Calculating Model Parameters Using Gaussian Mixture Models; Based on Vector Quantization in Speaker Identification

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1 IJCSNS Inernaonal Journal of Comuer Scence and Newor Secury, VOL.7 No., February 07 3 Calculang Model Parameers Usng Gaussan Mxure Models; Based on Vecor Quanzaon n Seaer Idenfcaon Hamdeh Rezae-Nezhad h.rezae@au.ac.r Dearmen of Comuer Engneerng, Qeshm Branch, Islamc Azad Unversy, Qeshm, Iran. Summary he use of Gaussan Mxure Model (GMM) s mos common n seaer denfcaon. he mos of he comuaonal rocessng me n GMM s requred o comue he lelhood of he es seech of he unnown seaer wh consder o he seaer models n he daabase. he me requred for seaer denfcaon s deendng o he feaure vecors, her dmensonaly and he number of seaers n he daabase. In hs aer, we focused on omzng he erformance of Gaussan mxure (GMM) and adaed Gaussan mxure model (GMM-UBM) based seaer denfcaon sysem and roosed a new aroach for calculaon of model arameers by usng vecor quanzaon (VQ) echnques o ncrease recognon accuracy and reduce he rocessng me. Our roosed modelng s based on formng clusers and assgnng weghs o hem accordng o uon he number of mxures used for modelng he seaer. he advanage of hs mehod s n he reducon n comuaon me whch deends uon how many mxures are used for ranng he seaer model by a subsanal value comared wh aroaches whch use execaon maxmzaon (EM) algorhm for comung he model arameers. Key words: Seaer denfcaon, Gaussan mxure model, EM algorhm, Vecor quanzaon, Feaure exracon.. Inroducon Sascal models such as Hdden Marov Models (HMM), Neural Newors (NN), Suor Vecor Machnes (SVM) and Gaussan Mxure Models (GMM) have been used n seaer recognon n he as several years. Usng a Gaussan mxure model due o havng a number of advanages has become a classc and successful mehod n seaer recognon and maes suable for modelng he robably dsrbuons over vecors of nu feaures []. Generally, seaer denfcaon sysem consss of hree hases [-3]. Feaure exracon s he frs se and followed by feaure selecon where he seech sgnal s exraced o feaure vecors. Seech can be characerzed n erms of he sgnal carryng message Informaon and also hs nd of sgnal has been very useful n some alcaons. Feaure exracon could ge hree man yes of nformaon: Seech ex, Language and Seaer Ideny. he second se s seaer modelng and develong a seaer model daabase. By usng feaure vecors exraced from a gven seaer s ranng uerance(s), a seaer model s raned and sored no he sysem daabase. In ex-deenden mode, he model s uerance-secfc and ncludes he emoral deendences beween he feaure vecors. he las se s decson mang. hs aer focused on he calculaon of model arameer n ex-ndeenden seaer denfcaon sysems usng Gaussan mxure model and adaed Gaussan mxure model. We are oms n searchng an aroach o reduce he comuaonal me n seaer modelng [4-6]. he mos moran se of seaer modelng s he calculaon of model arameers [7]. In hs aer EM algorhm s used for he calculaon of model arameers for boh GMM and GMM-UBM aroaches. We consder a seaer denfcaon sysem based on he EM algorhm for calculang he model arameers and we have nvesgaed anoher mehod by usng he VQ echnque o calculae he model arameers. For hese aroaches,.e., GMM based on EM and GMM based on VQ (GMM-UBM based on EM and GMM-UBM based on VQ), he recognon raes and comuaon me are comared. I has been shown ou ha even hough he recognon accuracy of wo mehods s nearly equal bu he comuaon me s consderably reduced n he new mehod. In Secon II, we dscuss how o use Mel- Frequency Cesral Coeffcens (MFCC) for feaure exracon of seech and exlan he fron-end rocessng echnque n shor [8-0]. Secon III and IV exlan he Gaussan mxure model based seaer denfcaon and maxmum lelhood arameer esmaon o comue model arameers resecvely [-4]. Adaed Gaussan mxure model s exlaned n secon V. he sxh secon s dedcaed o nroducng he new mehod for comung model arameers usng Vecor Quanzaon. Exermenal resuls and s dscusson are resened In Secon VII, and conclusons are shown n las Secon. Manuscr receved February, 07 Manuscr revsed February 0, 07

2 36 IJCSNS Inernaonal Journal of Comuer Scence and Newor Secury, VOL.7 No., February 07. Seech Feaure Exracon For all he recognon sysems, here are wo man hases. he frs hase s called ranng hase and he nex hase s called denfcaon or (esng) hase. ranng and esng are wo moran ses of an denfcaon sysem. ranng hase s o ge he seaer models or vocerns for seaer daabase. In hs hase, he mos useful feaures are exraced from seech sgnal for seaer denfcaon or verfcaon, and ran models o ge omal sysem arameers. Feaure exracon s he hear of he seaer denfcaon sysem. In esng hase, he same mehod for exracng feaures as n he frs hase s used for he ncomng seech sgnal, and hen he seaer models geng from enrollmen hase are used o calculae he smlary beween he new seech sgnal model and all he seaer models n he daabase. Fg. shows he ranng and esng hases for seaer denfcaon. he human seech sgnal conveys many levels of nformaon rangng from honec conen o seaer deny and even emoonal saus. Human voce before s fnal form asses hrough wo dfferen sysems. he frs sysem s vocal folds and he second sysem s vocal rac []. he am of feaure exracon sage s o exrac he seaer arcular nformaon as feaure vecors. Fg. (a) ranng hase, (b) esng hase. he MFCC s a mehod ha analyzes how he Fourer ransform exracs frequency comonens of a sgnal n he me-doman. Poular feaures for descrbng seech sgnal are MFCC. In hs aer, MFCCs s used for feaure exracon whch ae human ear's frequency resonse no consderaon. Process of feaure exracon s shown n Fg. and he comrehensve mehod s exlaned n [6-7]. In he frame blocng he nu seech waveform s dvded no frames of aroxmaely 30 mllseconds. he wndowng bloc mnmzes he dsconnues of he sgnal by aerng he begnnng and end of each frame o zero. Fg. Mel-frequency Cesral Coeffcens feaure exracon rocess.

3 IJCSNS Inernaonal Journal of Comuer Scence and Newor Secury, VOL.7 No., February Each frame convers from he me doman o he frequency doman by he FF bloc hen he magnude secrum of he uerance s assed hrough a ban of rangular-shaed flers. he energy ouu of each fler s comressed and ransformed o he Cesral doman va he DC. Cesrum, c(n) n s smles form s he dscree cosne s(n) ransformaon of he Mel-secrum of a sgnal, n logarhmc amludes and can be mahemacally defned as ( n) ff lof ff( s( n) ) ( ) c = () Seech sgnal consss of many feaures ha all of hem are no moran for seaer dscrmnaon [], [4]. An deal feaure would: have large beween-seaer varably and small whn-seaer varably be robus agans nose and dsoron occur frequenly and naurally n seech be easy o measure from seech sgnal be dffcul o mersonae/mmc No be affeced by he seaer s healh or longerm varaons n voce. 3. Gaussan Mxure Model GMM s a classc aramerc mehod bes used for seaer modelng due o he fac ha Gaussan comonens have he caably of reresenng some general seaer deenden secral shaes. Modelng echnques le GMM are o generae seaer models from Feaure vecors ha obaned from he above se by usng sascal varaons of he feaures. A GMM s a aramerc robably densy funcon reresened as a weghed sum of Gaussan comonen denses ha s shown o rovde a smooh aroxmaon o he underlyng long-erm samle dsrbuon of observaons obaned from uerances by a gven seaer [8]. An moran se n he mlemenaon of he lelhood rao deecor s selecon of he acual lelhood funcon. he choce of hs funcon s largely deenden on he feaures beng used as well as secfcs of he alcaon. For ex-ndeenden seaer recognon, where here s no ror nowledge of wha he seaer wll say, he mos successful lelhood funcon has been Gaussan mxure models. A Gaussan mxure model s generaed from a mxure of a fne number of Gaussan dsrbuons ha each dsrbuon s robably dsrbuon densy gven by he followng equaon: Where x s a D-dmensonal random b x = vecor, ( ),,, M, are he comonen denses, = and ( π ),, M, are he mxure weghs. b ( x) = ex D µ / / Σ ' ( x µ ) Σ ( x ) Mean vecors, covarance marces and mxure weghs arameerze he comlee Gaussan mxure densy. hese arameers are reresened by λ = {, µ, }, =,.., M. Each seaer n a seaer denfcaon sysem can be reresened by a GMM and s referred o by he seaer s resecve model λ. he arameers of a GMM model can be esmaed usng maxmum lelhood (ML) esmaon. he man objecve of he ML esmaon s o derve he omum model arameers ha can maxmze he lelhood of GMM. 4. Maxmum Lelhood Parameer Esmaon Unforunaely drec maxmzaon usng ML esmaon s no ossble and herefore a secal case of ML esmaon nown as Execaon-Maxmzaon (EM) algorhm s used o exrac he model arameers. he goal of hs echnque s o maxmze he followng formula wh bes maches n dsrbuon of ranng vecors. M ( x λ) = b ( x) = ( X λ) = ( x λ) = Where X { x },..., x () (3) (4) = s a se of ranng vecors. he EM algorhm s used o esmae arameers. he goal of he EM algorhm s o comue he model arameers + X λ X λ. eravely ll ( ) ( ) o guaranee he above condon, he followng formulae are used: defned by a mean vecor µ, a covarance marx = M and a mxure wegh. In a GMM model, he

4 38 IJCSNS Inernaonal Journal of Comuer Scence and Newor Secury, VOL.7 No., February 07 Mxure weghs: = ( = x,λ) MEANS: VARIANCES: µ σ = = = = = = = ( = x, λ) ( = x, λ) x ( = x, λ) Where for acousc class s gven by λ ( x, ) = M = b b ( x ) ( x ) ( = x, λ) x () (6) (7) (8) usng he seaer s ranng seech and a form of Bayesan adaaon Unle he sandard aroach of maxmum lelhood ranng of a model for he seaer ndeendenly of he UBM, he basc dea n he adaaon aroach s o derve he seaer s model by udang he well-raned arameers n he UBM va adaaon. Le he EM algorhm, he adaaon s a wo ses esmaon rocess. he frs se s dencal o he execaon se of he EM algorhm. Unle he second se of he EM algorhm, for adaaon hese new suffcen sasc esmaes are hen combned wh he old suffcen sascs from he UBM mxure arameers usng a daadeenden mxng coeffcen. For mxure n he UBM, we comue equaon (3) ha s he same as he execaon se n he EM algorhm. Fnally, hese new suffcen sascs from he ranng daa are used o udae he old UBM suffcen sascs for mxure o creae he adaed arameers for mxure wh he equaons: w w [ α n / + ( α ) w ]γ wˆ = (0) m µ = α E µ m ( x) + ( α ) ˆ () A grou of S seaers S={,,,S} s reresened by GMM s { λ,...,λ s } For seaer denfcaon. Fndng he seaer model whch has he maxmum a oseror robably of a gven observaon sequence s he denfcaon's am. S = arg max S ( X λ ) ˆ (9). Adaed Gaussan mxure model In he GMM-UBM sysem we use a sngle, seaer ndeenden bacground model o reresen ( X λ). he UBM s a large GMM raned o reresen he seaerndeenden dsrbuon of feaures. Secfcally, we wan o selec seech ha s reflecve of he execed alernave seech o be encounered durng recognon. hs ales o boh he ye and he qualy of seech, as well as he comoson of seaers. here are many aroaches ha can be used o oban he fnal model o ran he UBM [9]. he smles s o merely ool all he daa o ran he UBM va he EM algorhm. One should be careful ha he ooled daa are balanced over he suboulaons whn he daa. In hs sysem, we derve he hyoheszed seaer model by adang he arameers of he UBM ˆ σ v V ( xx ) + ( α )( σ + µ ) ˆ I α E µ = () he adaaon coeffcens conrollng he balance w m beween old and new esmaes are { α v, α, α } for he weghs, means and varances, resecvely. he scale facor γ s comued over all adaed mxure weghs o ensure hey sum o uny. For each mxure and each arameer, a daa-deenden adaaon coeffcen α, { w, m, v}, s used n he above equaons. hs s defned as α Where n n + r = (3) r s a fxed relevance facor for arameer. 6. Vecor Quanzaon Aroach For calculang model arameers, he vecor quanzaon (VQ) mehod and s uses are nroduced n hs secon [0]. Vecor quanzaon s an aroach o mang vecors o a fne number of regons n he sace as shows n Fg. 3. Regons are called clusers and can be reresened by her ceners. Each cener called a code

5 IJCSNS Inernaonal Journal of Comuer Scence and Newor Secury, VOL.7 No., February word and he collecon of all code words s a code boo. he VQ codeboo has a small number of hghly reresenave vecors ha effcenly reresen he seaer secfc characerscs. hs s a mehod used for reducng or comressng he number of ranng vecors requred n a recognon sysem. In hs new aroach, VQ as a modelng echnque was used n seaer denfcaon []. Afer obanng he feaure vecors of he nu seech segmen, feaure vecors are dvded no a ceran number of clusers, M ha nroduced as a codeboo sze usng he aroach n []. Each cluser has one cenrod whch reresenng he mean of all he feaure vecors relaed o ha cluser. he denfcaon error ercenage s drecly deendng on he sze of he codeboo [3]. hs echnque was used o fnd he M clusers such ha each cluser has a wegh of a leas /M. In equaon (3), we have used he cenrods of hese clusers as a mean. By usng feaure vecors belongng o each of he M clusers he covarance marx s obaned. By hs way all he arameers are obaned n equaon (3) daabase conanng seech daa from 00 seaers. Dsrbuon of male and female seaers on he seaer daabase s almos equal. wo sessons for ranng and esng sessons were used. Our exermens oerae on Cesral feaures, exraced usng a 4-ms Hammng wndow wh 0 mllseconds overlang. he sgnal was re emhaszed by he fler H (z) =-0.97 z- and slence frame was removed before he feaure exracon. MFCCs ogeher wh log energy were calculaed usng a ban of 3 flers as menoned n [4]. hus we have obaned -dmensonal feaure vecors. For ranng hase, ranng was done n dfferen duraons: 30sec and 60sec. Sysem was esed usng 0sec es frames. wo ses of exerence were done; EM algorhm s used for ranng he model n he frs se of exermens for GMM and GMM-UBM aroaches. In he second se, Vecor Quanzaon have used for comung he model arameers. able: Idenfcaon accuracy and runnng me for EM-GMM and VQ-GMM aroach (ranng wh 30sec and esng wh 0sec) M EM-GMM VQ-GMM Accuracy me Accuracy me Fg. 3 Mang vecors n he sace usng VQ aroach. he means for M mxures are randomly nalzed n he revous aroach (usng EM for calculang model arameers). In a -dmensonal feaure vecor sace, may hs sace be dense n ceran regons where mos of he feaure vecors are locaed and some feaure vecors are a larger dsances from feaure vecors n he dense area, so could devoe feaure vecors whch are a hgher dsances from oher feaure vecors, as a means bu VQ echnque aes no consderaon feaure vecors belongng o ha cluser only by usng cluserng aroach. hs mnmzes he value of ( x - µ ) n equaon (3). hs aroach dese eeng all he advanages Gaussan Mxure Modelng echnque has effcen resul for calculang model arameer. 7. Exermens seu, resul and dscusson As a es maeral for our exermens we used he Farsda daabase. he exermens were made usng a seaer able: Idenfcaon accuracy and runnng me for EM-GMM and VQ- GMM aroach (ranng wh 60sec and esng wh 0sec) M EM-GMM VQ-GMM Accuracy me Accuracy me If he cluser for every cenrod has wegh of /M (M s he number of mxures), sos slng bu f he cluser has a wegh less han /M, he cenrods are sl agan. Selecon of M s moran for shorer ranng daa. he covarance s comued based on he daa for each cluser. Idenfcaon accuracy s calculaed for 0sec esng daa usng ranng model arameers obaned from he above ses. ables and able show a comarson of consderng he accuracy and melnes requred beween GMM based on EM and GMM based on VQ for dfferen ranng and esng mes. Furhermore, able 3 shows GMM-UBM based on EM and GMM-UBM based on VQ for ranng and esng mes as for able and.

6 IJCSNS Inernaonal Journal of Comuer Scence and Newor Secury, VOL.7 No., February 07 able3: Idenfcaon accuracy and runnng me for EM-GMM-UBM and VQ-GMM-UBM aroach (ranng wh 30sec and esng wh 0sec) M EM-GMM-UBM VQ-GMM-UBM Accuracy me Accuracy me DE curve duraon s of 0sec. We can see ha, VQ-GMM and VQ- GMM-UBM aroaches have a slghly beer erformance raher han EM-GMM and EM-GMM-UBM resecvely. We comare he effec of model sze usng VQ-GMM and VQ-GMM-UBM aroaches on seaer denfcaon erformance n he nex exermen. he ranng s 60sec and esng s 0sec. Referrng o Fg. 6 and Fg. 7, he curves showed ha he ncrease n he number of mxures ncreases he erformance of he sysem. DE curve 0 0 Mss robably (n %) 0 VQ-GMM 8.3 EM-GMM 7. Mss robably (n %) 0 0. M=64 M=8 M=3 M=6 M=8 M= False Alarm robably (n %) False Alarm robably (n %) Fg. 4 Comarson of VQ-GMM and EM-GMM aroach for 8 mxures. Fg. 6 Effec of model sze on seaer denfcaon usng VQ-GMM aroach. DE curve DE curve 0 0 Mss robably (n %) 0 Mss robably (n %) 0 M=64 M=3 VQ-GMM-UBM 6.3 EM-GMM-UBM M=6 M= M=6 M= False Alarm robably (n %) False Alarm robably (n %) Fg. : Comarson of VQ-GMM-UBM and EM-GMM-UBM aroach for 8 mxures. Fg. 4 and Fg. show he above se of exermens whch are loed on he DE curve. 8 mxures are used n hs exermen. ranng duraon s of 60sec and es Fg. 7 Effec of model sze on seaer denfcaon usng VQ-GMM- UBM aroach.

7 IJCSNS Inernaonal Journal of Comuer Scence and Newor Secury, VOL.7 No., February Concluson he mlemenaon of GMM based seaer denfcaon has been addressed n hs aer. Four aroaches were used for ranng he seaer model. I has been shown ha usng VQ-GMM and VQ-GMM-UBM n he model arameers calculaon have a slgh mrovemen n denfcaon accuracy. Consderable mrovemen s observed n comuaonal me. able I and able III showed a seedu facor of 7 was acheved n he frs se of exermens wh 8 mxures and ranng duraon of 30 Sec, whle n he second se of exermens a seedu facor was acheved wh 6 mxures and ranng daa of 60sec as shown n he able II. References [] D. A. Reynolds and R. C. Rose, Robus ex-ndeenden seaer denfcaon usng Gaussan seaer models, IEEE rans. Seech Audo Process , 99. [] J. Yamagsh,. Nose, H. Zen, Z.-H. Lng,. oda, K. ouda, S. Kng, and S. Renals, A robus seaer-adave HMM based ex-o-seech synhess, IEEE rans. Seech, Audo & Language Process., Vol. 7, No. 6, , Aug [3] om Knnuen e al., "Real-me seaer denfcaon and verfcaon", IEEE ransacons on audo, seech and language rocessng, Vol. 4, No., Jan [4] D. A. Reynolds,. F. Quaer and R. B. Dunn, Seaer Verfcaon Usng Adaed Gaussan Mxure Models, Dgal Sgnal Processng, Vol. 0,. 9-4, 000. [] Xong, Z., Zheng,.F., Song, Z., Soong, F., Wu, W., A ree-based ernel selecon aroach o effcen Gaussan mxure model unversal bacground model based seaer denfcaon, Seech Communcaon, Vol. 48,. 73 8, 006. [6] Saed, R., Sadegh Mohammad, H.R., Rodman, R.D., Knnunen,., A new segmenaon algorhm combned wh ransen frames ower for ex ndeenden seaer verfcaon, In: Proc. ICASSP 007, Vol., , Arl 007. [7] Arhur Chan e al., Four-layer caegorzaon scheme of fas GMM comuaon n large vocabulary connuous seech recognon sysems, n Proc. Of Inerseech, , 004. [8] N. Deha, P. Kenny, R. Deha, P. Dumouchel, and P. Ouelle, Fron-end facor analyss for seaer verfcaon, IEEE rans. Audo, Seech, and Lang. Process., Vol. 9, No. 4, , 0 [9] Sandan Charobory, Anndya Roy and Gouam Saha Imroved Closed Se ex- Indeenden Seaer Idenfcaon by Combnng MFCC wh Evdence from Fled Fler Bans Inernaonal Journal of Sgnal Processng, Vol. 4,.4-, Nov [0] M. Sahdullah and G. Saha, Desgn, Analyss and Exermenal Evaluaon of Bloc Based ransformaon n MFCC Comuaon for Seaer Recognon, Seech Communcaon, Vol. 4, No. 4, 0, [] D. A. Reynolds,. F. Quaer and R. B. Dunn, Seaer Verfcaon Usng Adaed Gaussan Mxure Models, Dgal Sgnal Processng, Vol. 0, No.,. 9-4, 000 [] D. A. Reynolds, Gaussan Mxure Models, echncal Reor, MI Lncoln Laboraory, Cncnna, 00. [3] Reynolds D. A, Rose R. C., Robus ex Indeenden Seaer Idenfcaon Usng Gaussan Mxure Seaer Models, IEEE rans. Seech Audo Processng, Vol. 3,. 7 83, 99. [4] A.P. Demser, N.M. Lard, and D.B. Rubn, Maxmum Lelhood from Incomlee Daa va EM Algorhm, J. Royal Sas. Soc., Vol. 39, No.,. -38, 997. [] O. Schleusng,. Knnunen, B. Sory, J.-M. Vesn, Jon Source-Fler Omzaon for Accurae Vocal rac Esmaon Usng Dfferenal Evoluon, IEEE ransacons on Audo, Seech and Language Processng, Vol., No. 8, , Augus 03. [6] D. A. Reynolds, A Gaussan mxure modelng aroach o ex-ndeenden seaer denfcaon, Ph.D. hess, Georga Insue of echnology, Seember 99. [7]. Knnunen, R. Saed, F. Sedla, K.A. Lee, J. Sandberg, M. Hansson-Sandsen, H. L, Low-Varance Mulaer MFCC Feaures: a Case Sudy n Robus Seaer Verfcaon, IEEE ransacons on Audo, Seech and Language Processng, Vol. 0, No. 7, , Seember 0. [8] F. Bmbo e al., A uoral on ex-indeenden Seaer Verfcaon, EURASIP J. Al. Sgnal Process., No. 4, , 004. [9]. Knnunen, E. Karov, and P. Fran, Real-me seaer denfcaon and verfcaon, IEEE rans. Audo, Seech, and Language Process., Vol. 4, No., , Jan [0] A.Srnvasan, "Seaer Idenfcaon and verfcaon usng Vecor Quanzaon and Mel frequency Cesral Coeffcens", Research Journal of Aled Scences, Engneerng and echnology, Vol. 4(I),. 33-, 0. [] Memon, S., M. Lech and N. Maddage, 009., Seaer verfcaon based on dfferen vecor quanzaon echnques wh gaussan mxure models, Proceedngs of he 3rd Inernaonal Conference on Newor and Sysem Secury, Oc. 9-, Gold Coas, Queensland, Ausrala, : 3-8. [] Y. Lnde, A. Buzo, and R. M. Gray, An algorhm for Vecor Quanzaon, IEEE rans. on Communcaons, Vol. COM48, No.,. 84-9, January 980. [3] A. Revah, R. Ganaahy and Y. Venaaraman, ex Indeenden Seaer Recognon and Seaer Indeenden Seech Recognon Usng Ierave Cluserng Aroach, Inernaonal Journal of Comuer Scence & Informaon echnology, Vol., No.,. 30-4, 009. [4] Premaanhan and W.B. Mhael, Seaer verfcaon/ recognon and he morance of selecve feaure exracon: Revew, Proceedngs of he 44h IEEE 00, Mdwes Symosum, Vol.,. 4-7, 00.