{"id":4480,"date":"2026-07-29T16:56:13","date_gmt":"2026-07-29T14:56:13","guid":{"rendered":"https:\/\/ellistat.com\/?post_type=guide-dutilisateur&#038;p=4480"},"modified":"2026-07-30T10:31:31","modified_gmt":"2026-07-30T08:31:31","slug":"fokomponens-elemzes-pca","status":"publish","type":"guide-dutilisateur","link":"https:\/\/ellistat.com\/hu\/guide-dutilisateur\/analyse-en-composantes-principales-acp\/","title":{"rendered":"F\u0151komponens-elemz\u00e9s (FKE)"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Az ACP t\u00f6bb, egym\u00e1ssal \u00f6sszef\u00fcgg\u0151 mennyis\u00e9gi v\u00e1ltoz\u00f3t n\u00e9h\u00e1ny tengelybe foglal \u00f6ssze, amelyeket&nbsp;<strong>f\u0151 komponensek<\/strong>, amelyeket CP1, CP2, CP3 jel\u00f6l\u00e9ssel l\u00e1ttunk el. Minden tengely a teljes variabilit\u00e1s egy r\u00e9sz\u00e9t magyar\u00e1zza; az els\u0151k a legnagyobb r\u00e9sz\u00e9t magyar\u00e1zz\u00e1k.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 Az \u201e\u00d6sszefoglal\u00e1s\u201d f\u00fcl<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. z\u00f3na<\/strong>&nbsp;: a megjelen\u00edt\u00e9si be\u00e1ll\u00edt\u00e1sok.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>Egy\u00e9nek megjelen\u00edt\u00e9se<\/strong>&nbsp;: az egy\u00e9nek felh\u0151j\u00e9t r\u00e1helyezi a korrel\u00e1ci\u00f3s k\u00f6rre.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>C\u00edmk\u00e9k megjelen\u00edt\u00e9se<\/strong>&nbsp;: \u00edrja le az egyes szem\u00e9lyek nev\u00e9t a hozz\u00e1juk tartoz\u00f3 pont mell\u00e9.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>Fel\u00fcgyelet n\u00e9lk\u00fcli oszt\u00e1lyoz\u00e1s (K-Means)<\/strong>&nbsp;: sz\u00ednezd be az egyedeket csal\u00e1donk\u00e9nt, \u00e9s jel\u00f6ld meg az egyes csal\u00e1dok k\u00f6zpontjait.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>Csoportok sz\u00e1ma<\/strong>&nbsp;: a keresett csal\u00e1dok sz\u00e1ma.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>\u00c1bra t\u00edpusa<\/strong>&nbsp;: 2D vagy 3D. 3D eset\u00e9n hozz\u00e1ad\u00f3dik a CP3 tengely.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>A c\u00edmk\u00e9k elhelyezked\u00e9se<\/strong>&nbsp;: csak egy c\u00edmke \u00e1thelyez\u00e9se ut\u00e1n jelenik meg, \u00e9s lehet\u0151v\u00e9 teszi, hogy mindent vissza\u00e1ll\u00edtsunk a hely\u00e9re.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. z\u00f3na<\/strong>&nbsp;: a grafikon. Az 1-es sugar\u00fa k\u00f6r a&nbsp;<strong>korrel\u00e1ci\u00f3s k\u00f6r<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. z\u00f3na<\/strong>&nbsp;: a grafikon alatt a saj\u00e1tvektorok t\u00e1bl\u00e1zata tartalmazza az egyes v\u00e1ltoz\u00f3k tengelyeken m\u00e9rt koordin\u00e1t\u00e1it.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"644\" height=\"480\" src=\"https:\/\/ellistat.com\/wp-content\/uploads\/userguide3-1.png\" alt=\"\" class=\"wp-image-4481\" srcset=\"https:\/\/ellistat.com\/wp-content\/uploads\/userguide3-1.png 644w, https:\/\/ellistat.com\/wp-content\/uploads\/userguide3-1-300x224.png 300w, https:\/\/ellistat.com\/wp-content\/uploads\/userguide3-1-16x12.png 16w\" sizes=\"auto, (max-width: 644px) 100vw, 644px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udca1&nbsp;<strong>A c\u00edmk\u00e9k \u00e1thelyezhet\u0151k.<\/strong>&nbsp;2D-ben az eg\u00e9rrel fogja meg a v\u00e1ltoz\u00f3 vagy a m\u00f3d neve, majd h\u00fazza el: ez a legegyszer\u0171bb m\u00f3dja az egym\u00e1st \u00e1tfed\u0151 c\u00edmk\u00e9k sz\u00e9tv\u00e1laszt\u00e1s\u00e1nak. A poz\u00edci\u00f3k megmaradnak, \u00e9s a grafikonnal egy\u00fctt ment\u0151dnek, ha azt elmenti.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2 A korrel\u00e1ci\u00f3s k\u00f6r \u00e9rtelmez\u00e9se<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Minden v\u00e1ltoz\u00f3 egy, az orig\u00f3b\u00f3l kiindul\u00f3 ny\u00edl. Helyzet\u00e9t k\u00e9t szempont alapj\u00e1n lehet meghat\u00e1rozni.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A hossz<\/strong>&nbsp;m\u00e9ri az \u00e1br\u00e1zol\u00e1s min\u0151s\u00e9g\u00e9t. Egy olyan ny\u00edl, amely szinte el\u00e9ri a k\u00f6rt, j\u00f3l van \u00e1br\u00e1zolva a megjelen\u00edtett s\u00edkon: \u00e9rtelmezhet\u0151. Egy r\u00f6vid, a k\u00f6zponthoz k\u00f6zeli ny\u00edl viszont rosszul van \u00e1br\u00e1zolva ezen a s\u00edkon \u2014&nbsp;<strong>ezt itt nem szabad \u00fagy \u00e9rtelmezni, hogy<\/strong>, a k\u00f6vetkez\u0151 szempontokat kell figyelembe venni.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>K\u00e9t ny\u00edl k\u00f6z\u00f6tti sz\u00f6g<\/strong>&nbsp;megm\u00e9ri a k\u00f6z\u00f6tt\u00fck l\u00e9v\u0151 korrel\u00e1ci\u00f3t, felt\u00e9ve, hogy mindkett\u0151 hossz\u00fa:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2 k\u00e9t egym\u00e1s mellett \u00e1ll\u00f3 ny\u00edl: pozit\u00edv korrel\u00e1ci\u00f3j\u00fa v\u00e1ltoz\u00f3k; ;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2 k\u00e9t egym\u00e1ssal ellent\u00e9tes ny\u00edl: negat\u00edvan korrel\u00e1l\u00f3 v\u00e1ltoz\u00f3k; ;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2 k\u00e9t, 90\u00b0-os sz\u00f6gben elhelyezked\u0151 ny\u00edl: f\u00fcggetlen v\u00e1ltoz\u00f3k.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Egy v\u00e1ltoz\u00f3 koordin\u00e1t\u00e1ja egy tengelyen&nbsp;<strong>a<\/strong>&nbsp;a tengellyel val\u00f3 korrel\u00e1ci\u00f3ja. \u00c9rt\u00e9ke teh\u00e1t mindig \u22121 \u00e9s 1 k\u00f6z\u00f6tt van, ami magyar\u00e1zza a k\u00f6r alakj\u00e1t.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.3 Az egy\u00e9nek felh\u0151j\u00e9nek \u00e9rtelmez\u00e9se<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">K\u00e9t, a t\u00e9rben egym\u00e1shoz k\u00f6zel elhelyezked\u0151 egy\u00e9n az elemzett v\u00e1ltoz\u00f3k tekintet\u00e9ben hasonl\u00edt egym\u00e1sra. A felh\u0151 k\u00f6zepe a kiindul\u00e1si pont: a k\u00f6zpontt\u00f3l t\u00e1vol es\u0151 egy\u00e9n atipikus.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u26a0\ufe0f A felh\u0151&nbsp;<strong>a k\u00f6r m\u00e9retar\u00e1ny\u00e1ra visszavezetve<\/strong>&nbsp;hogy egym\u00e1sra helyezhet\u0151 legyen. Az egyedek k\u00f6z\u00f6tti t\u00e1vols\u00e1gok \u00e9s azok ir\u00e1nya pontosan megegyeznek, de m\u00e9retar\u00e1nyuk nem egyezik meg a korrel\u00e1ci\u00f3k\u00e9val: egy&nbsp;<strong>ir\u00e1ny<\/strong>&nbsp;(\u00abez a szem\u00e9ly a nyom\u00e1s ir\u00e1ny\u00e1ba halad\u00bb), nem pedig egy \u00e9rt\u00e9k.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.4 A \u201ePareto\u201d f\u00fcl<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Minden tengely eset\u00e9ben megadja a&nbsp;<strong>saj\u00e1t t\u0151ke<\/strong>, a&nbsp;<strong>magyar\u00e1zott variancia<\/strong>&nbsp;\u00e9s a&nbsp;<strong>kumul\u00e1lt variancia<\/strong>, a hozz\u00e1 tartoz\u00f3 k\u0151oml\u00e1ssal egy\u00fctt.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itt d\u00f6ntj\u00fck el, h\u00e1ny tengelyt tartunk meg. A kumul\u00e1lt variancia piros sz\u00ednnel jelenik meg, am\u00edg 80 % alatt van, e felett pedig z\u00f6ld sz\u00ednnel: annyi tengelyt kell megtartani, hogy a kijelz\u00e9s z\u00f6ldre v\u00e1ltson.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udca1 Egy m\u00e1sik klasszikus ir\u00e1nyelv: csak azokat a tengelyeket tartsuk meg, amelyek saj\u00e1t\u00e9rt\u00e9ke nagyobb, mint 1; egy olyan tengely, amely kevesebbet magyar\u00e1z, mint egy \u00f6n\u00e1ll\u00f3 v\u00e1ltoz\u00f3, nem ny\u00fajt \u00f6sszefoglal\u00e1st.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.5 A \u201eV\u00e1ltoz\u00f3k\u201d f\u00fcl<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">V\u00e1ltoz\u00f3nk\u00e9nt egy sor, \u00e9s minden tengelyhez n\u00e9gy oszlop:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>C1, C2, C3<\/strong>&nbsp;: a v\u00e1ltoz\u00f3 \u00e9s a tengely k\u00f6z\u00f6tti korrel\u00e1ci\u00f3; ;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>Hozz\u00e1j\u00e1rul\u00e1s<\/strong>&nbsp;: a v\u00e1ltoz\u00f3 s\u00falya a tengely kialak\u00edt\u00e1s\u00e1ban, sz\u00e1zal\u00e9kban kifejezve. Egy tengely egyes elemeinek \u00f6sszege 100; ;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>Cos\u00b2<\/strong>&nbsp;: a v\u00e1ltoz\u00f3 tengelyen val\u00f3 \u00e1br\u00e1zol\u00e1s\u00e1nak min\u0151s\u00e9ge; ;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2&nbsp;<strong>p<\/strong>&nbsp;: annak a val\u00f3sz\u00edn\u0171s\u00e9ge, hogy a megfigyelt korrel\u00e1ci\u00f3 v\u00e9letlen eredm\u00e9nye. Az \u00e9rt\u00e9k sz\u00ednez\u00e9ssel jelzi a \u201enagyon szignifik\u00e1ns\u201d \u00e9s a \u201enem szignifik\u00e1ns\u201d k\u00f6z\u00f6tti fokozatokat.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udca1 Ahhoz, hogy egy tengelyt elnevezz\u00fcnk, meg kell hat\u00e1roznunk azokat a v\u00e1ltoz\u00f3kat, amelyeknek a&nbsp;<strong>hozz\u00e1j\u00e1rul\u00e1s<\/strong>&nbsp;j\u00f3l l\u00e1that\u00f3an meghaladja az \u00e1tlagot (100 \/ v\u00e1ltoz\u00f3k sz\u00e1ma), \u00e9s amelynek a&nbsp;<strong>Cos\u00b2<\/strong>&nbsp;magas. Ezek az elemek adj\u00e1k meg a tengely \u00e9rtelm\u00e9t.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.6 Az \u201eEgy\u00e9nek\u201d f\u00fcl<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Ugyanez a logika, egyenk\u00e9nti vonalak: a k\u00f6z\u00e9ppontt\u00f3l m\u00e9rt t\u00e1vols\u00e1g, a koordin\u00e1t\u00e1k, a hozz\u00e1j\u00e1rul\u00e1sok \u00e9s a Cos\u00b2-\u00e9rt\u00e9kek.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Olyan szem\u00e9ly, akinek hozz\u00e1j\u00e1rul\u00e1sa messze meghaladja a t\u00f6bbiek\u00e9t&nbsp;<strong>egyed\u00fcl h\u00fazza ki a tengelyt<\/strong>&nbsp;: miel\u0151tt k\u00f6vetkeztet\u00e9st vonn\u00e1nk le, ellen\u0151rizz\u00fck, hogy nem be\u00edr\u00e1si hiba-e.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Egy adott pont Cos\u00b2-\u00e9rt\u00e9keinek \u00f6sszege az \u00f6sszes tengelyen 1-et ad ki. A megjelen\u00edtett tengelyeken teh\u00e1t ezek \u00f6sszege jelzi, hogy a pont helyzet\u00e9nek mekkora r\u00e9sze l\u00e1that\u00f3 val\u00f3j\u00e1ban.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.7 Tov\u00e1bbi v\u00e1ltoz\u00f3k \u00e9s c\u00edmk\u00e9k<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. z\u00f3na<\/strong>&nbsp;A k\u00e9perny\u0151n (a f\u00fclek felett) k\u00e9t v\u00e1laszt\u00f3gomb tal\u00e1lhat\u00f3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tov\u00e1bbi v\u00e1ltoz\u00f3k<\/strong>&nbsp;\u2014 m\u00e1s n\u00e9ven szeml\u00e9ltet\u0151 k\u00e9pek. Ezek&nbsp;<strong>tervezett<\/strong>&nbsp;a tengelyeken jelennek meg, de nem vesznek r\u00e9szt azok kialak\u00edt\u00e1s\u00e1ban. Ez a megfelel\u0151 m\u00f3dszer arra, hogy egy eredm\u00e9nyt egy k\u00fcls\u0151 v\u00e1ltoz\u00f3val \u00f6sszehasonl\u00edtsunk an\u00e9lk\u00fcl, hogy az befoly\u00e1soln\u00e1 az elemz\u00e9st.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2 Egy tov\u00e1bbi v\u00e1ltoz\u00f3&nbsp;<strong>mennyis\u00e9gi<\/strong>&nbsp;egy tov\u00e1bbi ny\u00edlk\u00e9nt jelenik meg a k\u00f6rben, valamint a \u00abTov\u00e1bbi mennyis\u00e9gi v\u00e1ltoz\u00f3k\u00bb f\u00fcl\u00f6n, az egyes tengelyekhez tartoz\u00f3 korrel\u00e1ci\u00f3j\u00e1val egy\u00fctt.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d2 Egy tov\u00e1bbi v\u00e1ltoz\u00f3&nbsp;<strong>min\u0151s\u00e9gi<\/strong>&nbsp;helyezd a&nbsp;<strong>barycentrum<\/strong>&nbsp;az egyes kateg\u00f3ri\u00e1k eset\u00e9ben a t\u00e9rk\u00e9pen: az azokat k\u00e9pvisel\u0151 egy\u00e9nek k\u00f6z\u00e9p\u00e9rt\u00e9ke. A szimb\u00f3lum m\u00e9rete ar\u00e1nyos a kateg\u00f3ria l\u00e9tsz\u00e1m\u00e1val.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u00abTov\u00e1bbi kvalitat\u00edv v\u00e1ltoz\u00f3k\u00bb f\u00fcl minden modalit\u00e1s eset\u00e9ben megadja a k\u00f6z\u00e9ppontt\u00f3l m\u00e9rt t\u00e1vols\u00e1got, a koordin\u00e1t\u00e1kat, a Cos\u00b2-\u00e9rt\u00e9keket, valamint egy&nbsp;<strong>p-\u00e9rt\u00e9k tengelyenk\u00e9nt<\/strong>. Ez a p-\u00e9rt\u00e9k arra a k\u00e9rd\u00e9sre ad v\u00e1laszt: ez a v\u00e1ltoz\u00f3 elv\u00e1lasztja-e az egy\u00e9neket ezen a tengelyen? Az alacsony p-\u00e9rt\u00e9k azt jelenti, hogy a kateg\u00f3ri\u00e1k egy\u00e9rtelm\u0171en elt\u00e9r\u0151 poz\u00edci\u00f3kat foglalnak el a tengelyen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C\u00edmke<\/strong>&nbsp;megjel\u00f6li az egy\u00e9neket: a pontjuk a kiv\u00e1lasztott m\u00f3d sz\u00edn\u00e9t veszi fel, \u00e9s a nev\u00fck megjelenik, ha a \u00abC\u00edmk\u00e9k megjelen\u00edt\u00e9se\u00bb jel\u00f6l\u0151n\u00e9gyzet be van jel\u00f6lve. Ez a legegyszer\u0171bb m\u00f3dja annak, hogy l\u00e1ssuk, kialakul-e egy csal\u00e1d.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udca1 Ne jel\u00f6lj\u00f6n meg egy v\u00e1ltoz\u00f3t egyszerre akt\u00edvnak \u00e9s kieg\u00e9sz\u00edt\u0151nek: ilyenkor a rendszer megalkotn\u00e1 a tengelyt, majd ezen a tengelyen \u00e9rt\u00e9keln\u00e9 a v\u00e1ltoz\u00f3t, ami semmit sem bizony\u00edt.<\/p>","protected":false},"featured_media":0,"menu_order":0,"template":"","meta":{"_acf_changed":true},"menu-guide-dutilisateur":[40],"class_list":["post-4480","guide-dutilisateur","type-guide-dutilisateur","status-publish","hentry","menu-guide-dutilisateur-6-statistiques-multivariees"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Analyse en composantes principales (ACP) - Ellistat<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrez comment le module Data Analysis d&#039;Ellistat identifie l&#039;origine des d\u00e9rives qualit\u00e9 gr\u00e2ce \u00e0 l&#039;analyse statistique multivari\u00e9e.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/hu\/hasznaloi-utmutato\/fokomponens-elemzes-pca\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Analyse en composantes principales (ACP) - 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