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Component Score Weighting for GMM based Text-Independent Speaker Verification
Liang Lu
SNLP Unit, France Telecom R&D Beijing
2008-01-21
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Outline
IntroductionConventional LLR and Motivation for
detailed score processingComponent Score WeightingExperimental ResultsConclusion
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Introduction
State of the art GMM-UBM framework
GMM based model construction
Log-likelihood Ratio (LLR) based decision making
Score Normalisation (Tnorm, Hnorm, etc) for robustesses
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Introduction
wc
| |ˆ argmax| |
T bcT wc
bc () ()1
1 TJ j jbc jj NN
()11 J jwc jj NN
Major challenges
Limited data for speaker model training
Mismatch between training and testing data
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Motivation for Component Score Weighting
Motivation The insufficiency of training data and mismatch
between training and testing condition make the mixtures in GMM different in discriminative capability
The LLR just sum the score of each mixture without considering its reliability
Does it helpful if LLR considers the discriminative capability of each mixture?
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T bcT wc
bc () ()1
1 TJ j jbc jj NN
()11 J jwc jj NN
QuestionIf it does, how to explore the discriminative capabilities of Gaussian Component Mixtures
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Component Score Weighting
Our MethodFirst, scatter the LLR to each Gaussian mixture
Where, the k-th mixture is dominant for frame , namely, tx
ktkt
tk
tiM
kii k
itkk
M
kiitiitkkt
ss
xp
xp
w
w
Txpw
T
xpwxpwT
xpT
~
1log1
log1
log1
log1
,1
,1
.,,1, kiMixpwxpw tiitkk
Let we call is the dominant score and is the residual score
kts
kts~
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in original LLR
Component Score Weighting
Extend the original LLR After doing this, the original LLR will be spitted
into two score serials, dominant score serial and residual score serial
Original:
If we consider the discriminative capacity of each Gaussian mixture
Extended:
Md sssS ,,, 21
Mr sssS ~,,~,~~21
~ M
1k
kk ssXLLR
M
kkkrkkd ssWssWXf ~~
.1,1 rd WW
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Component Score Weighting
Now the question is: How can we know the discriminative capability of
each Gaussian mixture and what the should be?
Our assumption: We believe that the high dominant scores will
have better discriminative capability and should be highlighted.
W
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Component Score Weighting
Why the high dominant scores?
If the test utterance is from the target speaker, then more components in GMM should get high value compared with UBM.
If the utterance is form imposter, then high-valued components in GMM are hardly more UBM.
If the test utterance is from the target speaker, the low-valued components in GMM is due to the mixtures are not well trained or mismatch exists between training and testing data.
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Component Score Weighting
xxW exp
Restrained Emphasized
We simply used an exponential function as the weighting function
The residual scores have little importance and we ignore them finally.
The final LLR score is as follows:
M
k
ubmk
ubmk
spkk
spkk ssssXf
1
expexp
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Experimental Results
0.1 0.2 0.5 1 2 5 10 20 40
0.1
0.2
0.5
1
2
5
10
20
40
False Alarm probability (in %)
Mis
s p
robabili
ty (
in %
)
Cepstral GMM-UBM
Cepstral GMM-UBM with CSW Cepstral GMM-UBM with TNorm
Cepstral GMM-UBMwith CSW&TNorm
system EER (%) MinDCF(x100)
GMM baseline 7.64 4.16
GMM with CSW 7.45 3.66
GMM with TNorm 6.96 3.48
GMM with CSW&TNorm
7.14 3.10
Table: Results for GMM baseline and GMM with Component Score Weighting with TNorm
Experiments are performed in the 1conv4w-1conv4w task of the
2006 NIST SRE corpora
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Conclusion Split the LLR score and consider the discriminative capacity of Gaussian mixtures is helpful to cope with the insufficiency of training data and mismatch between training and testing condition.
The score weighting function should be coincident with the component score distribution and discriminative capacity.
The exponential weighting function used in this investigation is not universal and also may not optimal. More work is needed to explore an optimal weighting function.
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