Learning Radial Basis Function Model with Matching Score Quality for Person Authentication in Multimodal Biometrics

Hyunsoek Choi and Miyoung Shin*,† Dept. of Electronic Engineering, Kyungpook National University, Daegu, South Korea

choihs@ee.knu.ac.kr *School of Electrical Engineering & Computer Science, Kyungpook National University, Daegu,

South Korea shinmy@knu.ac.kr

† Corresponding author.

Abstract

Recently multimodal biometrics technology that employs more than two types of biometrics data has been popularly used for person authentication and verification. In particular, the score-level fusion approach which combines matching scores from unimodal systems to make final decision has gained lots of attentions. In most of these works, however, they assume all the matching scores to be of the same quality. This assumption may cause the problem not to reflect such situation that the qualities of the matching scores from certain unimodal systems are relatively low. To deal with this problem, we propose the RBF based score-level fusion approach which incorporates the quality information of the scores in developing classification models. According to our experimental results, the proposed method using quality information showed its superiority in the performance of person authentication to the usual RBF based score-level fusion without using quality information.

1. Introduction

Recently the multimodal biometrics technology that employs more than two types of biometrics data has been widely used for person authentication and verification[1]. In particular, the score-level fusion approach has gained many attentions which combine matching scores from unimodal systems to make final decision by using either combination rules such as weighted-sum, min, max, etc., or pattern classifiers such as SVM, MLP, etc[2][3][4]. In most of these works, however, all the matching scores are assumed to be of the same quality. This assumption may cause

the problem not to reflect such situation that the qualities of the matching scores from certain unimodal systems are relatively low. Especially, in FVC (Fingerprint Verification Competitions) 2004, it has been revealed that the performance of biometrics system could be degraded by low quality of samples which have the noises caused by a variety of factors. Since then there have been many studies about how the quality can be measured and applied in biometrics system. In Bengio[5], the authors introduced the measure of matching score’s confidence which is similar to quality and showed its usefulness with the combined matching scores. Later Poh and Bengio[6] proposed the method to measure the confidence based on the margin between genuine and impostor distribution. Also, Bigun[7] proposed the expert conciliation scheme which considers the accuracy of the unimodal expert as well as the confidence of each input sample. In Fierrez [8], authors showed that the performance of Bayesian and SVM classifiers could be improved for the multimodal biometrics by using quality information.

In this paper, our interests is to develop radial basis function (RBF) model for person authentication in multimodal biometrics system when the qualities of matching scores are assumed to be available to use. This paper is organized as follows. In Section 2, we describe the proposed the RBF model approach for score-level fusion which incorporates quality information of matching scores in the multimodal biometrics system, along with the learning algorithm. In Section 3, experiment procedure and results are presented and summarized. Finally, we conclude the paper with some discussions.

2009 First Asian Conference on Intelligent Information and Database Systems

978-0-7695-3580-7/09 $25.00 © 2009 IEEE

DOI 10.1109/ACIIDS.2009.49

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2009 First Asian Conference on Intelligent Information and Database Systems

978-0-7695-3580-7/09 $25.00 © 2009 IEEE

DOI 10.1109/ACIIDS.2009.49

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2. Learning RBF model with matching score quality

2.1 RBF model for score-level fusion

RBF model is a type of neural network model in

which the activation of a hidden unit is determined by the distance between an input vector and a prototype vector (or center). Especially, it represents the nonlinearity by the mapping from the input vector to basis functions via kernel and the linearity by the weights between the basis function outputs and the model output. Consequently RBF model is known to have the performance similar to the MLP or other nonlinear neural networks while being computationally faster than MLP or other nonlinear neural networks [9][10]. Gaussian RBF model is the most popularly used and represented in the following functional form: for a given input x , the estimate of the output y is

( )2

21 1

( ) exp2

m mj

j j j jj j j

y f ω ωσ= =

⎛ ⎞−⎜ ⎟= = Φ − = −⎜ ⎟⎝ ⎠

∑ ∑x μ

x x μ (1)

where m is the number of basis functions, jμ and

jσ are the center and width of the jth basis function, respectively, and jω is the weight of the jth basis function to produce model output.

For score-level fusion, we assume a dataset ( ){ }, , 1, ,i iD i n= =x q is given where ( )1, ,i i ids s=x

is an input score vector of the ith sample and 1( , , )i i idq q=q is its corresponding quality vector. In

the score vector ( )1, ,i i ids s=x , the component ijs , 1, ,j d= , corresponds to a matching score of the jth

unimodal biometrics system for the ith sample while the component ijq , 1, ,j d= , denotes the quality of the matching score of the jth unimodal system for the ith sample. Here our goal is to develop a RBF model that seeks the optimal decision boundary to classify the score vector x into the genuine or impostor classes. So, we need to determine model parameters ( ), , ,P m μ σ ω= from D with learning algorithm.

2.2 Learning algorithm

For the learning of the RBF model, we used the

modified OLS (Orthogonal Least Squares) algorithm to incorporate the quality information. The original OLS algorithm[11] determines RBF model parameters by constructing a set of orthogonal vectors in the space spanned by the vectors of hidden unit outputs for the training set and then finding at each step the center of an additional basis function such that it gives the

greatest error reduction ratio. This procedure is iteratively computed until a chosen model selection criterion is satisfied. The widths of basis functions here are kept constant at some predetermined values. For incorporating the quality information in learning phase of RBF model, we reflected the quality values into the computation of error reduction ratio at each step in such a way that the lower quality samples are less likely to be chosen as centers of basis functions. That is, in our approach, the error reduction ratio is computed as

[ ] [ ] , 1Q i i ierr Q err i M= ⋅ ≤ ≤ (2)

where iQ is the fused quality value obtained from the matching score qualities of unimodal systems and defined as

1/

1

, 0 1d

d

i ij ij

Q q Q=

⎛ ⎞= ≤ ≤⎜ ⎟⎜ ⎟⎝ ⎠∏ (3)

By the equation (2) and (3), therefore, we can reduce the influence of training samples of low quality on the selection of basis function centers. A summary of our learning algorithm is as follows.

Modified OLS Learning algorithm

Step 1. Construct design matrix with the basis functions having each of all the samples as the centers and orthogonalize it by the Gram-Schmidt methods.

Step 2. (a) Compute the error reduction ratio ( Qerr )

for each basis vector as follows.

( ) ( ) ( )2

1 1 1 1[ ] / , 1Ti i i i T

Qerr Q g i M⎡ ⎤= ⋅ ≤ ≤⎢ ⎥⎣ ⎦u u y y

1( , , )nQ Q Q= : quality vector g : the OLS solution

iu : the orthogonal columns, 1 i M≤ ≤ y : desired output

(b) Find { }11 1[ ] max [ ] , 1i i

Q Qerr err i M= ≤ ≤

and select 11 1

iu u= Step 3.

(a) For the kth iteration, where 1 12, , , kk i i i i −≥ ≠ ≠ , obtain

( ) ( ) ( )2[ ] / , 1

Ti i i i TQ k k k kerr Q g i M⎡ ⎤= ⋅ ≤ ≤⎢ ⎥⎣ ⎦

u u y y

(b) Find { }1 1[ ] max [ ] , 1 , , ,ki i

Q k Q k kerr err i M i i i i −= ≤ ≤ ≠ ≠

and select kik ku u=

Step 4. Terminate the procedure until the chosen model selection criterion is satisfied.

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2.3 Authentication of the RBF based score-level fusion using quality.

Up to now, in the learning phase, we determined

RBF model parameters by taking into consideration the qualities of matching scores. Although the model parameters are obtained so as to reduce the low quality sample’s influence, it is not possible to reflect the quality of new samples for authentication. To solve this problem, therefore, we employ the quality-based trade-off coefficient approach[8]. In [8], the authors proposed the quality-based trade-off coefficient based on multiple SVM classifiers. Similarly we first learned multiple RBF classifiers and then made final output by combining the multiple RBF classifiers with the quality-based trade-off coefficient as the below.

When the d is the number of unimodal biometrics systems, one RBF model RBFf is learned with all uses of d unimodal system outputs and d RBF model (

1RBFf to

dRBFf ) are learned with use of d-1 unimodal system outputs, leaving out scores 1 to d, respectively. For the authentication, the score vector and quality vector of each test sample are re-indexed in order to have

,1 ,T T dq q≤ ≤ and ( ),1 ,, ,T T T dx x=x . Thus, for a given test sample Tx , the combined RBF model

QRBFf for authentication is as follows:

1( )

1 111

1

( ) ( ) (1 ) ( )Q j

dj j

RBF T RBF T RBF Tdj

rr

f f fβ

β ββ

−

−=

=

= + −∑∑

x x x (4)

Here ( ),1 , 1 , 1 ,, , , , ,j

T T T j T j T dx x x x− += ⎡ ⎤⎣ ⎦x and jβ is obtained by

( ), , , 1, , 1j T d T jq q j dβ = − = − (5)

By the equation (4) and (5), the unimodal system producing higher (or lower) quality of matching score is likely to provide higher (or lower) contribution to the final output of the combined RBF model.

The proposed strategy is graphically represented as in Figure 1. Also the detailed steps of our modeling procedure are given as below.

3. Experiment and Result

3.1 Data description

For our experiments, we used the NIST Biometrics

Scores Set (BSSR1) [12] which is generally recommended for the study of score-level fusion in multimodal, multi algorithm, and multi-instance system. BSSR1 is a set of raw matching scores from two face

Figure 1. The proposed strategy for incorporating the quality of matching scores in learning RBF

model for person authentication.

Learning Phase Step 1. Normalize the data using Min-Max method. Step 2. Compute the fused quality iQ for each

sample by (3) Step 3. For a given width

(a) Find , ,m μ ω using the modified OLS (b) Repeat this with different widths and

select an optimal width using MSE of train and validation data.

Authentication Phase Step 4. Calculate the trade-off coefficient with

quality using (5) Step 5. Compute the combined RBF model with (4) Step 6. Decide Accept or Reject.

recognition systems (anonymous face system C and G) and one fingerprint system (NIST VTB Bozorth matcher). BSSR1 includes three subsets Set1, Set2, and Set3 and we used Set1 only here. BSSR1-Set1 consists of two face (C, G) scores and two fingerprint (LI, RI) scores from the 517 individuals and so there are 517 genuine scores and 266,772 impostor scores in each system. For experiment, we randomly selected 31,000 samples (500 genuine, 30,500 impostor) from BSSR1 Set1. Out of these sampled data, 500 samples which consist of 100 genuine and 400 impostors are used for the training. Validation data are chosen in the same way. The remaining samples which consist of 300 genuine and 29,700 impostors are used for the test. Additionally, in order to study the benefits of using matching score quality for RBF model development, we mapped a quality value {0.2, 0.5, 0.8 or 1} to each matching score in a strategic way. That is, the mapping

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of quality value was done in the way that the matching scores closer to 0 (impostor) or 1 (genuine) get assigned as of higher quality while the matching scores farther to 0 or 1 get assigned as of lower quality, as shown in Table 1. Thus, due to this mapping strategy, we can evaluate the model in terms of classification performance, without much concern of score quality distribution. Before assigning quality values to matching scores, we normalized matching scores with min-max normalization method to make them in the range of [0,1].

Table 1. The mapping of quality

Normalized matching scores Quality

0.4 ~ 0.6 0.2 0.3 ~ 0.4 and 0.6 ~ 0.7 0.5 0.1 ~ 0.3 and 0.7 ~ 0.9 0.8

0 ~ 0.1 and 0.9 ~ 1 1

3.2 Experiment procedure and Result To determine the RBF model parameters by the

modified OLS algorithm, we used the width from 0.1 to 0.7 by 0.1 steps and finally selected as the optimal one the width giving minimum means squared error on validation data. The experiments were done for two-modal system (face C + fingerprint LI), three-modal system (face C + fingerprint LI, RI), and four-modal system (face C, G + fingerprint LI, RI), respectively. For each case, two RBF models were developed with using quality and without using quality.

For performance evaluation, we use ROC (Receiver Operating Characteristic) curve. The ROC curve is a graphical approach for displaying the tradeoff between true positive rate and false alarm rate of a classifier. Generally the horizontal axis of ROC curve represents the false alarm rate while the vertical axis represents true positive rate. The advantage of ROC curve is that the evaluation of which model is better on the average can be made by the analysis of area under the curve (AUC) analysis. When the model is perfect, its area under the ROC curve would equal 1[13].

Figure 2 shows the results of our experiments with the proposed method. In the figures, the solid line corresponds to the RBF model with quality and the dashed line corresponds to the RBF model without quality. Also, the dashed-dot-line corresponds to the unimodal system. We presented the horizontal axis in log scale to show the difference of the results clearly and also changed the scale of the vertical axis for the same reason. According to Figures 2(a), (b) and (c), the

(a) Face C + Fingerprint LI

(b) Face C + Fingerprint LI, RI

(c) Face C, G + Fingerprint LI, RI Figure 2. RBF-based score-level fusion multi-

modal biometrics model using quality

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our proposed method shows better performance than the results by other methods. Also, we can observe that the increasing number of biometric modals makes more reliable performance. However, this observation may not be true for the general case. Just in this case of BSSR1-Set1, four- modal system seems to be better than two-modal system for person authentication.

4. Discussion

In this paper, we introduced the RBF based score-

level fusion method which incorporates the quality information of matching scores from unimodal biometrics systems to make final decision for person authentication. In fact, there are many cases that the qualities of matching scores obtained from unimodal systems can be various due to a variety of factors, such as system quality, biometrics data quality, and etc. By taking into consideration this quality information in the modeling process with the modified OLS algorithm, therefore, we tried to improve the performance of classification model for person authentication in multimodal biometrics systems. Also, to make the use of the quality information in the authentication phase, we employed the quality-based trade-off coefficient approach. As a result, the contribution of each matching score to final output is controlled by the quality value of each matching score. Lower quality of matching scores make less effect on the final decision while higher quality of matching scores make more effect on the decision.

For the evaluation of our proposed method, we conducted experiments in two-modal, three-modal, and four-modal systems with NIST BSSR1-Set1 dataset. According to our experiment results, the proposed method showed its superiority in the classification performance of all three cases to the usual RBF based score-level fusion without consideration of the quality. In this paper, however, since we assumed the qualities of matching scores to be given in advance, we need to investigate the method to obtain them as future works by considering biometric data sample qualities, unimodal biometric system qualities, and etc.

5. Acknowledgement

This work was supported by the Korea Science and

Engineering Foundation (KOSEF) grant funded by the Korea Government (MEST) (No.R01-2008-000-11089-0).

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