{"id":1420,"date":"2019-06-24T19:48:00","date_gmt":"2019-06-24T17:48:00","guid":{"rendered":"https:\/\/revista.newprojects.org\/?p=1420"},"modified":"2023-05-21T23:14:00","modified_gmt":"2023-05-21T21:14:00","slug":"analiza-masuratorilor-de-diagnosticare-a-diabetului-folosind-algoritmul-kmeans","status":"publish","type":"post","link":"https:\/\/revista.newprojects.org\/?p=1420","title":{"rendered":"Analiza m\u0103sur\u0103torilor de diagnosticare a diabetului folosind algoritmul KMEANS"},"content":{"rendered":"\n<h5 class=\"wp-block-heading\"><em>\u2013 Prof. T\u0103b\u00eerc\u0103 Angelica-Ioana, informatic\u0103 \u0219i TIC, Liceul Teoretic \u201eIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te<br>\u2013 Prof. T\u0103b\u00eerc\u0103 Nicolae-Radu, informatic\u0103 \u0219i TIC, Liceul Teoretic \u201eIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te<\/em><\/h5>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Conform studiului efectuat de Jain et al. (1999)[1]<\/em>, clusterizarea reprezint\u0103 o tehnic\u0103 fundamental\u0103 \u00een analiza datelor, care implic\u0103 gruparea obiectelor sau instan\u021belor similare \u00een clusteri sau grupuri distincte. Algoritmul K-Means este unul dintre cei mai r\u0103sp\u00e2ndi\u021bi \u0219i utilizati algoritmi de clusterizare.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Scopul clusteriz\u0103rii este de a identifica structurile sau tiparele ascunse \u00eentr-un set de date, facilit\u00e2nd \u00een\u021belegerea \u0219i extragerea informa\u021biilor relevante. Prin gruparea datelor similare, K-Means ofer\u0103 o metod\u0103 simpl\u0103 \u0219i eficient\u0103 de a rezuma \u0219i analiza seturile de date complexe.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Algoritmul K-Means se bazeaz\u0103 pe principiul c\u0103 un cluster este reprezentat de un centroid, care reprezint\u0103 media sau centrul geometric al datelor din acel cluster. Scopul algoritmului este s\u0103 atribuie fiecare instan\u021b\u0103 din setul de date unui cluster astfel \u00eenc\u00e2t suma p\u0103tratelor distan\u021belor dintre fiecare instan\u021b\u0103 \u0219i centroidul corespunz\u0103tor s\u0103 fie minim\u0103.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">K-Means utilizeaz\u0103 o strategie iterativ\u0103 pentru a g\u0103si centroizii optimi \u0219i pentru a atribui instan\u021bele la clusterii corespunz\u0103tori. Algoritmul \u00eencepe prin ini\u021bializarea aleatoare a centroizilor \u0219i apoi alterneaz\u0103 \u00eentre dou\u0103 metode: atribuirea instan\u021belor la clusterul cu cel mai apropiat centroid \u0219i recalcularea pozi\u021biilor centroizilor pe baza instan\u021belor alocate.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p class=\"wp-block-paragraph\">\u00cen timpul itera\u021biilor, algoritmul K-Means tinde s\u0103 minimizeze func\u021bia obiectiv\u0103 cunoscut\u0103 sub numele de sum of squared errors (SSE), care reprezint\u0103 suma p\u0103tratelor distan\u021belor dintre fiecare instan\u021b\u0103 \u0219i centroidul corespunz\u0103tor. Algoritmul converge atunci c\u00e2nd pozi\u021biile centroizilor nu mai sufer\u0103 modific\u0103ri semnificative sau c\u00e2nd criteriul de oprire specificat este \u00eendeplinit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Algoritmul K-Means are diverse aplica\u021bii practice, inclusiv analiza datelor, segmentarea imaginilor, recunoa\u0219terea de tipare, gruparea social\u0103 \u0219i multe altele. Capacitatea sa de a identifica structuri \u0219i rela\u021bii \u00een seturile de date \u00eel face o unealt\u0103 valoroas\u0103 \u00een domeniul \u0219tiin\u021bific \u0219i \u00een luarea deciziilor \u00een diverse industrii.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00cen continuare, voi explora detaliile implement\u0103rii algoritmului K-Means \u0219i voi analiza metodele de evaluare a performan\u021bei \u0219i limit\u0103rile acestui algoritm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Importan\u021ba \u0219i aplica\u021biile algoritmului K-Means<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Potrivit lui Jiawei Han (2011)[2],<\/em> algoritmul K-Means este extrem de important \u00een domeniul analizei datelor \u0219i clusteriz\u0103rii. Prin capacitatea sa de a grupa datele asem\u0103n\u0103toare \u00een clusteri, K-Means ofer\u0103 o modalitate eficient\u0103 de a extrage informa\u021bii semnificative \u0219i de a identifica tipare \u0219i structuri ascunse \u00een seturile de date.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplica\u021biile algoritmului K-Means sunt vaste \u0219i se \u00eentind pe mai multe domenii.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Segmentarea imaginilor<\/strong>: K-Means poate fi utilizat pentru segmentarea imaginilor, adic\u0103 \u00eemp\u0103r\u021birea imaginilor \u00een regiuni semnificative bazate pe caracteristici similare. Aceast\u0103 abordare poate fi utilizat\u0103 \u00een analiza medical\u0103, analiza imaginilor satelitare sau \u00een domeniul computer vision (ramur\u0103 a inteligen\u021bei artificiale).<\/li>\n\n\n\n<li><strong>Marketing \u0219i segmentarea clien\u021bilor:<\/strong> K-Means poate fi aplicat \u00een domeniul marketingului pentru segmentarea clien\u021bilor \u00een grupuri cu caracteristici similare, cum ar fi preferin\u021bele de cump\u0103rare, comportamentul de consum sau caracteristicile demografice. Aceasta permite personalizarea strategiilor de marketing \u0219i dezvoltarea de campanii mai eficiente.<\/li>\n\n\n\n<li><strong>Recunoa\u0219terea de modele:<\/strong> K-Means poate fi folosit pentru recunoa\u0219terea de modele \u00een seturile de date, cum ar fi recunoa\u0219terea de modele de fraud\u0103 \u00een tranzac\u021biile financiare, recunoa\u0219terea de modele de comportament \u00een re\u021bele sociale sau recunoa\u0219terea de modele \u00een analiza datelor biologice.<\/li>\n\n\n\n<li><strong>\u00cen\u021belegerea comportamentului consumatorilor:<\/strong> K-Means poate fi utilizat pentru a \u00een\u021belege \u0219i analiza comportamentul consumatorilor \u00een diverse industrii, cum ar fi retail, comer\u021b electronic sau turism. Prin identificarea segmentelor de consumatori \u0219i caracteristicilor lor comune, se pot dezvolta strategii de marketing \u0219i abord\u0103ri personalizate.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Concepte de baz\u0103 \u00een clusterizare<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Clusterizarea este o tehnic\u0103 utilizat\u0103 \u00een analiza datelor pentru a grupa obiecte sau instan\u021be similare \u00een clusteri sau grupuri distincte. Scopul clusteriz\u0103rii este de a identifica structuri sau tipare ascunse \u00eentr-un set de date \u0219i de a facilita \u00een\u021belegerea \u0219i extragerea informa\u021biilor relevante.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00cen clusterizare, principalele concepte de baz\u0103 sunt:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Clusterul<\/strong>: Un cluster reprezint\u0103 un grup sau o colec\u021bie de obiecte sau instan\u021be care sunt similare \u00eentre ele. Obiectele din acela\u0219i cluster prezint\u0103 o similaritate mai mare \u00eentre ele dec\u00e2t cu obiectele din al\u021bi clusteri.<\/li>\n\n\n\n<li><strong>Centroidul<\/strong>: Un centroid reprezint\u0103 un punct central sau un reprezentant al unui cluster. Este adesea calculat ca medie sau ca centru geometric al obiectelor din acel cluster \u0219i serve\u0219te ca referin\u021b\u0103 pentru atribuirea instan\u021belor la clusteri.<\/li>\n\n\n\n<li><strong>Similaritatea\/Distan\u021ba<\/strong>: Similaritatea sau distan\u021ba m\u0103soar\u0103 gradul de asem\u0103nare sau diferen\u021b\u0103 \u00eentre dou\u0103 obiecte sau instan\u021be. Exist\u0103 diverse m\u0103suri de similaritate \u0219i distan\u021b\u0103 utilizate \u00een clusterizare, cum ar fi distan\u021ba euclidian\u0103, distan\u021ba Manhattan sau coeficientul de similaritate cosinus.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Algoritmul K-Means: principii \u0219i etape<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Algoritmul K-Means este un algoritm iterativ utilizat pentru clusterizare. Principiul de baz\u0103 al algoritmului K-Means este de a atribui fiecare instan\u021b\u0103 din setul de date unui cluster, astfel \u00eenc\u00e2t suma p\u0103tratelor distan\u021belor dintre fiecare instan\u021b\u0103 \u0219i centroidul corespunz\u0103tor s\u0103 fie minim\u0103 [3].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Etapele principale ale algoritmului K-Means sunt urm\u0103toarele:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Ini\u021bializare<\/strong>: Se alege num\u0103rul dorit de clusteri, K, \u0219i se ini\u021bializeaz\u0103 aleator centroizii pentru fiecare cluster.<\/li>\n\n\n\n<li><strong>Atribuirea la clusteri<\/strong>: Fiecare instan\u021b\u0103 din setul de date este atribuit\u0103 clusterului cu cel mai apropiat centroid. Aici, similaritatea sau distan\u021ba \u00eentre instan\u021b\u0103 \u0219i centroid este calculat\u0103 folosind o m\u0103sur\u0103 specific\u0103.<\/li>\n\n\n\n<li><strong>Recalcularea centroizilor<\/strong>: Dup\u0103 atribuirea ini\u021bial\u0103, se recalculeaz\u0103 pozi\u021biile centroizilor pe baza instan\u021belor alocate. Centroidul este actualizat ca medie sau centrul geometric al instan\u021belor din acel cluster.<\/li>\n\n\n\n<li><strong>Itera\u021bie<\/strong>: Pa\u0219ii 2 \u0219i 3 sunt repeta\u021bi p\u00e2n\u0103 c\u00e2nd pozi\u021biile centroizilor nu mai sufer\u0103 modific\u0103ri semnificative sau p\u00e2n\u0103 c\u00e2nd criteriul de oprire specificat este \u00eendeplinit.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Algoritmul K-Means converge la o solu\u021bie local\u0103, iar rezultatul final depinde de ini\u021bializarea aleatoare a centroizilor \u0219i de num\u0103rul de clusteri selectat.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Exemplu model teoretic<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"219\" height=\"234\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS1.png\" alt=\"\" class=\"wp-image-1427\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS1.png 219w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS1-140x150.png 140w\" sizes=\"auto, (max-width: 219px) 100vw, 219px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a>Figur\u0103 <\/a>1. Set de date bisimensional<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pentru a demonstra modul \u00een care func\u021bioneaz\u0103 algoritmul K-Means, voi utiliza un exemplu simplificat. S\u0103 presupunem c\u0103 avem un set de date bidimensional compus din \u0219apte puncte: A(1, 1), B(1, 2), C(2, 1), D(4, 3), E(5, 4), F(4, 5) \u0219i G(5, 5).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pentru a aplica algoritmul K-Means, trebuie specificat num\u0103rul de clusteri k. S\u0103 alegem k = 2 pentru acest exemplu.<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li><strong>Ini\u021bializarea<\/strong>: Se selecteaz\u0103 aleatoriu dou\u0103 puncte din setul de date ca centroizi ini\u021biali. Presupunerea este c\u0103 primii doi centroizi ini\u021biali sunt C\u2081(1, 1) \u0219i C\u2082(4, 5).<\/li>\n\n\n\n<li><strong>Atribuirea<\/strong>: Fiecare punct din setul de date este atribuit clusterului reprezentat de cel mai apropiat centroid. \u00cen acest caz, A, B \u0219i C sunt mai apropia\u021bi de C\u2081, iar D, E, F \u0219i G sunt mai apropia\u021bi de C\u2082.<\/li>\n\n\n\n<li><strong>Recalcularea<\/strong>: Se calculeaz\u0103 noi pozi\u021bii pentru centroizi pe baza punctelor atribuite. Noile pozi\u021bii sunt determinate prin calcularea mediei aritmetice a coordonatelor punctelor din fiecare cluster. Astfel, C\u2081 se va reloca la (1.33, 1.33), iar C\u2082 la (4.5, 4.25).<\/li>\n\n\n\n<li><strong>Itera\u021bii<\/strong>: Pa\u0219ii de atribuire \u0219i recalculare se repet\u0103 p\u00e2n\u0103 c\u00e2nd pozi\u021biile centroizilor nu se mai modific\u0103 sau se atinge un num\u0103r maxim de itera\u021bii. \u00cen acest exemplu, dup\u0103 c\u00e2teva itera\u021bii, algoritmul converge la urm\u0103toarele pozi\u021bii pentru centroizi: C\u2081(1.33, 1.33) \u0219i C\u2082(4.5, 4.25).<\/li>\n\n\n\n<li><strong>Rezultat<\/strong>: Dup\u0103 ce algoritmul K-Means converge, rezult\u0103 doi clusteri: clusterul 1 format din punctele A, B \u0219i C, \u0219i clusterul 2 format din punctele D, E, F \u0219i G.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS2.png\"><img loading=\"lazy\" decoding=\"async\" width=\"213\" height=\"236\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS2.png\" alt=\"\" class=\"wp-image-1428\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS2.png 213w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS2-135x150.png 135w\" sizes=\"auto, (max-width: 213px) 100vw, 213px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a>Figur\u0103 <\/a>2. Rezultat kMeans<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Algoritmul K-Means \u00eemparte setul de date \u00een clusteri disjunc\u021bi, cu scopul de a minimiza suma p\u0103tratelor distan\u021belor dintre punctele de date \u0219i centroizii clusterilor lor. \u00cen exemplul dat, am ob\u021binut doi clusteri prin aplicarea algoritmului K-Means.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>M\u0103surile de similaritate \u0219i distan\u021b\u0103 utilizate \u00een K-Means<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00cen algoritmul K-Means, m\u0103surile de similaritate sau distan\u021b\u0103 sunt utilizate pentru a calcula gradul de asem\u0103nare sau diferen\u021b\u0103 \u00eentre instan\u021be. Aceste m\u0103suri sunt esen\u021biale \u00een etapa de atribuire a instan\u021belor la clusteri \u0219i \u00een recalcularea centroizilor.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exist\u0103 mai multe m\u0103suri de similaritate \u0219i distan\u021b\u0103 utilizate \u00een K-Means, iar alegerea lor depinde de natura datelor \u0219i cerin\u021bele specifice ale problemei [4].<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Distan\u021ba euclidian\u0103:<\/strong> Este m\u0103sura cea mai utilizat\u0103 \u0219i se calculeaz\u0103 ca r\u0103d\u0103cina p\u0103trat\u0103 a sumei p\u0103tratelor diferen\u021belor dintre valorile caracteristicilor a dou\u0103 instan\u021be.<\/li>\n\n\n\n<li><strong>Distan\u021ba Manhattan<\/strong>: Aceast\u0103 m\u0103sur\u0103 calculeaz\u0103 suma valorilor absolute ale diferen\u021belor dintre valorile caracteristicilor a dou\u0103 instan\u021be.<\/li>\n\n\n\n<li><strong>Coeficientul de similaritate cosinus:<\/strong> Aceast\u0103 m\u0103sur\u0103 m\u0103soar\u0103 unghiul dintre doi vectori \u00eentr-un spa\u021biu multidimensional \u0219i este utilizat\u0103 \u00een special pentru date reprezentate ca vectori de caracteristici [4].<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Alegerea m\u0103surii de similaritate sau distan\u021b\u0103 adecvat\u0103 este important\u0103 pentru ob\u021binerea unor rezultate bune \u00een algoritmul K-Means \u0219i trebuie adaptat\u0103 la specificul problemei \u0219i tipul de date utilizat.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ini\u021bializarea centroizilor<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u00cen studiul lui Arthur \u0219i Vassilvitskii (2007)[5], se propune o metod\u0103 de ini\u021bializare a centroizilor numit\u0103 K-means++ care \u00eembun\u0103t\u0103\u021be\u0219te performan\u021ba algoritmului K-Means prin selec\u021bia atent\u0103 a punctelor ini\u021biale.<\/em> \u00cen implementarea algoritmului K-Means, prima etap\u0103 este ini\u021bializarea centroizilor. Ini\u021bializarea poate fi realizat\u0103 \u00een mai multe moduri:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ini\u021bializarea aleatoare: Centroizii sunt ale\u0219i aleatoriu din setul de date. Aceast\u0103 metod\u0103 este simpl\u0103 \u0219i rapid\u0103, dar poate duce la convergen\u021b\u0103 la minime locale \u0219i poate necesita mai multe itera\u021bii pentru a ob\u021bine rezultate bune.<\/li>\n\n\n\n<li>Ini\u021bializarea pe baza unor euristici: Se utilizeaz\u0103 euristici specifice pentru a alege pozi\u021biile ini\u021biale ale centroizilor. De exemplu, se pot alege instan\u021be care au o dispersie maxim\u0103 sau se pot folosi alte metode specifice domeniului de aplicare.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Etapele atribuirii \u0219i recalcul\u0103rii<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Algoritmul K-Means, a\u0219a cum a fost prezentat de Lloyd (1982)[6], const\u0103 \u00een iterarea etapelor de atribuire a instan\u021belor la clusteri \u0219i de recalculare a centroizilor pentru a ob\u021bine o solu\u021bie convergent\u0103<\/em>. Dup\u0103 ini\u021bializarea centroizilor, algoritmul K-Means parcurge urm\u0103toarele etape iterative pentru a atribui instan\u021bele la clusteri \u0219i pentru a recalcula centroizii:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Atribuirea la clusteri: Fiecare instan\u021b\u0103 din setul de date este atribuit\u0103 la cel mai apropiat centroid \u00een func\u021bie de o m\u0103sur\u0103 de distan\u021b\u0103 sau similaritate. De obicei, se folose\u0219te distan\u021ba euclidian\u0103.<\/li>\n\n\n\n<li>Recalcularea centroizilor: Dup\u0103 ce toate instan\u021bele sunt atribuite, centroizii sunt recalcula\u021bi pe baza instan\u021belor aflate \u00een clusterii respectivi. Recalcularea se face prin calcularea mediei valorilor caracteristicilor pentru instan\u021bele din fiecare cluster.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Aceste dou\u0103 etape (atribuirea \u0219i recalcularea) sunt repetate p\u00e2n\u0103 c\u00e2nd algoritmul converge \u0219i nu mai are loc o schimbare semnificativ\u0103 \u00een pozi\u021biile centroizilor \u0219i atribu\u021biilor instan\u021belor.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Criterii de oprire \u0219i convergen\u021b\u0103<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>MacQueen (1967) define\u0219te criteriile de oprire \u0219i convergen\u021b\u0103 utilizate \u00een algoritmul K-Means, care se bazeaz\u0103 pe schimb\u0103rile minime \u00een pozi\u021biile centroizilor \u0219i atribu\u021biile instan\u021belor \u00eentre itera\u021bii consecutive [7].<\/em> Algoritmul K-Means utilizeaz\u0103 anumite criterii de oprire pentru a determina c\u00e2nd s-a atins convergen\u021ba \u0219i algoritmul poate fi oprit.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Num\u0103rul maxim de itera\u021bii: Se specific\u0103 un num\u0103r maxim de itera\u021bii dup\u0103 care algoritmul se opre\u0219te, indiferent dac\u0103 a convergat sau nu.<\/li>\n\n\n\n<li>Schimbarea minim\u0103 a pozi\u021biilor centroizilor: Algoritmul se opre\u0219te atunci c\u00e2nd diferen\u021ba dintre pozi\u021biile centroizilor la itera\u021biile consecutive este mai mic\u0103 dec\u00e2t o valoare de prag predefinit\u0103.<\/li>\n\n\n\n<li>Convergen\u021ba complet\u0103: Algoritmul se opre\u0219te atunci c\u00e2nd nu mai are loc nicio schimbare \u00een atribu\u021biile instan\u021belor \u0219i pozi\u021biile centroizilor \u00eentre dou\u0103 itera\u021bii consecutive.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Aceste criterii de oprire asigur\u0103 c\u0103 algoritmul K-Means se opre\u0219te \u00eentr-un punct \u00een care rezultatele sunt stabile \u0219i converge la o solu\u021bie acceptabil\u0103.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>M\u0103suri de evaluare a calit\u0103\u021bii clusteriz\u0103rii (ex: SSE, Silhouette score)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>SSE \u0219i coeficientul Silhouette sunt m\u0103suri larg acceptate \u00een evaluarea clusteriz\u0103rii, conform studiului lui Jain (2010) [8] \u0219i Jain et al. (1999)[9].<\/em> Pentru a evalua calitatea clusteriz\u0103rii ob\u021binute folosind algoritmul K-Means, exist\u0103 o serie de m\u0103suri utilizate \u00een literatura de specialitate. Dou\u0103 dintre cele mai comune m\u0103suri sunt Suma P\u0103tratelor Erorilor (SSE) \u0219i coeficientul Silhouette.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Suma P\u0103tratelor Erorilor (SSE): SSE este o m\u0103sur\u0103 a varia\u021biei din interiorul clusterilor \u0219i se calculeaz\u0103 ca suma p\u0103tratelor distan\u021belor dintre fiecare punct \u0219i centrul clusterului s\u0103u asignat. Un SSE mai mic indic\u0103 o clusterizare mai bun\u0103, \u00een care punctele din fiecare cluster sunt mai apropiate de centrul lor.<\/li>\n\n\n\n<li>Coeficientul Silhouette: Silhouette este o m\u0103sur\u0103 a separa\u021biei \u0219i coeziunii \u00eentre clusteri. Acest coeficient este calculat pentru fiecare punct, lu\u00e2nd \u00een considerare distan\u021ba medie fa\u021b\u0103 de celelalte puncte din acela\u0219i cluster (a) \u0219i distan\u021ba medie fa\u021b\u0103 de ceilal\u021bi clusteri (b). Coeficientul Silhouette variaz\u0103 \u00eentre -1 \u0219i 1, unde valori mai mari indic\u0103 o clusterizare mai bun\u0103, cu separare mai mare \u00eentre clusteri \u0219i coeziune mai mare \u00een cadrul aceluia\u0219i cluster.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Aceste m\u0103suri pot fi utilizate pentru a evalua \u0219i compara rezultatele diferitelor rul\u0103ri ale algoritmului K-Means sau pentru a compara performan\u021ba acestuia cu al\u021bi algoritmi de clusterizare.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Compararea cu al\u021bi algoritmi de clusterizare<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Pentru o compara\u021bie \u00eentre algoritmul K-Means \u0219i al\u021bi algoritmi de clusterizare, se poate consulta studiul lui Jain (2010) [8], care ofer\u0103 o perspectiv\u0103 cuprinz\u0103toare asupra diferitelor metode de clusterizare \u0219i a performan\u021bei lor. <\/em>Algoritmul K-Means este doar unul dintre numero\u0219ii algoritmi de clusterizare disponibili \u00een literatura de specialitate. Exist\u0103 \u0219i al\u021bi algoritmi care pot fi utiliza\u021bi \u00een func\u021bie de specificul setului de date \u0219i obiectivele cercet\u0103rii. C\u00e2teva exemple de algoritmi de clusterizare care pot fi compara\u021bi cu K-Means includ:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>DBSCAN (Density-Based Spatial Clustering of Applications with Noise): Acest algoritm utilizeaz\u0103 densitatea punctelor pentru a identifica regiuni dense \u00een spa\u021biul de caracteristici \u0219i separ\u0103 punctele din zonele dense de cele din zonele mai pu\u021bin dense.<\/li>\n\n\n\n<li>Hierarchical Clustering: Acest tip de algoritm construie\u0219te o ierarhie a clusterilor prin unirea sau divizarea acestora \u00een func\u021bie de m\u0103surile de similaritate \u00eentre puncte sau clusteri.<\/li>\n\n\n\n<li>Gaussian Mixture Models (GMM): Acest algoritm asociaz\u0103 fiec\u0103rui punct o probabilitate de a apar\u021bine unui anumit cluster, folosind o combina\u021bie de distribu\u021bii gaussiene. GMM poate fi utilizat pentru a identifica clusteri cu forme complexe \u0219i distribu\u021bii de probabilitate diferite.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Compararea \u00eentre algoritmul K-Means \u0219i al\u021bi algoritmi de clusterizare poate fi realizat\u0103 pe baza performan\u021bei lor \u00een func\u021bie de m\u0103suri specifice, cum ar fi SSE sau coeficientul Silhouette. \u00cen plus, se pot lua \u00een considerare \u0219i caracteristicile specifice ale algoritmului, precum capacitatea de a gestiona date cu zgomot sau capacitatea de a identifica clusteri de form\u0103 \u0219i dimensiune variate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Avantaje \u0219i aplica\u021bii specifice:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Avantajele \u0219i aplica\u021biile specifice ale algoritmului K-Means sunt prezentate \u00een conformitate cu studiul lui Jain (2010)[8] \u0219i Jain et al. (1999) [10].<\/em> Algoritmul K-Means are mai multe avantaje care \u00eel fac util:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplitate \u0219i eficien\u021b\u0103: K-Means este un algoritm simplu \u0219i eficient \u00een timpul de execu\u021bie, ceea ce \u00eel face potrivit pentru seturi mari de date.<\/li>\n\n\n\n<li>Interpretabilitate: Rezultatele algoritmului K-Means sunt u\u0219or de interpretat, deoarece clusterii ob\u021binu\u021bi pot fi reprezenta\u021bi prin centroizi.<\/li>\n\n\n\n<li>Scalabilitate: Algoritmul K-Means poate fi aplicat \u0219i pe seturi de date de dimensiuni mari \u0219i poate fi paralelizat pentru a accelera procesul de clusterizare.<\/li>\n\n\n\n<li>Aplica\u021bii practice: K-Means este folosit \u00een diverse domenii, cum ar fi analiza datelor, segmentarea pie\u021belor, recunoa\u0219terea de tipare, analiza imaginilor \u0219i multe altele.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Limit\u0103ri \u0219i cazuri \u00een care K-Means poate fi mai pu\u021bin eficient:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Limit\u0103rile \u0219i cazurile \u00een care K-Means poate fi mai pu\u021bin eficient sunt discutate pe baza cercet\u0103rilor lui Jain (2010)[8] \u0219i Jain et al. (1999) [10]. <\/em>Cu toate acestea, algoritmul K-Means are \u0219i c\u00e2teva limit\u0103ri \u0219i exist\u0103 cazuri \u00een care poate fi mai pu\u021bin eficient:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sensibilitate la ini\u021bializare: Performan\u021ba K-Means poate varia \u00een func\u021bie de ini\u021bializarea centroizilor. Ini\u021bializarea necorespunz\u0103toare poate duce la ob\u021binerea de solu\u021bii suboptimale.<\/li>\n\n\n\n<li>Dependen\u021b\u0103 de num\u0103rul de clusteri: Trebuie specificat num\u0103rul de clusteri \u00een avans, ceea ce poate fi o provocare \u00een anumite situa\u021bii \u00een care acest lucru nu este cunoscut \u00een prealabil sau nu este evident.<\/li>\n\n\n\n<li>Sensibilitate la forme \u0219i dimensiuni diferite: K-Means poate avea dificult\u0103\u021bi \u00een gestionarea seturilor de date cu clusteri de forme \u0219i dimensiuni variate sau cu densit\u0103\u021bi inegale.<\/li>\n\n\n\n<li>Sensibilitate la date cu zgomot: Prezen\u021ba datelor cu zgomot poate afecta performan\u021ba algoritmului K-Means, determin\u00e2nd formarea de clusteri incorec\u021bi sau dispersa\u021bi.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Este important s\u0103 se ia \u00een considerare aceste limit\u0103ri \u0219i s\u0103 se evalueze corespunz\u0103tor adecvarea utiliz\u0103rii algoritmului K-Means \u00eentr-un context specific.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Rezultate<\/strong><strong><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Setul de date \u0219i prelucrarea acestuia<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Setul de date utilizat \u00een acest studiu provine de la Institutul Na\u021bional al Diabetului \u0219i al Bolilor Digestive \u0219i Renale, care face parte din Institutul Na\u021bional de S\u0103n\u0103tate al Statelor Unite. Acesta este disponibil pe platforma Kaggle la urm\u0103toarea adres\u0103: <a href=\"https:\/\/www.kaggle.com\/datasets\/mathchi\/diabetes-data-set.\">https:\/\/www.kaggle.com\/datasets\/mathchi\/diabetes-data-set.<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Acest set de date este alc\u0103tuit din m\u0103sur\u0103tori privind diabetul pentru pacientele de gen feminin, \u00een v\u00e2rst\u0103 de cel pu\u021bin 21 de ani, de origine indian\u0103. Scopul studiului este de a analiza gruparea acestor paciente utiliz\u00e2nd algoritmi de clusterizare, \u00een func\u021bie de indicatorii specifici diabetului. Setul de date con\u021bine urm\u0103toarele variabile:<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li><strong>ID<\/strong>: id-ul unic al fiec\u0103rei paciente;<\/li>\n\n\n\n<li><strong>Pregnancies<\/strong>: Num\u0103rul de sarcini;<\/li>\n\n\n\n<li><strong>Glucose<\/strong>: Concentra\u021bia de glucoz\u0103 plasmatic\u0103 la 2 ore \u00een cadrul unui test de toleran\u021b\u0103 la glucoz\u0103 oral\u0103;<\/li>\n\n\n\n<li><strong>BloodPressure<\/strong>: Tensiunea arterial\u0103 diastolic\u0103 (mm Hg);<\/li>\n\n\n\n<li><strong>SkinThickness<\/strong>: Grosimea pliului cutanat al tricepsului (mm);<\/li>\n\n\n\n<li><strong>Insulin<\/strong>: Insulin\u0103 seric\u0103 la 2 ore (mu U\/ml);<\/li>\n\n\n\n<li><strong>BMI<\/strong>: Indicele de mas\u0103 corporal\u0103 (greutate \u00een kg\/(\u00een\u0103l\u021bime \u00een m)^2);<\/li>\n\n\n\n<li><strong>DiabetesPedigreeFunction<\/strong>: Func\u021bia pedigree pentru diabet;<\/li>\n\n\n\n<li><strong>Age<\/strong>: v\u00e2rsta \u00een ani.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u00cenainte de a aplica algoritmii de clusterizare, setul de date a fost prelucrat pentru a asigura calitatea \u0219i consisten\u021ba acestuia. Acest proces de prelucrare a implicat urm\u0103torii pa\u0219i:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Cur\u0103\u021barea datelor<\/strong>: Identificarea \u0219i eliminarea eventualelor erori sau anomalii, precum valorile lips\u0103 sau incorecte.<\/li>\n\n\n\n<li><strong>Transformarea datelor<\/strong>: Conversia datelor \u00eentr-un format adecvat pentru aplicarea algoritmilor de clusterizare, cum ar fi normalizarea sau scalarea variabilelor.<\/li>\n\n\n\n<li><strong>Reducerea dimensiunilor<\/strong>: Selec\u021bionarea celor mai relevante variabile pentru analiza clusteriz\u0103rii, elimin\u00e2nd variabilele redundante sau coliniare, prin tehnici precum analiza componentelor principale (PCA) sau selec\u021bia univariat\u0103 a caracteristicilor.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Dup\u0103 prelucrarea \u0219i preg\u0103tirea setului de date, acesta a fost folosit pentru aplicarea \u0219i evaluarea algoritmului de clusterizare kMeans. Algoritmul a fost implementat \u00een limbajul de programare Python, folosindu-se biblioteci \u0219i pachete software specifice, cum ar fi scikit-learn \u0219i NumPy.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Rezultatele ob\u021binute prin kMeans \u00een Python<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analiza clusterilor prin histograme<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Prezentarea clusterilor<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Conform studiului lui Jain et al. (1999)[1], clusterizarea datelor este un domeniu de cercetare vast \u0219i exist\u0103 multiple metode \u0219i seturi de date utilizate pentru exemplificarea algoritmului K-Means.<\/em> Pentru a exemplifica aplicarea algoritmului K-Means, voi aplica algoritmul pe setul de date \u00een Python.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Alegerea valorii k<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u00cen lucrarea lui Tibshirani et al. (2001), se propune o metod\u0103 de estimare a num\u0103rului optim de clusteri, cunoscut\u0103 sub numele de gap statistic, care poate fi utilizat\u0103 \u00een procesul de alegere a valorii k \u00een algoritmul K-Means [11].<\/em> Pentru a aplica algoritmul K-Means, este necesar\u0103 alegerea valorii k, care reprezint\u0103 num\u0103rul de clusteri \u00een care dorim s\u0103 grup\u0103m obiectele. Aceast\u0103 alegere poate fi realizat\u0103 prin diverse metode, precum analiza exploratorie a datelor, expertiza de domeniu sau utilizarea unor metode statistice.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Biblioteca scikit-learn, men\u021bionat\u0103 \u00een lucrarea lui Pedregosa et al. (2011) [13], ofer\u0103 func\u021bionalit\u0103\u021bi pentru implementarea algoritmului K-Means \u00een Python \u0219i va fi folosit\u0103 \u00een exemplul nostru de implementare.<\/em> Pentru implementarea algoritmului K-Means, voi folosi limbajul de programare Python \u0219i biblioteca scikit-learn, care ofer\u0103 func\u021bionalit\u0103\u021bi pentru clusterizare. Voi utiliza urm\u0103torii pa\u0219i:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Importarea bibliotecilor necesare: import\u0103m biblioteca scikit-learn \u0219i alte biblioteci utile, cum ar fi numpy \u0219i matplotlib.<\/li>\n\n\n\n<li>\u00cenc\u0103rcarea setului de date: \u00eenc\u0103rc\u0103m setul de date \u00eentr-o variabil\u0103 pentru a-l putea utiliza \u00een algoritmul K-Means.<\/li>\n\n\n\n<li>Ini\u021bializarea algoritmului: ini\u021bializ\u0103m algoritmul K-Means, specific\u00e2nd num\u0103rul de clusteri dorit (k = x).<\/li>\n\n\n\n<li>Aplicarea algoritmului: aplic\u0103m algoritmul K-Means asupra setului de date pentru a ob\u021bine rezultatele.<\/li>\n\n\n\n<li>Vizualizarea rezultatelor: reprezent\u0103m grafic rezultatele ob\u021binute, afi\u0219\u00e2nd punctele din setul de date colorate \u00een func\u021bie de clusterii atribui\u021bi de algoritm.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Interpretarea rezultatelor \u0219i analiza clusterilor ob\u021binu\u021bi<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dup\u0103 aplicarea algoritmului K-Means \u0219i ob\u021binerea rezultatelor, urmeaz\u0103 interpretarea \u0219i analiza clusterilor ob\u021binu\u021bi. Acest lucru poate implica:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Vizualizarea centroizilor: reprezentarea grafic\u0103 a pozi\u021biilor centroizilor \u00een spa\u021biul caracteristicilor, pentru a ob\u021bine o imagine a distribu\u021biei acestora.<\/li>\n\n\n\n<li>Analiza caracteristicilor clusterilor: evaluarea valorilor medii sau alte statistici relevante ale caracteristicilor pentru fiecare cluster \u00een parte, pentru a \u00een\u021belege diferen\u021bele \u0219i similarit\u0103\u021bile \u00eentre clusteri.<\/li>\n\n\n\n<li>Interpretarea rezultatelor: interpretarea \u0219i \u00een\u021belegerea semnifica\u021biei fiec\u0103rui cluster \u00een contextul studiului, identificarea caracteristicilor distinctive ale fiec\u0103rui cluster \u0219i posibilele concluzii extrase din analiza clusterilor.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><br>\u00cen continuare, voi detalia implementarea exemplului de aplicare a algoritmului K-Means \u00een Python, urm\u00e2nd pa\u0219ii men\u021biona\u021bi mai sus.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS01.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"480\" height=\"352\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS01.jpg\" alt=\"\" class=\"wp-image-1430\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS01.jpg 480w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS01-300x220.jpg 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS01-150x110.jpg 150w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 1. Codul surs\u0103 &#8211; implementarea algoritmului kMeans \u00een Python<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicarea algoritmului kMeans \u00een Python pe setul de date conduce la histogramele urm\u0103toare specifice celor 5 clusteri:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>V\u00e2rsta<\/strong> \u2013 pacien\u021bii care au v\u00e2rsta cea mai mare se situeaz\u0103 \u00een clusterul 1<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS02.png\"><img loading=\"lazy\" decoding=\"async\" width=\"521\" height=\"321\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS02.png\" alt=\"\" class=\"wp-image-1431\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS02.png 521w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS02-300x185.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS02-150x92.png 150w\" sizes=\"auto, (max-width: 521px) 100vw, 521px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 2. Histogram\u0103 kMeans (id = v\u00e2rst\u0103)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Probabilitatea de diabet pe baza antecedentelor familiale &#8211; <strong>pacien\u021bii care au probabilitatea de diabet<\/strong> cea mai mare se situeaz\u0103 \u00een clusterii 1 \u0219i 5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS03.png\"><img loading=\"lazy\" decoding=\"async\" width=\"543\" height=\"322\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS03.png\" alt=\"\" class=\"wp-image-1432\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS03.png 543w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS03-300x178.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS03-150x89.png 150w\" sizes=\"auto, (max-width: 543px) 100vw, 543px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 3. Histogram\u0103 kMeans (id = pb. de diabet)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Indicele de mas\u0103 corporal\u0103<\/strong> &#8211; pacien\u021bii care au indicele de mas\u0103 corporal\u0103 cel mai mare se situeaz\u0103 \u00een clusterul 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS04.png\"><img loading=\"lazy\" decoding=\"async\" width=\"567\" height=\"333\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS04.png\" alt=\"\" class=\"wp-image-1433\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS04.png 567w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS04-300x176.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS04-150x88.png 150w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 4. Histogram\u0103 kMeans (id = indicele de mas\u0103 corporal\u0103)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Insulin\u0103<\/strong> &#8211; pacien\u021bii care au insulina cea mai mare se situeaz\u0103 \u00een clusterul 5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS05.png\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"327\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS05.png\" alt=\"\" class=\"wp-image-1434\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS05.png 600w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS05-300x164.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS05-150x82.png 150w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 5. Histogram\u0103 kMeans (id = insulin\u0103)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Grosimea pielii &#8211; <\/strong>pacien\u021bii care au grosimea pielii cea mai mare se situeaz\u0103 \u00een clusterul 1.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS06.png\"><img loading=\"lazy\" decoding=\"async\" width=\"577\" height=\"334\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS06.png\" alt=\"\" class=\"wp-image-1435\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS06.png 577w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS06-300x174.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS06-150x87.png 150w\" sizes=\"auto, (max-width: 577px) 100vw, 577px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 6. Histogram\u0103 kMeans (id = grosimea pielii)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Presiunea arterial\u0103 &#8211; <\/strong>pacien\u021bii care au presiunea arterial\u0103 cea mai mare se situeaz\u0103 \u00een clusterii 1, 2 \u0219i 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS07.png\"><img loading=\"lazy\" decoding=\"async\" width=\"542\" height=\"343\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS07.png\" alt=\"\" class=\"wp-image-1436\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS07.png 542w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS07-300x190.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS07-150x95.png 150w\" sizes=\"auto, (max-width: 542px) 100vw, 542px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 7. Histogram\u0103 kMeans (id = presiune arterial\u0103)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Cantitatea de glucoz\u0103<\/strong> &#8211; pacien\u021bii care au cantitatea de glucoz\u0103 cea mai mic\u0103 se situeaz\u0103 \u00een clusterul 1.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS08.png\"><img loading=\"lazy\" decoding=\"async\" width=\"539\" height=\"338\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS08.png\" alt=\"\" class=\"wp-image-1437\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS08.png 539w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS08-300x188.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS08-150x94.png 150w\" sizes=\"auto, (max-width: 539px) 100vw, 539px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 8. Histogram\u0103 kMeans (id = cantitatea de glucoz\u0103)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Num\u0103rul de na\u0219teri<\/strong> &#8211; pacien\u021bii care au num\u0103rul de na\u0219teri cea mai mic\u0103 se situeaz\u0103 \u00een clusterul 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS09.png\"><img loading=\"lazy\" decoding=\"async\" width=\"589\" height=\"322\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS09.png\" alt=\"\" class=\"wp-image-1438\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS09.png 589w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS09-300x164.png 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS09-150x82.png 150w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 9. Histogram\u0103 kMeans (id = nr. de na\u0219teri)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Graficul parti\u021biei eviden\u021biaz\u0103 grup\u0103rile cele mai bine format\u0103 pentru clusterii c3 \u0219i c4.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS10.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"514\" height=\"328\" src=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS10.jpg\" alt=\"\" class=\"wp-image-1439\" srcset=\"https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS10.jpg 514w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS10-300x191.jpg 300w, https:\/\/revista.newprojects.org\/wp-content\/uploads\/KMEANS10-150x96.jpg 150w\" sizes=\"auto, (max-width: 514px) 100vw, 514px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Figur\u0103 10. Graficul parti\u021biei kMeans<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Referin\u021be bibliografice<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[1]: <\/strong><a href=\"https:\/\/dl.acm.org\/doi\/10.1145\/331499.331504\">https:\/\/dl.acm.org\/doi\/10.1145\/331499.331504<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Jain, A. K., Murty, M. N., &amp; Flynn, P. J. (1999). Data clustering: A review. ACM Computing Surveys (CSUR), 31(3), 264-323.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[2]: <\/strong><a href=\"https:\/\/www.sciencedirect.com\/book\/9780123814791\/data-mining-concepts-and-techniques\">https:\/\/www.sciencedirect.com\/book\/9780123814791\/data-mining-concepts-and-techniques<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Han, J., Kamber, M., &amp; Pei, J. (2011). Data Mining: Concepts and Techniques (3rd ed.). Morgan Kaufmann.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[3]: <\/strong><a href=\"https:\/\/projecteuclid.org\/ebooks\/berkeley-symposium-on-mathematical-statistics-and-probability\/Proceedings-of-the-Fifth-Berkeley-Symposium-on-Mathematical-Statistics-and\/chapter\/Some-methods-for-classification-and-analysis-of-multivariate-observations\/bsmsp\/1200512992\">https:\/\/projecteuclid.org\/ebooks\/berkeley-symposium-on-mathematical-statistics-and-probability\/Proceedings-of-the-Fifth-Berkeley-Symposium-on-Mathematical-Statistics-and\/chapter\/Some-methods-for-classification-and-analysis-of-multivariate-observations\/bsmsp\/1200512992<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>MacQueen, J. (1967). Some Methods for classification and Analysis of Multivariate Observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1, pp. 281-297). University of California Press. <\/em><em><\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[4]: <\/strong><a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC4686108\/\">https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC4686108\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>A Comparison Study on Similarity and Dissimilarity Measures in Clustering Continuous Data (<\/em><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/?term=Shirkhorshidi%20AS%5BAuthor%5D\"><em>Ali Seyed Shirkhorshidi<\/em><\/a><em>,&nbsp;<\/em><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/?term=Aghabozorgi%20S%5BAuthor%5D\"><em>Saeed Aghabozorgi<\/em><\/a><em>, <\/em><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/?term=Wah%20TY%5BAuthor%5D\"><em>Teh Ying Wah<\/em><\/a><em>)<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[5]: <\/strong><a href=\"https:\/\/dl.acm.org\/doi\/10.5555\/1283383.1283494\">https:\/\/dl.acm.org\/doi\/10.5555\/1283383.1283494<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Arthur, D., &amp; Vassilvitskii, S. (2007). K-means++: The advantages of careful seeding. In Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1027-1035). SIAM<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[6]: <\/strong><a href=\"https:\/\/ieeexplore.ieee.org\/document\/1056489\">https:\/\/ieeexplore.ieee.org\/document\/1056489<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Lloyd, S. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[7]: <\/strong><a href=\"https:\/\/projecteuclid.org\/ebooks\/berkeley-symposium-on-mathematical-statistics-and-probability\/Proceedings-of-the-Fifth-Berkeley-Symposium-on-Mathematical-Statistics-and\/chapter\/Some-methods-for-classification-and-analysis-of-multivariate-observations\/bsmsp\/1200512992\">https:\/\/projecteuclid.org\/ebooks\/berkeley-symposium-on-mathematical-statistics-and-probability\/Proceedings-of-the-Fifth-Berkeley-Symposium-on-Mathematical-Statistics-and\/chapter\/Some-methods-for-classification-and-analysis-of-multivariate-observations\/bsmsp\/1200512992<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>MacQueen, J. (1967). Some Methods for classification and Analysis of Multivariate Observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1, pp. 281-297). University of California Press<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[8]: <\/strong><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0167865509002323?via%3Dihub\">https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0167865509002323?via%3Dihub<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Jain, A.K. (2010). Data clustering: 50 years beyond K-means. Pattern Recognition Letters, 31(8), 651-666.<\/em><em><\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[9]: <\/strong><a href=\"https:\/\/dl.acm.org\/doi\/10.1145\/331499.331504\">https:\/\/dl.acm.org\/doi\/10.1145\/331499.331504<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Jain, A.K., Murty, M.N., &amp; Flynn, P.J. (1999). Data clustering: a review. ACM Computing Surveys (CSUR), 31(3), 264-323<\/em><em><\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[10]: <\/strong><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0167865509002323?via%3Dihub\">https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0167865509002323?via%3Dihub<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Jain, A.K. (2010). Data clustering: 50 years beyond K-means. Pattern Recognition Letters, 31(8), 651-666<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[11]: <\/strong><a href=\"https:\/\/rss.onlinelibrary.wiley.com\/doi\/abs\/10.1111\/1467-9868.00293\">https:\/\/rss.onlinelibrary.wiley.com\/doi\/abs\/10.1111\/1467-9868.00293<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>R. Tibshirani, G. Walther, and T. Hastie, &#8222;Estimating the number of clusters in a data set via the gap statistic,&#8221; Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 63, no. 2, pp. 411-423, 2001.<\/em><em><\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[12]: <\/strong><a href=\"https:\/\/jmlr.csail.mit.edu\/papers\/v12\/pedregosa11a.html\">https:\/\/jmlr.csail.mit.edu\/papers\/v12\/pedregosa11a.html<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>F. Pedregosa et al., &#8222;Scikit-learn: Machine learning in Python,&#8221; Journal of Machine Learning Research, vol. 12, pp. 2825-2830, 2011.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[13]: <\/strong><a href=\"https:\/\/docs.oracle.com\/en\/database\/oracle\/machine-learning\/oml4sql\/21\/dmcon\/expectation-maximization.html#GUID-7FE19F37-3A08-4C17-9D60-98413A31E0F2\">https:\/\/docs.oracle.com\/en\/database\/oracle\/machine-learning\/oml4sql\/21\/dmcon\/expectation-maximization.html#GUID-7FE19F37-3A08-4C17-9D60-98413A31E0F2<\/a><strong><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u2013 Prof. T\u0103b\u00eerc\u0103 Angelica-Ioana, informatic\u0103 \u0219i TIC, Liceul Teoretic \u201eIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te\u2013 Prof. T\u0103b\u00eerc\u0103 Nicolae-Radu, informatic\u0103 \u0219i TIC, Liceul Teoretic \u201eIon Heliade R\u0103dulescu\u201d T\u00e2rgovi\u0219te Conform studiului efectuat de Jain et al. (1999)[1], clusterizarea reprezint\u0103 o tehnic\u0103 fundamental\u0103 \u00een analiza datelor, care implic\u0103 gruparea obiectelor sau instan\u021belor similare \u00een clusteri sau grupuri distincte. Algoritmul K-Means&#8230;<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1420","post","type-post","status-publish","format-standard","hentry","category-fara-categorie"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts\/1420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1420"}],"version-history":[{"count":2,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts\/1420\/revisions"}],"predecessor-version":[{"id":1440,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=\/wp\/v2\/posts\/1420\/revisions\/1440"}],"wp:attachment":[{"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/revista.newprojects.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}