DIFFUSION MAPS FOR PLDA-BASED SPEAKER VERIFICATION

Transcription

1 DIFFUSION MAPS FOR PLDA-BASED SPEAKER VERIFICATION Ore Barka,, Haga Aroowz IBM Research Hafa, Israel School of Compuer Scece, Tel Avv Uversy, Israel ABSTRACT Durg he las few years, -vecors have become a mpora compoe mos sae-of-he-ar speaker recogo sysems. I- vecor eraco s base o a assumpo ha GMM supervecors rese o a low mesoal space, whch s moele usg Facor Aalyss. I hs paper we replace he above assumpo wh a assumpo ha he GMM supervecors rese o a low mesoal mafol a propose o use Dffuso Maps o lear ha mafol. The lear mafol mples a mappg of spoke sessos o a mofe -vecor space whch we call - vecor space. D-vecors ca furher be processe usg saar echques such as LDA, WCCN, cose sace scorg or Probablsc Lear Dscrma Aalyss (PLDA). We emosrae he usefuless of our approach o he elephoe core coos of NIST 00, a oba sgfca error reuco. Ie Terms Speaker verfcao, Dffuso Maps, - vecors, o-lear mesoaly reuco. INTRODUCTION Durg he las few years -vecors have become he saar froe layer mos of sae-of-he-ar speaker verfcao sysems. I [3] he auhors showe ha mos of he speaker varably he hgh mesoal GMM space may be capure by a low mesoal subspace ame as he Toal Varably space. Therefore, he -vecor framework proves a way o map he hgh mesoal GMM supervecors o a relavely low mesoal vecors, ame -vecors. I a commo seup, - vecors are use as a fro-e processg whch s followe by a subseque cha of lear proecos, LDA a WCCN [3]. Recely, a eve more successful echque ame PLDA [9, 0] has bee rouce o he speaker recogo commuy a currely -vecor eraco followe by PLDA s regare as a eremely robus a accurae framework for speaker verfcao. However, was o ul recely ha Karam e al. [] showe ha he GMM supervecors he GMM space are lyg o a low mesoal mafol a ha by he use of mafol learg echques such as graph geoescs a ISOMAP [8] s possble o mprove classfcao error. A furher aemp for o-lear mesoaly reuco for speaker recogo has bee oe [4]. I ha work, he auhors use a mafol learg echque ame Dffuso Maps (DM) [6], however hey abaoe he GMM framework. Isea, hey use 78 mesoal feaure vecors cossg of MFCC a ela MFCC mea, varace, m a ma sascs erace from a sesso. I hs paper we propose a alerave o-lear way for - vecor eraco we ame -vecor eraco. The propose algorhm s base o he DM framework a may furher be processe usg saar echques such as PLDA. We emosrae he effecveess of our algorhm a compare s resuls wh he sae-of-he-ar -vecor base PLDA algorhm o he NIST 00 Evaluao aa. Our work ffers from he prevous oes several aspecs. Frs, ulke [8], we choose o use he DM framework ue o s beer moelg of relaos bewee aa pos a he relavely easy way ca be eee o ew aa pos usg geomerc harmocs [7]. Secoly, as oppose o he approach presee [4] we o use he GMM framework as a basele represeao of he aa a cosequely use a more approprae merc fuco ha a smple Euclea sace orer o moel he relaos bewee he GMM supervecors. Lasly, boh [4] a [8], he epermes focuse o cluserg a aa mg asks whch are base o he assumpo ha he evaluao aa or par of s gve a pror o he recogo sysem. Hece, hese seups are o suable for he scearo whe he evaluao aa s ukow a s gve oly o es me. The paper s orgaze as follows: I Seco we prove a overvew of he DM framework. I Seco 3 we prese eal he propose -vecor eraco algorhm. I Seco 4 we escrbe he epermeal seup a resuls. I Seco 5 we coclue.. DIFFUSION MAPS Dffuso Maps (DM) [6] s a mache learg echque for olear mesoaly reuco. Dffere from oher mesoaly reuco mehos such as prcple compoe aalyss (PCA), mul-mesoal scalg (MDS), a facor aalyss (FA), DM s a o-lear meho ha focuses o scoverg he uerlyg mafol ha he aa has bee sample from. I hs meho a affy mar s bul whch s use o geerae a ffuso process. As he ffuso process progress, egraes local geomery o reveal geomerc srucures of he aa a ffere scales. Base o he reveale geomery, oe ca measure he smlary bewee wo aa samples a a specfc scale. A ffuso map embes he hgh mesoal aa a lowermesoal space D, such ha he Euclea sace bewee pos D appromaes he ffuso sace he orgal feaure space. The meso of D s eerme by he geomerc srucure uerlyg he aa, a he accuracy by whch he ffuso sace s appromae.

2 I our seup, he hgh mesoal feaure vecors are he GMM supervecors ha represe ffere sessos he GMM supervecor space G, we oe hem as g-vecors. DM s performe orer o map he g-vecors o l -mesoal -vecors he ffuso space D. From ow o, we wll use hese oaos o ffer bewee he orgal hgh mesoal feaure space, a he low mesoal ffuso space. The res of hs seco scusses he DM algorhm more eal. Gve a evelopme se of g-vecors { } = G he frs sep he DM algorhm s o efe a affy merc c( ) over G. The hs merc shoul be covere o a smlary measure. A commo approach for hs ype of coverso s usg he Gaussa kerel: c( ) k( ) = ep () σ where he σ parameer eermes he scale or sze of he eghborhoo we rus our local smlary measure o be accurae. I pracce, σ s chose emprcally or accorg o pror kowlege of he geomerc srucure a esy of he aa. Therefore, for a rcae, o lear a ese srucure, σ shoul be se o a small value, whle for a sparse srucure large values mgh be cosere as more suable. I hs way, we ca efe a full urece graph where he g- vecors are he oes, a he weghs of he eges are eerme accorg o he ffuso kerel (). We he efe a raom walk o hs graph by coverg he smlary measure o a probably fuco as follows: p( ) = k( ) / z( ) where = z( ) = k( ). The e sep s o efe a raso Markov mar P whch he ery P, = p( ) s he probably of raso from oe sep. I he same way, o oe a sgle P s a mar whch he ery, P s he probably of raso from oe o oe seps. Base o he above cosruco, a ffuso sace afer seps s efe as follows: =, k k k= Q ( ) ( P P ). By specral ecomposo of P we ge a complee se of egevalues = λ0 λ... λ a lef a rgh egevecors sasfyg: Pψ = λϕ. We he efe a mappg M :{ } = D accorg o: M ( ) = λψ,..., λψ l l, where ψ k caes he -h eleme of he k -h egevecor of P a l s he meso of he ffuso space D. I has bee show [6] ha for l = m he followg equao hols: M ( ) M ( ) = Q ( ). Ths resul usfe he use of square Euclea sace he ffuso space. Of course pracce oe shoul pck l< m accorg o he ecay of { λ } =. Ths ecay s relae o he compley of he rsc mesoaly of he aa a he choce of he parameers σ a. T Fgure : Travellg alog he blue pah (whch follows he rsc geomery of he mafol) has hgher probably ha ravellg alog he re pah as he ffuso process progress. Fgure shows a llusrave eample for a ffuso process. Two alerave pahs are coecg bewee pos o he mafol. The blue pah s he loger oe bu s he oe whch follows he geomerc srucure of he mafol whle he re pah s he shor oe bu oes o follow he mafol srucure. As he umber of seps he ffuso process,, creases, he probably of ravellg alog he blue pah also creases, sce cosss of may shor sace umps. However, he probably of ravellg alog he re pah says always small (a become smaller a smaller as he creases) as s cosss of a log sace umps. So far we aresse he suao whe all g-vecors are gve a-pror. However, we ee o also aress he suao where a ew g-vecor { } + = s rouce a we are aske o erac s correspog -vecor. A aïve approach woul be o repea he whole process escrbe above from he begg. Alhough hs mgh be praccal offle applcaos, s eremely effce a resuls large amou overhea. Ths ou-of-sample eeso problem s well-sue he mafol learg commuy a recely, may successful mehos [5] have bee propose o allevae. I hs work we chose o use he Geomerc harmoc [7] approach whch s base o Nysrom eeso: ψ k ( + ) P +, ψ k λk = =. () Ths eeso ees each of he egevecors wh oe aoal ery correspog o he ew g-vecor whle s cosse o he evelopme se { } =. Ths resuls a + + eee mappg: M :{ } = D. 3. D-VECTOR EXTRACTION FOR SPEAKER VERIFICATION Our ma corbuo hs work s he ulzao of he DM framework for a o-lear meho for -vecor eraco for speaker verfcao. Ths ype of eraco resuls a -vecor. Ths -vecor ca be use epeely or couco wh he raoal -vecor. The propose meho s ve o wo phases: DM rag a -vecor eraco. 3.. DM rag

3 I hs phase we ra he DM moel. The pu o hs phase s a evelopme se of g-vecors (GMM supervecors meas) { } g =, where each g-vecor correspos o a evelopme sesso. Frs, followg [3] we ormalze each g as follows : ( ) / / =Σ ( w Im ) g µ where Σ s he { g } µ s he { g } = sample mea vecor, = agoal sample covarace mar, w s he vecor of sacke mure GMM weghs correspog o he -h g-vecor, s he Kroecker prouc a I s he ey mar of sze m, whch s he g-vecor meso. Noe ha hs ype of ormalzao geeraes a ew se of ormalze g- vecors { } = = G G. The, by applyg he DM algorhm o G, we lear he srucure of he uerlyg speaker mafol ha reses G. Ths s oe by efg a mappg M : G D as escrbe Seco. I hs work we chose o use he followg ffuso kerel: ( c( )) k( ) = ep (3) σ where G a c(, ) s he cose sace [3]. I hs way each g-vecor s mappe o a correspog l - mesoal - vecor. The compuaoal compley of he rag phase s reuce o he compley of specral ecomposo of he raso mar P. Noe ha he ecomposo s carre ou oly for he frs l egevecors a egevalues, for a selece parameer l. The sze of P s eerme by he sze of he evelopme se. 3.. D-vecor eraco As eplae Seco, he mappg M s efe oly o he oma G (he ormalze evelopme se). Therefore, case of a ew es g-vecor G \ G, M has o be eee o M : G { } D orer o esmae he ew cooraes of D. For hs ask we use he geomerc harmoc echque escrbe Seco. Therefore, as alreay eplae Seco, he ffuso sace bewee a par of g-vecors G ca be appromae by he square Euclea sace bewee he correspog par of -vecors D. The compuaoal compley of -vecor eraco s eerme by he sze of he evelopme se a he compley of he chose ffuso kerel. Gve a ew g-vecor he eeso s oe accorg o (). Therefore s ecessary o compue a ew row he raso mar whch s correspog o he probably of umpg from he ew es g-vecor o each of he evelopme g-vecors separaely. I s mpora o clarfy ha oher eeso mehos ca be also cosere. For eample, he meho propose [5] have bee prove o be more robus a compuaoal effce ha he oe use our paper. 4. EXPERIMENTAL SETUP AND RESULTS 4. Fro-e m The fro-e we use hroughou hs paper s base o Melfrequecy cepsral coeffces (MFCC). A eergy base voce acvy eecor s use o locae a remove o-speech frames. The fal feaure se cosss of cepsral coeffces augmee by ela a ela-ela cepsral coeffces erace every 0ms usg a 3ms wow. Feaure warpg [] s apple wh a 300 frame wow. We use a GMM orer of 04 for esmag suffce sascs for -vecor eraco a for esmao supervecors for -vecor eraco. 4.. Gaussa-PLDA PLDA oly moels speaker a chael varably he - vecor (or -vecor) space. A speaker a chael epee - vecor (or -vecor) ca be efe as w = w +Vy + U + ε (4) where w eoes he observe -vecor (-vecor), w s a global mea -vecor (-vecor), y a are he speaker a chael facor respecvely, V a U are he egespeaker a egechael marces. ε s a resual vecor ha s assume o be srbue accorg o he saar ormal srbuo. The PLDA moel s rae o a evelopme aa for a gve egespeaker rak a a gve egechael rak. I verfcao phase, he verfcao score has a close form epresso whch ca be fou []. 4.3 I-vecor PLDA basele sysem Our basele sysem s a geer-epee -vecor base Gaussa-PLDA sysem spre by []. We se he meso of he -vecors o 400 (600 mesoal -vecors o show mproveme o our seup). The Gaussa-PLDA backe processes legh-ormalze -vecors by frs applyg LDA for obag a mesoaly reuco o 50. The PLDA moel we use s cofgure o have 00 egespeakers a 00 egechaels. We o o apply ay sor of score ormalzao (as we fou score ormalzao o egrae accuracy) D-vecor PLDA sysem The geer-epee -vecor base PLDA sysem s smlar o he -vecor base PLDA sysem escrbe he prevous seco ecep for he subsuo of he -vecors wh -vecors. I he DM rag phase we chose he followg se of parameers: l (meso) = 800, σ = 6 a = 0. We fou ou ha 300 egespeakers a 300 egechaels were opmal for our seup The fuse sysem We fuse boh he -vecor base PLDA sysem a he -vecor base PLDA sysem by og a smple average (wh equal weghs) o he score level Daases We rae a geer-epee UBM o,7 sessos from Swchboar-II, NIST 004 speaker recogo evaluao (SRE) a NIST-006-SRE. For rag he -vecor a -vecor

4 eracors we use 6989 (female) a 45 (male) elephoe sessos from NIST a 008 SREs. We ra epermes o he hree elephoe-oly core coos of NIST-00-SRE (5, 6, a 8) Resuls Tables -3 prese comparsos of he basele -vecor base PLDA sysem wh he propose -vecor base PLDA sysem. The resuls are measure Equal Error Rae (EER), ol-mdcf [] a ew-mdcf [] respecvely. Table. A comparso of -vecor PLDA o -vecor PLDA o NIST-00 elephoe oly coos. Resuls are EER (%) Sysem Coo 5 Coo 6 Coo 8 -vecor PLDA vecor PLDA Fuse sysem vecor PLDA vecor PLDA Fuse sysem Table 4 summarzes he gas we ge usg he -vecor base PLDA sysem a usg he fuse sysem compare o he basele -vecor base PLDA sysem. We see ha he -vecor base PLDA sysem mproves over he basele by a average of 8.5%, 3.5% a 9% for EER, ol-mdcf a ew-mdcf respecvely, a he fuse sysem mproves over he basele by 40%, 3% a 8.5% for EER, ol-mdcf a ew-m-dcf respecvely. Table 4. Summary of he mprovemes for he -vecor PLDA sysem a he fuse sysem compare o he basele -vecor PLDA sysem. Resuls for he separae coos are average. Resuls are relave mproveme ( %) Measure -vecor PLDA sysem Fuse sysem EER 9 44 Ol m-dcf 7 40 New m-dcf 4 4 EER 8 36 Ol m-dcf 0 4 New m-dcf CONCLUSION Table. A comparso of -vecor PLDA o -vecor PLDA o NIST-00 elephoe oly coos. Resuls are ol m-dcf Sysem Coo 5 Coo 6 Coo 8 -vecor PLDA vecor PLDA Fuse sysem vecor PLDA vecor PLDA Fuse sysem Table 3. A comparso of -vecor PLDA o -vecor PLDA o NIST-00 elephoe oly coos. Resuls are ew-m-dcf. Sysem Coo 5 Coo 6 Coo 8 -vecor PLDA vecor PLDA Fuse sysem vecor PLDA vecor PLDA Fuse sysem I hs paper we rouce he use of Dffuso Maps for he applcao of -vecor eraco for speaker verfcao sysems. We presee he -vecor eraco algorhm. Ths algorhm ca be use as a o-lear alerave o he raoal -vecor eraco algorhm. We emosrae he effecveess of - vecor eraco algorhm whe s use as a fro-e layer for a PLDA base speaker verfcao sysem. We maage o oba reuce error usg he -vecor base meho compare o usg -vecors. The error reuco was he rage of 4-9%, epeg o he geer a error measure. Furhermore, a smple fuso of he -vecor base sysem a he -vecor base sysem resule error reucos of 3-44% compare o he basele, epeg o he geer a error measure.. 6. REFERENCES [] J. Pelecaos a S. Srhara, Feaure warpg for robus speaker verfcao, Proc. of Speaker Oyssey Workshop, 00. [] Z. N. Karam a W. M. Campbell, Graph-embeg for speaker recogo, Proc. Ierspeech, 00. [3] N. Dehak, P. Key, R. Dehak, P. Dumouchel, a P. Ouelle, Fro-E Facor Aalyss for Speaker Verfcao, IEEE Trasacos o Auo, Speech, a Lauage Processg, vol. 9, o. 4, pp , 0. [4] Y. Mchalevsky, R. Talmo, a I. Cohe. "Speaker efcao usg ffuso maps", Proc. Euspco, 0. [5] A. Bermas, A. Averbuch, a R.R. Cofma. "Mulscale aa samplg a fuco eeso", Apple a Compuaoal Harmoc Aalyss, 0. DOI:0.06/.acha

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