情報論的学習理論テクニカルレポート 2009
Technical Report on Information-Based Induction Sciences 2009 (IBIS2009)

局所 MFCC 特徴量の最適線形結合によるテキスト独立型話者照合

Text-Independent Speaker Verification using
Optimized Linear Combination of Local MFCC Features
坂井俊亮∗
Shunsuke Sakai

亀山啓輔†
Keisuke Kameyama

Abstract: In recent years, studies of speaker veriﬁcation have been conducted as a means
for biometric person authentication. However, because of the overall veriﬁcation performance, only few actual implementations exist. This paper focuses on the text-independent
speaker veriﬁcation system. We propose an eﬀective method for speaker veriﬁcation by
adaptive weighting of local Mel Frequency Cepstrum Coeﬃcient (MFCC) features. For agiven set of registered persons, an optimal linear weightings of multiple speech frames aresearched based on the likelihood ratio error, generalizing the scheme of the conventionaluse of Δ parameters [1]. It was observed that using the proposed adaptive parameters,
superior veriﬁcation performance was achieved compared with the cases using conventionalfeatures.
Keywords: text-independent speaker veriﬁcation, biometric authentication, adaptive feature weighting, inter-frame feature.

1

Introduction
In recent years, as a technology to verify individuals,

studies for authentication using human biometrics havebeen conducted actively [2]. In password authentication conventionally often used, there are problems thatthe users forget the phrase and impostor can be easily
veriﬁed due to leakage or theft. Therefore, biometrics
technology verifying the individuals using physical information such as ﬁngerprint, vein pattern, iris, face,and speech is in the spotlight [3]. Speaker veriﬁcation technology to verify the speaker by speech features
can be useful as it does not require special veriﬁcation∗ 筑 波 大 学 シ ス テ ム 情 報 工 学 研 究 科, 305-8573 茨 城 県 つ
8480, e-mail
く ば 市 天 王 台 1-1-1, tel. 029-853-6200 ext.
sakai@adapt.cs.tsukuba.ac.jp,
Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573,
Japan† 筑 波 大 学 シ ス テ ム 情 報 工 学 研 究 科, 305-8573 茨 城 県 つ
8480, e-mail
く ば 市 天 王 台 1-1-1, tel. 029-853-6200 ext.
Keisuke.Kameyama@cs.tsukuba.ac.jp,
Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573,
Japan

hardware, is less stressful for the users, and can beused from remote places across the telephone network.
However, actual use of speaker veriﬁcation technology
is still less common. The main reason is due to thefact that the veriﬁcation performance is still low whencompared with the use of other modalities.
This study proposes a framework of speaker modeling to use the inter-frame dynamics in addition to perframe Mel Frequency Cepstrum Coeﬃcient (MFCC)
speech feature aiming to improve the veriﬁcation precision. While ΔMFCC feature [1] is known to take asimilar approach, it uses ﬁxed weights of local MFCC
features. In contrast, the proposed feature employs
adaptive weights optimized for improving the veriﬁcation performance. Also, some methods that present
mel-cepstral analysis method and its adaptive algorithm [4], and method which optimizes the weights foreach likelihood such that the overall expected loss canbe minimized [5], have been reported. In this work,
we examine the improvement of speaker discrimination ability by using an optimized linear combination

of relatively long-term features.

Text-independent speaker veriﬁcation㻲㼑㼍㼠㼡㼞㼑㻌
㼑㼤㼠㼞㼍㼏㼠㼕㼛㼚㻿㼜㼑㼑㼏㼔㻌㼒㼞㼛㼙㻌㼟㼑㼢㼑㼞㼍㼘㻌㼟㼜㼑㼍㼗㼑㼞㻲㼑㼍㼠㼡㼞㼑㻌
㼑㼤㼠㼞㼍㼏㼠㼕㼛㼚࣭࣭࣭

2㻿㼜㼑㼑㼏㼔㻌㼒㼞㼛㼙㻌㼍㻌㼓㼕㼢㼑㼚㻌㼟㼜㼑㼍㼗㼑㼞㼀㼕㼙㼑㻙㼟㼑㼞㼕㼑㼟㼒㼑㼍㼠㼡㼞㼑㻌㼢㼑㼏㼠㼛㼞㻱㼟㼠㼕㼙㼍㼠㼕㼛㼚㻌㼛㼒㻌㼟㼜㼑㼍㼗㼑㼞㻌㼙㼛㼐㼑㼘㻌㼜㼍㼞㼍㼙㼑㼠㼑㼞㼟㻌㻿㼜㼑㼍㼗㼑㼞㻌
㼙㼛㼐㼑㼘㻱㼟㼠㼕㼙㼍㼠㼕㼛㼚㻌㼛㼒㻌㼎㼍㼏㼗㼓㼞㼛㼡㼚㼐㻌㼙㼛㼐㼑㼘㻌㼜㼍㼞㼍㼙㼑㼠㼑㼞㼟㻮㼍㼏㼗㼓㼞㼛㼡㼚㼐㻌㼙㼛㼐㼑㼘

図 1: Modeling phase

The methods of speaker veriﬁcation is divided into
three main groups [6]. Text-dependent system speciﬁes
the veriﬁcation text in beforehand, text-independent㼀㼕㼙㼑㻙㼟㼑㼞㼕㼑㼟㼒㼑㼍㼠㼡㼞㼑㻌㼢㼑㼏㼠㼛㼞㻿㼜㼑㼑㼏㼔㻌㼐㼍㼠㼍㻌㼒㼞㼛㼙㻌㼍㼚㻌㼡㼚㼗㼚㼛㼣㼚㻌㼟㼜㼑㼍㼗㼑㼞X㼀㼕㼙㼑㻙㼟㼑㼞㼕㼑㼟㻌㼒㼑㼍㼠㼡㼞㼑㻌㼢㼑㼏㼠㼛㼞㻲㼑㼍㼠㼡㼞㼑㻌
㼑㼤㼠㼞㼍㼠㼕㼛㼚p ( X | λC )system does not limit the text, and text-prompted system prompts the text at each veriﬁcation. In general, it㻯㼍㼘㼏㼡㼘㼍㼠㼕㼛㼚㻌㼛㼒㻌㼘㼕㼗㼑㼘㼕㼔㼛㼛㼐ΛC ( X )㻰㼑㼏㼕㼟㼕㼛㼚㻌㼎㼥㻌㼠㼔㼑㻌㼘㼕㼗㼑㼘㼕㼔㼛㼛㼐㻌㼞㼍㼠㼕㼛㻯㼍㼘㼏㼡㼘㼍㼠㼕㼛㼚㻌㼛㼒㻌㼘㼕㼗㼑㼘㼕㼔㼛㼛㼐㻯㼘㼍㼕㼙㼑㼐㻌
㼟㼜㼑㼍㼗㼑㼞㻌㼙㼛㼐㼑㼘 λC

is known that text-dependent and text-prompted systems indicate higher performance, because the system㻯㼘㼍㼕㼙㼑㼐㻌㻵㻰㻿㼑㼢㼑㼞㼍㼘㻌
㼟㼜㼑㼍㼗㼑㼞㻌㼙㼛㼐㼑㼘 㻮㼍㼏㼗㼓㼞㼛㼡㼚㼐㻌㼙㼛㼐㼑㼘C㻭㼏㼏㼑㼜㼠 (Λ ≥ θ )㼛㼞㻾㼑㼖㼑㼏㼠 (Λ < θ )p ( X | λC )λC

can use the speaker information depending on phonological line describing the text [7]. Recently, the study

図 2: Test phaseof text-independent speaker veriﬁcation having an advantage of not limiting the speech text, has been themainstream research topic [6]. This paper discusses

deﬁned asTlog p(X | λC ) =text-independent veriﬁcation as well.

2.1

1
log p (x(t) | λC ) .
T t=1

(2)

As a speech feature, Mel Frequency Cepstrum Coeﬃ-

Procedure

The general ﬂow of text-independent speaker veriﬁ-

cient (MFCC) is used commonly [9]. Here, MFCC feature of D component cepstrum coeﬃcients is describedcation system is shown in Figs. 1 and 2 [6]. At ﬁrst, inthe modeling phase, the model of each speaker λC andas x = [c1 , c2 , ..., cD ] .

the background model λC̄ are obtained based on the
speech signals. The speaker model λC uses a collection

2.2

Gaussian mixture speaker model

the authentic speech, whereas the background model

Text-independent speaker veriﬁcation does not havea limitation about the speech contents by the speaker.

(Universal Background Model [8]) uses speeches by
various speakers (average feature) in the training. In

Therefore, in the speaker modeling, likelihood function of speech feature is modeled as a density function,

the test phase, the log-likelihood ratio of input speechfeature vectors to the claimed speaker model λC andfor example with Gaussian Mixture Model (GMM) [9].
Here, if x is a D-dimensional feature vector, likelihood

the background model λC̄ is calculated, and this value
is compared to the predetermined threshold value θ.

function of a registered speaker s (s = 1, ..., N ) is deﬁned as

The speaker is accepted if the value is higher than thethreshold value, and is rejected otherwise. The log-p(x | λs ) =M

wsj bsj (x).

(3)

j=1

likelihood ratio is deﬁned as

This is a linear combination of M Gaussian functions
ΛC (X) = log p(X | λC ) − log p(X | λC̄ ).

(1)

Here, if x(i) is a feature vector in frame i (i = 1, 2, ..., T ),p(X | λC ) indicates the likelihood that speech X ={x(1), ..., x(T )} is from the claimed speaker giving themodel λC . On the other hand, p(X | λC̄ ) indicatesthe likelihood that speech X is not from the claimed
speaker.
Additionally, the likelihood that the model of theclaimed speaker gives the input speech collection X is

bsj (x), each computed as
11 ×(2π) |Σsj | 2


1

−1
exp − (x − µsj ) (Σsj ) (x − µsj ) , (4)2bsj (x) =D2which is determined by a mean vector µsj , a covariance matrix Σsj , and weights wsj (j = 1, ..., M ). Here,the parameter set of speaker s is denoted as λs ={(ws1 , µs1 , Σs1 ), ..., (wsM , µsM , ΣsM )}. The speakermodel parameters are estimated using the ExpectationMaximization (EM) algorithm [10].

3Adaptive weighting of local
MFCC featuresi

It has been reported that, by adding inter-frame dynamic information to short-time per-frame speech fea-iture as MFCC, there are cases that the veriﬁcation
performances are improved [1]. This feature known asΣthe ΔMFCC regression coeﬃcient of change along thetime axis of MFCC, is sometimes used together withsi

MFCC [6]. However, it only uses restrictive weights oflocal MFCC features.

i

s
s

s

図 3: Extraction of weighted feature cF si . Each hori-zontal bar denotes the period for a single frame.

We propose an adaptive method for weighting the
local MFCC features that searches the optimal linear

Xu

weightings of multiple speech frames based on the likelihood ratio error, generalizing the strategy taken by

Δ

Xs
as

as

the Δ parameters employing restrictive weights.

3.1

Generalization of ΔMFCC featureλs

The inter-frame regression coeﬃcient known as
ΔMFCC is computed aslk · ci (m + k)
, (i = 1, ..., D)
Δci (m) = k=−ll2
k=−l kλ UBM(5)
Λ(X u )

where l is the frame range that regression coeﬃcient iscalculated, c is the cepstrum coeﬃcient [1], and m isdthe frame index. In this work, we propose to generalize Eq. (5), searching for an arbitrary dynamic feature

Δas

to improve veriﬁcation precision among linear combi-

図 4: The training process. This modiﬁcation is ap-

nations of cepstrum coeﬃcients in neighboring frames.
Therefore, 2l + 1 parameters {as (−l), ..., as (l)} in

plied to the GMM parameter set λs and coeﬃcient
vector as of each registrant s (s = 1, . . . , N ), itera-cF si (m) =l

tively.
as (k)ci (m + k) (i = 1, ..., D)

(6)

k=−l

are adjusted. Here, in the case of ΔMFCC, parameteras (k) amounts to the special case ofaΔ (k) = lkis updated by steepest descent method to minimize
the error in log-likelihood ratio for the teacher signal.
Besides, each speaker has his/her own individual pa-(k = −l, ..., l)(7)rameter vector. Figure 4 shows the whole procedure ofparameter vector modiﬁcation.

Figure 3 shows the schematic for calculating the fea-

For a speech Xu attributed to speaker u, the T
frames in Xu is converted to a feature vector arrayk=−l k2.

ture cF si .

3.2

Coeﬃcient search based on likelihood ratio error

The veriﬁcation precision can be evaluated by loglikelihood ratio. Therefore, in the proposed method,
the coeﬃcient parameter vector for each speakeras = [as (−l), as (−l + 1), ..., as (l)] ∈ R

2l+1

(8)

gs (1), . . . , gs (T ) ∈ R2D , using the parameters as andλs of a registrant s. The feature vector gs (t) which
concatenates MFCC features x = [c1 , c2 , ..., cD ] and FMFCC features ys = [cF s1 , cF s2 , ..., cF sD ] , is denotedasgs (t) = [x , ys ] = M (t)as + b(t) ∈ R2D .

(9)

⎡

0
..
.
0

⎢
⎢
⎢
⎢
⎢
M (t) = ⎢⎢ c (t − l)
⎢ 1
⎢
..
⎢
.
⎣

···
..
.

⎤

0
..
.
0

∂σ(Λ)
∂gs (t)

⎥
⎥
⎥
⎥
⎥
···
⎥
· · · c1 (t + l) ⎥
⎥
⎥
..
..
⎥
.
.
⎦
cD (t − l) · · · cD (t + l)
∈ R2D×(2l+1)

and

(10)

b(t) = [c1 (t), ..., cD (t), 0, ..., 0] ∈ R2D .

(11)

Eq. (1). Additionally, Λ(Xu ) is converted to a valuein (0, 1) by the sigmoid function deﬁned asσ(Λ) =

1
1 + exp(−β · Λ)3) Calculate Δas to minimize the error
ELLR based on the teacher signal d, and(14)

update as .
4) Train the speaker model (λs ) using(15)(MFCC+F-MFCC) for Xu by the updated
model, and calculate the log-likelihood ratio.

(16)

Each partial diﬀerentiation is computed as follows basedon the deﬁnition above.
∂ELLR
∂ 1
=
(d − σ(Λ))2 = −(d − σ(Λ)), (17)∂σ(Λ)∂σ(Λ) 2T
∂σ(Λ) =∂as
t=1

∂σ(Λ) ∂gs (t)∂gs (t) ∂as


,

(22)

* Training of individual weight as and GMM(13)speech Xs again.
5) Verify using the new feature vector

6) Repeat 3-5 for the whole training set for

where, η is the learning coeﬃcient. The log-likelihood
ratio error ELLR is deﬁned as
1(d − σ(Λ))2 .
2∂gs (t)∂={M (t)as + b(t)} = M (t).
∂as∂asusing feature vector (MFCC+ΔMFCC) derived from speech Xu .

by the amount of correction deﬁned as

ELLR =(21)

tor (MFCC+ΔMFCC).
2) Calculate the log-likelihood ratio Λ(Xu )Vector as is updated as∂ELLR∂ELLR ∂σ(Λ)
= −η
,
∂as
∂σ(Λ) ∂aswhere, csj (t) = wsj bsj (gs (t)) , and

1) Train the background model (λUBM ) andall the speaker model (λs ) using feature vec-to minimize the error between the log-likelihood ratio
σ(Λ) and teacher signal. The teacher signal d is set as,Δas = −η(20)

* Initialization{aΔ (−l), ..., aΔ (l)}.
Next, the coeﬃcient parameter vector as is modiﬁed

+1)
)
a(τ
= a(τ
s
s + Δas ,(19)

Training procedure

initial as will be set identical to ΔMFCC coeﬃcients0 (s = u) (Impostor)).

1 ∂log p(gs (t) | λk ),T ∂gs (t)dated using the amount of correction Δas in Eq. (15)by the following steps.

(12)

1 (s = u) (Authentic speaker)=

Coeﬃcient vector as for each registered speaker is up-

considering the convergence performance in the next
training phase. Here, β is the slope parameter. The

d=

T
∂ 1 
log p(gs (i) | λk )∂gs (t) T i=1∂
log p(gs (t) | λs ) =∂gs (t)M−1
j=1 csj (t){gs (t) − µsj } (Σsj )−M
j=1 csj (t)Then, the likelihoods for the background model andthe corresponding speaker model are calculated by Eq.
(3), and the log-likelihood ratio Λ(Xu ) is obtained as

=

(18)

a predetermined time.

4

Experiment

We evaluated the proposed method in four experiments. In Experiment 1, the optimal number of Gaussian component for our dataset is determined. In Experiment 2, the iteration number of learning as is determined. Experiment 3 compares the veriﬁcation performance for the conventional method and the proposed method, and Experiment 4 is the same comparison using telephone speech.

4.1

Experimental condition

All speech data used in the experiments are sampled

表 1: Exp.1 Comparison of EER by Gaussian compo-

nent

at 16kHz, in 16 bit. The speech data is extracted fromthe ASJ Continuous Speech Corpus by the Acoustical

GaussianSociety of Japan [11].

component

The number of clients are 10 (5 male, 5 female), andthe speech length for speaker modeling is 60sec. The

EER (%)

size of the training set is 100 trials (10 authentic, 90
impostor). The size of the test set is 10000 trials (500

16

32

64

128

256

512

2.53

2.53

2.45

2.20

2.20

2.40



speech for the training and testing are from diﬀerent
texts. In the training and test phases, if one speaker is
set to a client, all other speakers are set to impostors.
The frame number l in Eq. (8) is set to l = 2, andthe slope β in Eq. (12) is set to β = 1.0. All theexperiments were conducted on a 3.6 GHz Intel Xeon
computer with 3.0 GB of RAM, running Windows XP.

4.2
4.2.1

Experiment 1: Optimal number ofGaussian components













ProcedureIn this experiment, we determined the optimal number of Gaussian component for our dataset. The background model and the speaker model with 16 to 512
Gaussian components were trained and evaluated using the same training and test data with clean (∞dB)
speech. Equal Error Rate (EER) and the detection error tradeoﬀ (DET) curve [12] are used as the index forevaluation.
4.2.2

0LVVSUREDELOLW\ LQauthentic, 9500 impostor), with the speech length of
3sec. There are 50 speech clips from each speaker. The

Result

The comparison of each case is shown in Table 1 andFigure 5. 128 and 256 Gaussian components achieved
the best among all in EER, and 128 appears slightly
better than all others in DET curves. These results
show that more Gaussian components are not always
better.
From this result, we use 128 Gaussian components
in the following experiments.

)DOVH$ODUPSUREDELOLW\ LQ

図 5: Exp.1 Comparison of DET curves by Gaussiancomponent
invetigated. Mean-squared error (MSE) ELLR for the
training and test sets were recorded at each training
round (100 trials). Normal speech in Experiment 3
and telephone speech in Experiment 4 are used, theseinclude the same three cases of S/N as Experiment 3
and 4.
4.3.2

ResultFigure 6 shows the case of normal speech in ∞dB
test set and Figure 7 shows the case of telephone speech
in ∞dB test set. These results show that the MSE of
the test sets is minimum at the early stage in contrast
to the monotonically decreasing training set error. The
same tendency of these was seen in 30dB and 20dB test
sets.

4.3

Experiment 2: Change in MSE with
the iteration number of learning

From this result, we set the iteration number of learning as varying GMM parameters at the same time to

4.3.1

Procedure

400 (4 rounds of 100) in Experiment 3 and to 200 (2rounds of 100) in Experiment 4. The value 400 was

In order to determine the appropriate training iteration, the change of error ELLR during training was

also used in Experiment 1.

0.025

表 2: Exp.3 Comparison of EER (%)

MSE

0.02

∞dB

30dB

20dB

MFCC

2.80

2.60

2.20

MFCC+ΔMFCC

2.69

1.94

2.05

MFCC+F-MFCC

2.20

1.89

1.34

0.015
0.01

training set

0.005

test set0
1 2 3 4 5 6 7 8 9 10
iteraon number(round of 100 trials)

(normal, ∞dB)
0.02

MSE

0.015
0.01
training set

0.005

0LVVSUREDELOLW\ LQ

図 6: Exp.2 Change in MSE for training and test sets

test set0
1 2 3 4 5 6 7 8 9 10




iteraon number(round of 100 trials)

0)&&0)&&Ǽ0)&&0)&&)̻0)&&)DOVH$ODUPSUREDELOLW\ LQ

図 8: Exp.3 DET curves in ∞dB test set.

図 7: Exp.2 Change in MSE for training and test sets(phone, ∞dB)

4.4

Experiment 3: Comparison of theveriﬁcation performance

noisy speech, the proposed feature indicates higher performance than the conventional ones. Thus, the superiority of adaptively choosing the weighting of local
MFCC features (MFCC+F-MFCC) has been veriﬁed.

4.4.1

Procedure

The conventional feature of MFCC, MFCC with
ΔMFCC, and the proposed feature of MFCC with FMFCC are compared in terms of the veriﬁcation performance. The veriﬁcation speech include three casesof S/N,
namely, ∞dB which is the ideal case, and levels common in usual veriﬁcation use (30dB and 20dB). EER
and DET curves are used as the index for evaluationas Experiment 1.
4.4.2

Result

The comparison using the EER(%) measure is shownin Table 2. Figs. 8-10 show the DET curves obtainedfor each S/N. In the case of training and testing withclean speech, the proposed method is superior to theconventional ones for veriﬁcation speech with ∞dB.
Additionally, in the case of training and testing with

4.5

Experiment 4: Comparison of theveriﬁcation performance (telephone
speech)4.5.1

Procedure

The same procedure as Experiment 3 is conductedwith telephone speech. The frequency range of 3003400 Hz was extracted from the same dataset, andwas used as the simulated voice through a telephoneline. The simulated telephone speech were used in bothtraining and testing.
4.5.2

Result

The comparison using the EER(%) measure is shownin Table 3, and the DET curves are shown in Figs. 1113. Here, the results also imply the superiority of using
the proposed feature MFCC+F-MFCC in veriﬁcation

0LVVSUREDELOLW\ LQ

0LVVSUREDELOLW\ LQ








0)&&
0)&&Ǽ0)&&0)&&)̻0)&&
)DOVH$ODUPSUREDELOLW\ LQ

図 9: Exp.3 DET curves in 30dB test set.
表 3: Exp.4 Comparison of EER (%)

∞dB

30dB

20dB

MFCC

1.80

3.20

2.80

MFCC+ΔMFCC

1.60

2.20

1.74

MFCC+F-MFCC

1.40

1.46

1.40

through the telephone line.

5

Conclusion

In this paper, we proposed a method for speaker
veriﬁcation using adaptive weighting of local MFCC
features. The core idea was to determine the optimal frame coeﬃcient parameter to minimize the veri-






0)&&
0)&&Ǽ0)&&0)&&)̻0)&&
)DOVH$ODUPSUREDELOLW\ LQ

図 10: Exp.3 DET curves in 20dB test set.

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Springer, 2008.

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ﬁcation error. In the experiments, it was shown thatalternative hypothesis via minimum veriﬁcation
error training with applications to speaker veri-

this mechanism gives lower veriﬁcation error than theconventional methods under clean and certain level ofﬁcation,” Pattern Recognition, vol. 42, no. 7, pp.
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noise environment, including authentication via a telephone line.
In future works, we consider methods that the present
linear combination of local MFCC is extended to nonlinear transformation and indices other than the likelihood ratio error are used.

参考文献[1] S. Furui, “Comparison of speaker recognition
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図 11: Exp.4 DET curves in ∞dB test set.
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[8] D. A. Reynolds, T. F. Quatieri, and R. B.
Dunn, “Speaker veriﬁcation using adapted Gaus-0)&&0)&&Ǽ0)&&0)&&)̻0)&&
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図 12: Exp.4 DET curves in 30dB test set.

sian mixture models,” Digital Signal Processing,no. 10, pp. 19–41, 2000.
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N.M.Laird,

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[12] A. Martin, G. Doddington, T. Kamm, M. Or-

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dowski, and M. Przybocki, “The DET curve inassessment of detection task performance,” Proceedings of European Conference on Speech Communication and Technology, pp. 1895–1898, 1997.

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図 13: Exp.4 DET curves in 20dB test set.

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