Local Variability Vector for Text-Independent Speaker Verification

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1 Loal Vaiabiliy Veo fo ex-inepenen Speake Veifiaion Liping Chen 1 Kong Aik Lee 2 Bin Ma 2 Wu Guo 1 Haizhou Li 2 an Li Rong Dai 1 1 Naional Engineeing Laboaoy fo Speeh an Language Infomaion Poessing Univesiy of Siene an ehnology of China (USC) 2 Insiue fo Infoomm Reseah Ageny fo Siene ehnology an Reseah (A*SAR) lp2011@mail.us.eu.n kalee@i2.a-sa.eu.sg Absa oal vaiabiliy moeling has shon o be effeive fo exinepenen speake veifiaion ask. I povisions a aable ay o esimae he so-alle i-veo hih esibes he speake an session vaiabiliy enee in an ueane. Due o he lo imensionaliy of he i-veo hannel ompensaion ehniques suh as linea isiminan analysis (LDA) an pobabilisi LDA an be applie fo he pupose of hannel ompensaion. his pape poposes he loal vaiabiliy moeling ehnique he enal iea of hih is o apue he loal vaiabiliy assoiae ih iniviual imension of he aousi spae. We analyze he laen suue assoiae ih boh he i-veo an loal vaiabiliy veo an sho ha he o epesenaions omplemen eah ohe base on he expeimen onue on NIS SRE 08 an SRE 10 aases. Inex ems speake eogniion fao analysis session vaiabiliy 1. Inouion Ove he pas fe yeas many appoahes base on he Gaussian mixue moel (GMM) in a GMM-UBM fameok [1] have been popose fo ex-inepenen speake veifiaion ask [2]. Folloing he same fomulaion as in he join fao analysis (JFA) [3] he oal vaiabiliy moel [4] onfines he speake an hannel vaiabiliy ihin a lo-imensional subspae leaing o a fixe an eue imension epesenaion fo speeh ueanes i.e. he so-alle i-veo. eaing an i- veo as a ompa epesenaion of a speeh ueane hannel ompensaion ehniques fo insane ihin-lass ovaiane nomalizaion [5] linea isiminan analysis (LDA) [6] an pobabilisi LDA (PLDA) [7] an hen be applie effeively on he lo-imensional i-veos. An i-veo oul be seen as a eue-imension epesenaion of a GMM mean supeveo (obaine by onaenaing he mean veos in he GMM). hough imension euion oul be pefome on he supeveo using eeminisi ehniques e.g. piniple omponen analysis (PCA) [6] he i-veo exaion is fomulae in pobabilisi ems base on a laen vaiable moel [6]. One obvious benefi is ha in aiion o obaining he i-veo as he poseio mean of he laen vaiable e oul also ompue he poseio ovaiane hih quanifies he uneainy of he esimae an fol in he infomaion in subsequen moeling [8]. Among ohes pobabilisi PCA an fao analysis ae o ommonly use laen vaiable moels in speeh appliaions. he oal vaiabiliy moel an he JFA alike is an exension o he lassial fao analysis ih aiional ying of mixues an fames of an ueane oniione on he same laen vaiable. his ill be fuhe illusae in Seion 2. In his pape e analyze he ying sheme use in he oal vaiabiliy moel (VM) an popose a iffeen appoah by elaxing he ying of mixues suh ha eah iniviual imension of aousi feaue is oniione on is on laen vaiable. A speeh ueane is heeby epesene by a se of loal vaiabiliy veos insea of a single i-veo. We efe o he popose moel as he loal vaiabiliy moel (LVM) he enal iea of hih is o apue he loal vaiabiliy assoiae ih iniviual imension of he aousi spae. In his pape e eive he poseio infeene an give he maximum likelihoo esimae of he moel paamees using he expeaion-maximizaion (EM) algoihm. We also emonsae he use of he popose moel fo ex-inepenen speake veifiaion ask. he es of he pape is oganize as follos. Seion 2 pesens a bief ovevie of he oal vaiabiliy moel an he i-veo exaion poess. Seion 3 poposes he loal vaiabiliy moel an shos ho o use loal vaiabiliy veos fo speake veifiaion ih PLDA. Seion 4 gives some expeimen esuls. Finally Seion 5 onlues he pape. 2. he i-veo paaigm his session gives a bief ovevie of he i-veo exaion poess. In paiula e emphasize on he analysis of laen vaiable ying aoss fames an mixues so as o esablish he onneion o he ne ying sheme popose in his pape I-veo exaion he pupose of i-veo exaion is o fin a fixe-lengh lo-imensional epesenaion fo vaiable-lengh ueanes. he funamenal assumpion of i-veo is ha he feaue veo sequene of an ueane is geneae fom a session-speifi GMM hose mean supeveo m is onsaine o lie in a lo imensional subspae ih oigin μ as follos m μ. (1) Hee is he session inex hee a laen vaiable is assoiae o eah ueane. he oal vaiabiliy maix moels he speake an hannel vaiabiliy leane fom a aining se. An i-veo is hen aken as he poseio mean of he laen vaiable epesening boh he speake an hannel infomaion of an ueane [4].

2 μ Σ 1 C μ V Σ 1 D o o 1 N Figue 1: Pobabilisi gaphial moel illusaing he oal vaiabiliy moel (VM). N is he numbe of fames fom session ha assoiae ih he -h Gaussian omponen hee C is he numbe of Gaussian omponens an R is he numbe of ueanes. An i-veo is aken as he poseio mean of he laen vaiable oal vaiabiliy moel 1 C 1 R Figue 1 shos he oal vaiabiliy moel (VM) in he fom of a pobabilisi gaphial moel. Hee C enoes he numbe of Gaussian omponens hile μ an Σ ae he mean veo an ovaiane maix of he -h Gaussian espeively. In Fig. 1 he obsevaions ae he aousi feaue veos o epesene ih a shae ile. he eangula box suouning he ile ih he value N a is boom igh one iniaes ha hee ae N numbe of obseve veos fom he -h Gaussian fo he -h speeh segmen: po o μ Σ fo N. (2) Noie ha e eompose he oal vaiabiliy maix 1 2 C o is omponen maies one assoiae ih eah Gaussian. In Fig. 1 he oue box iniaes ha he same opeaion is epeae fo all Gaussian omponens fo C. Eah Gaussian omponen aouns fo N numbe of obseve veos o 1 o N N olleively epesene as he union of hih gives ise o he obseve sequene. Fo given a aase he numbe of segmens is enoe as R. One impoan feaue of he oal vaiabiliy moel (an he join fao analysis alike) is ying of he obseve isibuions oniione on he same laen vaiable aoss fames an mixues. Fo he uen ase he ying appeas a o plaes. Fisly he laen vaiable is ie aoss obsevaions o fo 1... N peaining o a Gaussian. Seonly he same laen vaiable is ie aoss he C Gaussian omponens. In Fig. 1 he ying of vaiable is eflee by plaing ousie he o eangula boxes hih essenially iniaes ha he same laen vaiable (un-shae ile) is ie aoss mixues an aoss fames of a given speeh segmen. In mahemaial noaion his is eflee by opping he mixue inex on he laen vaiable. he noion of ying he laen vaiable aoss fames is base on he assumpion ha he hannel an speake being onsan houghou a given speeh segmen (e.g. spoken by Figue 2: Pobabilisi gaphial moel illusaing he loal vaiabiliy moel (LVM). he same imension aoss iffeen Gaussians shae he same loal vaiabiliy veo. he same peson using he same hanse). his assumpion leas o he folloing likelihoo funion: lvm o μ Σ I. 0 (3) Noie ha in (3) he laen vaiable ~ 0 II is assume o follos sana nomal pio. Fuhemoe he same vaiable is ie aoss fames an mixues fo a single session hile sepaae vaiables ae use fo he R speeh segmens o sessions available fo aining. Noie also epesens he se of moel paamees μ Σ; 12 C C hee he mean veos an ovaiane maies ae geneally aken as hose of he UBM. hough i is possible o upae he mean veos an ovaiane maies hey ae usually fixe. Essenially he loaing maies fo 1 2 C C ae he emaining paamees o be opimize. Conaenaing hese maies one afe anohe in a olumn ise manne e fom he so-alle oal vaiabiliy maix. 3. Loal vaiabiliy veo As shon in Seion 2 an i-veo epesens boh he speake an session vaiabiliy onaine in an ueane. o moel he loal vaiabiliy speifi o eah imension of he aousi spae e popose o emove he ying of laen vaiable aoss imensions hile eaining he ying aoss fames an mixues. his fomulaion leas o imension-eni vaiabiliy moeling hih e efe o as he loal vaiabiliy moel. In he folloing e sho ho suh ying sheme oul be aomplishe Loal vaiabiliy moel 1 D 1 R he objeive of loal vaiabiliy moel is o exa he loal vaiabiliy assoiae ih eah iniviual imension of he aousi feaues by eiaing one laen vaiable o evey single imension. Le m m m m D enoes he D 1 veo epesening he mean of he -h Gaussian hee D is he imension of aousi feaue veos. Wih his noaion he mean supeveo m on he lef-han-sie of (1) is obaine by onaenaing he mean veos in he GMM suh ha m m1 m2... m C foms he CD 1 supeveo.

3 o moel he loal vaiabiliy assoiae ih eah iniviual imension of he aousi spae e e-oganize he elemens in he supeveo o fom D sub-veos m m 1 m2... mc fo = 1 2 D eah onsising of C elemens. Essenially he veos m un hough all he C Gaussian omponens of he GMM one imension a a ime. In he above e have oppe he session inex fo beviy. aking he session inex ino aoun e onfine m o lie in a lo-imensional subspae: m m μ V. (4) In (4) he global mean μ is fome in simila manne as m hile V an ae he subspae an laen vaiable apuing he loal vaiabiliy assoiae ih he -h imension of he aousi spae. Figue 2 shos he LVM in he fom of gaphial moel. hee ae o majo iffeenes fom ha of he VM of Fig. 1. Fisly he LVM is imension-eni insea of mixueeni. his is eflee by he hange of subsip fom o a he boom igh one of he seon eangula box. Seonly he ile epesening he laen vaiable is no loae insie he seon eangula box. By his e assign sepaae laen vaiables o he D aousi feaues hile ie aoss mixues an fames of an ueane. Moe speifially he popose ying sheme leas o he folloing likelihoo funion: o o 0. (5) l o V I I LVM he iffeene beeen LVM fom VM an be obseve in hei likelihoo funions in (3) an (5). Noably he laen vaiable in LVM is maginalize sepaaely fo eah imension of he aousi spae as oppose o maginalizaion ove he pou aoss mixues in (3) fo he ase of VM. Like VM he loal vaiabiliy spaes V fo = 1 2 D ae he only moel paamees e nee o esimae. Also he pio of he laen vaiable is assume o follo he sana nomal isibuion. A pe-poessing sep is essenial fo he fomulaion in (5) o be possible. ha is he obseve veo o has o be enalize an hiene in avane hee o epesens he esuling veo. Fom he implemenaion pespeive his oul be aomplishe by enalizing an hiening he fis-oe saisis as esibe in [10] Poseio infeene an paamee esimaion In (5) similaly in (3) e assume ha he alignmen of fames o Gaussian omponens is knon. In paie his infomaion is given by he zeo-oe an fis-oe saisis F exae ih he UBM [3]. In paiula he zeo-oe saisis oul be olleively epesene in a maix fom as Γ (6) C hee iniaes he numbe of fames in ha falls ino he -h Gaussian omponens of he UBM. Given he imension-eni naue of he LVM he poseio mean an ovaiane of he laen vaiable eah assoiae ih an iniviual imension of he aousi spae oul be infee sepaaely as follos: y E L V F (7) L 1 1 L I V Γ V. (8) 1 Noie ha in (7) F is he imension-eni fis-oe suffiien saisis obaine in a o-sep poess. In he fis sep he inpu saisis F is hiene an enalize fo eah Gaussian suh ha F Σ 12 F μ hee μ an Σ ae he mean veo an ovaiane maix of he -h mixue of he UBM. In he seon sep F is fome base on he hiene an enalize saisis F in a simila manne as m in (4). he seon sep oespons o he sap fom mixue-eni o imension-eni as iniae by he hange of subsip in Fig. 1 o in Fig. 2 (a he boom igh one of he seon eangula box). Sine eah iniviual imension of he aousi feaue has is on laen vaiable a speeh ueane oul heeby be epesene by a se of poseio mean veos y 1 y2 y D D hih e efee o as he loal vaiabiliy veos in a simila vein as he i-veo exaion. he expeaion maximizaion (EM) algoihm is use o esimae he loaing maies V fo = 1 2 D. he loaing maies V oul be obaine by ieaively maximizing he folloing auxiliay funion: 1 R D QE V F V ΓV. (9) aking he eivaive of (9) ih espe o V an seing he eivaive o zeo e obain he fomula fo esimaing V hih onsiues he M-sep of he EM ieaion: E E ΓV F. (10) Moe speifially he -h o of V an be upae as: 1 v Φ K (11) hee Φ F E an K E. In (11) he supesip in Φ enoes he -h o of Φ an is he oupany of session in he -h Gaussian as (6) PLDA fo loal vaiabiliy veos Simila o i-veos he loal vaiabiliy veos also onain boh speake an hannel vaiabiliy making i neessay fo some fom of hannel ompensaion o be applie [11]. his objeive is ahieve ih PLDA [12]. Reall ha hee ae D loal vaiabiliy veos fo eah given ueane. We fom a loal vaiabiliy supeveo by onaenaing iniviual elemens as y1 y2 y D. Compae o he GMM mean supeveo one avanage of

4 his loal vaiabiliy supeveo is ha i has a muh loe imensionaliy hih allos he PLDA o be applie iely. I is oh menioning ha he imension euion is ahieve pe imension aoss all mixues. he ask of speake veifiaion is o eemine hehe o no an enollmen ueane an a es ueane ae fom he same speake [13 14]. In his pape e fisly obain an enollmen speake PLDA moel hough aapaion on he univesal moel [15]. hen he log-likelihoo aio of he es ueane beeen he enollmen an he univesal PLDA moels is ompue as: p e p l e log. (12) Hee he subsips e an enoe he enollmen an es sessions espeively. Deaile seps o evaluae he likelihoo an be foun in [15]. 4. Expeimens Expeimens ee aie ou on he elephone ials of he sho2-sho3 ask of NIS SRE 08 an he oe-oe ask of SRE 10. he nominal uaion of he aining an es segmens as abou o an a half minues. he pefomane as evaluae base on he equal-eo-ae (EER) an he minimum eeion os funion (mindcf). We onsie he mindcf a o iffeen opeaion poins namely mindcf08 an mindcf10. he aousi feaues ee 57-imensional veos of mel fequeny epsal oeffiiens (MFCC) ih fis an seon eivaives appene. We aine gene-epenen UBMs of 512 Gaussians ih full ovaiane maies using NIS SRE 04 aase. Fo i-veo e aine he oal vaiabiliy maix ih a ank of J = 400 using he elephone aa fom NIS SRE an 06. As suh he i-veo ha a imensionaliy of 400. he same aase as use o ain he PLDA moel ih an eigenvoie maix of ank 200 an eigenhannel maix of ank 50 an a full ovaiane maix. Fo he loal vaiabiliy moel D = 57 loaing maies V ih a ank of J = 20 ee aine using he same aase. his onfiguaion esule in 57 loal vaiabiliy veos of 20 imensions i.e. a loal vaiabiliy supeveo ih a imensionaliy of l140 is fome fo eah inpu ueane. he loal supeveos ee hen moele ih a PLDA moel ih F of ank 400 G of ank 300 an a iagonal esiual maix. he same aase as use fo he aining he PLDA fo boh ases. able I an able II ompae he pefomanes of VM an LVM on NIS SRE 08 an NIS SRE 10 espeively. Also shon in he ables ae he fusion esuls by a simple summaion of hei soes. VM folloe by PLDA (i.e. an i- veo PLDA sysem) is use as he baseline. he esuls onfim ha he loal vaiabiliy veos exae ih LVM ae effeive fo speake haaeizaion even hough hee is sill a mino gap ompae o he baseline i-veo PLDA. he fusion sysem oupefoms he baseline i-veo sysem in mos ases espeially in male ials shoing ha he loal able I: Pefomane ompaison of oal vaiabiliy moel (VM) loal vaiabiliy moel (LVM) an soe fusion on DE6 of sho2-sho3 ask in NIS SRE 08. Male VM LVM fusion Female VM LVM fusion able II: Pefomane ompaison of oal vaiabiliy moel (VM) loal vaiabiliy moel (LVM) an soe fusion on CC5 of oe-oe ess in NIS SRE 10. Male VM LVM fusion Female VM LVM fusion vaiabiliy veos aiional infomaion omplemenay o ha of he i-veo. his suggess ha he popose LVM moel he speake an session vaiabiliy ha is absen in he VM. 5. Conlusion We popose he loal vaiabiliy moel (LVM) fo exaing he loal vaiabiliy assoiae ih eah imension of he aousi feaues fo ex-inepenen speake veifiaion. he majo iffeene beeen he LVM an oal vaiabiliy moel (VM) lies a hehe o no o ie he mixues aoss iffeen imensions of he aousi feaues oniione on some laen vaiables. his iffeene is illusae ih he use of pobabilisi gaphial moel in he pape. We also eive he poseio infeene an he EM seps fo paamee leaning. Expeimenal esuls onfim he effiay of he loal vaiabiliy veos in haaeizing he voal popey of a speake. he esuls also sugges ha he popose LVM moel he vaiabiliy ha is absen in he VM. 7. Aknolegemens his ok of Liping Chen as paially suppoe by he Naional Naue Siene Founaion of China (Gan No ) an he eleoni infomaion inusy evelopmen fun of China (Gan No ).

5 8. Refeenes [1] D.A. Reynols.F. Quaiei an R.B. Dumn Speake veifiaion using aape Gaussian mixue moel Digial Signal Poessing vol. 10 no. 1-3 pp [2]. Kinnunen an H. Li An ovevie of ex-inepenen speake eogniion: fom feaues o supeveos Speeh Communiaion vol. 52 no. 1 pp Jan [3] P. Kenny G. Boulianne P. Ouelle an P. Dumouhel Speake an session vaiabiliy in GMM-Base speake veifiaion IEEE ans. Auio Speeh an Language Poessing vol. 15 no. 4 pp May [4] N. Dehak P. Kenny R. Dehak P. Dumouhel an P. Ouelle Fon-en fao analysis fo speake veifiaion IEEE ans. Auio Speeh an Language Poessing vol. 19 no. 4 pp May [5] A. Hah S. Kajaeka an A. Solke Wihin-lass ovaiane nomalizaion fo SVM-base speake eogniion in Inenaional Confeene on Spoken Language Poessing Pisbugh PA USA Sepembe [6] C. M. Bishop Paen Reogniion an Mahine Leaning. Spinge [7] S. J. D. Pine an J. H. Ele Pobabilisi linea isiminan analysis fo infeenes abou ieniy in Po. Inenaional Confeene on Compue Vision [8] P. Kenny. Safylakis P. Ouelle M. J. Alam an P. Dumouhel PLDA fo speake veifiaion ih ueane of abiay uaion in Po. IEEE ICASSP 2013 pp [9] P. Kenny A Small Foopin i-veo Exao in Po. Oyssey: Speake an Language Reogniion Wokshop June [10] P. Maejka O. Glembek F. Casalo J. Alam O. Plho P. Kenny L. Buge an J. Cenoky Full-ovaiane ubm an heavy-aile pla in i-veo speake veifiaion in Po. IEEE ICASSP 2011 pp [11] P. Kenny Bayesian speake veifiaion ih heavy-aile pios in Po. Oyssey: Speake an Language Reogniion Wokshop Jun [12] S. J. D. Pine Compue vision: moels leaning an infeene. Cambige Univesiy Pess [13] Y. Jiang K. A. Lee Z. ang B. Ma A. Lahe an H. Li PLDA moeling in i-veo an supeveo spae fo speake veifiaion in Po. INERSPEECH 2012 pape 198. [14] K. A. Lee A. Lahe C. H. You B. Ma H. Li Muli-session PLDA soing of i-veo fo paially open-se speake eeion in Po. INERSPEECH 2013 pp [15] L. Chen K. A. Lee B. Ma W. Guo H. Li an L. R. Dai Minimum ivegene esimaion of speake pio in muli-session PLDA soing in Po. ICASSP 2014 pp [16] N. Bümme an J. u Peez Appliaion-inepenen evaluaion of speake eeion Compue Speeh & Language vol. 20 no. 2 pp

LOCAL VARIABILITY MODELING FOR TEXT-INDEPENDENT SPEAKER VERIFICATION

LOCAL VARIABILITY MODELING FOR TEXT-INDEPENDENT SPEAKER VERIFICATION Odyssey 2014: he Speake and Language eognition Wokshop 16-19 June 2014, Joensuu, Finland LOAL VAIABILIY MODELING FO EX-INDEPENDEN SPEAKE VEIFIAION Liping hen 1, Kong Aik Lee 2, Bin Ma 2, Wu Guo 1, Haizhou