
kernel fisher discriminant vishakalanam

staattistiksil, generalised discriminant analysis ennum kernel discriminant analysis ennum ariyappedunna kernel fisher discriminant analysis (keey. eph. dii), leanier discriminant anaalisisinte (ell. dii. eiii) carnelised pathippaanu. ronald fisherinte perilaanu ithu ariyappedunnathu.
leanier discriminant vishakalanam.
avabodhajanyamaayi, klaas seppareshan paramavadhi vardhippikkunna oru projection kandethuka ennathaanu ldaude ashayam. formula _ 1, formula _ 2 ennee rund settu label cheytha daatta nalkiyaal, oro klaasinteyum sharashari moolyam, formula _ 3, formula _ 4 enniva namukk kanakkakkaam.
ivide formula _ 6 ennathu klaas formula _ 7-nte udaaharanangalude ennamaanu. leanier discriminant vishakalanathinte lakshyam klaas maarggangalude valia verthiriv nalkuka ennathaanu, athesamayam inn-klaas vyathiyaanam cheruthaakkuka ennathaanu. formula _ 8-maayi bandhappett, inipparayunna anupatham paramavadhi vardhippikkunnathaayi ithu roopappeduthunnu
ivide formula _ 10 ennathu klaas-thammilulla covarians matrix formula _ 11 ennathu motham klaas-ullile covarians matrix aannu
melpparanja anupaathatthinte paramavadhi nedunnathu
lagranch multiplier reethi (thelivukalude rekhaachithram) kaanikkunnathupole
formula _ 14 paramavadhi vaykkunnathu paramavadhi vaykkunnathinu thulyamaanu.
vishayamaayi 
ithu, formula _ 17 paramavadhi vardhippikkunnathinu thulyamaanu, ivide formula _ 18 ennathu lagranch gunakamaanu. 
paramavadhi, formula _ 8, formula _ 18 ennivayumaayi bandhappett formula _ 19-nte derivateevukal poojyamaayirikkanam. formula _ 22 vilavu edukkunnu 
formula _ 24, formula _ 25 ennivayaal nissaaramaayi thripthippeduthunnu
lda vipuleekarikkunnu.
lda noonn-leanier maappingukalilekku vyaapippikkunnathin, formula _ 26 pooyint formula _ 27 aayi nalkiyirikkunna daatta, eee puthiya feature speysile chila function formula _ 29 vazhi formula _ 28 enna puthiya feature speysilekku mapp cheyyaan kazhiyum, paramavadhi cheyyenda function ithaanu 
evide
oppam
koodaathe, formula _ 33. mapping formula _ 34 vyakthamaayi kanakkukoottukayum thudarnnu lda nadathukayum cheiyunnathu computational chelaveriyathum pala kesukalilum asaadhyavumaanennu shradhikkuka. udaaharanathinu, formula _ 35 ananthamaaya alavilayirikkaam. athinaal, formula _ 35 lake daatta vyakthamaayi mapp cheiyunnathinupakaram, dott uthppannangalude adisthaanathil algoritam maattiyezhuthunnathiloode puthiya feature speysile dott uthppannathin pakaram oru kernel function, formula _ 37 upayogichu kernel functionukal upayogikkunnathiloodeyum daatta parokshamaayi ulcherkkaan kazhiyum.
formula _ 8 nuu oru vipuleekaranamundaakumenna aadyam shradhichukondu dott uthppannangalude kaaryatthil lda punarnirmikkaan kazhiyum.
roopam 
appol athu shradhikkuka
evide
formula _ 42-nte numerator ingane ezhuthaam
athupole, denominator ingane ezhuthaam
formula _ 46-nte formula _ 45 gadakathil formula _ 47 ennu nirvachikkappedunna aidantitti matricks aanu, formula _ 49-nuu thulyamaaya ellah entrikalumulla matricks formula _ 48 aanu. formula _ 50-nte padaprayogatthil ninnu aarambhich formula _ 8-nte vipuleekaranavum formula _ 52, formula _ 53 ennivayude nirvachanangalum upayogichu eee aidantitti nedaam.
formula _ 42-nte numeratorinum denominatorinum eee samavaakyangal upayogichu, formula _ 56-nte samavaakyam ingane ezhuthaam
appol, poojyathinu thulyamaaya deferentiate krameekaranavum nalkunnu
formula _ 8-nte disha maathram aayathinal, formula _ 60-nte disha pradhaanamaayathinaal, mukalil paranjava formula _ 61-nuu ingane pariharikkan kazhiyum
praayogikamaayi, formula _ 63 saadhaaranayaayi ekavachanamaanennum athinaal aidantittiyude oru multiple athilekku cherkkunnuvennum shradhikkuka. 
formula _ 61-nulla pariharam nalkumbol, oru puthiya dattaa pooyintinte projection nalkunnathu 
multy klaas keey. eph. dii.
randil kooduthal klaasukalulla kesukalilekkulla vipuleekaranam thaarathamyena nereyaanu. formula _ 67 klaasukalude ennamaayirikkatte. appol multy-klaas keey. eph. dii. yill formula _ 68 discriminant functionukal upayogichu daattaye oru formula _ 68-dimensional speysilekku project cheiyunnathu ulppedunnu.
ithu matricks notteshanil ezhuthaam.
ivide soothravaakyam _ 72 ennathu soothravaakyam _ 73-nte nirakalaanu. koodaathe, klaas coverians matricks ippol
ivide formula _ 75 ennathu puthiya feature speysile ellah daattayudeyum sharashari aanu. inn-klaas covarians matricks
paramavadhi vardhippichaanu ippol pariharam labhikkunnath.
kernel trick veendum upayogikkaam, multy-klaas keey. eph. diyude lakshyam maarunnu 
evide soothravaakyam _ 79 umm
81 enna soothravaakyam melpparanja vibhaagathil nirvachichirikkunnathupo nirvachichirikkunnu, 82 enna soothravaakyam ingane nirvachichirikkunnu 
formula 86-nte formula 68 leading egenvectorukal kandethi formula 84 kanakkakkaam. koodaathe, oru puthiya inputtinte projection, formula 87, nalkunnu 
ivide formula _ 90-nte formula _ 89 ghadakam formula _ 91 nalkunnu.
keey. eph. dii. upayogichu vargeekaranam.
rund klaas, multy klaas keey. eph. dii. ennivayil, oru puthiya inputtinte klaas label ingane nalkaam 
ivide formula _ 93 ennathu klaas formula _ 94-nte projected meane aanu, formula _ 95 oru disttans functionaanu.
aaplikkeshanukal.
kernel discriminant vishakalanam vividha aaplikkeshanukalil upayogichittundu. ivayil ulppedunnu