DTIC ADA494622: Iterated Class-Specific Subspaces for Speaker-Dependent Phoneme Classification

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ITERATED CLASS-SPECIFIC SUBSPACES FOR SPEAKER-DEPENDENT
PHONEME CLASSIFICATION
PaulM. Baggenstoss
NavalUnderseaWarfareCenter
NewportRI,02841,USA
phone:[phone]
email: [email protected]
web:www.npt.nuwc.navy.mil/csf
ThisworkwassupportedbyOfficeofNavalResearchONR321US
ABSTRACT transformationsavailabletoeachphoneme.UnderCSM,the
“commonfeaturespace” is the time-series(raw data)itself.
The features based on the MEL cepstrum have long dom-
FeaturePDFs,evaluatedondifferentfeaturespacesarepro-
inated probabilistic methods in automatic speech regogni-
jectedbacktotherawdataspacewherethelikelihoodcom-
tion(ASR).Thisfeaturesethasevolvedtomaximizegeneral
parison is done. Besides its generality, the CSM paradigm
ASRperformancewithinaBayesianclassifierframeworkus-
has manyadditionaladvantagesas well. Forexamplethere
ingacommonfeaturespace. Now,however,withtheadvent
isaquantitativeclass-dependentmeasuretooptimizethatal-
of the PDF projectiontheorem (PPT) and the class-specific
lowsthedesignofthe class-dependentfeaturesinisolation,
method (CSM), it is possible to design features separately
withoutregardtotheotherclasses.
for each phonemeand compare log-likelihoodvalues fairly
across various feature sets. In this paper, class-dependent
features are found by optimizing a set of frequency-band 2. CLASS-SPECIFICAPPROACH
functions for projection of the spectral vectors, analogous
When applyingCSM, one must find class-dependentsignal
totheMELfrequencybandfunctions,individuallyforeach
processing to produce features that characterize each class
class. Using this method, we show significant improve-
orsub-class. Weseekanautomaticmeansofoptimizingthe
ment overstandard MEL cepstrum methods in speaker and
matrixAforagivensubclass. WefirstreviewCSM.
phonemespecificrecognition.
2.1 Class-SpecificMethod(CSM)
1. INTRODUCTION
Lettherebe M classesamongwhichwe wouldlike toclas-
TheMELcepstrumfeatures[1]anditsderivativeshavelong sify. Theclass-specificclassifier,basedonthePPT,isgiven
been the staple of automatic speech recogniton (ASR) sys- by
tems. OnemaywritetheMELcepstrumfeaturesas argmaxp (x|H ),
p m
m
z=DCT(log(A′y)), (1) where p (x|H ) is the projected PDF (projected from the
p m
feature space to the raw data space). The projectedPDF is
where vector y is the length-N/2+1 spectral vector, the givenby
magnitude-squared DFT output and the columns of A are
theMELbandfunctions[1]. Thelogarithmandthediscrete p (x|H )=J (x,A ,H )pˆ(z |H ), (3)
p m m m 0,m m m
cosine transform (DCT) are invertible functions. There is
no dimensionreductionor informationloss so they may be where pˆ(z |H )isthefeaturePDFestimate(estimatedfrom
m m
consideredafeatureconditioningstepwhichresultsinmore trainingdata)andtheJ-functionisgivenby
Gaussian-likeandindependentfeatures. Thus,wemaycon-
centrateourattentiononthematrixmultiplication p(x|H )
J (x,A ,H )= 0,m , (4)
m m 0,m p(z |H )
w=A′y. (2) m 0,m
and H are class-dependent reference hypotheses. The
0,m
Thekeyoperationhereisdimensionreductionbylinearpro-
class-dependentfeaturesz arecomputedfromthespectral
m
jection onto a lower-dimensional space. Now, with the in-
vectorythroughtheclass-dependentsubspacematricesA ,
m
troductionoftheclass-specific method(CSM) andthePDF
as
projection theorem (PPT) [2], one is free to explore class- z =C(A′ y), (5)
dependentfeatures within the rigid framework of Bayesian m m
classification. Someworkhasbeendoneinclass-dependent whereCisthefeatureconditioningtransformation.Notethat
features[3],[4]howeverexistingapproachesareonlyableto the J-function is a fixed function of x precicely defined by
usedifferentfeaturesthroughtheuseofcompentationfactors thefeaturetransformationfrom xtozandthereferencehy-
tomakelikelihoodcomparisonsfair. Suchapproacheswork pothesesH . Itisthe“correctionterm”thatallowsfeature
0,m
iftheclass-dependentfeauretransformationsarerestrictedto PDFsfromvariousfeaturespacestobecomparedfairlybe-
certainlimitedsets. Bothmethodsfallshortofthepotential cause the resulting log-likelihood function is a PDF on the
ofthePPTwhichmakesnorestrictiononthetypeoffeature raw data space x. The J-function is a generalization of the
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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Iterated Class-Specific Subspaces for Speaker-Dependent Phoneme
5b. GRANT NUMBER
Classification
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
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14. ABSTRACT
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determinantoftheJacobianmatrixinthecaseofa1:1trans- • Orthonormality. The columnsof A are an orthonor-
m
formation.ThePPTguaranteesthatp (x|H )givenby(3)is mal set of vectors. We use a orthonormality under the
p m
aPDF,soitintegratesto1overxregardlessofthereference innerproduct
hypothesisH orthe featuretransformationproducing z
0,m m
from x. It is up to the designer to choose H and A to N/2
make pp(x|Hm)asgoodanestimateof p(x|H0m,m)aspossimble. <x,y>= (cid:229) eixiyi,
Thedesignerisguidedbytheprinciplethatifzmisasuffient i=0
statisticforH vs. H ,then p (x|H )willequal p(x|H )
m 0,m p m m where e has the value 2 except for the end bins (0 and
(provided pˆ(z |H )is a goodestimate). We can also think i
m m N/2) where it has value 1. Ortho-normality under this
ofitasawayofimbeddingalow-dimensionalPDFwithina
innerproductmeansthatthespectralvectorswillbeor-
high-dimensionalPDF.
thonormalifextendedtothefullNbins.Useoforthonor-
We havegoodreason,asweshallsee, touseacommon
malityhelpstostabilizetheterm pˆ(z |H )asA isvar-
referencehypothesis,H ,whichsimplifiestheclassifierto m m m
0 ied.
argmaxJ (x,A ,H )p(z |H ) (6) • Energy sufficiency. The energy sufficiency constraint
m m 0 m m
m meansthatthetotalenergyinx,
wheretheJ-functionJ (x)nowdependsonlyonA . Note
m m N
thatincontrasttootherclass-dependentschemesusingpair- E=(cid:229) x2
i
wise or tree tests, CSM is a Bayesian classifier and has
i=1
the promise CSM of providing a “drop-in” replacement to
theMEL-cepstrumbasedfeatureprocessorsinexistingASR can be derived from the features. Energy sufficiency is
systems. importantinthecontextoffloatingreferencehypotheses
[2]. In order that the classifier result is scale invariant,
2.2 Findingaclass-specificsubspace weneedenergysufficiency. Withenergysufficiency,the
term
We are interested in adapting the matrix A to an individ- p(x|H )
0
ualclass. We proposethe strategyof selecting A to max-
m p(z |H )
imize the total log-likelihood of the training data using the m 0
projectedPDF.Let will be independentof the variance used on the H ref-
0
erence hypothesis. Note that E =e′y/N, where e =
1 1
L(x1,x2...xK;A )=(cid:229)K logp (xi|H ) (7) [1,2,2,2...,2,1]′, which is composed of the numberof
m p m degreesoffreedomineachfrequencybin. Thus,energy
i=1 sufficiencymeansthatthecolumnspaceofA needsto
m
containthevectore .
where K is the number of training vectors. If we expand 1
p (x|H ),
p m 2.2.1 Class-specificiteratedsubspace(CSIS)
p(x|H ) Since we would like the feature set created by projecting
0
p (x|H )= pˆ(z |H ),
p m (cid:20)p(z |H )(cid:21) m m onto the columns of A to characterize the statistical varia-
m 0
tions within the class, a naturalfirst step is to use principal
whereH istheindependentGaussiannoisehypothesis,we componentanalysis(PCA).Todothis,wearrangethespec-
0
see that the term p(x|H ) is independent of A . Thus, to tralvectorsfromthetrainingsetintoamatrix
0 m
maximizeL,weneedtomaximizetheaveragevalueof
X=[y1y2···yK],
logpˆ(z |H )−logp(z |H ). (8)
m m m 0
where K isthe numberof trainingvectors. To meetthe en-
Our approach is to assume that the first term in (8) is only ergysufficiencyconstraint,wefixthefirstcolumnofAtobe
weakly dependent on Am and concentrate on the second thenormalizede1
e
term.GiventhesimplicityofthereferencehypothesisH0,the e˜ = 1 .
1
secondterm p(zm|H0)canbeknown,eitherinanalyticform ke1k
orinanaccurateanalyticapproximation[5]. Thus,itiseasy
To find the best linear subspace orthogonal to e , we first
toanalyzeitsbehaviorasA changes.Wehaveobtainedthe 1
m orthogonalizethecolumnsofXtoe X =X−e˜ (e˜ ′X).
firstderivativesoflogp(z |H )withrespecttoeachelement 1 n 1 1
m 0 LetUbethelargestPsingularvectorsofX ,orequivalently
ofA . Weproceed,thenbyignoringtheterm pˆ(z |H )and n
m m m thelargestPeigenvectorsofX X′.WethensetA=[e˜ U].
maximizingthefunction n n 1
Wethenproceedtomaximize(9)usinganiterativeapproach.
We use the term class-specific iterated subspace (CSIS) to
K
Q(x1,x2...xK;Am)=−(cid:229) logp(zim|H0). (9) refertothecolumnsofAm obtainedinthisway.
i=1
3. EXPERIMENTALAPPROACH
Thechangeinpˆ(z |H )canbeminimizedasA ischanged
m m m 3.1 DataSet
byinsistingonanorthonormalformforA . Thus,bymax-
m
imizing L (7) under the restriction that A is orthonormal, We used the TIMIT [6] data set as a source of phonemes,
m
weapproximatelymaximizeL. Weapplythefollowingcon- drawingall of ourdata from the “training”portion. TIMIT
straintstoA : consists of sampled time-series (in 16 kHz .wav files) of
m
scriptedsentencesreadbyawidevarietyofspeakersandin- 3.3.5 SubspaceProjection(MatrixMultiplication)
cludes index tables that point to start and stop samples of
Next,thespectralvectors,denotedbyy,wereprojectedonto
eachspokenphonemeinthetext. Thereare61phonemesin
alowerdimensionalsubspacebyamatrixasin(2)resulting
thedatabase,havinga1to4charactercode.Weusetheterm
infeaturevectors,denotedbyw.
dataclassto representthe collection of all the phonemesof
ForMFCC,thecolumnsofAwereMELfrequencyband
a given type from a given speaker. The average numberof
functions. The numberof columnsin matrix A was N +2
samples (utterences) of a given speaker/phonemecombina- c
includingthezeroandNyquisthalf-bands.
tionis about10andrangesfrom1 upto about30forsome
For CSIS, A was an orthonormal matrix determined
ofthemostcommonphonemes. We usedspeaker/phoneme
from the optimization algorithm. For CSIS, the number of
combinationswithnofewerthan10samples.
columnsofAwasP+1wherePisthenumberofbasisfunc-
tionsinadditiontothefirstcolumne˜ .
1
3.2 Cross-Validation
3.3.6 FeatureConditioning
In all of our classification experiments, the utterences of
a given speaker/phoneme were divided into two sets, even From a statistical point of view, feature conditioning has
(samples2,4,6...) andodd(samples1,3,5...). Weconducted effect on the information content of the features. It does,
two sub-experiments,trainingoneven, testing onodd, then however,makeprobabilitydensityfunction(PDF)estimation
trainingonodd,testingoneven. Wereportedthesumofthe easieriftheresultingfeaturesareapproximatelyindependent
classificationcountsfromthetwoexperiments. andGaussian. ForMFCC,thefeatureswereconditionedby
taking the log and DCT as in (1). For CSIS, features were
conditionedfirstbydividingfeatures2throughP+1bythe
3.3 Processing
first feature. This effectively normalizes the features since
WenowdescribetheprocessingforthefeaturesoftheMEL the firstfeature, beinga projectiononto e , isa poweresti-
1
frequency cepstral coefficient (MFCC) classifier and CSIS. mate for the segment. Lastly, the log of the first feature is
Inordertoconcentrateonthebasicdimensionreductionstep taken. Mathematically,wehaveforCSIS
(equation2),thesimplestpossibleprocessingandPDFmod-
elingwasused. Eachstepintheprocessingisdescribedbe- w=A′y,
low,intheorderinwhichitisprocessed.
z =log(w ),
1 1
z =w/w , i=2,3,...P+1.
3.3.1 Resampling i i 1
We pre-processedall TIMIT .wav files by resampling from 3.3.7 J-functioncalculation
16 kHz down to 12 kHz. Phoneme endpoints were corre-
J-function contributions must be included for FFT
spondinglyconvertedandusedtoselectdatafromthe12kHz
magnitude-squared, spectral normalization, matrix mul-
time-series.
tiplication, and feature conditioning. See [7] for details of
theseclass-specificmodules.
3.3.2 Truncation
3.3.8 PDFmodelingandClassification
The phonemedata was truncatedto a multiple of 384 sam-
ples by truncating off the end. Those phoneme events that We used a simple multivariate Gaussian PDF model, or
were below 384 samples at 12 kHz were dropped. Doing equivalently a Gaussian mixture model (GMM) with a sin-
this allowed us to use FFT sizes of 48, 64, 96, 128, or 192 gle mixturecomponent. We assume independencebetween
samples,whichareallfactorsof384. the membersof the sequencewithin a givenutterence, thus
disregardingthe time ordering. The log-likelihoodvalue of
asamplewasobtainedbyevaluatingthetotallog-likelihood
3.3.3 FFTprocessing
of the feature sequence from the phoneme utterance. The
We computed non-overlapped unshaded (rectangular win- reason we used such simplified processing and PDF mod-
dow function) FFTs resulting in a sequence of magnitude- els was to concentrate ourdiscussion on the featuresthem-
squaredFFTspectralvectorsoflength N/2+1,whereN is selves. Classificationwasaccomplishedbymaximizationof
theFFTsize. ThenumberofFFTsinthesequencedepended log-likelihoodacross class models. For CSS and CSIS, we
on how many non-overlappedFFTs fit within the truncated addedthelogJ-functionvaluetothelog-likelihoodvalueof
phonemeutterance. theGMM[2],implementing(6)inthelogdomain.
4. EXPERIMENTALRESULTS
3.3.4 Spectralnormalization
4.1 DataDescription
SpectralvectorswerenormalizedafterFFTprocessing. For
non-speaker-dependent(MEL cepstrum) features, the spec- We selected fourteen phonemes for our experiments. For
tralvectorswere normalizedbythe averagespectrumofall eachphoneme,wechoseasetoffromfourtosevenindivid-
availabledata. ualspeakersofthesamesex. Weselectedphoneme/speaker
ForCSIS(speaker-dependent)features,thespectralval- combinations that had large numbers of utterences per
uesforeachspeaker/phonemecombinationwerenormalized speaker - a minimum of ten utterences per speaker. Thus,
bytheaveragespectrumforthatspeaker/phoneme. In clas- eachphonemesetconsistedofabout60utterences.Phoneme
sification experiments the average spectrum was computed sets were arrangedinto sevenpairsforusein two-phoneme
fromthetrainingdatatoavoidissuesofdataseparation. individualspeakerexperiments.
4.2 BasisFunctionoptimization 1. E istheconfusionmatrixerrormetricwhichisthenum-
c
ber of off-diagonal elements in the confusion matrix.
4.2.1 ValidationofAssumptions
Thus, it is a measure of speaker identity errors without
An important experiment to perform is to validate the as- regardtothephoeneme.
sumption used in section 2.2, that maximizing L (equation 2. Inter-phoneme error E counts the number of inter-
ip
7) can be achieved by maximizing Q in equation (9). Al- phonemeerrors.
thoughspacedoesnotpermitpresentingtheresults,wehave
Allof ourexperimentsused strictseparationbetweentrain-
obtainedoverwhelmingevidencethatthesecondtermin(9)
ingandtestingdata(section3.2). Inallcases,datawassep-
doesinfactdominate.
aratedintoevenandoddevents(utterences).Firstallmodels
were trained on odd events, events1,3,5, etc, and tested on
4.2.2 ChoiceofFFTsizeandmodelorder
evenevents,2,4,6,etc.,thenallmodelsweretrainedoneven
TheCSISapproachisparameterizedbytwoparameters,the events and tested on odd events. The error were added to
FFT size N, and the model order P. The MFCC method is obtaintheaggregateerrorcount.
parameterized by the FFT size N, and the numberof MEL
bandsNc. We chose to use the same value of N forMFCC 4.3.2 Two-PhonemeExperiments.
and CSIS. This ensured that the only significant difference
Thetwo-phonemeexperimentsweredesignedtotesttheabil-
between MFCC and CSIS would be the ability to choose
ity to distinguish speakers of a given phoneme as well as
matrix A as a function of class thanks to the PPT. Fea-
m
classify two phonemes in a limited multi-speaker environ-
tureconditioningisalsodifferentbutisnotexpectedtocon-
ment. In each of seven the two-phoneme experiments, we
tributegreatlytoperformancedifferences. Forfaircompari-
testedbothCSISandMFCCundertwoconditions.Insingle-
son,weselectedtheFFT sizetomaximizetheperformance
speaker (SS) classifier training, we separately trained a
of MFCC, which turned out to be N =96. For MFCC, we
modeloneachspeaker/phonemecombination. Inphoneme-
usedalwaystheoptimumN =10.
c
class (PC) classifier training, we grouped all speakers of a
For CSIS, we are left with deciding on the model or-
givenphonemeintoasinglephonemeclass. FortheSSclas-
der P. Refer to figure 1. In which we see the total log-
sifiers, we measured E which included all errors, and E
c ip
whichcountsonlyinter-phonemeerrors. ForthePC classi-
−1.705x 104
fiers,wecouldonlymeasureE .
ip
−1.71
Toprovidethemostmeaninfulperformancecomparison,
Total log−likelihood Q−−−11..177.217552 wcoemobpitnimatiiozendotfhpeaprearmfoertmerasnNceaonfdMNFcCoCvebryalfilnsdeivnegnthexepbeersi-t
ments.MetricE wasataminimumatN =10,N=96.For
−1.73 ip c
E , it was close to the minimumat the same parameterset-
−1.7353 4 5 Model 6order P 7 8 9 tincg. Thus,wechoseN =10,N=96asthebenchmarkfor
c
Figure 1: Total log-likelihood (with even-odd cross- comparison.
validation)as a function of P for speaker MGRL0 phoneme The seven experiments tested phonemes “IY” versus
“N”withCSIS. “EH”, “AE” versus “EH” , “R” versus “L” , “AX” ver-
sus “AXR” , “IX” versus “IH” , “N” versus “M” , and
“DCL”versus“TCL”. Betweenfourandsevenspeakersper
likelihoodLofspeakerMGRL0,phoneme“N”,asafunction phonemewere used with an averageof about12 utterences
ofP. Even-oddcross-validationis used(section 3.2). Note perspeaker/phonemecombination.Theresultsareplottedin
thatthelikelihoodincreasesuptoP=5thenexhibitsasteep figure 2. First, CSIS-SS, with P chosenseparatelyforeach
decline. This suggests that a dimension-5subspace is opti- classperformedgenerallybetterthanCSIS-SS(5)whichuses
maltorepresentthisspeaker/phonemecombination. Forthe modelorderfixedat P=5. Thisindicatesthatindividually
individual speaker experiments, we chose model order for optimizedmodelorderisbetter. Thefactthatthemodelor-
eachspeaker/phonemecombinationinthesameway. ders were determined individually without regard to other
Toaddressthephoneme-classexperimentswewillneed classes validates is an important observation. In compari-
toexpandthedatatoincludeallspeakersofagivenphoneme. sontoMFCC-SS,CSS-SSachievedalowerE inallexper-
c
We expanded the data to all male speakers of “N”. and at- iments. Asameansofcomparison,MFCCproducedhigher
tainedapeakatP=8.Thisindicatesthatanincreaseinsub- values of E by 14, 22, 38, 22, 7.5, 59, 12 and 12 percent,
c
spacedimensionisrequired. Inphoneme-classexperiments, an averageof 25.5percenthigher. Using the E errormet-
ip
weusedaconstantvalueofP=8forallphonemeclasses. ric, for which we have no space to report detailed results,
therewasnotmuchdifferencebetweenCSS-SSandMFCC-
4.3 ClassificationExperiments
SS. For multi-speakertraining, MFCC-PC was consistently
Weconductedsevenindividualspeakerexperiments,eachin- betterthanCSS-PC.
volvingtwophonemes(seesection4.1).
4.3.3 Single-SpeakerExperiments.
4.3.1 Performancemetrics
The single-speaker experiments were designed to test the
Because in each experiment we used a number of individ- abilitytodistinguishphonemesofagivenspeaker.Ineachof
ual speakers of each phoneme, it is possible to measure the seventeensingle-speakerexperiments,we gathereddata
bothinter-speakererrors(speakeridentity errors)and inter- fromasinglespeakerandbetweenfourandsevenphonemes
phonemeerrors. We definethefollowingperformancemet- intooneclassificationexperimentandmeasuredE . There-
c
rics: sultsaresummarizedinfigure3. CSISdoesgenerallybetter
100 40
90
35 MCC
80
30 CSS(5)
70
60 25 CSIS
Ec 4500 Total errors (E)c20
15
30 MCC−SS
120001 IY vs EH 2 AE vs EH CCSSIISS3−−SSSSR vs L(5) 4 AX vs AXR 5 IX vs IH 6 N vs M DCL vs TCL7 1005 fmem0 fceg0 mkag0 fapb0 mcxm0 mmea0 fdaw0 mgrl0 mkdd0 msat1 mbma1 mprk0 fklh0 mjma0 mbth0 mbcg0 mmlm0
0 2 4 6 8 10 12 14 16
Experiment Number
Figure2: ComparisonofMFCC andCSIS usingindividual
speakererrormetric E . TheexperimentnumberisontheX Figure3: ComparisonofMFCCandCSISinsingle-speaker
c
axisinthefollowingorder: “IY”versus“EH”,“AE”versus experimentsusingerrormetric Ec. The experimentnumber
“EH” , “R” versus “L” , “AX” versus “AXR”, “IX” versus isontheXaxisinthefollowingorder: fmem0fceg0mkag0
“IH”, “N” versus“M” , “DCL” versus“TCL”. CSIS-SS(5) fapb0 mcxm0 mmea0 fdaw0 mgrl0 mkdd0 msat1 mbma1
indicatesCSISwithmodelorderfixedatP=5. mprk0 fklh0 mjma0 mbth0 mbcg0 mmlm0, which is in or-
derofincreasingMFCCerror. CSIS(5)indicatesCSISwith
modelorderfixedatP=5.
thanMFCC exceptin two experimentswhereit doesworse
and one where it is the same. The total number of errors
to clusterspeakersinto like-soundinggroups, which can be
across the seventeen experiments was 435 for MFCC. We
representedbyseparatelow-dimensionalCSISmodels.
first tried CSIS with model order fixed at P=5 (indicated
as CSIS(5) in the figure) and acheived total errors of 385.
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AerospaceandElectronicSystemsMagazine,specialTu-
phonemediscrimination,itperformsbetterthanCSISinthe
torialaddendum,vol.19,pp.37–52,January2002.
inter-phomemeareas. Whentwophonemesareverysimilar,
discriminationoccurs“nearthepeak”whereCSISperforms
better.
Future work should determine how can the strengths of
bothCSISandMFCCbebestutilized.Theevidencewepro-
videdsuggeststhatthe mostpromisingapproachforapply-
ingCSIStomulti-speakerexperimentsmaylieintheability