Hidden Markov Model for Speech Recognition. Using Modified Forward-Backward Re-estimation Algorithm

Transcription

1 IJCSI Inernaonal Journal of Compuer Scence Issues Vol. 9 Issue 4 o 2 July 22 ISS (Onlne): IJCSI.org 242 Hdden Markov Model for Speech Recognon Usng Modfed Forard-Backard Re-esmaon Algorhm Balan A. Sonkamble and Dr. D. D. Doye 2 Pune Insue of Compuer echnology Dhankaad Pune Maharashra Sae Inda 2 Professor E&C Deparmen SGGSIE& Vshnupur anded Maharashra Sae Inda Absrac here are varous knds of praccal mplemenaon ssues for he HMM. he use of scalng facor s he man ssue n HMM mplemenaon. he scalng facor s used for obanng smoohened probables. he proposed echnue called Modfed Forard-Backard Re-esmaon algorhm used o recognze speech paerns. he proposed algorhm has shon very good recognon accuracy as compared o he convenonal Forard-Backard Re-esmaon algorhm. Keyords: Forard-Backard Algorhm; Speech Recognon Parameer Esmaon Verb Algorhm Baum-Welch Algorhm.. Inroducon here as a drasc change n he performance and success of auomac speech recognon sysems. he reason s he use of effcen echnues proposed by he researchers me o me. In he early days he convenonal approach uses grammars and emplaes n he speech recognon sysem developmen. he emplae based approaches are ell developed provdng he good recognon performance bu lack of flexbly as he lmaon. he sochasc approaches called Hdden Markov Models (HMM) are he mos promsng echnues for developng speech recognon sysems []. HMM s a sascal model generaes he model parameers as a collecon of values n hch he saonary process as approxmaed by Markov model. he HMMs are very popular due o s smple srucure and ease of use. he HMMs key feaures are s mahemacal racable srucure useful o characerze he speech sgnal very effcenly. An HMM can be used as a maxmum lkelhood classfer o compue he probably of a seuence of ords gven a seuence of acousc observaons. he Forard-Backard recursons ere used n HMM as ell as compuaons of margnal smoohng probables. he frs applcaon of HMMs as speech recognon. he Forard-Backard algorhms are belongng o he general class of algorhms and can be operaed on seuence models. here are varous praccal mplemenaon ssues n HMM ncludng scalng mulple observaon seuences nal parameer esmaes mssng daa and choce of model sze and ype [ 4]. In hs paper he man obecve s o solve he scalng ssue of HMM effcenly usng Lef-Rgh model. In he paper organzaon Secon-II explans bref abou he HMM. Secon-III descrbes abou he Modfed Forard- Backard Re-esmaon algorhm. he expermenaon and her resuls ll be dscussed n he Secon-IV. he concluson and fuure ork ll be explaned n Secon-V. 2. Hdden Markov Model [ 2 3 5] he HMM are aced as a more conrolled approaches n he recognon/classfcaon based sysems. he HMM are he sae of ar echnues o represen varous speech uns characerscs hn he model parameers. he HMMs are lke Markov Chans n hch he oupu symbols and he ransons are probablsc. he HMMs represen speech as a seuence of observaon vecors derved from a probablsc funcon of a frs-order Markov chan. In speech recognon he HMMs ould oupu a seuence of n-dmensonal real-valued vecors. In Copyrgh (c) 22 Inernaonal Journal of Compuer Scence Issues. All Rghs Reserved.

2 IJCSI Inernaonal Journal of Compuer Scence Issues Vol. 9 Issue 4 o 2 July 22 ISS (Onlne): IJCSI.org 243 each sae sascal dsrbuon gves lkelhood for each observed vecor.e. for each ord ll have a dfferen oupu dsrbuon. he decodng of he speech means compung he mos lkely ord from an unknon uerance. he HMM are generave models he sae space of he hdden varables s dscree hle he observaons hemselves can eher be dscree generaed from a caegorcal dsrbuon or connuous generaed from a Gaussan dsrbuon. he HMM has o parameers for modelng. he on dsrbuon of observaons and hdden saes means he pror dsrbuon of hdden saes called ranson probables and condonal dsrbuon of observaons gven saes called emsson probables. In he sandard HMM he algorhm mplcly assumes a unform pror dsrbuon over he ranson probables. he ranson probables are conrolled by he hdden saes. he Lef-Rgh model also knon as Baks model sasfes he propery ha as me ncreases he sae ndex ncreases or says he same.e. he saes proceed from lef o rgh. I can easly model sgnals hose properes change over me n a successve manner.e. speech. he fundamenal propery of all he lef-rgh HMMs s ha he sae ranson coeffcens have he propery a ha s no ransons are alloed o saes hose ndces are loer han he curren sae. he nal sae probables have he propery oherse snce he sae seuence mus begn n sae and end n sae. In Lef-Rgh model addonal consrans are placed on he sae ranson coeffcens n he form of a here 2.e. no umps of more han 2 saes are alloed. he las sae n lef-rgh model s specfed by sae ranson coeffcens are a a. he consrans are useful o make sure ha large changes n sae ndces do no occur. here s no effec on he re-esmaon procedure due o consrans on lef-rgh model because any HMM parameer se o zero hroughou he re-esmaon procedure. he goal of HMM parameer esmaon s o maxmze he lkelhood of he daa under he gven parameer seng [3]. he HMM h dscree probably dsrbuons can be denoed as ( A B ). he HMM has hree man basc problems Frsly he Evaluaon problem n hch gven an HMM and a seuence of observaons O o o o o ha s he probably of he gven observaons generaed by he model p {O )? hs problem s solved usng he Forard-Backard Algorhm. Secondly he decodng problem here gven a model and a seuence of observaons O o o o o ha s he mos lkely sae seuence n he model ha produced he observaons? hs problem s solved usng Verb algorhm or usng he alernave Verb algorhm called logarhmc approach. hrdly he learnng problem also called ranng here gven a model and a seuence of observaons O o o o o. he model parameers ( A B ) are adused o maxmze p {O ). he problem s solved usng Forard- Backard Re-esmaon algorhm. 3. he Modfed Forard-Backard Reesmaon algorhm [7 8 9 ] he Forard-Backard algorhm acs as an nference algorhm called smoohng based on he prncple of dynamc programmng hch effcenly compues he probably dsrbuon of all hdden sae varables gven a seuence of observaons / emssons. he Forard- Backard algorhm can be used o fnd he mos lkely sae for any pon n me. he Forard-Backard algorhm dvded no o sages. In he frs sage he Forard-Backard algorhm compues a se of forard probables usng auxlary varable () called forard varable. he forard varable defnes he probably of he paral observaon seuence o o2 o3... o has lo complexy. I ermnaes a he sae and he mahemacal represenaon s n he form of o o2 o () he recursve funcon can be ren as here here ( ) b ( o ) a (2) ( ) b ( o ) can be calculaed and he reured probably s gven by Copyrgh (c) 22 Inernaonal Journal of Compuer Scence Issues. All Rghs Reserved.

3 IJCSI Inernaonal Journal of Compuer Scence Issues Vol. 9 Issue 4 o 2 July 22 ISS (Onlne): IJCSI.org 244 p { O ( ) (3) In he second sage he backard varable () s used as he probably of he paral observaon seuence o o 2 o 3... o hch s he probably of he paral observaon seuence from me o he end gven sae a me and model. I s mahemacally represened as o o 2 o (4) and for calculang he () effecvely he represenaon can be gven by here gven by Where ( ) ab ( o ) (5) and he reured probably s p { O ( ) b ( o ) ( ) (6) ) ( O (7) he follong represenaon used o calculae p {O by usng boh forard and backard varables O O (8) he fnal probably s compued usng he smoohed probably values of he forard and backard probables. he smoohed probably values mus be scaled and s enres sum o. hese are obaned by applyng scalng facor. In he sandard HMM mplemenaon no need o use scalng facor n he logarhmc approach. We are proposng o apply scale o he backard probables. he backard probably vecors acually represen he lkelhood of each sae a me gven he fuure observaons. hese vecors are proporonal o he acual backard probables and he resul has o be scaled an addonal me. As per many researchers he forard are suffcen o calculae he mos lkely fnal sae bu omng he scalng facor appled on he backard probables decreases he performance. In he proposed expermen he speech recognon accuracy as ncreased by addng scalng facor o he backard probables. hese backard probables are combned h he nal sae vecor o provde he mos probable nal sae for gven he observaons. he forard and backard probables need only be combned o nfer he mos probable saes beeen he nal and fnal pons. he scalng facor can be expressed as c appled h boh he forard and backard probables. By addng scalng facor he expressons becomes c and c. he Baum-Welch algorhms key feaure as o provde guaraneed convergence. he Baum-Welch algorhm uses he opmzng crera based on he maxmum lkelhood (ML). he ML crera maxmzes he probably of a gven seuence of observaons O belongng o a gven class gven he HMM o he parameers of he model of he class h respec. hs probably s he oal lkelhood of he observaons for all classes or ords and can be expressed mahemacally as L O (9) he ML creron for one class or ord can be ren as L O () Hoever here s no knon ay o analycally solve for he model ( A B ) hch maxmze he uany L. he model parameers are chosen hch are locally maxmzed. he erave procedure appled derved from smple occurrence counng argumens or hrough calculus o maxmze he auxlary uany Q( ) O log[ O ] () Where = []. he Baum-Welch algorhm also knon as Forard-Backard Re-esmaon algorhm can be descrbed by defnng o more auxlary varables n addon o he forard and backard varables. hese varables can be expressed n erms of he forard and backard varables. Copyrgh (c) 22 Inernaonal Journal of Compuer Scence Issues. All Rghs Reserved.

4 IJCSI Inernaonal Journal of Compuer Scence Issues Vol. 9 Issue 4 o 2 July 22 ISS (Onlne): IJCSI.org 245 he frs varable s defned as he probably of beng n sae a and n sae a. hs can be formally represened as ( ) O (2) a ( ) (9) he above expresson can be reren as ( ) O O (3) Usng forard and backard varables hs can be expressed as b ( k) o vk ( ) ( ) k M (2) ( ) a a ( ) b ( o ) ( ) b ( o (4) ) he second varable s he a poseror probably O (5) ha s he probably of beng n sae a gven he observaon seuence and he model. In forard and backard varables hs can be expressed by he preprocessng par of he sysem gves ou a seuence of observaon vecors O { 2 o o o (2) he nal observaon vecor parameer values for each of he HMMs are (22) ( ) (6) Lasly he lkelhoods can be calculaed usng he forard and backard varables hrough he follong euaon L lkelhood (23) he relaonshp beeen () and ( ) s gven by ( ) ( ) M (7) he parameers of he HMM are updaed o maxmze he uany of O n he Baum-Welch learnng process. he sarng model ( A B ) calculaes he ' ' s ' ' s ' and hen ' ' s ' ' s. he HMM parameers are updaed usng he follong seps knon as re-esmaon formulas. ( ) (8) 4. he Expermenaon and Resuls he I46 daabase [2] s used for expermenaon. here are 6 speakers from hem 8 male speakers and 8 female speakers. he numbers of replcaons are 26 for uerance by each person. he oal daabase sze s 46 uerances of hch6 samples used for ranng and remanng samples are used for esng of ords ha are numbers n Englsh o 9 and are sampled a a rae of 8 Hz. A vecor of 2 Lnear Predcng Codng Cepsrum coeffcens as obaned and provded as an npu o vecor uanzaon o fnd codeords for each class. he VQ codebook [9 ] maps each connuous observaon vecor no a dscree codebook ndex. he vecor uanzed values are provded o Lef-Rgh model for modelng. In he recognon phase lkelhoods ll be calculaed for machng and recognzng he dgs. Copyrgh (c) 22 Inernaonal Journal of Compuer Scence Issues. All Rghs Reserved.

5 IJCSI Inernaonal Journal of Compuer Scence Issues Vol. 9 Issue 4 o 2 July 22 ISS (Onlne): IJCSI.org 246 able- shos he resuls obaned from Lef-Rgh model usng 3-saes from hch e can see ha he average accuracy s ncreased by 4% as compared o he proposed algorhm. able- Accuracy n % for Lef-Rgh model usng 3-saes Accuracy for s=3 a LoR usng fb Accuracy for s=3 a LoR usng mfb dgs LRfb3 LRmfb Avg able-2 shos he resuls obaned from Lef-Rgh model usng 5-saes from hch e can see ha he average accuracy s more compared o he proposed algorhm he reason s ha he uerances consdered n solaon. Accuracy for s=3 a LoR usng fb -5 5 Accuracy for s=3 a LoR usng mfb -5 5 Fg. 3 he Recognon Accuracy for 3-sae Lef-Rgh Model. Fg. 4 shos he recognon accuracy usng Modfed Forard-Backard Re-esmaon algorhm compared h he convenonal Forard-Backard Re-esmaon algorhm h 5-saes. Accuracy for s=5 a LoR usng fb Accuracy for s=5 a LoR usng mfb able-2 Accuracy n % for Lef-Rgh model usng 5-saes dgs LRfb5 LRmfb Avg Accuracy for s=5 a LoR usng fb Accuracy for s=5 a LoR usng mfb -5 5 Fg. 4 he Recognon Accuracy for 5-sae Lef-Rgh Model. Fg. 3 shos he recognon accuracy usng Modfed Forard-Backard Re-esmaon algorhm compared h he convenonal Forard-Backard Re-esmaon algorhm h 3-saes. Copyrgh (c) 22 Inernaonal Journal of Compuer Scence Issues. All Rghs Reserved.

6 IJCSI Inernaonal Journal of Compuer Scence Issues Vol. 9 Issue 4 o 2 July 22 ISS (Onlne): IJCSI.org Conclusons he proposed Modfed Forard-Backard Re-esmaon algorhm has shon mproved recognon accuracy as compared o convenonal Forard-Backard Reesmaon algorhm usng Lef-Rgh model. he recognon accuracy s ncreased by 4% n he 3-sae model hereas he recognon accuracy of 5-sae model obaned h he convenonal algorhm s more because Lef-Rgh model used as sngle observaon seuence. he expermenaon s done for solaed ords hch reures mnmum number of saes and hence he recognon accuracy for 5-sae model consan. he saes above 5-saes can be used n connuous speech recognon sysems. References [] Larence R. Rabner A uoral on Hdden Markov Model and Seleced Applcaon n Speech Recognon Proceedngs of he IEEE Vol. 77 o. 2 pp [2] Qysen Brkenesomoko Masu Kuno anabe Sabao Marco Snscalch or Andre Myrvoll and Magne Hallsen Johnsen Penalzed Logsc Regresson h HMM Log- Lkelhood Regressors for Speech Recognon IEEE ransacons on Audo Speech and Language Processng Vol. 8 o. 6 pp Augus 2. [3] Xong Xao Jnyu L Eng Song Chng Hazhou L Chn- Hu Lee A Sudy on Hdden Markov Models Generalzaon Capably for Speech Recognon Proceedngs of ASRU-29 pp [4] Shun-Zheng Yu and Hsash Kobayash Praccal Implemenaon of an Effcen Forard Backard Algorhm for an Explc-Duraon Hdden Markov Model IEEE ransacons on Sgnal Processng Vol. 54 no. 5 pp May 26. [5] Mark Gales and Seve Young he Applcaon of Hdden Markov Models n Speech Recognon Journal of Foundaons and rends n Sgnal Processng Vol. o. 3 pp [9] Cheung Y. Leung S. Speaker-ndependen Isolaed Word Recognon usng ord-based vecor uanzaon and hdden Markov models Proceedngs of ICASSP' 87 Vol. 2 pp [] Falkhausen M. Euler S.A. Wolf D. Improved ranng and recognon algorhms h VQ-based hdden Markov models Proceedngs of ICASSP-9 Vol. pp [] Penado A.M.; Lopez J.M.; Sanchez V.E.; Segura J.C.; Rubo Ayuso A.J. Improvemens n HMM-based solaed ord recognon sysem IEE Proceedngs of Communcaons Speech and Vson Vol. 38 o. 3 pp [2] IS I46 CD Sepember 99. Balan A. Sonkamble receved hs BE (Compuer scence and Engneerng n 994 and M. E. (Compuer Engneerng) n 24. Currenly he s research scholar a SGGS College of Engneerng and echnology Vshnupur anded (MS) IDIA. He s orkng as a Assocae Professor n Compuer Engneerng a Pune Insue of Compuer echnology Pune Inda. Hs research areas are Speech Recognon and Arfcal Inellgence. D D Doye receved hs BE (Elecroncs) degree n 988 ME (Elecroncs) degree n 993 and Ph. D. n 23 from SGGS College of Engneerng and echnology Vshnupur anded (MS) IDIA. Presenly he s orkng as Professor n deparmen of Elecroncs and elecommuncaon Engneerng SGGS Insue of Engneerng and echnology Vshnupur anded. Hs research felds are speech processng fuzzy neural neorks and mage processng. [6] Levnson S. Rabner L. Sondh M. Speaker ndependen solaed dg recognon usng hdden Markov models Proceedngs of ICASSP '83 Vol. 8 pp [7] Juang B. Rabner L. Levnson S. Sondh M. Recen developmens n he applcaon of hdden Markov models o speaker-ndependen solaed ord recognon Proceedngs of ICASSP '85 Vol. pp [8] Sugaara K. shmura M. oshoka K. Okoch M. Kaneko. Isolaed ord recognon usng hdden Markov models Proceedngs of ICASSP '85 Vol. pp Copyrgh (c) 22 Inernaonal Journal of Compuer Scence Issues. All Rghs Reserved.