IMPROVED HYBRID MODEL OF HMM/GMM FOR SPEECH RECOGNITION. Poonam Bansal, Anuj Kant, Sumit Kumar, Akash Sharda, Shitij Gupta

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1 Inernaional Book Series "Inforaion Science and Copuing" 69 IMPROVED HYBRID MODEL OF HMM/GMM FOR SPEECH RECOGIIO Poona Bansal, Anu Kan, Sui Kuar, Akash Sharda, Shii Gupa Absrac: In his paper, we propose a speech recogniion engine using hybrid odel of Hidden Markov Model (HMM) and Gaussian Mixure Model (GMM). Boh he odels have been rained independenly and he respecive likelihood values have been considered oinly and inpu o a decision logic which provides ne likelihood as he oupu. his hybrid odel has been copared wih he HMM odel. raining and esing has been done by using a daabase of 20 Hindi words spoken by 80 differen speakers. Recogniion raes achieved by noral HMM are 83.5% and i ges increased o 85% by using he hybrid approach of HMM and GMM. Keywords: Speech Recogniion, GMM, HMM ACM Classificaion Keywords: I5.4 Paern Recogniion- Applicaions- Conference proceedings Conference: he paper is seleced fro Inernaional Conference "Inelligen Inforaion and Engineering Syses" IFOS 2008, Varna, Bulgaria, June-July 2008 Inroducion Speech signal priarily conveys he words or essage being spoken. Area of speech recogniion is concerned wih deerining he underlying eaning in he uerance. Success in speech recogniion depends on exracing and odeling he speech dependen characerisics which can effecively disinguish one word fro anoher. A general paern recogniion syse consiss of 4 pars, he feaure exracor, paern rainer, paern classifier and decision logic. One of he os coon and successful feaure exracion processes is MFCC [Konik, 2002] which has been ipleened in his odel. Of he various speech/ speaker recogniion odels available, he os coonly used are Arificial eural eworks (A), Hidden Markov Model (HMM) and Gaussian Mixure Model (GMM). Presenly HMM is widely used as one of he successful speech recogniion process. HMM considers he speech signal as quasi- saic for shor duraions and odels hese fraes for recogniion. I breaks he feaure vecor of he signal ino a nuber of saes and finds he probabiliy of a signal o ransi fro one sae o anoher [Rabiner, Juang, 993]. Vierbi search, forward-backward and Bau-Welch algorihs are used for paraeer esiaion and opiizaion [Rabiner, 989], [Rabiner, Juang, 99]. GMM on he oher hand considers a signal o conain differen coponens ha are independen of each oher. hese coponens represen he broad acousic classes ha represen cerain vocal rac configuraions [Reynolds, Rose, 995]. hus i is ore inclined owards odeling feaures concerning o words having specific characerisics. Each coponen is opiized using EM algorih [Depser, 977]. Various ways of cobining hese odels have been proposed. One way is o use a 3 sae HMM and ipleen GMM on he iddle sae o obain he observaion probabiliies for ha sae [Rodriguez, 2003]. Here we have proposed a novel odel cobining GMM and HMM o provide ore enhanced speech recogniion engine, which we call as he hybrid odel. We have proposed he exracion of likelihood value by cobining he likelihood values of boh he odels using decision logic. In he res of he paper we discuss individually abou he HMM, he GMM and how he hybrid odel was developed. A he end, we copare he HMM odel wih he hybrid odel using a 20 word, 80 uerances daa se. Hidden Markov Model Hidden Markov odel (HMM) is a saisical odel in which he syse being odeled is assued o be a Markov process wih unknown paraeers, and he challenge is o deerine he hidden paraeers fro he observable paraeers. he exraced odel paraeers can hen be used o perfor furher analysis, for exaple for paern/speech recogniion applicaions. In a hidden Markov odel, he saes are no direcly visible, bu variables influenced by he sae are visible. Each sae has a probabiliy disribuion over he possible oupu okens. Also, he sae ransiions are probabilisic in naure. herefore, he sequence of okens generaed by an HMM gives soe inforaion abou he sequence of saes. he coplee HMM odel is denoed as λ (A,B,π ).

2 70 Inelligen echnologies and Applicaions HMM Model Paraeers. A, he sae probabiliy disribuion, A {ai}. 2. B, he observaion sybol probabiliy densiy, B {b(k)}. 3. π, he iniial sae disribuion, π { πi}. he HMM raining procedure requires codebook o esiae odel paraeers. In codebook, he large nuber of observaional vecors of he raining daa is clusered ino M observaional vecors clusers using K-eans ieraive procedure. Based on his clusered observaional vecors, esiaes of he odel paraeers are generaed during HMM raining. he HMM raining procedure ries o esiae he value of sae probabiliy disribuion (A), observaion sybol probabiliy densiy (B), and iniial sae disribuion (π). he observaional vecors of raining sequences are segened for each of he saes, a axiu likelihood esiaes of he se of he observaions ha occur wihin each sae each of he observaion vecors wihin a sae is coded using he M code word codebook. Before proper esiaion of he odel paraeers hey are iniialized o good iniial esiaes ha are essenial for rapid and proper convergence of he re-esiaion forulas. he paraeers are re-esiaed using Vierbi Algorih, Forward- Backward Algorih and Bau/Welch Algorih. Forward- Backward Algorih Forward Algorih he forward variable α(i) is defined as α(i) P(o,o2,,o,q i λ) i.e. he probabiliy of he parial observaion sequence (unil ie ) and sae i a ie, given he odel λ. α(i) is inducively copued by following seps: Iniializaion: α() ι πibi( ο), ι Ν () Inducion: α ( ) [ α () i a ] b ( ο ), (2) + i + erinaion: P(O λ) α (i) (3) Backward Algorih he backward variable β(i) is defined as β(i) P(o+,o+2,,o,q i λ) i.e. he probabiliy of he parial observaion sequence fro + o he end, given he sae i a ie and he odel λ. β(i) is inducively solved as follows: Iniializaion: β () i, i Ν (4) Inducion: β ( i) a b b ( o ) β ( ), Τ, Τ 2,...,, i Ν (5) i + + Cobining Forward and Backward variables, we ge: P(O λ) α ( i) β ( i), Τ (6) he Vierbi Algorih o find he single bes sae sequence, for he given observaion sequence, δ(i) ax P[qq2 q-, q i, oo2 o λ], δ(i) is he highes probabiliy and ψ(i) is he rack for pah. Iniializaion: δ i) b ( o ), i ( π i i ψ () i 0 (7) Recursion: δ ) ax[ δ ( i) a ] b ( o ),2, (8) ( i

3 Inernaional Book Series "Inforaion Science and Copuing" 7 erinaion: ψ ( ) arg ax[ ( i) a ],2, δ i P * ax [ δ(i) ] i Ν q * arg ax [ δ (i)] i Ν Pah (sae sequence) backracking q* (q* ), Τ,Τ 2,... (0) ψ + + (9) he Bau/Welch Algorih o adus he odel paraeers o saisfy a cerain opiizaion crieria is done by he Bau/Welch algorih. ξ (i,) α i (i)aib (o + )ß + () α iab o β () i ( + ) + ( ) ( i ) ξ (i,) (2) a b i i ξ i o v k (, i ) () ( ) ( ) Using he final re-esiaed A, B and π, he value of LIHMM is calculaed wih respec o all he word odels available wih he recogniion engine by using Vierbi algorih. he Vierbi algorih akes odel paraeers and he observaional vecors of he word as inpu and reurns he value of aching wih all paricular word odels. his is he likelihood values of he word (LIHMM) passed o hybrid raining odel. he Gaussian Mixure Model he GMM can be viewed as a hybrid beween paraeric and non- paraeric densiy odels. Like a paraeric odel, i has srucure and paraeers ha conrol he behavior of densiy in known ways. Like non-paraeric odel i has any degrees of freedo o allow arbirary densiy odeling. he GMM densiy is defined as weighed su of Gaussian densiies: M p ( x) w g ( x, μ, C ) (5) GM Here is he Gaussian coponen ( M), and M is he oal nuber of Gaussian coponens. w are he coponen probabiliies ( w ), also called weighs. We consider K-diensional densiies so he arguen is a vecor x (x,..., xk ). he coponen pdf, g(x, µ, C), is a K-diensional Gaussian probabiliy densiy funcion (pdf). ( x μ ) ( ) (,, ) 2 C x μ g x μ C e K /2 /2 (6) C ( 2π ) () (3) (4)

4 72 Inelligen echnologies and Applicaions where µ is he ean vecor, and C is he covariance arix. ow, a Gaussian ixure odel probabiliy densiy funcion is copleely defined by a paraeer lis given by θ {w, µ, C... w, µ, C} M Organizing he daa for inpu o he GMM is iporan since he coponens of GMM play a vial role in he aking of word odels. For his purpose, we use K- Means clusering echnique o break he daa ino 256 cluser cenroids. hese cenroids are hen grouped ino ses of 32 and hen passed ino each coponen of GMM. As a resul we obain a se of 8 coponens for GMM. Once he coponen inpus are decided, he GMM odeling can be ipleened. EM Algorih he expecaion axiizaion (EM) algorih is an ieraive ehod for calculaing axiu likelihood disribuion paraeer esiaes fro incoplee daa (eleens issing in feaure vecors). he EM updae equaions are used which gives a procedure o ieraively axiize he log-likelihood of he raining daa given he odel. he EM algorih is a wo sep process: Esiaion Sep in which curren ieraion values of he ixure are uilized o deerine he values for he nex ieraion ( i) ( i) ( i) w g ( X, μ, C ) (, ) M ( i) ( i) ( i) (7) w g ( X, μ, C ) Maxiizaion sep in which he prediced values are hen axiized o obain he real values for he nex ieraion. μ ( i + ), X, (8) W ( i + ), (9) λ ( i+ ), ( i+ ) 2, ( x, μ, ), EM algorih is well known and highly appreciaed for is nuerical sabiliies under a hreshold values of λin. Using he final re-esiaed w, µ and C, he value of LIGMM is calculaed wih respec o all he word odels available wih he recogniion engine as: L log P ( x ) (2) he Hybrid Model GMM GM he GMM/HMM hybrid odel has he abiliy o find he oin axiu probabiliy aong all possible reference words W given he observaion sequence O. In real case, he cobinaion of he GMMs and he HMMs wih a weighed coefficien ay be a good schee because of he difference in raining ehods. he i h speaker independen GMM produces likelihood L i GMM, I, 2,, W, where W is he nuber of words. he i h speaker independen HMM also produces likelihood L i HMM, I, 2,, W. All hese likelihood values are passed o he so called likelihood decision block, where hey are ransfored ino he new cobined likelihood L (W): L '( W ) ( x( W )) L i ( ) i GMM + x W L HMM (22) where x(w) denoes a weighing coefficien. (20)

5 Inernaional Book Series "Inforaion Science and Copuing" 73 he value of x is calculaed during raining of he Hybrid Model. In Hybrid esing, he subse of raining daa is used and i s HMM & GMM likelihood values are calculaed which are cobined using weighing coefficien. Saic values of weighed coefficien are also used in order o ge higher recogniion rae. Resuls and Conclusions he HMM odel developed had been esed for differen cobinaions of cluser sizes and nuber of saes. he success rae (%) wih differen cobinaions of clusers and saes are shown in figure 2. I was observed ha as he cluser size increases success rae also increases, because of he reducion in quanizaion disorion, while increasing he nuber of clusers. Secondly he Figure : Hybrid Model Block Diagra ie coplexiy of he recogniion engine is also copued wih various cluser sizes, and i was observed ha 3- sae HMM odel having 28 cluser size has he leas ie coplexiy as coparing wih oher cobinaions. Since is ie coplexiy is sall i can be useful in applicaions where speed is he deciding facor. he GMM/HMM Hybrid odel creaed has 8 coponens and 256 clusering size in GMM and 3 saes and 28 clusering size in HMM. Success rae wih fixed as well as varying values of weighed coefficien was esed and is shown in figure 4. I was observed, ha wih he varying value of he weighed coefficien x,he success rae of word recogniion by using hybrid odel has increased o 84.38%, which earlier was 83.6% wih HMM alone. And by fixing he value of x o 0.9 success rae furher increased o 85%. he coplexiy curve for differen cluser size is shown in figure 3. Success Rae (%) Clusers 256 Clusers 52 Cluse o. of saes Figure 2: Success Rae verses differen cobinaions of clusers and saes ie (seconds) Clusers 256 Clusers o. of Saes Figure 3: Coplexiy v/s clusers and saes

6 74 Inelligen echnologies and Applicaions Success Rae (%) variable x Weighing Coefficien (X) Figure 4: Success Rae v/s weighing coefficien Bibliography [Depser, 977] A. P. Depser,. M. Laird, and D. B. Rubin. Maxiu likelihood fro incoplee daa via he EM algorih. In: Journal of he Royal Saisical Sociey: Series B, 39() pp. 38, oveber 977. [Konik, 2002] B. Konik, D. Vla, Z. Kačič, B. Horva. Robus MFCC Feaure Exracion Algorih Using Efficien Addiive and Convoluional oise Reducion procedures.in: ICSLP 02 Proceedings, Denver, Colorado, USA pp , [Rabiner, Juang, 993] L. Rabiner and B. H. Juang. Fundaenals of Speech Recogniion. Prenice Hall, ew Jersey, 993. [Rabiner, Juang, 99] B. H. Juang, L. R. Rabiner. Hidden Markov Models for Speech Recogniion. In: echnoerics, Vol. 33, o. 3, pp , Augus 99. [Rabiner, 989] L. Rabiner. A uorial on Hidden Markov Models and Seleced Applicaions in Speech Recogniion, In: Proceedings of IEEE Volue 77 o. 2 pp , February 989. [Reynolds, Rose, 995] D. A. Reynolds and R.C. Rose. Robus ex-independen speaker idenificaion using Gaussian ixure speaker odels. In: IEEE ransacions on Speech and Audio Processing, 3(), pp , 995 [Rodriguez, 2003] E. Rodriguez, B. Ruiz, A. G. Crespo, F. Garcia. Speech/Speaker Recogniion Using a HMM/GMM Hybrid Model. In: Proceedings of he Firs Inernaional Conference on Audio- and Video-Based Bioeric Person Auhenicaion, pp , April 2003 Auhors' Inforaion Poona Bansal Assisan Professor, Deparen of Copuer Science and Engineering, Aiy School Of Engineering and echnology, 580, Delhi Pala Vihar Road, Biwasan, ew Delhi 006, India ; Meber IHEA. e-ail: pbansal89@yahoo.co.in Anu Kan Deparen of Copuer Science and Engineering, Aiy School Of Engineering and echnology, 580, Delhi Pala Vihar Road, Biwasan, ew Delhi 006, India. Akash Sharda Deparen of Copuer Science and Engineering, Aiy School Of Engineering and echnology, 580, Delhi Pala Vihar Road, Biwasan, ew Delhi 006, India. Sui Kuar Deparen of Copuer Science and Engineering, Aiy School Of Engineering and echnology, 580, Delhi Pala Vihar Road, Biwasan, ew Delhi 006, India. Shii Gupa Deparen of Copuer Science and Engineering, Aiy School Of Engineering and echnology, 580, Delhi Pala Vihar Road, Biwasan, ew Delhi 006, India.