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.
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