],{"className":1498},[718,1499],"sqrt",[675,1501,1503,1802],{"className":1502},[1111,1112],[675,1504,1506,1799],{"className":1505},[1116],[675,1507,1510,1776],{"className":1508,"style":1509},[1120],"height:0.9839em;",[675,1511,1515,1519],{"className":1512,"style":1514},[1513],"svg-align","top:-3.2em;",[675,1516],{"className":1517,"style":1518},[1128],"height:3.2em;",[675,1520,1523,1526,1566,1569,1572,1575,1615,1646,1649,1652,1655,1658,1698,1701,1704,1707,1747],{"className":1521,"style":1522},[718],"padding-left:1em;",[675,1524,905],{"className":1525},[953],[675,1527,1529,1532],{"className":1528},[718],[675,1530,1050],{"className":1531},[718,719],[675,1533,1535],{"className":1534},[1107],[675,1536,1538,1558],{"className":1537},[1111,1112],[675,1539,1541,1555],{"className":1540},[1116],[675,1542,1544],{"className":1543,"style":1121},[1120],[675,1545,1546,1549],{"style":1124},[675,1547],{"className":1548,"style":1129},[1128],[675,1550,1552],{"className":1551},[1133,1134,1135,1136],[675,1553,1040],{"className":1554},[718,719,1136],[675,1556,1144],{"className":1557},[1143],[675,1559,1561],{"className":1560},[1116],[675,1562,1564],{"className":1563,"style":1151},[1120],[675,1565],{},[675,1567],{"className":1568,"style":999},[964],[675,1570,927],{"className":1571},[1003],[675,1573],{"className":1574,"style":999},[964],[675,1576,1578,1581],{"className":1577},[718],[675,1579,1050],{"className":1580},[718,719],[675,1582,1584],{"className":1583},[1107],[675,1585,1587,1607],{"className":1586},[1111,1112],[675,1588,1590,1604],{"className":1589},[1116],[675,1591,1593],{"className":1592,"style":1121},[1120],[675,1594,1595,1598],{"style":1124},[675,1596],{"className":1597,"style":1129},[1128],[675,1599,1601],{"className":1600},[1133,1134,1135,1136],[675,1602,1219],{"className":1603,"style":1255},[718,719,1136],[675,1605,1144],{"className":1606},[1143],[675,1608,1610],{"className":1609},[1116],[675,1611,1613],{"className":1612,"style":1151},[1120],[675,1614],{},[675,1616,1618,1621],{"className":1617},[972],[675,1619,915],{"className":1620},[972],[675,1622,1624],{"className":1623},[1107],[675,1625,1627],{"className":1626},[1111],[675,1628,1630],{"className":1629},[1116],[675,1631,1634],{"className":1632,"style":1633},[1120],"height:0.7401em;",[675,1635,1637,1640],{"style":1636},"top:-2.989em;margin-right:0.05em;",[675,1638],{"className":1639,"style":1129},[1128],[675,1641,1643],{"className":1642},[1133,1134,1135,1136],[675,1644,1421],{"className":1645},[718,1136],[675,1647],{"className":1648,"style":999},[964],[675,1650,1424],{"className":1651},[1003],[675,1653],{"className":1654,"style":999},[964],[675,1656,905],{"className":1657},[953],[675,1659,1661,1664],{"className":1660},[718],[675,1662,1059],{"className":1663,"style":1166},[718,719],[675,1665,1667],{"className":1666},[1107],[675,1668,1670,1690],{"className":1669},[1111,1112],[675,1671,1673,1687],{"className":1672},[1116],[675,1674,1676],{"className":1675,"style":1121},[1120],[675,1677,1678,1681],{"style":1181},[675,1679],{"className":1680,"style":1129},[1128],[675,1682,1684],{"className":1683},[1133,1134,1135,1136],[675,1685,1040],{"className":1686},[718,719,1136],[675,1688,1144],{"className":1689},[1143],[675,1691,1693],{"className":1692},[1116],[675,1694,1696],{"className":1695,"style":1151},[1120],[675,1697],{},[675,1699],{"className":1700,"style":999},[964],[675,1702,927],{"className":1703},[1003],[675,1705],{"className":1706,"style":999},[964],[675,1708,1710,1713],{"className":1709},[718],[675,1711,1059],{"className":1712,"style":1166},[718,719],[675,1714,1716],{"className":1715},[1107],[675,1717,1719,1739],{"className":1718},[1111,1112],[675,1720,1722,1736],{"className":1721},[1116],[675,1723,1725],{"className":1724,"style":1121},[1120],[675,1726,1727,1730],{"style":1181},[675,1728],{"className":1729,"style":1129},[1128],[675,1731,1733],{"className":1732},[1133,1134,1135,1136],[675,1734,1219],{"className":1735,"style":1255},[718,719,1136],[675,1737,1144],{"className":1738},[1143],[675,1740,1742],{"className":1741},[1116],[675,1743,1745],{"className":1744,"style":1151},[1120],[675,1746],{},[675,1748,1750,1753],{"className":1749},[972],[675,1751,915],{"className":1752},[972],[675,1754,1756],{"className":1755},[1107],[675,1757,1759],{"className":1758},[1111],[675,1760,1762],{"className":1761},[1116],[675,1763,1765],{"className":1764,"style":1633},[1120],[675,1766,1767,1770],{"style":1636},[675,1768],{"className":1769,"style":1129},[1128],[675,1771,1773],{"className":1772},[1133,1134,1135,1136],[675,1774,1421],{"className":1775},[718,1136],[675,1777,1779,1782],{"style":1778},"top:-2.9439em;",[675,1780],{"className":1781,"style":1518},[1128],[675,1783,1787],{"className":1784,"style":1786},[1785],"hide-tail","min-width:1.02em;height:1.28em;",[1788,1789,1795],"svg",{"xmlns":1790,"width":1791,"height":1792,"viewBox":1793,"preserveAspectRatio":1794},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[1796,1797],"path",{"d":1798},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[675,1800,1144],{"className":1801},[1143],[675,1803,1805],{"className":1804},[1116],[675,1806,1809],{"className":1807,"style":1808},[1120],"height:0.2561em;",[675,1810],{},[598,1812,1813],{},"En Python :",[1815,1816,1821],"pre",{"className":1817,"code":1818,"language":1819,"meta":1820,"style":1820},"language-python shiki shiki-themes github-light github-light github-dark","import math\n\ndef distance(a, b):\n    \"\"\"Distance euclidienne entre deux points 2D.\"\"\"\n    return math.sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2)\n\nprint(distance((0, 0), (3, 4)))   # 5.0\n","python","",[1822,1823,1824,1836,1843,1856,1863,1922,1927],"code",{"__ignoreMap":1820},[675,1825,1828,1832],{"class":1826,"line":1827},"line",1,[675,1829,1831],{"class":1830},"s8jYJ","import",[675,1833,1835],{"class":1834},"sxrX7"," math\n",[675,1837,1839],{"class":1826,"line":1838},2,[675,1840,1842],{"emptyLinePlaceholder":1841},true,"\n",[675,1844,1846,1849,1853],{"class":1826,"line":1845},3,[675,1847,1848],{"class":1830},"def",[675,1850,1852],{"class":1851},"snPdu"," distance",[675,1854,1855],{"class":1834},"(a, b):\n",[675,1857,1859],{"class":1826,"line":1858},4,[675,1860,1862],{"class":1861},"sIIMD","    \"\"\"Distance euclidienne entre deux points 2D.\"\"\"\n",[675,1864,1866,1869,1872,1876,1879,1882,1885,1887,1890,1893,1896,1899,1902,1905,1907,1909,1911,1913,1915,1917,1919],{"class":1826,"line":1865},5,[675,1867,1868],{"class":1830},"    return",[675,1870,1871],{"class":1834}," math.sqrt((a[",[675,1873,1875],{"class":1874},"sBjJW","0",[675,1877,1878],{"class":1834},"] ",[675,1880,1881],{"class":1830},"-",[675,1883,1884],{"class":1834}," b[",[675,1886,1875],{"class":1874},[675,1888,1889],{"class":1834},"]) ",[675,1891,1892],{"class":1830},"**",[675,1894,1895],{"class":1874}," 2",[675,1897,1898],{"class":1830}," +",[675,1900,1901],{"class":1834}," (a[",[675,1903,1904],{"class":1874},"1",[675,1906,1878],{"class":1834},[675,1908,1881],{"class":1830},[675,1910,1884],{"class":1834},[675,1912,1904],{"class":1874},[675,1914,1889],{"class":1834},[675,1916,1892],{"class":1830},[675,1918,1895],{"class":1874},[675,1920,1921],{"class":1834},")\n",[675,1923,1925],{"class":1826,"line":1924},6,[675,1926,1842],{"emptyLinePlaceholder":1841},[675,1928,1930,1933,1936,1938,1941,1943,1946,1949,1951,1954,1957],{"class":1826,"line":1929},7,[675,1931,1932],{"class":1874},"print",[675,1934,1935],{"class":1834},"(distance((",[675,1937,1875],{"class":1874},[675,1939,1940],{"class":1834},", ",[675,1942,1875],{"class":1874},[675,1944,1945],{"class":1834},"), (",[675,1947,1948],{"class":1874},"3",[675,1950,1940],{"class":1834},[675,1952,1953],{"class":1874},"4",[675,1955,1956],{"class":1834},")))   ",[675,1958,1960],{"class":1959},"sCsY4","# 5.0\n",[1962,1963,1964,1967],"note",{},[598,1965,1966],{},"La distance euclidienne se généralise à un nombre quelconque de dimensions :",[675,1968,1970],{"className":1969},[884],[675,1971,1973,2048],{"className":1972},[678],[675,1974,1976],{"className":1975},[682],[684,1977,1978],{"xmlns":686,"display":893},[688,1979,1980,2045],{},[691,1981,1982,1984,1986,1988,1990,1992,1994,1996],{},[694,1983,900],{},[902,1985,905],{"stretchy":904},[694,1987,1040],{},[902,1989,910],{"separator":705},[694,1991,1219],{},[902,1993,915],{"stretchy":904},[902,1995,918],{},[1393,1997,1998],{},[691,1999,2000,2018,2020,2029,2031,2039],{},[2001,2002,2003,2006,2015],"munderover",{},[902,2004,2005],{},"∑",[691,2007,2008,2011,2013],{},[694,2009,2010],{},"i",[902,2012,918],{},[1419,2014,1904],{},[694,2016,2017],{},"n",[902,2019,905],{"stretchy":904},[2021,2022,2023,2025,2027],"msubsup",{},[694,2024,1050],{},[694,2026,2010],{},[694,2028,1040],{},[902,2030,927],{},[2021,2032,2033,2035,2037],{},[694,2034,1050],{},[694,2036,2010],{},[694,2038,1219],{},[1414,2040,2041,2043],{},[902,2042,915],{"stretchy":904},[1419,2044,1421],{},[698,2046,2047],{"encoding":700},"d(A, B) = \\sqrt{\\sum_{i=1}^{n}(x_i^A - x_i^B)^2}",[675,2049,2051,2087],{"className":2050,"ariaHidden":705},[704],[675,2052,2054,2057,2060,2063,2066,2069,2072,2075,2078,2081,2084],{"className":2053},[709],[675,2055],{"className":2056,"style":946},[713],[675,2058,900],{"className":2059},[718,719],[675,2061,905],{"className":2062},[953],[675,2064,1040],{"className":2065},[718,719],[675,2067,910],{"className":2068},[960],[675,2070],{"className":2071,"style":965},[964],[675,2073,1219],{"className":2074,"style":1255},[718,719],[675,2076,915],{"className":2077},[972],[675,2079],{"className":2080,"style":976},[964],[675,2082,918],{"className":2083},[980],[675,2085],{"className":2086,"style":976},[964],[675,2088,2090,2094],{"className":2089},[709],[675,2091],{"className":2092,"style":2093},[713],"height:3.1568em;vertical-align:-1.2777em;",[675,2095,2097],{"className":2096},[718,1499],[675,2098,2100,2363],{"className":2099},[1111,1112],[675,2101,2103,2360],{"className":2102},[1116],[675,2104,2107,2343],{"className":2105,"style":2106},[1120],"height:1.8791em;",[675,2108,2111,2115],{"className":2109,"style":2110},[1513],"top:-5.1168em;",[675,2112],{"className":2113,"style":2114},[1128],"height:5.1168em;",[675,2116,2119,2196,2199,2254,2257,2260,2263,2314],{"className":2117,"style":2118},[718],"padding-left:1.056em;",[675,2120,2124],{"className":2121},[2122,2123],"mop","op-limits",[675,2125,2127,2187],{"className":2126},[1111,1112],[675,2128,2130,2184],{"className":2129},[1116],[675,2131,2134,2156,2169],{"className":2132,"style":2133},[1120],"height:1.6514em;",[675,2135,2137,2141],{"style":2136},"top:-1.8723em;margin-left:0em;",[675,2138],{"className":2139,"style":2140},[1128],"height:3.05em;",[675,2142,2144],{"className":2143},[1133,1134,1135,1136],[675,2145,2147,2150,2153],{"className":2146},[718,1136],[675,2148,2010],{"className":2149},[718,719,1136],[675,2151,918],{"className":2152},[980,1136],[675,2154,1904],{"className":2155},[718,1136],[675,2157,2159,2162],{"style":2158},"top:-3.05em;",[675,2160],{"className":2161,"style":2140},[1128],[675,2163,2164],{},[675,2165,2005],{"className":2166},[2122,2167,2168],"op-symbol","large-op",[675,2170,2172,2175],{"style":2171},"top:-4.3em;margin-left:0em;",[675,2173],{"className":2174,"style":2140},[1128],[675,2176,2178],{"className":2177},[1133,1134,1135,1136],[675,2179,2181],{"className":2180},[718,1136],[675,2182,2017],{"className":2183},[718,719,1136],[675,2185,1144],{"className":2186},[1143],[675,2188,2190],{"className":2189},[1116],[675,2191,2194],{"className":2192,"style":2193},[1120],"height:1.2777em;",[675,2195],{},[675,2197,905],{"className":2198},[953],[675,2200,2202,2205],{"className":2201},[718],[675,2203,1050],{"className":2204},[718,719],[675,2206,2208],{"className":2207},[1107],[675,2209,2211,2245],{"className":2210},[1111,1112],[675,2212,2214,2242],{"className":2213},[1116],[675,2215,2218,2230],{"className":2216,"style":2217},[1120],"height:0.8231em;",[675,2219,2221,2224],{"style":2220},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[675,2222],{"className":2223,"style":1129},[1128],[675,2225,2227],{"className":2226},[1133,1134,1135,1136],[675,2228,2010],{"className":2229},[718,719,1136],[675,2231,2233,2236],{"style":2232},"top:-3.0448em;margin-right:0.05em;",[675,2234],{"className":2235,"style":1129},[1128],[675,2237,2239],{"className":2238},[1133,1134,1135,1136],[675,2240,1040],{"className":2241},[718,719,1136],[675,2243,1144],{"className":2244},[1143],[675,2246,2248],{"className":2247},[1116],[675,2249,2252],{"className":2250,"style":2251},[1120],"height:0.2769em;",[675,2253],{},[675,2255],{"className":2256,"style":999},[964],[675,2258,927],{"className":2259},[1003],[675,2261],{"className":2262,"style":999},[964],[675,2264,2266,2269],{"className":2265},[718],[675,2267,1050],{"className":2268},[718,719],[675,2270,2272],{"className":2271},[1107],[675,2273,2275,2306],{"className":2274},[1111,1112],[675,2276,2278,2303],{"className":2277},[1116],[675,2279,2281,2292],{"className":2280,"style":2217},[1120],[675,2282,2283,2286],{"style":2220},[675,2284],{"className":2285,"style":1129},[1128],[675,2287,2289],{"className":2288},[1133,1134,1135,1136],[675,2290,2010],{"className":2291},[718,719,1136],[675,2293,2294,2297],{"style":2232},[675,2295],{"className":2296,"style":1129},[1128],[675,2298,2300],{"className":2299},[1133,1134,1135,1136],[675,2301,1219],{"className":2302,"style":1255},[718,719,1136],[675,2304,1144],{"className":2305},[1143],[675,2307,2309],{"className":2308},[1116],[675,2310,2312],{"className":2311,"style":2251},[1120],[675,2313],{},[675,2315,2317,2320],{"className":2316},[972],[675,2318,915],{"className":2319},[972],[675,2321,2323],{"className":2322},[1107],[675,2324,2326],{"className":2325},[1111],[675,2327,2329],{"className":2328},[1116],[675,2330,2332],{"className":2331,"style":1633},[1120],[675,2333,2334,2337],{"style":1636},[675,2335],{"className":2336,"style":1129},[1128],[675,2338,2340],{"className":2339},[1133,1134,1135,1136],[675,2341,1421],{"className":2342},[718,1136],[675,2344,2346,2349],{"style":2345},"top:-3.8391em;",[675,2347],{"className":2348,"style":2114},[1128],[675,2350,2353],{"className":2351,"style":2352},[1785],"min-width:0.742em;height:3.1968em;",[1788,2354,2357],{"xmlns":1790,"width":1791,"height":2355,"viewBox":2356,"preserveAspectRatio":1794},"3.1968em","0 0 400000 3196",[1796,2358],{"d":2359},"M702 80H40000040\nH742v3062l-4 4-4 4c-.667.7 -2 1.5-4 2.5s-4.167 1.833-6.5 2.5-5.5 1-9.5 1\nh-12l-28-84c-16.667-52-96.667 -294.333-240-727l-212 -643 -85 170\nc-4-3.333-8.333-7.667-13 -13l-13-13l77-155 77-156c66 199.333 139 419.667\n219 661 l218 661zM702 80H400000v40H742z",[675,2361,1144],{"className":2362},[1143],[675,2364,2366],{"className":2365},[1116],[675,2367,2369],{"className":2368,"style":2193},[1120],[675,2370],{},[593,2372,2374],{"id":2373},"lalgorithme-k-nn-complet","L'algorithme k-NN complet",[1962,2376,2377,2391,2422],{},[598,2378,2379,2382,2383,2386,2387,2390],{},[602,2380,2381],{},"Boîte à outils Python."," Le code ci-dessous s'appuie sur quelques briques\nvues en ",[602,2384,2385],{},"PC"," (list-comprehension) et ",[602,2388,2389],{},"PG"," (lambda, opérateurs sur\nitérables) :",[2392,2393,2394,2404,2412],"ul",{},[658,2395,2396,2399,2400,2403],{},[1822,2397,2398],{},"zip(a, b)"," parcourt ",[602,2401,2402],{},"en parallèle"," deux listes (utile pour comparer\ncomposante par composante les coordonnées de deux points).",[658,2405,2406,2409,2410,722],{},[1822,2407,2408],{},"Counter(voisins).most_common(1)"," compte rapidement les occurrences et\nrenvoie la ",[602,2411,728],{},[658,2413,2414,2417,2418,2421],{},[1822,2415,2416],{},"[expr for x in liste]"," est une ",[602,2419,2420],{},"list-comprehension"," : on construit une\nnouvelle liste en une ligne.",[598,2423,2424,2425,2428],{},"Pas la peine de tout maîtriser pour comprendre l'algorithme — concentrez-vous\nsur les ",[602,2426,2427],{},"quatre étapes"," numérotées.",[1815,2430,2432],{"className":1817,"code":2431,"language":1819,"meta":1820,"style":1820},"import math\nfrom collections import Counter\n\ndef distance(a, b):\n    return math.sqrt(sum((ai - bi) ** 2 for ai, bi in zip(a, b)))\n\ndef knn(donnees, nouveau, k):\n    \"\"\"donnees : liste de tuples (point, classe).\n    nouveau : un point à classer.\n    k : nombre de voisins à considérer.\n    Retourne la classe prédite pour nouveau.\"\"\"\n    # 1. Distances entre nouveau et chaque point étiqueté\n    distances = [(distance(point, nouveau), classe) for point, classe in donnees]\n    # 2. Tri par distance croissante\n    distances.sort()\n    # 3. Récupération des classes des k plus proches\n    voisins = [classe for _, classe in distances[:k]]\n    # 4. Vote majoritaire\n    return Counter(voisins).most_common(1)[0][0]\n\n# Exemple : classifier un fruit par son poids et son diamètre\nfruits = [\n    ((150, 7), \"pomme\"),\n    ((170, 7.5), \"pomme\"),\n    ((140, 6.8), \"pomme\"),\n    ((120, 5.5), \"mandarine\"),\n    ((110, 5), \"mandarine\"),\n    ((130, 5.8), \"mandarine\"),\n]\ninconnu = (135, 6.2)\nprint(knn(fruits, inconnu, k=3))\n# 'mandarine' ou 'pomme' selon les plus proches\n",[1822,2433,2434,2440,2453,2457,2465,2502,2506,2516,2522,2528,2534,2540,2546,2568,2574,2580,2586,2607,2613,2636,2641,2647,2658,2681,2700,2719,2739,2758,2777,2782,2803,2821],{"__ignoreMap":1820},[675,2435,2436,2438],{"class":1826,"line":1827},[675,2437,1831],{"class":1830},[675,2439,1835],{"class":1834},[675,2441,2442,2445,2448,2450],{"class":1826,"line":1838},[675,2443,2444],{"class":1830},"from",[675,2446,2447],{"class":1834}," collections ",[675,2449,1831],{"class":1830},[675,2451,2452],{"class":1834}," Counter\n",[675,2454,2455],{"class":1826,"line":1845},[675,2456,1842],{"emptyLinePlaceholder":1841},[675,2458,2459,2461,2463],{"class":1826,"line":1858},[675,2460,1848],{"class":1830},[675,2462,1852],{"class":1851},[675,2464,1855],{"class":1834},[675,2466,2467,2469,2472,2475,2478,2480,2483,2485,2487,2490,2493,2496,2499],{"class":1826,"line":1865},[675,2468,1868],{"class":1830},[675,2470,2471],{"class":1834}," math.sqrt(",[675,2473,2474],{"class":1874},"sum",[675,2476,2477],{"class":1834},"((ai ",[675,2479,1881],{"class":1830},[675,2481,2482],{"class":1834}," bi) ",[675,2484,1892],{"class":1830},[675,2486,1895],{"class":1874},[675,2488,2489],{"class":1830}," for",[675,2491,2492],{"class":1834}," ai, bi ",[675,2494,2495],{"class":1830},"in",[675,2497,2498],{"class":1874}," zip",[675,2500,2501],{"class":1834},"(a, b)))\n",[675,2503,2504],{"class":1826,"line":1924},[675,2505,1842],{"emptyLinePlaceholder":1841},[675,2507,2508,2510,2513],{"class":1826,"line":1929},[675,2509,1848],{"class":1830},[675,2511,2512],{"class":1851}," knn",[675,2514,2515],{"class":1834},"(donnees, nouveau, k):\n",[675,2517,2519],{"class":1826,"line":2518},8,[675,2520,2521],{"class":1861},"    \"\"\"donnees : liste de tuples (point, classe).\n",[675,2523,2525],{"class":1826,"line":2524},9,[675,2526,2527],{"class":1861},"    nouveau : un point à classer.\n",[675,2529,2531],{"class":1826,"line":2530},10,[675,2532,2533],{"class":1861},"    k : nombre de voisins à considérer.\n",[675,2535,2537],{"class":1826,"line":2536},11,[675,2538,2539],{"class":1861},"    Retourne la classe prédite pour nouveau.\"\"\"\n",[675,2541,2543],{"class":1826,"line":2542},12,[675,2544,2545],{"class":1959},"    # 1. Distances entre nouveau et chaque point étiqueté\n",[675,2547,2549,2552,2554,2557,2560,2563,2565],{"class":1826,"line":2548},13,[675,2550,2551],{"class":1834},"    distances ",[675,2553,918],{"class":1830},[675,2555,2556],{"class":1834}," [(distance(point, nouveau), classe) ",[675,2558,2559],{"class":1830},"for",[675,2561,2562],{"class":1834}," point, classe ",[675,2564,2495],{"class":1830},[675,2566,2567],{"class":1834}," donnees]\n",[675,2569,2571],{"class":1826,"line":2570},14,[675,2572,2573],{"class":1959},"    # 2. Tri par distance croissante\n",[675,2575,2577],{"class":1826,"line":2576},15,[675,2578,2579],{"class":1834},"    distances.sort()\n",[675,2581,2583],{"class":1826,"line":2582},16,[675,2584,2585],{"class":1959},"    # 3. Récupération des classes des k plus proches\n",[675,2587,2589,2592,2594,2597,2599,2602,2604],{"class":1826,"line":2588},17,[675,2590,2591],{"class":1834},"    voisins ",[675,2593,918],{"class":1830},[675,2595,2596],{"class":1834}," [classe ",[675,2598,2559],{"class":1830},[675,2600,2601],{"class":1834}," _, classe ",[675,2603,2495],{"class":1830},[675,2605,2606],{"class":1834}," distances[:k]]\n",[675,2608,2610],{"class":1826,"line":2609},18,[675,2611,2612],{"class":1959},"    # 4. Vote majoritaire\n",[675,2614,2616,2618,2621,2623,2626,2628,2631,2633],{"class":1826,"line":2615},19,[675,2617,1868],{"class":1830},[675,2619,2620],{"class":1834}," Counter(voisins).most_common(",[675,2622,1904],{"class":1874},[675,2624,2625],{"class":1834},")[",[675,2627,1875],{"class":1874},[675,2629,2630],{"class":1834},"][",[675,2632,1875],{"class":1874},[675,2634,2635],{"class":1834},"]\n",[675,2637,2639],{"class":1826,"line":2638},20,[675,2640,1842],{"emptyLinePlaceholder":1841},[675,2642,2644],{"class":1826,"line":2643},21,[675,2645,2646],{"class":1959},"# Exemple : classifier un fruit par son poids et son diamètre\n",[675,2648,2650,2653,2655],{"class":1826,"line":2649},22,[675,2651,2652],{"class":1834},"fruits ",[675,2654,918],{"class":1830},[675,2656,2657],{"class":1834}," [\n",[675,2659,2661,2664,2667,2669,2672,2675,2678],{"class":1826,"line":2660},23,[675,2662,2663],{"class":1834},"    ((",[675,2665,2666],{"class":1874},"150",[675,2668,1940],{"class":1834},[675,2670,2671],{"class":1874},"7",[675,2673,2674],{"class":1834},"), ",[675,2676,2677],{"class":1861},"\"pomme\"",[675,2679,2680],{"class":1834},"),\n",[675,2682,2684,2686,2689,2691,2694,2696,2698],{"class":1826,"line":2683},24,[675,2685,2663],{"class":1834},[675,2687,2688],{"class":1874},"170",[675,2690,1940],{"class":1834},[675,2692,2693],{"class":1874},"7.5",[675,2695,2674],{"class":1834},[675,2697,2677],{"class":1861},[675,2699,2680],{"class":1834},[675,2701,2703,2705,2708,2710,2713,2715,2717],{"class":1826,"line":2702},25,[675,2704,2663],{"class":1834},[675,2706,2707],{"class":1874},"140",[675,2709,1940],{"class":1834},[675,2711,2712],{"class":1874},"6.8",[675,2714,2674],{"class":1834},[675,2716,2677],{"class":1861},[675,2718,2680],{"class":1834},[675,2720,2722,2724,2727,2729,2732,2734,2737],{"class":1826,"line":2721},26,[675,2723,2663],{"class":1834},[675,2725,2726],{"class":1874},"120",[675,2728,1940],{"class":1834},[675,2730,2731],{"class":1874},"5.5",[675,2733,2674],{"class":1834},[675,2735,2736],{"class":1861},"\"mandarine\"",[675,2738,2680],{"class":1834},[675,2740,2742,2744,2747,2749,2752,2754,2756],{"class":1826,"line":2741},27,[675,2743,2663],{"class":1834},[675,2745,2746],{"class":1874},"110",[675,2748,1940],{"class":1834},[675,2750,2751],{"class":1874},"5",[675,2753,2674],{"class":1834},[675,2755,2736],{"class":1861},[675,2757,2680],{"class":1834},[675,2759,2761,2763,2766,2768,2771,2773,2775],{"class":1826,"line":2760},28,[675,2762,2663],{"class":1834},[675,2764,2765],{"class":1874},"130",[675,2767,1940],{"class":1834},[675,2769,2770],{"class":1874},"5.8",[675,2772,2674],{"class":1834},[675,2774,2736],{"class":1861},[675,2776,2680],{"class":1834},[675,2778,2780],{"class":1826,"line":2779},29,[675,2781,2635],{"class":1834},[675,2783,2785,2788,2790,2793,2796,2798,2801],{"class":1826,"line":2784},30,[675,2786,2787],{"class":1834},"inconnu ",[675,2789,918],{"class":1830},[675,2791,2792],{"class":1834}," (",[675,2794,2795],{"class":1874},"135",[675,2797,1940],{"class":1834},[675,2799,2800],{"class":1874},"6.2",[675,2802,1921],{"class":1834},[675,2804,2806,2808,2811,2814,2816,2818],{"class":1826,"line":2805},31,[675,2807,1932],{"class":1874},[675,2809,2810],{"class":1834},"(knn(fruits, inconnu, ",[675,2812,696],{"class":2813},"sP4rz",[675,2815,918],{"class":1830},[675,2817,1948],{"class":1874},[675,2819,2820],{"class":1834},"))\n",[675,2822,2824],{"class":1826,"line":2823},32,[675,2825,2826],{"class":1959},"# 'mandarine' ou 'pomme' selon les plus proches\n",[2828,2829,2830],"python-snippet",{},[1815,2831,2833],{"className":1817,"code":2832,"language":1819,"meta":1820,"style":1820},"import math\nfrom collections import Counter\n\ndef distance(a, b):\n    return math.sqrt(sum((ai - bi) ** 2 for ai, bi in zip(a, b)))\n\ndef knn(donnees, nouveau, k):\n    distances = [(distance(p, nouveau), c) for p, c in donnees]\n    distances.sort()\n    voisins = [c for _, c in distances[:k]]\n    return Counter(voisins).most_common(1)[0][0]\n\n# Données : (poids en g, diamètre en cm) → classe\nfruits = [\n    ((150, 7), \"pomme\"),\n    ((170, 7.5), \"pomme\"),\n    ((140, 6.8), \"pomme\"),\n    ((120, 5.5), \"mandarine\"),\n    ((110, 5), \"mandarine\"),\n    ((130, 5.8), \"mandarine\"),\n]\n\nfor inconnu in [(135, 6.2), (160, 7.1), (115, 5.2)]:\n    print(f\"{inconnu} → {knn(fruits, inconnu, k=3)}\")\n",[1822,2834,2835,2841,2851,2855,2863,2891,2895,2903,2921,2925,2943,2961,2965,2970,2978,2994,3010,3026,3042,3058,3074,3078,3082,3123],{"__ignoreMap":1820},[675,2836,2837,2839],{"class":1826,"line":1827},[675,2838,1831],{"class":1830},[675,2840,1835],{"class":1834},[675,2842,2843,2845,2847,2849],{"class":1826,"line":1838},[675,2844,2444],{"class":1830},[675,2846,2447],{"class":1834},[675,2848,1831],{"class":1830},[675,2850,2452],{"class":1834},[675,2852,2853],{"class":1826,"line":1845},[675,2854,1842],{"emptyLinePlaceholder":1841},[675,2856,2857,2859,2861],{"class":1826,"line":1858},[675,2858,1848],{"class":1830},[675,2860,1852],{"class":1851},[675,2862,1855],{"class":1834},[675,2864,2865,2867,2869,2871,2873,2875,2877,2879,2881,2883,2885,2887,2889],{"class":1826,"line":1865},[675,2866,1868],{"class":1830},[675,2868,2471],{"class":1834},[675,2870,2474],{"class":1874},[675,2872,2477],{"class":1834},[675,2874,1881],{"class":1830},[675,2876,2482],{"class":1834},[675,2878,1892],{"class":1830},[675,2880,1895],{"class":1874},[675,2882,2489],{"class":1830},[675,2884,2492],{"class":1834},[675,2886,2495],{"class":1830},[675,2888,2498],{"class":1874},[675,2890,2501],{"class":1834},[675,2892,2893],{"class":1826,"line":1924},[675,2894,1842],{"emptyLinePlaceholder":1841},[675,2896,2897,2899,2901],{"class":1826,"line":1929},[675,2898,1848],{"class":1830},[675,2900,2512],{"class":1851},[675,2902,2515],{"class":1834},[675,2904,2905,2907,2909,2912,2914,2917,2919],{"class":1826,"line":2518},[675,2906,2551],{"class":1834},[675,2908,918],{"class":1830},[675,2910,2911],{"class":1834}," [(distance(p, nouveau), c) ",[675,2913,2559],{"class":1830},[675,2915,2916],{"class":1834}," p, c ",[675,2918,2495],{"class":1830},[675,2920,2567],{"class":1834},[675,2922,2923],{"class":1826,"line":2524},[675,2924,2579],{"class":1834},[675,2926,2927,2929,2931,2934,2936,2939,2941],{"class":1826,"line":2530},[675,2928,2591],{"class":1834},[675,2930,918],{"class":1830},[675,2932,2933],{"class":1834}," [c ",[675,2935,2559],{"class":1830},[675,2937,2938],{"class":1834}," _, c ",[675,2940,2495],{"class":1830},[675,2942,2606],{"class":1834},[675,2944,2945,2947,2949,2951,2953,2955,2957,2959],{"class":1826,"line":2536},[675,2946,1868],{"class":1830},[675,2948,2620],{"class":1834},[675,2950,1904],{"class":1874},[675,2952,2625],{"class":1834},[675,2954,1875],{"class":1874},[675,2956,2630],{"class":1834},[675,2958,1875],{"class":1874},[675,2960,2635],{"class":1834},[675,2962,2963],{"class":1826,"line":2542},[675,2964,1842],{"emptyLinePlaceholder":1841},[675,2966,2967],{"class":1826,"line":2548},[675,2968,2969],{"class":1959},"# Données : (poids en g, diamètre en cm) → classe\n",[675,2971,2972,2974,2976],{"class":1826,"line":2570},[675,2973,2652],{"class":1834},[675,2975,918],{"class":1830},[675,2977,2657],{"class":1834},[675,2979,2980,2982,2984,2986,2988,2990,2992],{"class":1826,"line":2576},[675,2981,2663],{"class":1834},[675,2983,2666],{"class":1874},[675,2985,1940],{"class":1834},[675,2987,2671],{"class":1874},[675,2989,2674],{"class":1834},[675,2991,2677],{"class":1861},[675,2993,2680],{"class":1834},[675,2995,2996,2998,3000,3002,3004,3006,3008],{"class":1826,"line":2582},[675,2997,2663],{"class":1834},[675,2999,2688],{"class":1874},[675,3001,1940],{"class":1834},[675,3003,2693],{"class":1874},[675,3005,2674],{"class":1834},[675,3007,2677],{"class":1861},[675,3009,2680],{"class":1834},[675,3011,3012,3014,3016,3018,3020,3022,3024],{"class":1826,"line":2588},[675,3013,2663],{"class":1834},[675,3015,2707],{"class":1874},[675,3017,1940],{"class":1834},[675,3019,2712],{"class":1874},[675,3021,2674],{"class":1834},[675,3023,2677],{"class":1861},[675,3025,2680],{"class":1834},[675,3027,3028,3030,3032,3034,3036,3038,3040],{"class":1826,"line":2609},[675,3029,2663],{"class":1834},[675,3031,2726],{"class":1874},[675,3033,1940],{"class":1834},[675,3035,2731],{"class":1874},[675,3037,2674],{"class":1834},[675,3039,2736],{"class":1861},[675,3041,2680],{"class":1834},[675,3043,3044,3046,3048,3050,3052,3054,3056],{"class":1826,"line":2615},[675,3045,2663],{"class":1834},[675,3047,2746],{"class":1874},[675,3049,1940],{"class":1834},[675,3051,2751],{"class":1874},[675,3053,2674],{"class":1834},[675,3055,2736],{"class":1861},[675,3057,2680],{"class":1834},[675,3059,3060,3062,3064,3066,3068,3070,3072],{"class":1826,"line":2638},[675,3061,2663],{"class":1834},[675,3063,2765],{"class":1874},[675,3065,1940],{"class":1834},[675,3067,2770],{"class":1874},[675,3069,2674],{"class":1834},[675,3071,2736],{"class":1861},[675,3073,2680],{"class":1834},[675,3075,3076],{"class":1826,"line":2643},[675,3077,2635],{"class":1834},[675,3079,3080],{"class":1826,"line":2649},[675,3081,1842],{"emptyLinePlaceholder":1841},[675,3083,3084,3086,3089,3091,3094,3096,3098,3100,3102,3105,3107,3110,3112,3115,3117,3120],{"class":1826,"line":2660},[675,3085,2559],{"class":1830},[675,3087,3088],{"class":1834}," inconnu ",[675,3090,2495],{"class":1830},[675,3092,3093],{"class":1834}," [(",[675,3095,2795],{"class":1874},[675,3097,1940],{"class":1834},[675,3099,2800],{"class":1874},[675,3101,1945],{"class":1834},[675,3103,3104],{"class":1874},"160",[675,3106,1940],{"class":1834},[675,3108,3109],{"class":1874},"7.1",[675,3111,1945],{"class":1834},[675,3113,3114],{"class":1874},"115",[675,3116,1940],{"class":1834},[675,3118,3119],{"class":1874},"5.2",[675,3121,3122],{"class":1834},")]:\n",[675,3124,3125,3128,3130,3133,3136,3139,3142,3145,3148,3150,3153,3155,3157,3159,3161,3163,3165],{"class":1826,"line":2683},[675,3126,3127],{"class":1874},"    print",[675,3129,905],{"class":1834},[675,3131,3132],{"class":1830},"f",[675,3134,3135],{"class":1861},"\"",[675,3137,3138],{"class":1874},"{",[675,3140,3141],{"class":1834},"inconnu",[675,3143,3144],{"class":1874},"}",[675,3146,3147],{"class":1861}," → ",[675,3149,3138],{"class":1874},[675,3151,3152],{"class":1834},"knn(fruits, inconnu, ",[675,3154,696],{"class":2813},[675,3156,918],{"class":1830},[675,3158,1948],{"class":1874},[675,3160,915],{"class":1834},[675,3162,3144],{"class":1874},[675,3164,3135],{"class":1861},[675,3166,1921],{"class":1834},[593,3168,3170,3171],{"id":3169},"choisir-kkk","Choisir ",[675,3172,3174,3187],{"className":3173},[678],[675,3175,3177],{"className":3176},[682],[684,3178,3179],{"xmlns":686},[688,3180,3181,3185],{},[691,3182,3183],{},[694,3184,696],{},[698,3186,696],{"encoding":700},[675,3188,3190],{"className":3189,"ariaHidden":705},[704],[675,3191,3193,3196],{"className":3192},[709],[675,3194],{"className":3195,"style":714},[713],[675,3197,696],{"className":3198,"style":720},[718,719],[598,3200,3201,3202,3230],{},"Le choix de ",[675,3203,3205,3218],{"className":3204},[678],[675,3206,3208],{"className":3207},[682],[684,3209,3210],{"xmlns":686},[688,3211,3212,3216],{},[691,3213,3214],{},[694,3215,696],{},[698,3217,696],{"encoding":700},[675,3219,3221],{"className":3220,"ariaHidden":705},[704],[675,3222,3224,3227],{"className":3223},[709],[675,3225],{"className":3226,"style":714},[713],[675,3228,696],{"className":3229,"style":720},[718,719]," influence fortement le résultat.",[2392,3232,3233,3290],{},[658,3234,3235,3289],{},[602,3236,3237],{},[675,3238,3240,3258],{"className":3239},[678],[675,3241,3243],{"className":3242},[682],[684,3244,3245],{"xmlns":686},[688,3246,3247,3255],{},[691,3248,3249,3251,3253],{},[694,3250,696],{},[902,3252,918],{},[1419,3254,1904],{},[698,3256,3257],{"encoding":700},"k = 1",[675,3259,3261,3279],{"className":3260,"ariaHidden":705},[704],[675,3262,3264,3267,3270,3273,3276],{"className":3263},[709],[675,3265],{"className":3266,"style":714},[713],[675,3268,696],{"className":3269,"style":720},[718,719],[675,3271],{"className":3272,"style":976},[964],[675,3274,918],{"className":3275},[980],[675,3277],{"className":3278,"style":976},[964],[675,3280,3282,3286],{"className":3281},[709],[675,3283],{"className":3284,"style":3285},[713],"height:0.6444em;",[675,3287,1904],{"className":3288},[718]," : on prend la classe du voisin le plus proche, point. Très\nsensible au bruit (un seul exemple aberrant peut faire basculer la\nclassification).",[658,3291,3292,3323,3324,3361,3362,3365],{},[602,3293,3294,3322],{},[675,3295,3297,3310],{"className":3296},[678],[675,3298,3300],{"className":3299},[682],[684,3301,3302],{"xmlns":686},[688,3303,3304,3308],{},[691,3305,3306],{},[694,3307,696],{},[698,3309,696],{"encoding":700},[675,3311,3313],{"className":3312,"ariaHidden":705},[704],[675,3314,3316,3319],{"className":3315},[709],[675,3317],{"className":3318,"style":714},[713],[675,3320,696],{"className":3321,"style":720},[718,719]," grand"," : on lisse, on moyenne, mais on perd la finesse locale. Si\n",[675,3325,3327,3343],{"className":3326},[678],[675,3328,3330],{"className":3329},[682],[684,3331,3332],{"xmlns":686},[688,3333,3334,3340],{},[691,3335,3336,3338],{},[694,3337,696],{},[902,3339,918],{},[698,3341,3342],{"encoding":700},"k = ",[675,3344,3346],{"className":3345,"ariaHidden":705},[704],[675,3347,3349,3352,3355,3358],{"className":3348},[709],[675,3350],{"className":3351,"style":714},[713],[675,3353,696],{"className":3354,"style":720},[718,719],[675,3356],{"className":3357,"style":976},[964],[675,3359,918],{"className":3360},[980]," nombre total d'exemples, on retombe sur la classe ",[602,3363,3364],{},"globalement\nmajoritaire"," quel que soit le nouveau point.",[763,3367,3368],{},[598,3369,3370,3371,3399,3400,3403,3404,3490,3491,3519],{},"En pratique, on choisit souvent ",[675,3372,3374,3387],{"className":3373},[678],[675,3375,3377],{"className":3376},[682],[684,3378,3379],{"xmlns":686},[688,3380,3381,3385],{},[691,3382,3383],{},[694,3384,696],{},[698,3386,696],{"encoding":700},[675,3388,3390],{"className":3389,"ariaHidden":705},[704],[675,3391,3393,3396],{"className":3392},[709],[675,3394],{"className":3395,"style":714},[713],[675,3397,696],{"className":3398,"style":720},[718,719]," ",[602,3401,3402],{},"impair"," (pour éviter les égalités\ndans le vote majoritaire) et autour de ",[675,3405,3407,3423],{"className":3406},[678],[675,3408,3410],{"className":3409},[682],[684,3411,3412],{"xmlns":686},[688,3413,3414,3420],{},[691,3415,3416],{},[1393,3417,3418],{},[694,3419,2017],{},[698,3421,3422],{"encoding":700},"\\sqrt{n}",[675,3424,3426],{"className":3425,"ariaHidden":705},[704],[675,3427,3429,3433],{"className":3428},[709],[675,3430],{"className":3431,"style":3432},[713],"height:1.04em;vertical-align:-0.2397em;",[675,3434,3436],{"className":3435},[718,1499],[675,3437,3439,3481],{"className":3438},[1111,1112],[675,3440,3442,3478],{"className":3441},[1116],[675,3443,3446,3461],{"className":3444,"style":3445},[1120],"height:0.8003em;",[675,3447,3450,3454],{"className":3448,"style":3449},[1513],"top:-3em;",[675,3451],{"className":3452,"style":3453},[1128],"height:3em;",[675,3455,3458],{"className":3456,"style":3457},[718],"padding-left:0.833em;",[675,3459,2017],{"className":3460},[718,719],[675,3462,3464,3467],{"style":3463},"top:-2.7603em;",[675,3465],{"className":3466,"style":3453},[1128],[675,3468,3471],{"className":3469,"style":3470},[1785],"min-width:0.853em;height:1.08em;",[1788,3472,3475],{"xmlns":1790,"width":1791,"height":3473,"viewBox":3474,"preserveAspectRatio":1794},"1.08em","0 0 400000 1080",[1796,3476],{"d":3477},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[675,3479,1144],{"className":3480},[1143],[675,3482,3484],{"className":3483},[1116],[675,3485,3488],{"className":3486,"style":3487},[1120],"height:0.2397em;",[675,3489],{}," où ",[675,3492,3494,3507],{"className":3493},[678],[675,3495,3497],{"className":3496},[682],[684,3498,3499],{"xmlns":686},[688,3500,3501,3505],{},[691,3502,3503],{},[694,3504,2017],{},[698,3506,2017],{"encoding":700},[675,3508,3510],{"className":3509,"ariaHidden":705},[704],[675,3511,3513,3516],{"className":3512},[709],[675,3514],{"className":3515,"style":846},[713],[675,3517,2017],{"className":3518},[718,719]," est le nombre\nd'exemples étiquetés.",[3521,3522,3524,3530],"self-eval-qcm",{"correct":1904,"slug":3523},"knn-c1",[3525,3526,3527],"template",{"v-slot:question":1820},[598,3528,3529],{},"Pourquoi choisit-on souvent k impair ?",[3525,3531,3532],{"v-slot:choices":1820},[2392,3533,3534,3537,3540],{},[658,3535,3536],{},"Pour aller plus vite",[658,3538,3539],{},"Pour éviter les égalités dans le vote",[658,3541,3542],{},"Pour augmenter la précision",[593,3544,3546],{"id":3545},"cest-un-algorithme-dapprentissage","C'est un algorithme d'apprentissage",[598,3548,3549,3550,3553,3554,3557,3558,3561,3562,722],{},"Le k-NN apprend ",[602,3551,3552],{},"à partir d'exemples étiquetés"," — il n'a pas besoin qu'on\nlui donne de règle explicite (« si poids > 140 alors pomme »). Il déduit ces\nrègles ",[602,3555,3556],{},"implicitement"," de la disposition des points. C'est ce qu'on\nappelle l'",[602,3559,3560],{},"apprentissage supervisé"," : on apprend à partir d'exemples\n",[602,3563,3564],{},"dont on connaît la classe",[3566,3567,3570,3590],"card",{"icon":3568,"title":3569},"i-lucide-brain","Trois grandes familles d'apprentissage automatique",[2392,3571,3572,3578,3584],{},[658,3573,3574,3577],{},[602,3575,3576],{},"Supervisé"," : exemples étiquetés (classe connue). Le k-NN en est un cas.",[658,3579,3580,3583],{},[602,3581,3582],{},"Non supervisé"," : exemples sans étiquette, on cherche des structures\n(groupes, regroupements).",[658,3585,3586,3589],{},[602,3587,3588],{},"Par renforcement"," : on apprend en interagissant avec un environnement,\npar essais et erreurs.",[598,3591,3592],{},"Le k-NN est l'un des plus simples — pas de phase d'entraînement à proprement\nparler, on garde juste tous les exemples en mémoire et on calcule au moment\nde la prédiction.",[593,3594,3596],{"id":3595},"coût-de-lalgorithme","Coût de l'algorithme",[598,3598,3599,3600,3603],{},"Pour classer ",[602,3601,3602],{},"un seul"," nouveau point :",[2392,3605,3606,3687,3789],{},[658,3607,3608,3609,3637,3638,3686],{},"on calcule ",[675,3610,3612,3625],{"className":3611},[678],[675,3613,3615],{"className":3614},[682],[684,3616,3617],{"xmlns":686},[688,3618,3619,3623],{},[691,3620,3621],{},[694,3622,2017],{},[698,3624,2017],{"encoding":700},[675,3626,3628],{"className":3627,"ariaHidden":705},[704],[675,3629,3631,3634],{"className":3630},[709],[675,3632],{"className":3633,"style":846},[713],[675,3635,2017],{"className":3636},[718,719]," distances : ",[675,3639,3641,3663],{"className":3640},[678],[675,3642,3644],{"className":3643},[682],[684,3645,3646],{"xmlns":686},[688,3647,3648,3660],{},[691,3649,3650,3654,3656,3658],{},[694,3651,3653],{"mathvariant":3652},"script","O",[902,3655,905],{"stretchy":904},[694,3657,2017],{},[902,3659,915],{"stretchy":904},[698,3661,3662],{"encoding":700},"\\mathcal{O}(n)",[675,3664,3666],{"className":3665,"ariaHidden":705},[704],[675,3667,3669,3672,3677,3680,3683],{"className":3668},[709],[675,3670],{"className":3671,"style":946},[713],[675,3673,3653],{"className":3674,"style":3676},[718,3675],"mathcal","margin-right:0.0278em;",[675,3678,905],{"className":3679},[953],[675,3681,2017],{"className":3682},[718,719],[675,3684,915],{"className":3685},[972]," ;",[658,3688,3689,3690,3759,3760,3788],{},"on les trie : ",[675,3691,3693,3721],{"className":3692},[678],[675,3694,3696],{"className":3695},[682],[684,3697,3698],{"xmlns":686},[688,3699,3700,3718],{},[691,3701,3702,3704,3706,3708,3711,3714,3716],{},[694,3703,3653],{"mathvariant":3652},[902,3705,905],{"stretchy":904},[694,3707,2017],{},[694,3709,3710],{},"log",[902,3712,3713],{},"⁡",[694,3715,2017],{},[902,3717,915],{"stretchy":904},[698,3719,3720],{"encoding":700},"\\mathcal{O}(n \\log n)",[675,3722,3724],{"className":3723,"ariaHidden":705},[704],[675,3725,3727,3730,3733,3736,3739,3742,3750,3753,3756],{"className":3726},[709],[675,3728],{"className":3729,"style":946},[713],[675,3731,3653],{"className":3732,"style":3676},[718,3675],[675,3734,905],{"className":3735},[953],[675,3737,2017],{"className":3738},[718,719],[675,3740],{"className":3741,"style":965},[964],[675,3743,3745,3746],{"className":3744},[2122],"lo",[675,3747,3749],{"style":3748},"margin-right:0.0139em;","g",[675,3751],{"className":3752,"style":965},[964],[675,3754,2017],{"className":3755},[718,719],[675,3757,915],{"className":3758},[972]," — ou on peut faire moins si on ne\nveut que les ",[675,3761,3763,3776],{"className":3762},[678],[675,3764,3766],{"className":3765},[682],[684,3767,3768],{"xmlns":686},[688,3769,3770,3774],{},[691,3771,3772],{},[694,3773,696],{},[698,3775,696],{"encoding":700},[675,3777,3779],{"className":3778,"ariaHidden":705},[704],[675,3780,3782,3785],{"className":3781},[709],[675,3783],{"className":3784,"style":714},[713],[675,3786,696],{"className":3787,"style":720},[718,719]," plus petites ;",[658,3790,3791,3792,722],{},"on fait un vote : ",[675,3793,3795,3815],{"className":3794},[678],[675,3796,3798],{"className":3797},[682],[684,3799,3800],{"xmlns":686},[688,3801,3802,3812],{},[691,3803,3804,3806,3808,3810],{},[694,3805,3653],{"mathvariant":3652},[902,3807,905],{"stretchy":904},[694,3809,696],{},[902,3811,915],{"stretchy":904},[698,3813,3814],{"encoding":700},"\\mathcal{O}(k)",[675,3816,3818],{"className":3817,"ariaHidden":705},[704],[675,3819,3821,3824,3827,3830,3833],{"className":3820},[709],[675,3822],{"className":3823,"style":946},[713],[675,3825,3653],{"className":3826,"style":3676},[718,3675],[675,3828,905],{"className":3829},[953],[675,3831,696],{"className":3832,"style":720},[718,719],[675,3834,915],{"className":3835},[972],[598,3837,3838,3839,3902],{},"Au total : ",[675,3840,3842,3867],{"className":3841},[678],[675,3843,3845],{"className":3844},[682],[684,3846,3847],{"xmlns":686},[688,3848,3849,3865],{},[691,3850,3851,3853,3855,3857,3859,3861,3863],{},[694,3852,3653],{"mathvariant":3652},[902,3854,905],{"stretchy":904},[694,3856,2017],{},[694,3858,3710],{},[902,3860,3713],{},[694,3862,2017],{},[902,3864,915],{"stretchy":904},[698,3866,3720],{"encoding":700},[675,3868,3870],{"className":3869,"ariaHidden":705},[704],[675,3871,3873,3876,3879,3882,3885,3888,3893,3896,3899],{"className":3872},[709],[675,3874],{"className":3875,"style":946},[713],[675,3877,3653],{"className":3878,"style":3676},[718,3675],[675,3880,905],{"className":3881},[953],[675,3883,2017],{"className":3884},[718,719],[675,3886],{"className":3887,"style":965},[964],[675,3889,3745,3891],{"className":3890},[2122],[675,3892,3749],{"style":3748},[675,3894],{"className":3895,"style":965},[964],[675,3897,2017],{"className":3898},[718,719],[675,3900,915],{"className":3901},[972]," par prédiction. Acceptable pour quelques\nmilliers d'exemples, lourd au-delà — d'où des structures de données plus\nmalines (arbres k-d, hashage de localité) qu'on rencontre en pratique réelle.",[3521,3904,3906,3911],{"correct":1875,"slug":3905},"knn-c2",[3525,3907,3908],{"v-slot:question":1820},[598,3909,3910],{},"Le k-NN appartient à quelle famille d'apprentissage ?",[3525,3912,3913],{"v-slot:choices":1820},[2392,3914,3915,3917,3919],{},[658,3916,3576],{},[658,3918,3582],{},[658,3920,3588],{},[593,3922,3924],{"id":3923},"pièges-courants","Pièges courants",[2392,3926,3927,3937,4052],{},[658,3928,3929,3932,3933,3936],{},[602,3930,3931],{},"Unités hétérogènes"," : si une coordonnée est en grammes (100 à 200) et\nl'autre en centimètres (5 à 8), le poids dominera la distance et la taille\nsera ignorée. On ",[602,3934,3935],{},"normalise"," souvent les coordonnées avant de calculer\ndes distances.",[658,3938,3939,3971,3972,4022,4023,4051],{},[602,3940,3941,3942,3970],{},"Choix de ",[675,3943,3945,3958],{"className":3944},[678],[675,3946,3948],{"className":3947},[682],[684,3949,3950],{"xmlns":686},[688,3951,3952,3956],{},[691,3953,3954],{},[694,3955,696],{},[698,3957,696],{"encoding":700},[675,3959,3961],{"className":3960,"ariaHidden":705},[704],[675,3962,3964,3967],{"className":3963},[709],[675,3965],{"className":3966,"style":714},[713],[675,3968,696],{"className":3969,"style":720},[718,719]," extrême"," : ",[675,3973,3975,3992],{"className":3974},[678],[675,3976,3978],{"className":3977},[682],[684,3979,3980],{"xmlns":686},[688,3981,3982,3990],{},[691,3983,3984,3986,3988],{},[694,3985,696],{},[902,3987,918],{},[1419,3989,1904],{},[698,3991,3257],{"encoding":700},[675,3993,3995,4013],{"className":3994,"ariaHidden":705},[704],[675,3996,3998,4001,4004,4007,4010],{"className":3997},[709],[675,3999],{"className":4000,"style":714},[713],[675,4002,696],{"className":4003,"style":720},[718,719],[675,4005],{"className":4006,"style":976},[964],[675,4008,918],{"className":4009},[980],[675,4011],{"className":4012,"style":976},[964],[675,4014,4016,4019],{"className":4015},[709],[675,4017],{"className":4018,"style":3285},[713],[675,4020,1904],{"className":4021},[718]," surajuste, ",[675,4024,4026,4039],{"className":4025},[678],[675,4027,4029],{"className":4028},[682],[684,4030,4031],{"xmlns":686},[688,4032,4033,4037],{},[691,4034,4035],{},[694,4036,696],{},[698,4038,696],{"encoding":700},[675,4040,4042],{"className":4041,"ariaHidden":705},[704],[675,4043,4045,4048],{"className":4044},[709],[675,4046],{"className":4047,"style":714},[713],[675,4049,696],{"className":4050,"style":720},[718,719]," trop grand sous-ajuste.",[658,4053,4054,4057],{},[602,4055,4056],{},"Base de données déséquilibrée"," : si vous avez 90 % de pommes et 10 % de\nmandarines, le vote majoritaire prédira presque toujours « pomme ». Il\nfaut équilibrer ou pondérer.",[593,4059,4061],{"id":4060},"pour-aller-plus-loin","Pour aller plus loin",[598,4063,4064,4065,4068],{},"Le k-NN est conceptuellement très simple. C'est souvent un ",[602,4066,4067],{},"baseline"," —\nun algorithme de référence facile à coder, contre lequel on compare des\nméthodes plus sophistiquées (arbres de décision, réseaux de neurones, etc.).\nSa simplicité reste sa force pédagogique : pour comprendre l'idée même\nd'apprentissage automatique, il est imbattable.",[4070,4071,4072],"style",{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":1820,"searchDepth":1838,"depth":1838,"links":4074},[4075,4076,4077,4078,4079,4081,4082,4083,4084],{"id":595,"depth":1838,"text":596},{"id":632,"depth":1838,"text":633},{"id":802,"depth":1838,"text":803},{"id":2373,"depth":1838,"text":2374},{"id":3169,"depth":1838,"text":4080},"Choisir kkk",{"id":3545,"depth":1838,"text":3546},{"id":3595,"depth":1838,"text":3596},{"id":3923,"depth":1838,"text":3924},{"id":4060,"depth":1838,"text":4061},"Un premier algorithme d'apprentissage — classer un point en regardant la classe majoritaire de ses k plus proches voisins.",null,"md",{},[4090,4094],{"slug":3523,"kind":4091,"question":3529,"choices":4092,"correct":1904,"multi":4093,"explanation":1820},"qcm",[3536,3539,3542],false,{"slug":3905,"kind":4091,"question":3910,"choices":4095,"correct":1875,"multi":4093,"explanation":1820},[3576,3582,3588],{"title":437,"description":4085},"uaI6WeTQY8hyJ7jpinF5bN22x-09jrNetbogD3R5ng4",{"id":4099,"title":4100,"bo":4101,"body":4102,"description":5023,"eval":4086,"extension":4087,"labo":4086,"meta":5024,"navigation":4093,"path":5025,"quizzes":5026,"readingTime":1827,"seo":5027,"stem":5028,"tp":4086,"__hash__":5029},"coursMemo\u002F1.nsi-1ere\u002Fph-algorithmique\u002F6.knn.memo.md","k plus proches voisins — l'essentiel",[588],{"type":590,"value":4103,"toc":5016},[4104,4108,4146,4150,4710,4714,4796,4798,4879,4883,5013],[593,4105,4107],{"id":4106},"en-une-phrase","En une phrase",[598,4109,4110,4111,4113,4114,4145],{},"Classer un nouveau point en regardant la ",[602,4112,728],{}," parmi ses\n",[602,4115,4116,4144],{},[675,4117,4119,4132],{"className":4118},[678],[675,4120,4122],{"className":4121},[682],[684,4123,4124],{"xmlns":686},[688,4125,4126,4130],{},[691,4127,4128],{},[694,4129,696],{},[698,4131,696],{"encoding":700},[675,4133,4135],{"className":4134,"ariaHidden":705},[704],[675,4136,4138,4141],{"className":4137},[709],[675,4139],{"className":4140,"style":714},[713],[675,4142,696],{"className":4143,"style":720},[718,719]," plus proches voisins"," dans un ensemble d'exemples étiquetés.",[593,4147,4149],{"id":4148},"à-mémoriser","À mémoriser",[2392,4151,4152,4161,4210,4517,4641],{},[658,4153,4154,4157,4158,722],{},[602,4155,4156],{},"Apprentissage supervisé"," : on apprend à partir d'exemples ",[602,4159,4160],{},"dont on\nconnaît la classe",[658,4162,4163,4166,4167],{},[602,4164,4165],{},"Quatre étapes"," :\n",[655,4168,4169,4172,4175,4207],{},[658,4170,4171],{},"Calculer la distance entre le nouveau point et chaque exemple.",[658,4173,4174],{},"Trier par distance croissante.",[658,4176,4177,4178,4206],{},"Garder les ",[675,4179,4181,4194],{"className":4180},[678],[675,4182,4184],{"className":4183},[682],[684,4185,4186],{"xmlns":686},[688,4187,4188,4192],{},[691,4189,4190],{},[694,4191,696],{},[698,4193,696],{"encoding":700},[675,4195,4197],{"className":4196,"ariaHidden":705},[704],[675,4198,4200,4203],{"className":4199},[709],[675,4201],{"className":4202,"style":714},[713],[675,4204,696],{"className":4205,"style":720},[718,719]," plus proches.",[658,4208,4209],{},"Voter à la majorité.",[658,4211,4212,3971,4215,722],{},[602,4213,4214],{},"Distance euclidienne",[675,4216,4218,4276],{"className":4217},[678],[675,4219,4221],{"className":4220},[682],[684,4222,4223],{"xmlns":686},[688,4224,4225,4273],{},[691,4226,4227,4229,4231,4233,4235,4237,4239,4241],{},[694,4228,900],{},[902,4230,905],{"stretchy":904},[694,4232,1040],{},[902,4234,910],{"separator":705},[694,4236,1219],{},[902,4238,915],{"stretchy":904},[902,4240,918],{},[1393,4242,4243],{},[691,4244,4245,4247,4249,4257,4259,4267],{},[902,4246,2005],{},[902,4248,905],{"stretchy":904},[2021,4250,4251,4253,4255],{},[694,4252,1050],{},[694,4254,2010],{},[694,4256,1040],{},[902,4258,927],{},[2021,4260,4261,4263,4265],{},[694,4262,1050],{},[694,4264,2010],{},[694,4266,1219],{},[1414,4268,4269,4271],{},[902,4270,915],{"stretchy":904},[1419,4272,1421],{},[698,4274,4275],{"encoding":700},"d(A, B) = \\sqrt{\\sum (x_i^A - x_i^B)^2}",[675,4277,4279,4315],{"className":4278,"ariaHidden":705},[704],[675,4280,4282,4285,4288,4291,4294,4297,4300,4303,4306,4309,4312],{"className":4281},[709],[675,4283],{"className":4284,"style":946},[713],[675,4286,900],{"className":4287},[718,719],[675,4289,905],{"className":4290},[953],[675,4292,1040],{"className":4293},[718,719],[675,4295,910],{"className":4296},[960],[675,4298],{"className":4299,"style":965},[964],[675,4301,1219],{"className":4302,"style":1255},[718,719],[675,4304,915],{"className":4305},[972],[675,4307],{"className":4308,"style":976},[964],[675,4310,918],{"className":4311},[980],[675,4313],{"className":4314,"style":976},[964],[675,4316,4318,4322],{"className":4317},[709],[675,4319],{"className":4320,"style":4321},[713],"height:1.24em;vertical-align:-0.2819em;",[675,4323,4325],{"className":4324},[718,1499],[675,4326,4328,4508],{"className":4327},[1111,1112],[675,4329,4331,4505],{"className":4330},[1116],[675,4332,4335,4492],{"className":4333,"style":4334},[1120],"height:0.9581em;",[675,4336,4338,4341],{"className":4337,"style":1514},[1513],[675,4339],{"className":4340,"style":1518},[1128],[675,4342,4344,4349,4352,4403,4406,4409,4412,4463],{"className":4343,"style":1522},[718],[675,4345,2005],{"className":4346,"style":4348},[2122,2167,4347],"small-op","position:relative;top:0em;",[675,4350,905],{"className":4351},[953],[675,4353,4355,4358],{"className":4354},[718],[675,4356,1050],{"className":4357},[718,719],[675,4359,4361],{"className":4360},[1107],[675,4362,4364,4395],{"className":4363},[1111,1112],[675,4365,4367,4392],{"className":4366},[1116],[675,4368,4370,4381],{"className":4369,"style":2217},[1120],[675,4371,4372,4375],{"style":2220},[675,4373],{"className":4374,"style":1129},[1128],[675,4376,4378],{"className":4377},[1133,1134,1135,1136],[675,4379,2010],{"className":4380},[718,719,1136],[675,4382,4383,4386],{"style":2232},[675,4384],{"className":4385,"style":1129},[1128],[675,4387,4389],{"className":4388},[1133,1134,1135,1136],[675,4390,1040],{"className":4391},[718,719,1136],[675,4393,1144],{"className":4394},[1143],[675,4396,4398],{"className":4397},[1116],[675,4399,4401],{"className":4400,"style":2251},[1120],[675,4402],{},[675,4404],{"className":4405,"style":999},[964],[675,4407,927],{"className":4408},[1003],[675,4410],{"className":4411,"style":999},[964],[675,4413,4415,4418],{"className":4414},[718],[675,4416,1050],{"className":4417},[718,719],[675,4419,4421],{"className":4420},[1107],[675,4422,4424,4455],{"className":4423},[1111,1112],[675,4425,4427,4452],{"className":4426},[1116],[675,4428,4430,4441],{"className":4429,"style":2217},[1120],[675,4431,4432,4435],{"style":2220},[675,4433],{"className":4434,"style":1129},[1128],[675,4436,4438],{"className":4437},[1133,1134,1135,1136],[675,4439,2010],{"className":4440},[718,719,1136],[675,4442,4443,4446],{"style":2232},[675,4444],{"className":4445,"style":1129},[1128],[675,4447,4449],{"className":4448},[1133,1134,1135,1136],[675,4450,1219],{"className":4451,"style":1255},[718,719,1136],[675,4453,1144],{"className":4454},[1143],[675,4456,4458],{"className":4457},[1116],[675,4459,4461],{"className":4460,"style":2251},[1120],[675,4462],{},[675,4464,4466,4469],{"className":4465},[972],[675,4467,915],{"className":4468},[972],[675,4470,4472],{"className":4471},[1107],[675,4473,4475],{"className":4474},[1111],[675,4476,4478],{"className":4477},[1116],[675,4479,4481],{"className":4480,"style":1633},[1120],[675,4482,4483,4486],{"style":1636},[675,4484],{"className":4485,"style":1129},[1128],[675,4487,4489],{"className":4488},[1133,1134,1135,1136],[675,4490,1421],{"className":4491},[718,1136],[675,4493,4495,4498],{"style":4494},"top:-2.9181em;",[675,4496],{"className":4497,"style":1518},[1128],[675,4499,4501],{"className":4500,"style":1786},[1785],[1788,4502,4503],{"xmlns":1790,"width":1791,"height":1792,"viewBox":1793,"preserveAspectRatio":1794},[1796,4504],{"d":1798},[675,4506,1144],{"className":4507},[1143],[675,4509,4511],{"className":4510},[1116],[675,4512,4515],{"className":4513,"style":4514},[1120],"height:0.2819em;",[675,4516],{},[658,4518,4519,4549,4550,722],{},[602,4520,3941,4521],{},[675,4522,4524,4537],{"className":4523},[678],[675,4525,4527],{"className":4526},[682],[684,4528,4529],{"xmlns":686},[688,4530,4531,4535],{},[691,4532,4533],{},[694,4534,696],{},[698,4536,696],{"encoding":700},[675,4538,4540],{"className":4539,"ariaHidden":705},[704],[675,4541,4543,4546],{"className":4542},[709],[675,4544],{"className":4545,"style":714},[713],[675,4547,696],{"className":4548,"style":720},[718,719]," : impair (pas d'égalité), souvent ",[675,4551,4553,4572],{"className":4552},[678],[675,4554,4556],{"className":4555},[682],[684,4557,4558],{"xmlns":686},[688,4559,4560,4569],{},[691,4561,4562,4565],{},[902,4563,4564],{},"≈",[1393,4566,4567],{},[694,4568,2017],{},[698,4570,4571],{"encoding":700},"\\approx \\sqrt{n}",[675,4573,4575,4588],{"className":4574,"ariaHidden":705},[704],[675,4576,4578,4582,4585],{"className":4577},[709],[675,4579],{"className":4580,"style":4581},[713],"height:0.4831em;",[675,4583,4564],{"className":4584},[980],[675,4586],{"className":4587,"style":976},[964],[675,4589,4591,4594],{"className":4590},[709],[675,4592],{"className":4593,"style":3432},[713],[675,4595,4597],{"className":4596},[718,1499],[675,4598,4600,4633],{"className":4599},[1111,1112],[675,4601,4603,4630],{"className":4602},[1116],[675,4604,4606,4618],{"className":4605,"style":3445},[1120],[675,4607,4609,4612],{"className":4608,"style":3449},[1513],[675,4610],{"className":4611,"style":3453},[1128],[675,4613,4615],{"className":4614,"style":3457},[718],[675,4616,2017],{"className":4617},[718,719],[675,4619,4620,4623],{"style":3463},[675,4621],{"className":4622,"style":3453},[1128],[675,4624,4626],{"className":4625,"style":3470},[1785],[1788,4627,4628],{"xmlns":1790,"width":1791,"height":3473,"viewBox":3474,"preserveAspectRatio":1794},[1796,4629],{"d":3477},[675,4631,1144],{"className":4632},[1143],[675,4634,4636],{"className":4635},[1116],[675,4637,4639],{"className":4638,"style":3487},[1120],[675,4640],{},[658,4642,4643,3971,4646,4709],{},[602,4644,4645],{},"Coût",[675,4647,4649,4674],{"className":4648},[678],[675,4650,4652],{"className":4651},[682],[684,4653,4654],{"xmlns":686},[688,4655,4656,4672],{},[691,4657,4658,4660,4662,4664,4666,4668,4670],{},[694,4659,3653],{"mathvariant":3652},[902,4661,905],{"stretchy":904},[694,4663,2017],{},[694,4665,3710],{},[902,4667,3713],{},[694,4669,2017],{},[902,4671,915],{"stretchy":904},[698,4673,3720],{"encoding":700},[675,4675,4677],{"className":4676,"ariaHidden":705},[704],[675,4678,4680,4683,4686,4689,4692,4695,4700,4703,4706],{"className":4679},[709],[675,4681],{"className":4682,"style":946},[713],[675,4684,3653],{"className":4685,"style":3676},[718,3675],[675,4687,905],{"className":4688},[953],[675,4690,2017],{"className":4691},[718,719],[675,4693],{"className":4694,"style":965},[964],[675,4696,3745,4698],{"className":4697},[2122],[675,4699,3749],{"style":3748},[675,4701],{"className":4702,"style":965},[964],[675,4704,2017],{"className":4705},[718,719],[675,4707,915],{"className":4708},[972]," par prédiction (à cause du tri).",[593,4711,4713],{"id":4712},"à-savoir-reconnaître","À savoir reconnaître",[4715,4716,4717,4730],"table",{},[4718,4719,4720],"thead",{},[4721,4722,4723,4727],"tr",{},[4724,4725,4726],"th",{},"Indice",[4724,4728,4729],{},"k-NN ?",[4731,4732,4733,4772,4780,4788],"tbody",{},[4721,4734,4735,4769],{},[4736,4737,4738,4739,4768],"td",{},"« classer un nouveau point parmi ",[675,4740,4742,4756],{"className":4741},[678],[675,4743,4745],{"className":4744},[682],[684,4746,4747],{"xmlns":686},[688,4748,4749,4754],{},[691,4750,4751],{},[694,4752,4753],{},"c",[698,4755,4753],{"encoding":700},[675,4757,4759],{"className":4758,"ariaHidden":705},[704],[675,4760,4762,4765],{"className":4761},[709],[675,4763],{"className":4764,"style":846},[713],[675,4766,4753],{"className":4767},[718,719]," classes »",[4736,4770,4771],{},"Oui",[4721,4773,4774,4777],{},[4736,4775,4776],{},"« base de données étiquetée disponible »",[4736,4778,4779],{},"Oui (supervisé)",[4721,4781,4782,4785],{},[4736,4783,4784],{},"« pas de données étiquetées, trouver des groupes »",[4736,4786,4787],{},"Non (non supervisé)",[4721,4789,4790,4793],{},[4736,4791,4792],{},"« agent qui apprend en jouant »",[4736,4794,4795],{},"Non (renforcement)",[593,4797,3924],{"id":3923},[2392,4799,4800,4805,4839,4873],{},[658,4801,4802,4804],{},[602,4803,3931],{}," → normaliser les coordonnées avant la distance.",[658,4806,4807,4838],{},[602,4808,4809,4837],{},[675,4810,4812,4825],{"className":4811},[678],[675,4813,4815],{"className":4814},[682],[684,4816,4817],{"xmlns":686},[688,4818,4819,4823],{},[691,4820,4821],{},[694,4822,696],{},[698,4824,696],{"encoding":700},[675,4826,4828],{"className":4827,"ariaHidden":705},[704],[675,4829,4831,4834],{"className":4830},[709],[675,4832],{"className":4833,"style":714},[713],[675,4835,696],{"className":4836,"style":720},[718,719]," trop petit"," (1) → sensible au bruit.",[658,4840,4841,4872],{},[602,4842,4843,4871],{},[675,4844,4846,4859],{"className":4845},[678],[675,4847,4849],{"className":4848},[682],[684,4850,4851],{"xmlns":686},[688,4852,4853,4857],{},[691,4854,4855],{},[694,4856,696],{},[698,4858,696],{"encoding":700},[675,4860,4862],{"className":4861,"ariaHidden":705},[704],[675,4863,4865,4868],{"className":4864},[709],[675,4866],{"className":4867,"style":714},[713],[675,4869,696],{"className":4870,"style":720},[718,719]," trop grand"," → lisse trop, perd la finesse locale.",[658,4874,4875,4878],{},[602,4876,4877],{},"Classes déséquilibrées"," → vote biaisé en faveur de la classe majoritaire\nglobale.",[593,4880,4882],{"id":4881},"syntaxe-python","Syntaxe Python",[1815,4884,4886],{"className":1817,"code":4885,"language":1819,"meta":1820,"style":1820},"import math\nfrom collections import Counter\n\ndef distance(a, b):\n    return math.sqrt(sum((x - y) ** 2 for x, y in zip(a, b)))\n\ndef knn(donnees, nouveau, k):\n    distances = 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var(--shiki-dark-text-decoration);}",{"title":1820,"searchDepth":1838,"depth":1838,"links":5017},[5018,5019,5020,5021,5022],{"id":4106,"depth":1838,"text":4107},{"id":4148,"depth":1838,"text":4149},{"id":4712,"depth":1838,"text":4713},{"id":3923,"depth":1838,"text":3924},{"id":4881,"depth":1838,"text":4882},"Mémo de révision sur l'algorithme k-NN et l'apprentissage supervisé.",{},"\u002Fnsi-1ere\u002Fph-algorithmique\u002Fknn.memo",[],{"title":4100,"description":5023},"1.nsi-1ere\u002Fph-algorithmique\u002F6.knn.memo","ANByV7XNiDu615UPuQclGSQt_3J2PcSpgGVNQX4YIyw",{"id":5031,"title":5032,"body":5033,"description":6391,"extension":4087,"meta":6392,"navigation":4093,"path":6393,"seo":6394,"stem":6395,"__hash__":6396},"coursSlides\u002F1.nsi-1ere\u002Fph-algorithmique\u002F6.knn.slides.md","k plus proches voisins — diapositives",{"type":590,"value":5034,"toc":6389},[5035,5039,5045,5048,5052,5070,5072,5076,5111,5113,5117,5163,5165,5168,5589,5621,5623,5627,5762,5764,5794,6011,6013,6016,6022,6040,6042,6046,6063,6065,6068,6073,6260,6329,6331,6335,6378,6380,6384,6387],[5036,5037,612],"h1",{"id":5038},"k-plus-proches-voisins",[598,5040,5041,5042,722],{},"Un premier algorithme d'",[602,5043,5044],{},"apprentissage",[5046,5047],"hr",{},[5036,5049,5051],{"id":5050},"le-problème","Le problème",[2392,5053,5054,5061,5067],{},[658,5055,5056,5057,5060],{},"Une base de points ",[602,5058,5059],{},"étiquetés"," (chat, chien, pomme, …)",[658,5062,5063,5064],{},"Un nouveau point ",[602,5065,5066],{},"sans étiquette",[658,5068,5069],{},"Quelle classe lui attribuer ?",[5046,5071],{},[5036,5073,5075],{"id":5074},"lidée","L'idée",[5077,5078,5079],"blockquote",{},[598,5080,5081,5082,5110],{},"Si mes ",[675,5083,5085,5098],{"className":5084},[678],[675,5086,5088],{"className":5087},[682],[684,5089,5090],{"xmlns":686},[688,5091,5092,5096],{},[691,5093,5094],{},[694,5095,696],{},[698,5097,696],{"encoding":700},[675,5099,5101],{"className":5100,"ariaHidden":705},[704],[675,5102,5104,5107],{"className":5103},[709],[675,5105],{"className":5106,"style":714},[713],[675,5108,696],{"className":5109,"style":720},[718,719]," voisins les plus proches sont majoritairement des chats,\nje suis probablement un chat.",[5046,5112],{},[5036,5114,5116],{"id":5115},"lalgorithme","L'algorithme",[655,5118,5119,5125,5128,5160],{},[658,5120,5121,5122,5124],{},"Calculer la distance entre le nouveau point et ",[602,5123,667],{}," exemple",[658,5126,5127],{},"Trier par distance croissante",[658,5129,4177,5130],{},[602,5131,5132,721],{},[675,5133,5135,5148],{"className":5134},[678],[675,5136,5138],{"className":5137},[682],[684,5139,5140],{"xmlns":686},[688,5141,5142,5146],{},[691,5143,5144],{},[694,5145,696],{},[698,5147,696],{"encoding":700},[675,5149,5151],{"className":5150,"ariaHidden":705},[704],[675,5152,5154,5157],{"className":5153},[709],[675,5155],{"className":5156,"style":714},[713],[675,5158,696],{"className":5159,"style":720},[718,719],[658,5161,5162],{},"Vote majoritaire → classe prédite",[5046,5164],{},[5036,5166,4214],{"id":5167},"distance-euclidienne",[675,5169,5171],{"className":5170},[884],[675,5172,5174,5249],{"className":5173},[678],[675,5175,5177],{"className":5176},[682],[684,5178,5179],{"xmlns":686,"display":893},[688,5180,5181,5247],{},[691,5182,5183,5185,5187,5189,5191,5193,5195,5197],{},[694,5184,900],{},[902,5186,905],{"stretchy":904},[694,5188,1040],{},[902,5190,910],{"separator":705},[694,5192,1219],{},[902,5194,915],{"stretchy":904},[902,5196,918],{},[1393,5198,5199],{},[691,5200,5201,5203,5209,5211,5217,5223,5225,5227,5233,5235,5241],{},[902,5202,905],{"stretchy":904},[1046,5204,5205,5207],{},[694,5206,1050],{},[694,5208,1040],{},[902,5210,927],{},[1046,5212,5213,5215],{},[694,5214,1050],{},[694,5216,1219],{},[1414,5218,5219,5221],{},[902,5220,915],{"stretchy":904},[1419,5222,1421],{},[902,5224,1424],{},[902,5226,905],{"stretchy":904},[1046,5228,5229,5231],{},[694,5230,1059],{},[694,5232,1040],{},[902,5234,927],{},[1046,5236,5237,5239],{},[694,5238,1059],{},[694,5240,1219],{},[1414,5242,5243,5245],{},[902,5244,915],{"stretchy":904},[1419,5246,1421],{},[698,5248,1449],{"encoding":700},[675,5250,5252,5288],{"className":5251,"ariaHidden":705},[704],[675,5253,5255,5258,5261,5264,5267,5270,5273,5276,5279,5282,5285],{"className":5254},[709],[675,5256],{"className":5257,"style":946},[713],[675,5259,900],{"className":5260},[718,719],[675,5262,905],{"className":5263},[953],[675,5265,1040],{"className":5266},[718,719],[675,5268,910],{"className":5269},[960],[675,5271],{"className":5272,"style":965},[964],[675,5274,1219],{"className":5275,"style":1255},[718,719],[675,5277,915],{"className":5278},[972],[675,5280],{"className":5281,"style":976},[964],[675,5283,918],{"className":5284},[980],[675,5286],{"className":5287,"style":976},[964],[675,5289,5291,5294],{"className":5290},[709],[675,5292],{"className":5293,"style":1495},[713],[675,5295,5297],{"className":5296},[718,1499],[675,5298,5300,5581],{"className":5299},[1111,1112],[675,5301,5303,5578],{"className":5302},[1116],[675,5304,5306,5566],{"className":5305,"style":1509},[1120],[675,5307,5309,5312],{"className":5308,"style":1514},[1513],[675,5310],{"className":5311,"style":1518},[1128],[675,5313,5315,5318,5358,5361,5364,5367,5407,5436,5439,5442,5445,5448,5488,5491,5494,5497,5537],{"className":5314,"style":1522},[718],[675,5316,905],{"className":5317},[953],[675,5319,5321,5324],{"className":5320},[718],[675,5322,1050],{"className":5323},[718,719],[675,5325,5327],{"className":5326},[1107],[675,5328,5330,5350],{"className":5329},[1111,1112],[675,5331,5333,5347],{"className":5332},[1116],[675,5334,5336],{"className":5335,"style":1121},[1120],[675,5337,5338,5341],{"style":1124},[675,5339],{"className":5340,"style":1129},[1128],[675,5342,5344],{"className":5343},[1133,1134,1135,1136],[675,5345,1040],{"className":5346},[718,719,1136],[675,5348,1144],{"className":5349},[1143],[675,5351,5353],{"className":5352},[1116],[675,5354,5356],{"className":5355,"style":1151},[1120],[675,5357],{},[675,5359],{"className":5360,"style":999},[964],[675,5362,927],{"className":5363},[1003],[675,5365],{"className":5366,"style":999},[964],[675,5368,5370,5373],{"className":5369},[718],[675,5371,1050],{"className":5372},[718,719],[675,5374,5376],{"className":5375},[1107],[675,5377,5379,5399],{"className":5378},[1111,1112],[675,5380,5382,5396],{"className":5381},[1116],[675,5383,5385],{"className":5384,"style":1121},[1120],[675,5386,5387,5390],{"style":1124},[675,5388],{"className":5389,"style":1129},[1128],[675,5391,5393],{"className":5392},[1133,1134,1135,1136],[675,5394,1219],{"className":5395,"style":1255},[718,719,1136],[675,5397,1144],{"className":5398},[1143],[675,5400,5402],{"className":5401},[1116],[675,5403,5405],{"className":5404,"style":1151},[1120],[675,5406],{},[675,5408,5410,5413],{"className":5409},[972],[675,5411,915],{"className":5412},[972],[675,5414,5416],{"className":5415},[1107],[675,5417,5419],{"className":5418},[1111],[675,5420,5422],{"className":5421},[1116],[675,5423,5425],{"className":5424,"style":1633},[1120],[675,5426,5427,5430],{"style":1636},[675,5428],{"className":5429,"style":1129},[1128],[675,5431,5433],{"className":5432},[1133,1134,1135,1136],[675,5434,1421],{"className":5435},[718,1136],[675,5437],{"className":5438,"style":999},[964],[675,5440,1424],{"className":5441},[1003],[675,5443],{"className":5444,"style":999},[964],[675,5446,905],{"className":5447},[953],[675,5449,5451,5454],{"className":5450},[718],[675,5452,1059],{"className":5453,"style":1166},[718,719],[675,5455,5457],{"className":5456},[1107],[675,5458,5460,5480],{"className":5459},[1111,1112],[675,5461,5463,5477],{"className":5462},[1116],[675,5464,5466],{"className":5465,"style":1121},[1120],[675,5467,5468,5471],{"style":1181},[675,5469],{"className":5470,"style":1129},[1128],[675,5472,5474],{"className":5473},[1133,1134,1135,1136],[675,5475,1040],{"className":5476},[718,719,1136],[675,5478,1144],{"className":5479},[1143],[675,5481,5483],{"className":5482},[1116],[675,5484,5486],{"className":5485,"style":1151},[1120],[675,5487],{},[675,5489],{"className":5490,"style":999},[964],[675,5492,927],{"className":5493},[1003],[675,5495],{"className":5496,"style":999},[964],[675,5498,5500,5503],{"className":5499},[718],[675,5501,1059],{"className":5502,"style":1166},[718,719],[675,5504,5506],{"className":5505},[1107],[675,5507,5509,5529],{"className":5508},[1111,1112],[675,5510,5512,5526],{"className":5511},[1116],[675,5513,5515],{"className":5514,"style":1121},[1120],[675,5516,5517,5520],{"style":1181},[675,5518],{"className":5519,"style":1129},[1128],[675,5521,5523],{"className":5522},[1133,1134,1135,1136],[675,5524,1219],{"className":5525,"style":1255},[718,719,1136],[675,5527,1144],{"className":5528},[1143],[675,5530,5532],{"className":5531},[1116],[675,5533,5535],{"className":5534,"style":1151},[1120],[675,5536],{},[675,5538,5540,5543],{"className":5539},[972],[675,5541,915],{"className":5542},[972],[675,5544,5546],{"className":5545},[1107],[675,5547,5549],{"className":5548},[1111],[675,5550,5552],{"className":5551},[1116],[675,5553,5555],{"className":5554,"style":1633},[1120],[675,5556,5557,5560],{"style":1636},[675,5558],{"className":5559,"style":1129},[1128],[675,5561,5563],{"className":5562},[1133,1134,1135,1136],[675,5564,1421],{"className":5565},[718,1136],[675,5567,5568,5571],{"style":1778},[675,5569],{"className":5570,"style":1518},[1128],[675,5572,5574],{"className":5573,"style":1786},[1785],[1788,5575,5576],{"xmlns":1790,"width":1791,"height":1792,"viewBox":1793,"preserveAspectRatio":1794},[1796,5577],{"d":1798},[675,5579,1144],{"className":5580},[1143],[675,5582,5584],{"className":5583},[1116],[675,5585,5587],{"className":5586,"style":1808},[1120],[675,5588],{},[598,5590,5591,5592,5620],{},"Généralisable à ",[675,5593,5595,5608],{"className":5594},[678],[675,5596,5598],{"className":5597},[682],[684,5599,5600],{"xmlns":686},[688,5601,5602,5606],{},[691,5603,5604],{},[694,5605,2017],{},[698,5607,2017],{"encoding":700},[675,5609,5611],{"className":5610,"ariaHidden":705},[704],[675,5612,5614,5617],{"className":5613},[709],[675,5615],{"className":5616,"style":846},[713],[675,5618,2017],{"className":5619},[718,719]," dimensions.",[5046,5622],{},[5036,5624,5626],{"id":5625},"le-code","Le code",[1815,5628,5630],{"className":1817,"code":5629,"language":1819,"meta":1820,"style":1820},"import math\nfrom collections import Counter\n\ndef distance(a, b):\n    return math.sqrt(sum((x-y)**2 for x,y in zip(a,b)))\n\ndef knn(donnees, nouveau, k):\n    distances = [(distance(p, nouveau), c)\n                 for p, c in donnees]\n    distances.sort()\n    voisins = [c for _, c in distances[:k]]\n    return Counter(voisins).most_common(1)[0][0]\n",[1822,5631,5632,5638,5648,5652,5660,5692,5696,5704,5713,5724,5728,5744],{"__ignoreMap":1820},[675,5633,5634,5636],{"class":1826,"line":1827},[675,5635,1831],{"class":1830},[675,5637,1835],{"class":1834},[675,5639,5640,5642,5644,5646],{"class":1826,"line":1838},[675,5641,2444],{"class":1830},[675,5643,2447],{"class":1834},[675,5645,1831],{"class":1830},[675,5647,2452],{"class":1834},[675,5649,5650],{"class":1826,"line":1845},[675,5651,1842],{"emptyLinePlaceholder":1841},[675,5653,5654,5656,5658],{"class":1826,"line":1858},[675,5655,1848],{"class":1830},[675,5657,1852],{"class":1851},[675,5659,1855],{"class":1834},[675,5661,5662,5664,5666,5668,5671,5673,5676,5678,5680,5682,5685,5687,5689],{"class":1826,"line":1865},[675,5663,1868],{"class":1830},[675,5665,2471],{"class":1834},[675,5667,2474],{"class":1874},[675,5669,5670],{"class":1834},"((x",[675,5672,1881],{"class":1830},[675,5674,5675],{"class":1834},"y)",[675,5677,1892],{"class":1830},[675,5679,1421],{"class":1874},[675,5681,2489],{"class":1830},[675,5683,5684],{"class":1834}," x,y ",[675,5686,2495],{"class":1830},[675,5688,2498],{"class":1874},[675,5690,5691],{"class":1834},"(a,b)))\n",[675,5693,5694],{"class":1826,"line":1924},[675,5695,1842],{"emptyLinePlaceholder":1841},[675,5697,5698,5700,5702],{"class":1826,"line":1929},[675,5699,1848],{"class":1830},[675,5701,2512],{"class":1851},[675,5703,2515],{"class":1834},[675,5705,5706,5708,5710],{"class":1826,"line":2518},[675,5707,2551],{"class":1834},[675,5709,918],{"class":1830},[675,5711,5712],{"class":1834}," [(distance(p, nouveau), c)\n",[675,5714,5715,5718,5720,5722],{"class":1826,"line":2524},[675,5716,5717],{"class":1830},"                 for",[675,5719,2916],{"class":1834},[675,5721,2495],{"class":1830},[675,5723,2567],{"class":1834},[675,5725,5726],{"class":1826,"line":2530},[675,5727,2579],{"class":1834},[675,5729,5730,5732,5734,5736,5738,5740,5742],{"class":1826,"line":2536},[675,5731,2591],{"class":1834},[675,5733,918],{"class":1830},[675,5735,2933],{"class":1834},[675,5737,2559],{"class":1830},[675,5739,2938],{"class":1834},[675,5741,2495],{"class":1830},[675,5743,2606],{"class":1834},[675,5745,5746,5748,5750,5752,5754,5756,5758,5760],{"class":1826,"line":2542},[675,5747,1868],{"class":1830},[675,5749,2620],{"class":1834},[675,5751,1904],{"class":1874},[675,5753,2625],{"class":1834},[675,5755,1875],{"class":1874},[675,5757,2630],{"class":1834},[675,5759,1875],{"class":1874},[675,5761,2635],{"class":1834},[5046,5763],{},[5036,5765,3170,5766],{"id":3169},[675,5767,5769,5782],{"className":5768},[678],[675,5770,5772],{"className":5771},[682],[684,5773,5774],{"xmlns":686},[688,5775,5776,5780],{},[691,5777,5778],{},[694,5779,696],{},[698,5781,696],{"encoding":700},[675,5783,5785],{"className":5784,"ariaHidden":705},[704],[675,5786,5788,5791],{"className":5787},[709],[675,5789],{"className":5790,"style":714},[713],[675,5792,696],{"className":5793,"style":720},[718,719],[2392,5795,5796,5849,5880,5911],{},[658,5797,5798,5848],{},[675,5799,5801,5818],{"className":5800},[678],[675,5802,5804],{"className":5803},[682],[684,5805,5806],{"xmlns":686},[688,5807,5808,5816],{},[691,5809,5810,5812,5814],{},[694,5811,696],{},[902,5813,918],{},[1419,5815,1904],{},[698,5817,3257],{"encoding":700},[675,5819,5821,5839],{"className":5820,"ariaHidden":705},[704],[675,5822,5824,5827,5830,5833,5836],{"className":5823},[709],[675,5825],{"className":5826,"style":714},[713],[675,5828,696],{"className":5829,"style":720},[718,719],[675,5831],{"className":5832,"style":976},[964],[675,5834,918],{"className":5835},[980],[675,5837],{"className":5838,"style":976},[964],[675,5840,5842,5845],{"className":5841},[709],[675,5843],{"className":5844,"style":3285},[713],[675,5846,1904],{"className":5847},[718]," : très sensible au bruit",[658,5850,5851,5879],{},[675,5852,5854,5867],{"className":5853},[678],[675,5855,5857],{"className":5856},[682],[684,5858,5859],{"xmlns":686},[688,5860,5861,5865],{},[691,5862,5863],{},[694,5864,696],{},[698,5866,696],{"encoding":700},[675,5868,5870],{"className":5869,"ariaHidden":705},[704],[675,5871,5873,5876],{"className":5872},[709],[675,5874],{"className":5875,"style":714},[713],[675,5877,696],{"className":5878,"style":720},[718,719]," grand : lissage, perte de finesse",[658,5881,5882,5910],{},[675,5883,5885,5898],{"className":5884},[678],[675,5886,5888],{"className":5887},[682],[684,5889,5890],{"xmlns":686},[688,5891,5892,5896],{},[691,5893,5894],{},[694,5895,696],{},[698,5897,696],{"encoding":700},[675,5899,5901],{"className":5900,"ariaHidden":705},[704],[675,5902,5904,5907],{"className":5903},[709],[675,5905],{"className":5906,"style":714},[713],[675,5908,696],{"className":5909,"style":720},[718,719]," impair : pas d'égalité dans le vote",[658,5912,5913,5914],{},"Heuristique : ",[675,5915,5917,5937],{"className":5916},[678],[675,5918,5920],{"className":5919},[682],[684,5921,5922],{"xmlns":686},[688,5923,5924,5934],{},[691,5925,5926,5928,5930],{},[694,5927,696],{},[902,5929,4564],{},[1393,5931,5932],{},[694,5933,2017],{},[698,5935,5936],{"encoding":700},"k \\approx \\sqrt{n}",[675,5938,5940,5958],{"className":5939,"ariaHidden":705},[704],[675,5941,5943,5946,5949,5952,5955],{"className":5942},[709],[675,5944],{"className":5945,"style":714},[713],[675,5947,696],{"className":5948,"style":720},[718,719],[675,5950],{"className":5951,"style":976},[964],[675,5953,4564],{"className":5954},[980],[675,5956],{"className":5957,"style":976},[964],[675,5959,5961,5964],{"className":5960},[709],[675,5962],{"className":5963,"style":3432},[713],[675,5965,5967],{"className":5966},[718,1499],[675,5968,5970,6003],{"className":5969},[1111,1112],[675,5971,5973,6000],{"className":5972},[1116],[675,5974,5976,5988],{"className":5975,"style":3445},[1120],[675,5977,5979,5982],{"className":5978,"style":3449},[1513],[675,5980],{"className":5981,"style":3453},[1128],[675,5983,5985],{"className":5984,"style":3457},[718],[675,5986,2017],{"className":5987},[718,719],[675,5989,5990,5993],{"style":3463},[675,5991],{"className":5992,"style":3453},[1128],[675,5994,5996],{"className":5995,"style":3470},[1785],[1788,5997,5998],{"xmlns":1790,"width":1791,"height":3473,"viewBox":3474,"preserveAspectRatio":1794},[1796,5999],{"d":3477},[675,6001,1144],{"className":6002},[1143],[675,6004,6006],{"className":6005},[1116],[675,6007,6009],{"className":6008,"style":3487},[1120],[675,6010],{},[5046,6012],{},[5036,6014,4156],{"id":6015},"apprentissage-supervisé",[598,6017,6018,6019,653],{},"Le k-NN appartient à la famille de l'apprentissage ",[602,6020,6021],{},"supervisé",[2392,6023,6024,6030,6033],{},[658,6025,6026,6027],{},"on apprend à partir d'",[602,6028,6029],{},"exemples étiquetés",[658,6031,6032],{},"pas besoin de règle explicite",[658,6034,6035,6036,6039],{},"les règles sont ",[602,6037,6038],{},"déduites"," de la disposition des points",[5046,6041],{},[5036,6043,6045],{"id":6044},"trois-familles-dapprentissage","Trois familles d'apprentissage",[2392,6047,6048,6053,6058],{},[658,6049,6050,6052],{},[602,6051,3576],{}," : exemples étiquetés (k-NN en fait partie)",[658,6054,6055,6057],{},[602,6056,3582],{}," : on cherche des regroupements",[658,6059,6060,6062],{},[602,6061,3588],{}," : essais et erreurs avec récompense",[5046,6064],{},[5036,6066,4645],{"id":6067},"coût",[598,6069,3599,6070,3603],{},[602,6071,6072],{},"un",[2392,6074,6075,6148,6214],{},[658,6076,6077,3637,6105],{},[675,6078,6080,6093],{"className":6079},[678],[675,6081,6083],{"className":6082},[682],[684,6084,6085],{"xmlns":686},[688,6086,6087,6091],{},[691,6088,6089],{},[694,6090,2017],{},[698,6092,2017],{"encoding":700},[675,6094,6096],{"className":6095,"ariaHidden":705},[704],[675,6097,6099,6102],{"className":6098},[709],[675,6100],{"className":6101,"style":846},[713],[675,6103,2017],{"className":6104},[718,719],[675,6106,6108,6127],{"className":6107},[678],[675,6109,6111],{"className":6110},[682],[684,6112,6113],{"xmlns":686},[688,6114,6115,6125],{},[691,6116,6117,6119,6121,6123],{},[694,6118,3653],{"mathvariant":3652},[902,6120,905],{"stretchy":904},[694,6122,2017],{},[902,6124,915],{"stretchy":904},[698,6126,3662],{"encoding":700},[675,6128,6130],{"className":6129,"ariaHidden":705},[704],[675,6131,6133,6136,6139,6142,6145],{"className":6132},[709],[675,6134],{"className":6135,"style":946},[713],[675,6137,3653],{"className":6138,"style":3676},[718,3675],[675,6140,905],{"className":6141},[953],[675,6143,2017],{"className":6144},[718,719],[675,6146,915],{"className":6147},[972],[658,6149,6150,6151],{},"tri : ",[675,6152,6154,6179],{"className":6153},[678],[675,6155,6157],{"className":6156},[682],[684,6158,6159],{"xmlns":686},[688,6160,6161,6177],{},[691,6162,6163,6165,6167,6169,6171,6173,6175],{},[694,6164,3653],{"mathvariant":3652},[902,6166,905],{"stretchy":904},[694,6168,2017],{},[694,6170,3710],{},[902,6172,3713],{},[694,6174,2017],{},[902,6176,915],{"stretchy":904},[698,6178,3720],{"encoding":700},[675,6180,6182],{"className":6181,"ariaHidden":705},[704],[675,6183,6185,6188,6191,6194,6197,6200,6205,6208,6211],{"className":6184},[709],[675,6186],{"className":6187,"style":946},[713],[675,6189,3653],{"className":6190,"style":3676},[718,3675],[675,6192,905],{"className":6193},[953],[675,6195,2017],{"className":6196},[718,719],[675,6198],{"className":6199,"style":965},[964],[675,6201,3745,6203],{"className":6202},[2122],[675,6204,3749],{"style":3748},[675,6206],{"className":6207,"style":965},[964],[675,6209,2017],{"className":6210},[718,719],[675,6212,915],{"className":6213},[972],[658,6215,6216,6217],{},"vote : ",[675,6218,6220,6239],{"className":6219},[678],[675,6221,6223],{"className":6222},[682],[684,6224,6225],{"xmlns":686},[688,6226,6227,6237],{},[691,6228,6229,6231,6233,6235],{},[694,6230,3653],{"mathvariant":3652},[902,6232,905],{"stretchy":904},[694,6234,696],{},[902,6236,915],{"stretchy":904},[698,6238,3814],{"encoding":700},[675,6240,6242],{"className":6241,"ariaHidden":705},[704],[675,6243,6245,6248,6251,6254,6257],{"className":6244},[709],[675,6246],{"className":6247,"style":946},[713],[675,6249,3653],{"className":6250,"style":3676},[718,3675],[675,6252,905],{"className":6253},[953],[675,6255,696],{"className":6256,"style":720},[718,719],[675,6258,915],{"className":6259},[972],[598,6261,6262],{},[602,6263,6264,6265,6328],{},"Total : ",[675,6266,6268,6293],{"className":6267},[678],[675,6269,6271],{"className":6270},[682],[684,6272,6273],{"xmlns":686},[688,6274,6275,6291],{},[691,6276,6277,6279,6281,6283,6285,6287,6289],{},[694,6278,3653],{"mathvariant":3652},[902,6280,905],{"stretchy":904},[694,6282,2017],{},[694,6284,3710],{},[902,6286,3713],{},[694,6288,2017],{},[902,6290,915],{"stretchy":904},[698,6292,3720],{"encoding":700},[675,6294,6296],{"className":6295,"ariaHidden":705},[704],[675,6297,6299,6302,6305,6308,6311,6314,6319,6322,6325],{"className":6298},[709],[675,6300],{"className":6301,"style":946},[713],[675,6303,3653],{"className":6304,"style":3676},[718,3675],[675,6306,905],{"className":6307},[953],[675,6309,2017],{"className":6310},[718,719],[675,6312],{"className":6313,"style":965},[964],[675,6315,3745,6317],{"className":6316},[2122],[675,6318,3749],{"style":3748},[675,6320],{"className":6321,"style":965},[964],[675,6323,2017],{"className":6324},[718,719],[675,6326,915],{"className":6327},[972]," par prédiction",[5046,6330],{},[5036,6332,6334],{"id":6333},"pièges","Pièges",[2392,6336,6337,6344,6375],{},[658,6338,6339,6340,6343],{},"Unités hétérogènes → ",[602,6341,6342],{},"normaliser"," d'abord",[658,6345,6346,6374],{},[675,6347,6349,6362],{"className":6348},[678],[675,6350,6352],{"className":6351},[682],[684,6353,6354],{"xmlns":686},[688,6355,6356,6360],{},[691,6357,6358],{},[694,6359,696],{},[698,6361,696],{"encoding":700},[675,6363,6365],{"className":6364,"ariaHidden":705},[704],[675,6366,6368,6371],{"className":6367},[709],[675,6369],{"className":6370,"style":714},[713],[675,6372,696],{"className":6373,"style":720},[718,719]," extrême → surajuste ou sous-ajuste",[658,6376,6377],{},"Classes déséquilibrées → vote biaisé",[5046,6379],{},[5036,6381,6383],{"id":6382},"à-retenir","À retenir",[598,6385,6386],{},"k-NN = baseline simple et intuitive de l'apprentissage automatique.\nConceptuellement clair, prêt à coder en quelques lignes 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