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1 ISCA Archve hp:// ODYSSEY4 - The Speaker and Language Recognon Workshop Toledo, Span May 3 - June 3, 4 Speaker Idenfcaon wh Dual Penalzed Logsc Regresson Machne Tomoko Masu and Kuno Tanabe The Insue of Sascal Mahemacs Tokyo, Japan {masu, anabe}@sm.ac.jp Absrac Ths paper proposes a novel speaker denfcaon mehod based on he dual Penalzed Logsc Regresson Machne (dplrm) for general mul-class dscrmnaon. The machne employs kernel funcons whch mplcly map an acousc feaure space o a hgher dmensonal space. Each speaker s dscrmnavely denfed n hs space mplcly. The penalzed logsc regresson model used n dplrm provdes a relable esmae of probably of each denfcaon decson. Tex-ndependen speech daa recorded by male speakers n four sessons over nne monhs was used o evaluae he new approach. The proposed mehod effecvely reduced he error rae of he convenonal GMM-based approach.. Inroducon Speaker recognon echnques are wdely appled no only o secure access conrols of nformaon servce sysems bu also o such problems as he speaker deecon problem n speech dalogue and speaker ndexng problem wh large audo archves. The demand has been ncreasng for echnques wh hgher-accuracy. The convenonal mehod for ex-ndependen speaker recognon s based on he Gaussan mxure model (GMM) []. In hs approach, uerance varaon s well capured by a mxure of a well-chosen number of Gaussan dsrbuons. However, he esmaon of he mxure dsrbuon end o be unrelable especally when he number of ranng daa s relavely small. In such a case addonal fne-unng process of he esmaed mxure s needed for ganng hgher dscrmnave power []. The suppor vecor machnes (SVMs) [3] have been successfully appled o varous paern recognon problems: handwren dg recognon, face deecon, ex caegorzaon and speaker recognon [4-8]. The SVMs are bascally desgned for wo-class dscrmnaon, and some specal echnques are necessary for mul-class dscrmnaon. The dual Penalzed Logsc Regresson Machne (dplrm), whch was employed n hs paper for he speaker denfcaon problem, was proposed by Tanabe [9,] based on penalzed logsc regresson model wh a specfc penaly erm for brngng abou nducon-generalzaon capacy of he machne. Maxmzaon of he dual penalzed logsc regresson lkelhood leads nrnccally o he kernel regressors as s he case wh SVMs whch employ a quadrac programmng model. One of he mos noable advanage of he machne over he oher mehods s ha can gve probablsc predcons. In hs paper, we show a new approach o he speaker denfcaon problem and demonsrae he power of dplrm. In he followng secon, we brefly skech he machne dplrm. In secon 3, we nroduce our speaker denfcaon procedure. In secon 4, our proposed mehod s evaluaed n exndependen speaker denfcaon expermens. In secon 5, we dscuss he choces of kernel funcons and assess he esmae of he probably on each denfcaon decson.. Dual penalzed logsc regresson machne Le x j s a column vecor of sze n and c j akes a value n he fne se {,,,K} of classes. The learnng machne dplrm feeds a fne number of ranng daa {( x j, c j )} j=, K,, and hen produces a condonal mulnomal dsrbuon n Μ( p ( ) of c gven x R, where p ( s a predcve probably vecor whose k-h elemen pk ( ndcaes he probably of c akng he value k. For mahemacal convenence, we code he class daa c j by j-h un column vecor ek (, K,, K) of sze K and defne an K consan marx Y by Y [ y ; L; y ] [ ec ; L; ec ] () whose j-h column vecor y j e c j ndcaes he class o whch he daa x j s aached. Whle SVM deermnes a sngle valued dchoomous dscrmnave funcon f ( vk( () where v s a row vecor of sze, we nroduce a mul-valued funcon f ( Vk( (3) K mappng R no R, where V s an K parameer marx whch s o be esmaed by usng he ranng daa se n {( x j, c j )} j =, K,, k( s a map from R no R defned by

2 k( ( K( x,, K, K( x, ), (4) and K(x, x ) s a ceran posve defne kernel funcon. Then we defne a model for mulnomal probablsc predcor p( by ˆ ˆ p( pˆ( f ( ) ( p( f ( ), K, p K ( f ( )), (5) exp( fk ( ) where pˆ k ( f ( ) s he logsc ransform. K exp( f ( ) = Under hs model assumpon, he negave-log-lkelhood funcon L (V) for p ( s gven by L( V ) log( pc ( x j )) = j log( pˆ c ( Vk( x j j ))) (6) j= j= whch s a convex funcon (see [9,]). Ths objecve funcon L(V) s of dscrmnave naure, and ha f he kernel funcon s appropraely chosen, he map f( can represen a wde varey of funcons so ha he resulng predcve probably p( can be expeced o be close o he realy. A predcve vecor p ( could be obaned by pung p ( = pˆ( ) where V s he he maxmum lkelhood esmae whch mnmze he funcon L(V) wh respec o V. However, over-learnng problems could occur wh V wh he lmed number of ranng daa. In order o oban an nducon power of dplrm, he penaly erm s nroduced and he negave-log-penalzed-lkelhood δ PL( V) L( V) + Γ VK (7) F s mnmzed o esmae V where s he Frobenus norm. F The marx Γ s an K K posve defne marx. A frequen choce of Γ s gven by Γ = YY (8) whch equlbraes a possble mbalance of classes n he ranng daa. The marx K s he consan marx, gven by K = [ K( x, x j )], j=, K,. (9) The δ s a regularzaon parameer and can be deermned by he emprcal Bayes mehod. oe ha by maxmzng he convex PL(V), our mehod can handle mul-class problem whou sufferng from he dffcules encounered by a parwse classfcaon mehod employed n SVM, whle SVM maxmzes he margn beween wo classes of daa, hence canno rea mul-class suaons a once. Due o he nroducon of he specfc quadrac penaly n (7), he mnmzer V of PL(V) s a soluon of he nea marx equaon, PL ( P ( V) Y + δ ΓV) K = Ο K,, () where P (V) s an K marx whose j-h column vecor s he probably vecor p( x j ) pˆ ( Vk( x j )). The marx Y s gven n (). The mnmzer V, whch gves he probablsc predcor ˆ p ( p( ), s eravely compued by he followng algorhm. Algorhm: Sarng wh an arbrary K marx V, we generae a sequence { V } of marces by where + V = V α V, =, K, () V s he soluon of he lnear marx equaon, Tranng daa se: {( x, j )} j K Tesng daa: x } Predcor: p ( x ) { =, K, M Probablsc predcon of speakers for each daa x : Calculae he summaon over samples and decde a deermnsc predcon of a sngle speaker: M c = arg max log( p ( x )) k x p ( ) = j c =,, Conver class daa {c j } no Y Learnng by dplrm Dual parameer marx: V Predcor : p ( pˆ( ) Fgure. Tranng procedure. k Fgure. Tesng procedure.

3 ([ p( x j )] p( x j )( p( x j )) ) V ( k( x j )( k( x j )) ) j= () + δ Γ V K = ( P( V ) Y + δγv ) K. The dealed algorhm for esmaon s shown n [9-]. oe ha we only need o solve an unconsraned opmzaon of a srcly convex funcon PL(V) or equvalenly, o solve he smple marx nonlnear equaon (). SVM, however, has o solve a seres of nequaly consraned maxmzaon problems n mul-class suaons. 3. dplrm-based Speaker denfcaon Fg. shows he ranng procedure. The ranng daa se {( x j, c j )} j =, K, whch covers all he speakers daa s colleced. The class daa {c j } s convered no marx Y. The key marx V s esmaed by dplrm. Fnally he predcor p ( s obaned. Fg. shows he esng procedure. The predcve probably p ( x ) s calculaed for each daa x. Then we sum up he log-probably for each class over samples and choose he class whch aans s maxmum as he speaker who uers he esng daa. 4. Expermens and resuls The proposed mehod was evaluaed n ex-ndependen speaker denfcaon. The performance was compared wh ha of he convenonal GMM-based mehod. 4.. Daa and sysem descrpon The daabase consss of male speakers. Each speaker uers several senences and words as lsed n Table. Each senence s approxmaely four seconds n duraon and each word one second. The exs are common for all speakers. The same se of senence and word speech was repeaedly recorded n four sessons (T o T3) over nne monhs and sampled a 6 khz. A feaure vecor of 6 componens, conssng of mel-frequency cepsral coeffcens plus normalzed log energy and her frs dervaves, was derved once every ms over a 5.6 ms Hammng-wndowed speech segmen. For he dplrm ranng, hree senences from sesson T ( second speech n oal) were used for esmang V. The followng polynomal funcon was used as he kernel funcon. s K ( x, x ) = ( x x + ) (3) The power s was nne. The dplrm parameers α and δ were expermenally se o. n () and 7.7e-5 n (7), respecvely. In he esng, fve senences and fve words from hree sessons T o T3 were ndvdually esed. The case number s 5 for each senence and word daa. The senences for esng were dfferen from hose for ranng and were he same for all esng sessons. In he GMM-based mehod, dagonal covarance models were used as speaker models. The parameers were nalzed Table. Tranng and esng senences and words (he Hepburn sysem of romaj for Japanese scrps) Tranng: senences Tesng: senences Tesng: words Conens. seno akasaha hyakunanajussech hodode mega ookku yaya fuoeru. oogoeo dashsuge kasuregoen nae shmau 3. ashza hkzaha deknakuemo eha kakeru. obujyuuo eru kooha jruno yume daa. hajmee ruuburubjusukae haanoha juuyonemaeno kooda 3. jbuno jsuryokuha jbuga chba yoku sheru hazuda 4. koremade shouneyakyuu mamasa bareenado chksupoosuo sasae shmn mcchakushe kanoha musuuno boraadaa 5. gzakeno amagoo yunyuushe fukasase kachuude sodaeru youshokumo hajmaeru. mouchdo. orkaesh 3. ese 4. horyuu 5. shouka usng all ranng speech for all speakers wh he HMM oolk (HTK) [], and hen esmaed wh he EM algorhm usng he hree senences for each speaker. For esng, he speaker who aaned he maxmum collecve log-lkelhood was regarded as he speaker who uered he esng daa. 4.. Resuls Tables lss he numbers of senences and words denfed correcly for each sesson and he accuracy raes and he confdence nervals (%) averaged over sessons T o T3 when compared wh he GMM-based mehod. For he GMM-based mehod, 6-Gaussan-mxure models were used for senence speech and 4-Gaussan-mxure models for word speech, snce hose models showed he bes performance n he prelmnary expermens usng 8, 6, 4 and 3-Gaussan-mxure models as lsed n Table 3. Our mehod ouperformed he GMM-based mehod especally for word speech. These resuls ndcae ha he dplrm can precsely capure he speaker characerscs wh a small amoun of daa and effecvely dscrmnae each speaker dsrbuon. Fgure 3 shows he speaker denfcaon raes averaged over sessons T o T3 for each speaker. Especally for word speech, he dsperson n he raes for our mehod was smaller han ha for he GMM-based mehod. I can be consdered ha our mehod ends o sably denfy any speakers.

4 Table. The numbers of (A) senences and (B) words denfed correcly for each sesson and he accuracy raes ± he confdence nervals (%) averaged over sessons T o T3. (A) senence speech Mehod T T T3 Average dplrm ±.9 GMM (6) ±. (B) word speech Mehod T T T3 Average dplrm ±.9 GMM (4) ± 3.5 Table 3. Accuracy raes (%) of speaker denfcaon averaged over sessons T o T3 usng he GMMbased mehod wh 8, 6, 4 and 3-Gaussan mxures. Tesng senence speech word speech Speaker ID (A) senence speech Speaker ID (B) word speech dplrm (sen.) GMM (sen.) dplrm (word) GMM (word) Fgure 3. Accuracy raes (%) of speaker denfcaon averaged over sessons T o T3 usng (A) senence and (B) word speech for each speaker. 5. Dscusson We nvesgae our dplrm-based mehod from he vewpons of he kernel funcons. The polynomal kernel funcons (3) wh several powers and he Gaussan kernel funcon, x x K ( x, x ) = exp h (4) were compared n performance n he case where he esmaon sep () was ermnaed a he -h eraon. Table 4 lss he accuracy raes of speaker denfcaon averaged over sessons T o T3 for he senence and word speech daa. The polynomal kernel funcon wh he power of nne performed he bes, and much beer han he Gaussan kernel funcon. For he polynomal kernel funcon, he performance wh he power of was worse han ha wh he power of nne because of he lack of precson wh 3-b compuers whch we used n he expermens. Table 4. Accuracy raes (%) of speaker denfcaon wh several kernel funcons. Kernel funcon Senence Word Polynomal s = s = s = Gaussan h = Conclusons Ths paper proposed a new speaker denfcaon mehod based on dplrm. In dplrm, he polynomal kernel funcon wh he power of nne was shown o be effecve for speaker dscrmnaon. In he expermens wh -second speech for ranng and speech wh several sessons for esng, our dplrm-based mehod was shown o perform beer han he convenonal GMM-based mehod. Our fuure work ncludes he evaluaon of dplrm wh a larger daase, he use for speaker verfcaon and end-pon deecon, and he comparson n performance wh convenonal dscrmnave mehods and SVM. 7. REFERECES [] D. A. Reynolds, Speaker Idenfcaon and Verfcaon Usng Mxure Speaker Models, Speech Communcaon, 7, pp. 9-8, 995. [] G. R. Doddngon, M. A. Przybock, A. F. Marn and D. A. Reynolds, The IST Speaker Recognon Evaluaon Overvew, Mehodology, Sysems, Resuls,

5 Perspecve, Speech Communcaon, 3, pp. 5-54,. [3] V.. Vapnk, The aure of Sascal Learnng Theory, Sprnger, 995. [4] M. Schmd and H. Gsh, Speaker Idenfcaon va Suppor Vecor Classfers, Proc. ICASSP, Alana, 996. [5] M. Schmd, Idenfyng Speakers Wh Suppor Vecor eworks, Proc. Inerface, Sydney, 996. [6] S. Fne, J. avral and R. A. Gopnah, A Hybrd GMM/SVM Approach o Speaker Idenfcaon, Proc. ICASSP, Sal Lake Cy,. [7] W. M. Campbell, A Sequence Kernel and s Applcaon o Speaker Recognon, IPS-4, pp ,. [8] V. Wan and S. Renals, SVMSVM: Suppor Vecor Machne Speaker Verfcaon Mehodology, Proc. ICASSP, Hong-Kong 3. [9] K. Tanabe, Penalzed Logsc Regresson Machnes: ew mehods for sascal predcon, ISM Cooperave Research Repor 43, pp ,. [] K. Tanabe, Penalzed Logsc Regresson Machnes: ew mehods for sascal predcon, Proc. IBIS, Tokyo, pp. 7-76,. [] K. Tanabe, Penalzed Logsc Regresson Machnes and Relaed Lnear umercal Algebra, KOKYUROKU 3, Insue for Mahemacal Scences, Kyoo Unversy, pp , 3. [] hp://hk.eng.cam.ac.uk, he hdden Markov model oolk (HTK).