Iterative Methods for Searching Optimal Classifier Combination Function

Transcription

1 htt:// Iteratve Method for Searchng Otmal Clafer Combnaton Functon Sergey Tulyakov Chaohong Wu Venu Govndaraju Unverty at Buffalo

2 Identfcaton ytem: Alce Bob htt:// Bometrc Alcaton Fngerrnt matchng 6 Face matchng f S f S arg max =... Verfcaton ytem: Alce 6.35 f S > θ Accet Reject f f f f Queton: f we fnd otmal and t necearly?

3 htt:// Handwrtten Word Recognton Identfcaton ytem: Amhert Buffalo WMR CMR.5.8 f S f S arg max =... Verfcaton ytem: Amhert f S > θ Accet Reject f f f f Queton: f we fnd otmal and t necearly?

4 htt:// Verfcaton Sytem Pattern clafcaton aroach clae genune and motor verfcaton attemt Bometrc core Imotor Genune Bometrc core Mnmum rk mnmzaton crtera: otmal decon boundare concde wth the contour of lkelhood rato functon: f gen lr = m f = The roblem eay can drectly recontruct dente or ue multle attern clafcaton algorthm SVM etc. f lr

5 htt:// Lkelhood Rato Combnaton Functon for Identfcaton Sytem Mnmzng mclafcaton cot: j ω ω > Clafy a rather than ω ω j Aume that core agned to dfferent clae are ndeendent: m gen m = = ω ω ω ω The nequalty become: m j j gen m m gen m >

6 htt:// Lkelhood Rato Combnaton Functon for Identfcaton Sytem Or: gen m > gen m j j j j Thu obtaned lkelhood rato combnaton rule: The nut hould be clafed a arg max =... f lr If core agned by clafer to dfferent clae are ndeendent then lkelhood rato combnaton rule the otmal combnaton rule for dentfcaton ytem

7 Exerment htt:// Handwrtten word recognzer: CMR WMR; lexcon of ze 680 word Bometrc matcher: fngerrnt l\v and face G from IST BSSR et; 988 enrolled eron Total Tral t Matcher Correct nd Matcher Correct Both Correct Ether Correct Lkelhood Rato Weghted Sum CMR & WMR l & C l & G Exermental error? - The erformance of lkelhood rato combnaton rule for handwrtten word recognzer wore than the erformance of a ngle WMR recognzer

8 htt:// Verfcaton Sytem: WMR & CMR

9 htt:// Verfcaton Sytem: bometrc l & C

10 htt:// Verfcaton Sytem: bometrc l & G

11 htt:// Deendence of Identfcaton Tral Score Lkelhood rato combnaton fal for dentfcaton ytem Thu we can not aume that dentfcaton tral core agned to dfferent clae are ndeendent Correlaton of genune core wth ome tattc of motor core dentfcaton tral et: t Im nd Im 3 rd Im mean CMR WMR l C G

12 htt:// Obervaton of Score Deendence T.K. Ho PhD the 993: mage qualty nfluence OCR core and rank rovde more nformaton durng combnaton OCR A.95 B.89 C.76 OCR A.80 B.54 C.43 convert core to rank ue to core

13 Hyothetcal dente of genune and motor core: htt:// Examle How uch dtrbuton were generated? Cae : genune and motor core are amled ndeendently from correondng dente Cae : n every dentfcaton tral: m = gen Verfcaton ytem : both cae have ame erformance Identfcaton ytem : econd cae ha erfect erformance genune core alway on to Concluon: erformance of a matcher n dentfcaton ytem can be dfferent from t erformance n verfcaton ytem

14 htt:// Examle Combne two matcher: one a n cae another a n cae Lkelhood rato combnaton rule: Incorrectly clafed dentfcaton tral: ω Cae matcher Cae matcher f + ω lr = = Wnner Concluon: the lkelhood rato combnaton rule mght have wore erformance n dentfcaton ytem than ngle matcher a n CMR&WMR ex

15 Genune core Imotor core Examle 3 = x y gen gen + m = xm + y htt:// xgen ~ X gen xm ~ X m y ~ gen X m Y - ndeendent dtrbuton X - gauan y - the ame for dentfcaton tral Can rove: the otmal combnaton functon for dentfcaton ytem wth uch dtrbuton f + lr =

16 Examle 3 htt:// Deendng on the dtrbuton of the otmal combnaton functon can dffer gnfcantly from the one of dentfcaton ytem. Y E.g.: Y unformly dtrbuted on [ 0 ] Concluon: genune and motor core dtrbuton mght not have enough nformaton to deduce the otmal combnaton functon for dentfcaton ytem.

17 htt:// Tranng Ung Identfcaton Tral Score Set Bometrc core Imotor Genune Bometrc core Imotor Genune Bometrc core Bometrc core o! Bometrc core Imotor Bometrc core Genune The tranng of the dentfcaton ytem combnaton hould roce core from one dentfcaton tral a a ngle tranng amle.

18 htt:// Aroxmatng Otmal Combnaton Functon n Identfcaton Sytem Algorthm: Intalze ome combnaton functon Do for all dentfcaton tral: Get core from ame dentfcaton tral Adjut combnaton functon Crtera for adjutng combnaton functon: genune core hould be obly better than any motor core of the ame dentfcaton tral et

19 htt:// Condered Algorthm Bet Imotor Lkelhood Rato: where motor denty traned ung the et of bet motor determned teratvely Sum of logtc functon Combnaton functon hould be monotonc o aroxmate t a a um of monotonc logtc functon The coeffcent are choen o that the genune core earated from the bet motor core n current dentfcaton tral teratve algorthm M f ' M m M gen M f = 0 + = j M M M M e l α α α α α

20 htt:// Identfcaton Sytem Performance Lkelhood Rato Weghted um Bet Imotor Lkelhood Rato Logtc Sum Weghted Sum + Identfcaton Model CMR&WMR l & C l & G

21 htt:// Bg Pcture Preented combnaton rule are of low comlexty combnaton tye. Ung other tye medum II dentfcaton model can gnfcantly mrove erformance. Identfcaton model nherently account for core deendence.

22 htt:// Identfcaton Model for l&c

23 htt:// Identfcaton Model for l&g

24 htt:// Identfcaton Model for WMR&CMR Verfcaton Sytem