Statistical feature selection for isolated word recognition

S15a.l STATISTICAL FEATURE SELECTION FOR ISOLATED WORD RECOGNITION E. Lleida, C. Nadeu, E. Mon e, J.B. Ma ino E.T.S.I. Telecomunicacion, T.S.C. Dep . Apdo. 30.002, 08080 Ba celona, Spain ABSTRACT In his pape we p esen a new p ocedu e o ea u e selec ion in isola ed wo d ecogni ion (IWR). The ea u e selec ion is pe o med in wo s eps. The i s s ep akes in o accoun he empo al co ela ion among ea u e ec o s in o de o ob ain a ans o ma ion ma ix which p ojec s he ini ial empla e o N ea u e ec o s o a new space whe e hey a e unco ela ed. This s ep gi es a new empla e o M ea u e ec o s, being MeN. The second s ep akes in o accoun he equency disc imina ion ea u es which disc imina e each wo d o he ocabula y om he o he s o a se o hem. An impo an cha ac e is ic o his p ocess is ha he new empla es do no need ime-alignmen wi h he e e ences in he compa ison s ep, a oiding he use o he dyn,amic ime- wa ping p ocess. The speech ecogni ion esul s show a signi ican imp o emen in he ecogni ion pe o mance wi h a digi da a base and he con usable E-se . I. INTRODUCTION The i s s ep in any speech ecogni ion sys em is he signal ea u e measu emen . Typically, he speech signal is modeled by a sequence o ea u e ec o s called 'Templa e' in he IWR en i onmen . Gene ally, ea u e measu emen me hods a e block p ocessing models gi ing N ec o s o P ea u es. In his wo k, he LPC echnique has been chosen as a ea u e measu emen me hod. The classic pa e n-ma ching app oach used in IWR assumes [l] ha he adjacen ea u e ec o s a e unco ela ed and ha he a iabili y o speech can be accoun ed o he same dis ance measu e o all wo ds. Howe e , hese assump ions a e no ue, and a ea u e selec ion p ocess is needed o deal wi h hese p oblems. Thus, speech signal has s a iona y pa s which a e ep esen ed by se e al ea u e ec o s, ha ing a g ea edundancy [2,3]. The e o e, we can look o a new model in which he co ela ion among ea u e ec o s is emo ed. Fo his pu pose we assume ha he e is an unde lying se o " eal" unco ela ed ea u es, and he ea u es we a e wo king on a e "impu e" in he sense ha is a linea combina ion o hose " eal" ea u es. Then, he objec i e is o ind a ans o ma ion which eco e s he "leal" ea u es [4]. Basically, he p oblem is o ep esen he sequence o spec a by a supe posi ion o he membe s o any o hogonal amily o unc ions whe e he inpu empla e is ep esen ed wi h less coe icien s. I y(n) is he n h LPC ec o , he ans o ma ion obey he ollowing o mula ion M This wo k was suppo ed by he PRONTIC g an nQ 105/88. whe e $m is he m h ans o ma ion unc ion and am is he new m h ea u e ec o . A ypical amily o unc ions which pe o ms his ans o ma ion is he Ka hunen-LoB e unc ions [5]. I minimizes he mean squa e e o be ween a ec o and i s es ima ion by a linea combina ion. In !his wo k, he Ka hunen-LoB e ans o m (KLT) is used o emo e he empo al co ela ion in o de o ob ain M unco ela ed ec o s, being M<<N. Thus, a new empla e is ob ained wi h M unco ela ed ec o s which a e a anged in a iance, no being equi ed ime-alignmen o compa e wo empla es. The empo al in o ma ion is e ained in he ans o ma ion unc ions ($m). These unc ions a e ound om a aining se . In o de o educe he wi hin-class a iabili y and inc ease he sepa abili y among wo ds, a new ans o ma ion is p oposed in he equency dimension. In his case, aking he M unco ela ed ec o s, a ans o ma ion ma ix associa ed wi h each ec o o a wo d is sough . I maximizes he dis ance among his ec o and he co esponding ec o s o he o he wo ds. This co espondence among ec o s is lineal because o he a iance o de o he ec o s. Thus, a new ec o 6m, called disc iminan ea u e ec o , will be ob ained by ans o ming he unco ela ed ec o am wi h a amily o disc iminan unc ions as ollows P i=l 6m(q)=C am (i) cpm,q(i) 1 qq10 (2) whe e qm,q is he q h disc iminan unc ion o he m h ec o which is ound om a aining se by op imizing a c i e ion unc ion ha uses he be ween-class and wi hin-class dis ance. A e hese p ocesses, a empla e o MxQ dimension is ob ained whe e M<<P and Q<<P, and he classi ica ion is done in his new space by compa ing he disc iminan ec o s by means o he Euclidean dis ance and wi hou ime alignmen . In sec ion 2 a desc ip ion o he ea u e selec ion p ocess is p esen ed. Sec ion 3 explains he aining p ocess and he es da a base. The ecogni ion expe imen s a e epo ed in sec ion 4. II. FEATURE SELECTION The ea u e selec ion p ocess is pe o med in wo s eps called Tempo al Selec ion and F equency Selec ion. TEMPORAL SELECTION Tempo al selec ion is he i s s ep in ou ea u e selec ion p ocess. I s pu pose is o ob ain a ime comp ession by emo ing he co ela ion o he empo al e olu ion o he spec um. Gi en a NxP ma ix Y o spec al pa ame e s {yi(n)} ep esen ing N ames o P ea u es, a ini e amily o o hogonal unc ions can be ound in acco dance wi h (1) by 757 CH2847-2/90/0000-0757 $1.00 0 1990 IEEE means o he KL-expansion, educing a la ge se o co ela ed ea u es in o a smalle numbe o unco ela ed ea u es. -1 I he co a iance ma ix o a empla e Y co esponding o a wo d 'w' is de ined as P n, I I whe e lP Y=FZYi 02 (4) I I hen he o hogonal unc ions a e ob ained in he aining s ep om he eigensys em Fiau e 1. Fi s h ee eigen ec o s o he wo d /se/. Cyy hn = km $m (5) whe e Cyy can be equal o an a e age o he Ck o each wo d o an a e age o all he co a iance ma ises o all ocabula y wo ds. F om his eigensys em, N eigen alues and hei co esponding eigen ec o s a e ob ained. Howe e , only he M eigen ec o wi h he la ges eigen alues a e e ained. Thus, he ans o ma ion ma ix is composed by he M eigen ec o s wi h he M la ges eigen alues, anking hem om he la ges o he smalles one. Then, he new coe icien s am ha e in o ma ion abou he in e dependency among he ea u e ec o s. I mus be no iced ha each o hogonal unc ion is compu ed using he P ea u es o each ame, hus, hese unc ions ca y in o ma ion o he co ela ion o he P ea u es. The i s eigen ec o ep esen s he empo al ajec o y o he spec um wi h he la ges a iance, he second one ep esen s he bes empo al ajec o y which can be ob ained i he i s eigen ec o in o ma ion is emo ed om he co a iance ma ix. As he eigen alue dec eases, he eigen ec o asocia ed ca ies in o ma ion o he small a ia ion o he empo al ajec o y o he spec um. Figu e 1 shows he i s h ee eigen ec o s compu ed a e aging en co a iance ma ix o he wo d /SE/. The speech signal was analized by an LPC p ocesso and 8 Log-A ea a ios was ex ac ed in each ame. I can be seen ha o his wo d, which is composed by an un oiced sound ollowed by a oiced sound, he i s eigen ec o ca ies in o ma ion o he un oiced sound Is/, he second one abou he oiced sound /E/ and he hi d one abou he ansi ions, specially he /s/-/E/ ansi ion. This esul shows ha he empo al e olu ion o he Log-A ea a ios o he un oiced sound is o hogonal o he oiced sound. When he wo d has only oiced sounds, he i s eigen ec o is qui e simila o an a e age o he empo al e olu ion o he i s log-A ea coe icien s [6]. The new ea u e ec o s a e ob ained p ojec ing he ini ial empla e wi h he ans o ma ion ma ix esul ing a sequence o unco ela ed ea u e ec o s. This sequence is he bes ep esen a ion o he ini ial empla e in he mean squa e e o sense wi h he leas numbe o ames. The new ea u e ec o s a e anked om he la ges o he smalles a iance so he new empla e needs no ime-alignmen o be compa ed wi h ano he empla e. FREQUENCY SELECTION The second s ep o he ea u e selec ion p ocess is o compu e a ans o ma ion ma ix o each new unco ela ed ea u e ec o ob ained in he empo al selec ion in o de o disc imina e be ween wo ds. In he p e ious s ep a ep esen a ion c i e ion was used in o de o ob ain a subse o M unco ela ed ec o which e ain as much in o ma ion as possible o he ini ial empla e. Howe e , his ans o ma ion does no ake in o accoun he disc iminan p ope ies o he ea u e ec o s. Thus, a e he empo al selec ion, a equency selec ion s ep is p oposed o ob ain a se o disc iminan ea u es. In his s ep, a se o Q disc iminan unc ions qm,q is asocia ed o each ec o am o a wo d which inc eases he sepa abili y o his ec o om he m h ec o s o he o he wo ds. The new ea u e ec o is ob ained by means o eq. (2) In o de o ind he disc iminan unc ions, wo classes o ec o s a e de ined. Fo a wo d 'w', he m h ea u e ec o o any u e ance o i , o ms he co ec class and he m h ea u e ec o o he o he wo ds o ms he inco ec class. Thus, he p oblem is o maximize he mean o he be ween-class dis ance minimizing a he same ime he mean o he wi hin-class dis ance. De ining he wi hin-class mean dis ance ma ix as P PP W = E{(ac-a cc ) (a -aC) ) and he be ween-class mean dis ance ma ix as (7) whe e ac is a ealiza ion o he co ec class, a: is he P P B = E{(ai-ac) (ai-ac) ) e e ence p o o ype o he co ec class and ai is a ealiza ion o he inco ec class, he c i e ion unc ion o be maximized is de ined as [4,5] whe e FC is he disc iminan ma ix o he co ec class ec o , Fc =[qm,i ,qm ,2,...,(~m, al. The solu ion o his op imiza ion p oblem is he eigensys em (W-l B) m,k=kk m,k. The e o e, he disc iminan ma ix is o med by he Q eigen ec o s wi h he Q la ges eigen alue o W-l B, whene e hei eigen alues we e g ea e han 1. I an eigen alue is smalle han 1 he wi hin-class mean dis ance is g ea e han he be ween-class mean dis ance. Thus, only hose eigen ec o s whose eigen alues a e g ea e han 1 can be used as disc iminan unc ions. As in [l], his p ocess can be seen as a me hod o inding an speci ic- ame dis ance, o a ing he equency dimension in o de o be e cha ac e ize each unco ela ed ea u e ec o o each wo d. 758 Ill. TRAINING PROCESS l3smak& A da a base consis s o en epe i ions o he Ca alan digi s (u,dos, es,kua a,sink,sis,sE , ui ,nou,ze u}u e ed by six male and h ee emale speake s (900 wo ds) and eco ded in a quie oom. A small E-se Spanish {b,c,d,e,g,p, } da a base consis ing o se en epe i ions u e ed by wo male and one emale speake s eco ded in a labo a o y en i omen we e also used. -u emen The speech signal was sampled a 8 KHz, p e- emphasized (H(z)=l-O.95~-~) and 8 Log-A ea a ios we e compu ed each 15 ms o he digi da a base and 10 ms o he E-se da a base using he LPC analysis o 30 ms o he speech signal. A ypical Hamming smoo hing window was applied o he da a. The beginning and end o e e y u e ance we e au oma ically de ec ed by mean o an algo i hm based on he signal ene gy. A e he LPC analysis, empla es we e no malized o a ixed numbe N o ames, being N equal o 30 o all he wo ds. The Log-A ea a ios we e chosen as ea u e because o hei s abili y p ope ies since any kind o ans o ma ion gi es an s able sys em. M Jable 1. Eigen alues o he ma ix W-lB o he i s h ee unco ela ed ec o s o he wo d /dos/. he new ea u e ec o ob ained in he ea u e selec p ocess and wo ans o ma ion ma ices. One o hem is used o selec he empo al ea u e ec o s and i can be he same o all he wo ds o speci ic o each wo d. The o he one is used o selec he equency ea u es and i is speci ic o each ame ob ained in he empo al selec ion s ep. Due o he small da a base a alaible, wo kinds o expe imen s we e made. The i s expe imen was made aking six epe i ions o he nine speake s digi da a base as aining. In each ecogni ion expe imen , an e idence measu e was compu ed as E =(D2-D1)100/DI; OsE s100; whe e D2 is he dis ance o he second candida e and D1 is he dis ance o he -ion aining i s candida e. Figu e 2 shows he ecogni ion esul s ob ained o di e en alues o M and Q using bo h ans o ma ion ma ices Tg and Tw.l can be seen ha he bes esul s, 0.22 ?& o e o a e wi h a mean e idence o 85,4 %, a e ob ained Two cases can be dis inguished in he empo al Selec ion aining: Case. A ans o ma ion ma ix Tg o all he wo ds o he ocabula y. In his case, he co a iance ma ix Cyy is ob ained a e aging he co a iance ma ix o each aining wo d. The esul s o his p ocess a e qui e simila o he Disc e e Cosine ans o m [ 61. Case 7. A ans o ma ion ma ix TW o each wo d o he ocabula y. Then, he co a iance ma ix CYY is ob ained using se e al epe i ions o a wo d 'W. In his case, each ans o m ma ix has in o ma ion abou he speci ic empo al a ia ion o he Log-A ea a ios which o m he wo d. The ou pu o he empo al selec ion a e empla es o M ea u e ec o s being M equal o all empla es. The equency selec ion s ep compu es a disc iminan ma ix o each ea u e ec o . Fo his pu pose, a mean ec o o he m h ea u e ec o is compu ed and used la e as e e ence. This mean ec o is he e e ence p o o ype o he m h ec o and i is used o compu e he wi hin-class and be ween-class mean dis ance ma ix. In o de o ake he bes disc iminan unc ions, he numbe Q can be adap ed o each wo d o can be ixed and equal o each wo d. The disc imina ion in o ma ion a e in he eigen alues o W-lB. A big eigen alue indica es a good disc imina ion p ope y o his ea u e. Table 1 shows he eigen alues when M equal o 3 o he wo d /dos/. I can be seen how he i s h ee eigen ec o s ha e good disc imina ion p ope ies. The e o e he wo d /dos/ can be ep esen ed by h ee ec o s o h ee ea u es. IV. RECOGNITION EXPERIMENTS A classical pa e n ecogni ion sys em which compa es an inpu empla e wi h a se o e e ence empla es by means o he Euclidean dis ance be ween ames was used. The sys em makes use o a linea ame o ame compa ison. The e e ences, ob ained in he aining p ocess, a e cons i u ed by wi h he ans o ma ion ma ix Tg when M=3 and Q=2, being M and Q equal o all he wo ds. These esul s show ha he TW ma ices do no ha e good disc imina ion p ope ies when a wo d w' di e en o w is p ojec ed wi h he ma ix co esponding o he wo d w. 1: R 1 2 3 Q5 FW,. E o a e o se e al alues o M and Q using a gene al empo al ans o ma ion ma ix Tg (GEN.) o an speci ic ans o ma ion ma ix TW (SPE.) in he empo al selec ion s ep. In o de o ha e signi ican esul s, en ecogni ion expe imen s we e made aking in each ecogni ion expe imen a aining se wi h (six) di e en epe i ions (mul ispeake expe imen ). In his way, all he da a base was used as es . In his expe imen M and Q we e ixed and equal o 3 and 2 espec i ely and he Tg ma ix was used o empo al selec ion. Table 2 shows he con usion ma ix o his expe imen . The wo s esul s a e ob ained by he wo d / esl,/ul and /sink/. Ne e heless, he e o a e is small, 759 1.19 % o u e ances ou o he aining se and 0.26 O/o o u e ances inside he aining se . An expe imen wi h only he empo al selec ion s ep shows a de e io a ion o he ecogni ion a e o 7 % showing he need o imp o ing his s ep. Recognized Wo d To al e o : 57 (14 ou o he aining se ) mean e idence: 85.4 Yo (0.22%) wi hin and 43 (1.19%) Jable 2. Con usion ma ix o he mul ispeake expe imen . The second expe imen was made wi h a speake independen app oach. In his case, he aining se was made up by en epe i ions o six speake s and h ee speake s we e used as es . The same expe imen was pe o med using a classical speake independen sys em as in [7] whe e he bes esul s we e ob ained using wo candida es pe wo d. The esul s a e shown in able 3. In ou sys em, each wo d has only one candida e in he e e ence se ,i.e. he mean ec o o he aining se , using a ans o ma ion ma ix Tg o all he wo ds o he ocabula y. The numbe o empo al ea u es M we e equal o 3 and he equency ea u es Q we e selec ed o each wo d in o den o minimize he e o a e. Wi h hese condi ions, he e o a e is 1,66 % wi h a mean e idence o 77 % in ou sys em and an e o a e o 2 Yo wi h an e idence o 45 Yo o he clasical sys em. I can be no ed he high e idence mean ob ained in ou app oach. I Yo e o I e idence I Clus e ing Sys em Fea u e Selec ion 45 Yo 77 Yo I I I W. Resul s o he speake independen expe imen s. Wi h he E-se da a base, he esul s a e qui e di e en . In his case, he op imal numbe M o empo al ea u es is 9 and Q equal o 4 wi h he Tg ma ix. These esul s show he di icul y o his da a base whe e he mos signi ican di e ences a e in he ansi ions and his in o ma ion needs se e al eigen ec o s o be e ained. Wi h hese alues o M and Q, he ecogni ion a e is 12.53 %, a e aging se en expe imen s whe e six di e en epe i ions we e used as aining in each expe imen . Table 4 shows he con usion ma ix. Recognized Wo d To al e o : 129 (12.53 %) mean e idence: 53 % Table 4. Con usion ma ix o he E-se expe imen . Wi h ega d o he compu a ional load, he numbe o mul iplica ions needed o ecognizing a wo d is e y low. Using empla es o NxP dimension wi h a ans o ma ion ma ix Tg wi h M ec o s, Q disc iminan ec o s and V ocabula y wo ds, he numbe o mul iplica ions is (NxPxM) o he empo al selec ion s ep VxMxPxQ o he equency selec ion s ep and VxMxQ o he compa ison s ep. Thus, in ou expe imen s wi h he digi da a base whe e N=30,P=8,M=3,Q=2 and V=10 he numbe o mul iplica ions is 1308, when in a classical sys em wi h dynamic ime wa ping and one empla e pe wo d e e ence is (N2/3)xVxP = 24000. IV. CONCLUSION A wo s ep ea u e selec ion p ocess is in oduced o isola ed wo d ecogni ion. The i s s ep akes in o accoun he co ela ion among he N ames o a empla e gi ing a new subse o unco ela ed ames. The second s ep akes in o accoun he disc imina ion p ope ies o he P ea u es o each unco ela ed ame, gi ing a new ame wi h Q disc imina ea u es. The ans o ma ion ma ices a e ob ained in a aining p ocess. Al hough he es da a base was small his app oach shows a po en ial imp o emen on an IWR sys em gi ing a small e o a e and a e y small compu a ional load. Fu he s udies will be made in o de o imp o e he ecogni ion a e in he empo al selec ion s ep. REFERENCES [l]E.L Bocchie i, G.R. Dodding on, "F ame-speci ic s a is ical ea u es o speake independen speech ecogni ion". IEEE ans. on ASSP, Vol 34, Ag. 1986. [2]E. Lleida, C. Nadeu, J.B. Ma i io, "Speech pa ame iza ion and ecogni ion using block and ecu si e linea p edic ion wi h da a comp ession", Eu opean Con e ence on Speech Technology, pp. 300-303, Edinbu gh- 1987. [3]R. Pie accini, R. Billi, "Expe imen al compa ison among da a comp ession echniques in IWR", ICASSP-83, Bos on. [4]E. Lleida, C. Nadeu, J.B. Ma i io, "Fea u e selec ion h ough o hogonal expansion in IWR", MELECON-89, Lisboa, 1989. [5]K. Fukunaga, ln oduc ion o s a is ical pa e n ecogni ion, Academic P ess, 1972. [6]E. Lleida, "Fea u e comp ession and selec ion in speech ecogni ion", Ph. D. hesis (in Spanish), Uni e sidad Poli ecnica de Ca alu ia, 1989. [7]L.R. Rabine e al. "Speake -Independen ecogni ion o isola ed wo ds using clus e ing echniques", T ans. on ASSP- 27, Ag. 1979. 760