A New Method for Computing EM Algorithm Parameters in Speaker Identification Using Gaussian Mixture Models

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1 0 IACSI Hong Kong Conferences IPCSI vol. 9 (0) (0) IACSI Press, Sngaore A New ehod for Comung E Algorhm Parameers n Seaker Idenfcaon Usng Gaussan xure odels ohsen Bazyar +, Ahmad Keshavarz, and Khaoon Bazyar 3 Dearmen of Communcaon, Bushehr Branch, Islamc Azad Unversy Bushehr, Iran Persan Gulf Unversy of Bushehr, Iran 3 Dearmen of Communcaon, Bushehr Branch, Islamc Azad Unversy Bushehr, Iran Absrac. In seaker denfcaon, mos of he comuaonal rocessng me s requred o calculae he lkelhood of he es uerance of he unknown seaker wh resec o he seaker models n he daabase. he me requred for denfyng a seaker s a funcon of feaure vecors and her dmensonaly and he number of seakers n he daabase. In hs aer, we focus on omzng he erformance of Gaussan mxure (G) based seaker denfcaon sysem. An mroved aroach for model arameer calculaon s resened. he advanage of roosed aroach les n he reducon n comuaonal me by a sgnfcan amoun over an aroach whch uses execaon maxmzaon (E) algorhm o calculae he model arameer values. hs aroach s based on formng clusers and assgnng weghs o hem deendng uon he number of mxures used for modelng he seaker. he reducon n comuaon me deends uon how many mxures are used for ranng he seaker model. Keywords: Seaker Recognon, Gaussan mxure model, Feaure exracon, Vecor quanzaon. Inroducon Over he as several years, here has been a sgnfcan amoun of research n he feld of seaker recognon. Varous algorhms have been develoed o model he seakers; hese nclude H (Hdden arkov odels), NN (Neural Neworks), SV (Suor Vecor achnes) and G (Gaussan xure odels).a seaker recognon sysem ycally consss of hree sages: feaure exracon, seaker modelng, and decson makng. In hs aer, we focus on he ex-ndeenden denfcaon ask usng G. In hs aer, we focus on an aroach o reduce he comuaonal me n seaker modelng. odel arameer calculaon s an moran se n seaker modelng. In hs aer, we roose seaker denfcaon usng he aroach descrbed n []. In [] he model arameers are calculaed usng he E algorhm. We have nvesgaed anoher aroach for calculang he model arameers. hs aroach s based on he VQ echnque. he denfcaon raes and comuaonal me for ranng he model are comared for boh aroaches,.e., G based on E and G based on VQ. I has been shown ha he denfcaon accuracy for boh aroaches s almos equal bu he comuaonal me has been grealy reduced n he new aroach. he res of he aer s organzed as follows: Secon nroduces he basc dea of G based seaker denfcaon. In hs secon, he fron-end rocessng echnque, FCC, used for feaure exracon of seech s also dscussed n shor. Secon 3 nroduces he aroach of model arameer calculaon usng Vecor Quanzaon. In Secon 4 exermenal resuls are resened, and conclusons are drawn n Secon5.. G Based Idenfcaon Sysem.. Seech Feaure Exracon + Corresondng auhor. el.: ; E-mal address: mohsenbazyar4@yahoo.com. 9

2 Seech secrum has been roven effecve for seaker denfcaon. Seech secrum reflecs user s vocal rac srucure whch dsngushes hm/her from ohers. Sudes done n he as have roven he flerbank echnque o be very effecve for seech recognon. In hs aer, we use FCCs whch ake human ear frequency resonse no consderaon Fg. llusraes he rocess of feaure exracon [] and he dealed rocedure s exlaned n [3]... Gaussan xure odel In G, we model he seaker daa (feaure vecors obaned from he above se) usng sascal varaons of he feaures. Hence, rovdes us a sascal reresenaon of how seaker roduces sounds. Gaussan mxure densy s shown o rovde a smooh aroxmaon o he underlyng long-erm samle dsrbuon of observaons obaned from uerances by a gven seaker. hese are he moran movaons for usng G as a modelng echnque []. Fg.: el-frequency Cesral Coeffcens feaure exracon rocess A Gaussan mxure densy s a weghed sum of comonen denses and s gven by he equaon x λ = b x. () Where x s a D-dmensonal random vecor, b ( x ), =,,, are he comonen denses and, =,,, are he mxure weghs. Each comonen densy s a D-varae Gaussan funcon of he form ' b = ( ) Σ ( ) x ex x μ D x μ / / π Σ = he comlee Gaussan mxure densy s arameerzed by he mean vecors, covarance marces and mxure weghs from all comonen denses. hese arameers are collecvely reresened by λ = {,μ, Σ}, =,..,.3. axmum Lkelhood Parameer Esmaon Gven a ranng daa, he goal of model ranng s o calculae model arameers, l, whch bes maches he dsrbuon of ranng vecors. he goal of he echnque s o maxmze Where X { x } ( X λ) = ( x λ) = =,..., s a se of ranng vecors. he arameers are esmaed usng E algorhm. he x k+ k goal of E algorhm s o comue he model arameers eravely ll ( X λ ) ( X λ ) he followng formulae are used o guaranee he above condon: xure weghs: = ( = x,λ) = ( = x, λ) x = eans: μ = = x, λ Varances: = = = = ( = x, λ) ( = x, λ) where he a oseror robably for acousc class s gven by σ x. () (3) (4) (5) (6) 30

3 x (, λ ) = k = b ( x ) b ( x) k k.4. Idenfcaon For seaker denfcaon a grou of S seakers S={,,,S} s reresened by G s { λ,...,λ s }. he goal n denfcaon s o fnd he seaker model whch has he maxmum a oseror robably for a gven observaon sequence. 3. Vecor Quanzaon Aroach S = arg max k S ( X λ ) ˆ (8) In hs secon, we wll nroduce he vecor quanzaon (VQ) aroach frs and s use for calculang model arameers. VQ was used as a modelng echnque for seaker recognon [5]. In hs echnque, he enre seech daa (feaure vecors obaned from fron-end rocessng) are dvded no ceran number of clusers,, also known as codebook sze usng he aroach n [4]. Each cluser has one cenrod assocaed wh reresenng he mean of all he feaure vecors belongng ha cluser. he sze of he codebook has drec effec on he denfcaon error ercenage as menoned n [5].We have used hs echnque o fnd he clusers such ha each cluser has a wegh of a leas /. he cenrods of hese clusers are used as means n equaon (). he covarance marx s calculaed usng feaure vecors belongng o each of he clusers. hs way all he arameers requred for equaon () are obaned. In he revous aroach, usng E based model arameer calculaons, he means for mxures are randomly nalzed. Random nalzaon could allocae feaure vecors, whch are a hgher dsance from oher feaure vecors, as means.hs mnmzes he value of ( x μ ) n equaon (). hs aroach s fas. hs resuls n an effcen aroach for calculang model arameer keeng all he advanages Gaussan xure odelng echnque has o offer. 4. Exermens he exermens were carred ou on a seaker daabase conanng 00 seakers. he daabase has almos equal dsrbuon of male and female seakers. wo sessons were carred ou o ge daa for ranng and esng sessons. Feaure exracon rocess s erformed as follows: Every ms seech sgnal s mulled by 4ms Hammng wndow. el-frequency cesral coeffcens are calculaed usng a bank of 3 flers as menoned n [3].hs may hamer denfcaon accuracy o some exen. hus we have obaned -dmensonal feaure vecors. For ranng hase, sysem was raned for dfferen duraons: 30s and 60s. esng was done usng 0s es frames. For frs se of exermens, E algorhm s used for ranng he model. In he nex se of exermens, we have used Vecor Quanzaon for calculang he model arameers. Afer fnal cenrods slng, s checked ha he cluser for every cenrod has wegh of / where reresens number of mxures. If he cluser has wegh less han /, hen he cenrods are sled agan. For shorer ranng daa, selecon of s moran. he covarance s calculaed based on he daa for each cluser. Idenfcaon accuracy s calculaed for 0s esng daa usng ranng model arameers obaned from above ses. he followng able shows comarson for boh aroaches consderng he accuracy and me requred for model arameer calculaons. able.: Idenfcaon Accuracy and runnng me for boh aroaches (ranng wh 30s and esng wh 0s) E-G Accuracy me k VQ-G Accuracy me (7) 3

4 he DE curve s also loed for he above se of exermens as shown n Fgure. he number of mxures used s 8. ranng duraon s of 60sec and es duraon sof 0sec. he curves show ha, a slghly beer erformance can s obaned usng VQ-G aroach. he nex se of exermens conssed of long he effec of model sze on seaker denfcaon erformance usng VQ-G aroach. he ranng duraon used was 60sec and esng duraon was 0sec. he curves n Fgure 3 show ha as we ncrease he number of mxures, he erformance of he sysem ncreases. able.: Idenfcaon Accuracy and runnng me for boh aroaches (ranng wh 60s and esng wh 0s) E-G Accuracy me VQ-G Accuracy me Concluson hs aer has addressed he mlemenaon of G based seaker denfcaon. We have mlemened wo aroaches for ranng he seaker model. I has been shown ha here s a slgh mrovemen n denfcaon accuracy usng VQ based model arameer calculaon. Consderable mrovemen s observed n comuaonal me. A seed-u facor of 7 was acheved n frs se of exermens: 8 mxures and ranng duraon of 30 sec, as shown n able., whle n he second se of exermens a seed-u facor 5 was acheved whch conaned 56 mxures and ranng daa of 60sec as shown n able.. DE curve 40 ss robably (n %) VQ-G 6.53 E-G False Alarm robably (n %) Fg.:comarson of VQ-G and E-G aroach for 8 mxures 3

5 DE curve References ss robably (n %) =64 =8 =3 =6 =8 = False Alarm robably (n %) Fg. 3: Effec of model sze on seaker denfcaon usng VQ-G aroach [] D. A. Reynolds and R. C. Rose, Robus ex-ndeenden seaker denfcaon usng Gaussan seaker models, IEEE rans. Seech Audo Process. (995) [] D. A. Reynolds, A Gaussan mxure modelng aroach o ex-ndeenden seaker denfcaon, Ph.D. hess, Georga Insue of echnology, Seember 99. [3] om Knnuen e. al,"real-me seaker denfcaon and verfcaon", IEEE ransacons on audo, seech and language rocessng, Vol. 4, No., Jan. 006 [4] Y. Lnde, A. Buzo, and R.. Gray, An algorhm for Vecor Quanzaon, IEEE rans. on Communcaon s, Vol. CO48, No., , January 980. [5] F. Soong e al., A vecor quanzaon aroach o seaker recognon, n Proc. IEEE ICASSP, 985, [6] D. A. Reynolds,. F. Quaer, and R. B. Dunn, Seaker Verfcaon Usng Adaed Gaussan xure odels, Dgal Sgnal Processng, vol. 0, 9-4, Jan