Preserving Complete Subspace Structure Projection for Face Recognition

Neural Information Processing – Letters and Reviews Vol. 11, No. 2, February 2007

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Preserving Complete Subspace Structure Projection for Face Recognition

Jun-Bao Li

Department of Automatic Test and Control Harbin Institute of Technology, Harbin, 150001,P.R. China

Phone: +86-451-6413531-8603, Fax: +86-451-6418083, E-mail: [email protected]

Jeng-Shyang Pan

Department of Electronic Engineering

National Kaohsiung University of Applied Sciences, D415 Chien-Kung Road, Kaohsiung 807, Taiwan Phone: +886-7-3814526 Ext. 5636，Fax:+886-7-3811182，Email: [email protected]

(Submitted on November 1, 2006)

Abstract — Subspace-based face recognition is one of the most successful methods for face

recognition. Eigenfaces, Fisherfaces, and Laplacianfaces methods, which are based on PCA, LPP and LDA that preserve global, local and cluster structure information respectively, are three representative methods of subspace-based face recognition approaches. In this paper, we propose a novel pattern classification namely Preserving Complete Subspace Structure Projection (PCSSP) for face recognition. First we analyze their contributions of extracting the discriminating information respectively firstly, and then we construct a 3D parameter space using three subspace dimensions as axes. We can take advantage of the global, local and cluster structure information provided by three subspaces through searching over the whole 3D parameter space instead of searching only in lines or local regions as the standard subspace methods. Finally based on the 3D parameter space, we propose a framework for PCA, LPP and LDA. The experimental results with the ORL and Yale face databases show that the proposed algorithm outperforms three standard subspace approaches, and the proposed algorithm can also improve the computational efficiency without influencing the recognition performance.

Keywords — Preserving complete subspace structure projection, face recognition, principal

component analysis, linear discriminant analysis, locality preserving projections, 3D parameter space

1. Introduction

Face recognition has become a very active research area in recent years due to its wide applications. Many approaches have been developed in the last years, and good surveys can be found in [8], [9], and [10]. Among various face recognition algorithms, one of the most successful techniques is the appearance-based method. Among the crucial issues of face recognition technology, the low-dimensional feature representation with enhanced discriminatory power is of paramount importance in face recognition systems. To resolve the too large dimension problem when using original face images, dimensionality reduction techniques are employed widely [1], [2].Two of the most popular algorithms of these dimensionality reduction techniques are Principal Component Analysis (PCA) [1] and Linear Discriminant Analysis (LDA) [2]. Additionally, Laplacianfaces [11] method based on PCA and Locality Preserving Projections (LPP) is another successful face recognition method. Recently, the nonlinear methods, KPCA [7] and KFD [3], [4], have been widely used since kernel machine techniques [5], [6] were applied to the face recognition. Especially, PCA aims to preserve the global structure, and LPP preserves local structure information, and LDA preserves the cluster structure. In order to take full advantage of all structure information, we construct a 3D parameter space using the three subspace dimensions as axes in this paper. In the 3D parameter space, all above three methods search in the lines or plane only, in

Preserving Complete Subspace Structure Projection for Face Recognition Jun-Bao Li and Jeng-Shyang Pan

26

other words, we only apply one kind of structure information when we only apply one of LPP, PCA and LDA. In our algorithm, we can search the optimal parameters through the 3D parameter space for apply three kinds of structure information enough, so it is reasonable to enhance the recognition performance with searching over 3D parameter space instead of only in lines or planes as three standard subspace methods.

The remainder of this paper is organized as follows. The proposed algorithm is introduced in Section 2. In Section 3, experiments with the Yale and ORL face databases are presented to demonstrate the effectiveness of proposed algorithm. Conclusions are summarized in Section 4.

2. Proposed Algorithm

In this section, firstly we analyze the contributions of LPP, PCA and LDA in feature extraction, and then we introduce our algorithm for face recognition.

Given a set of M training samplesx x1, 2,...,xM in

N

R , LPP seeks to preserve the intrinsic geometry of the local structure. The objective function of LPP is as following.

2 min (y_i y_j) S_ij ij − ∑ (1) where y

iis the one-dimensional representation of xi and S is a similarity matrix, which can be defined by

2 2 exp( / ) 0 x_i x_j t x_i x_j Sij otherwise ε ⎧⎪ − − − < =⎨ ⎪⎩ (2) where ε is sufficiently small, and ε >0. LPP is a general method for manifold learning by finding the projection matrix _WLPP which can be obtained by computing the eigenvectors and eigenvalues for the generalized eigenvector problem as follows.

T T

XLX w=λXDX w (3) where D is a diagonal matrix whose entries are column (or row) sums of S, D_ii S_ij

j

=∑ and L=D−S. Let , , ,

1 2

w w K_wm be the solutions of equation (3) corresponding to m largest eigenvalues. The LPP transformation matrix _WLPP can be obtained by

1 2

[ , , , _m]

LPP

W = w w _K w (4) Differently, PCA try to preserving the global structure information, which apply the covariance matrix defined as follows.

(

)(

)

1 1 M T j j j M C x

x

x

x

= − − ∑

=

v

v

(5) where 1 1 M x _{x j} M j = ∑ =

v _{denotes the mean vector of all training samples. The orthonormal eigenvectors , , ,}

1 2

w w K_wm of

C correspond to m largest eigenvalues. For a sample x , we can obtain the feature vector Y=(y y_{1 2}, ,_Kym)Tby 1,2,...,

T

y_j=w x_j j= m (6) In order to preserve the cluster structure information, we also apply LDA in our algorithm, which tries to find the subspace that best discriminates different face classes by maximizing the between-class scatter Sb and minimizing the within-class_Sw in the projective subspace. And _Sband_Swcan be defined as follows.

(

)(

)

1 L _T S_b n m_{i i} m m_i m i =∑ − − = (7)

(

)(

)

1 T L k i k i i y_k y_i w S y m y m = ∈ =∑ ∑ − − (8) The transformation matrix Wcan be obtained by solving the following equation.

Preserving Complete Subspace Structure Projection for Face Recognition Jun-Bao Li and Jeng-Shyang Pan

30

4. Conclusion

A novel face recognition method of using the complete subspace structure information, i.e., global, local and cluster structure information, is presented in this paper. Firstly we construct a 3D parameter space using the dimensions of three subspaces as axes. In the 3D parameter space, we can take advantage of the three kinds of subspace structure information through searching in the whole 3D parameter space instead of searching only lines or local region as the standard subspace methods. Then based on the 3D parameter space, we construct a framework for PCA, LPP and LDA, and the superiority of the proposed algorithm in recognition performance is tested with the ORL and Yale face databases.

References

[1] P.N. Belhumeur, J.P. Hespanha, and D.J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, July 1997.

[2] A.U. Batur and M.H. Hayes, “Linear Subspace for Illumination Robust Face Recognition,” Proc. IEEE Int’l Conf. Computer Vision and Pattern Recognition, Dec. 2001.

[3] Jian Yang, Alejandro F. Frangi, Jing-yu Yang, David Zhang, and Zhong Jin, “KPCA Plus LDA: A Complete Kernel Fisher Discriminant Framework for Feature Extraction and Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 2, Feb.2005.

[4] Qingshan Liu, Hanqing Lu, and Songde Ma, “Improving kernel Fisher discriminant analysis for face recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 1, pp. 42-49, Jan. 2004. [5] A. Ruiz and P. E. López de Teruel, “Nonlinear kernel-based statistical pattern analysis,” IEEE Trans. Neural

Networks, vol. 12, pp. 16–32, Jan. 2001.

[6] K. R. Müller, S. Mika, G. Rätsch, K. Tsuda, and B. Schölkopf, “An introduction to kernel-based learning algorithms,” IEEE Trans. Neural Networks, vol. 12, pp. 181–201, Mar. 2001.

[7] B. Scholkopf, A. Smola, and K. R. Muller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Computation, vol. 10, no. 5, pp. 1299–1319, 1998.

[8] M.Turk, “A random walk through eigenspace,” IEICE Trans. Inform. Syst., vol. E84-D, no. 12, pp. 1586– 1695, Dec. 2001.

[9] A. Samal and P. A. Iyengar, “Automatic recognition and analysis of human faces and facial expressions: A survey,” Pattern Recognition, vol. 25, pp. 65–77, 1992.

[10] D. Valentin, J. O. Toole Herve Abdi Alice, and G.W. Cottrell, “Connectionist models of face processing: A survey,” Pattern Recognition, vol. 27, no. 9, pp. 1209–1230, 1994.

[11] Xiaofei He, Shuicheng Yan, Yuxiao Hu, Partha Niyogi, and Hong-Jiang Zhang, “Face Recognition Using Laplacianfaces” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 3, pp. 328-340, March 2005.

Neural Information Processing – Letters and Reviews Vol. 11, No. 2, February 2007

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Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1222-1228, Sep. 2004.

[13] Jian Yang, Jing-Yu Yang, and Alejandro F. Frangi, “Combining Fisherfaces framework,” Image and Vision computing, vol. 21, pp. 1037-1044, July. 2003.

[14] F. Samaria and A. Harter, “Parameterisation of a stochastic model for human face identification,” Proceedings of 2nd IEEE Workshop on Applications of Computer Vision, 1994.

Jun-Bao Li received the B.Sc. and M.Sc. degree from Harbin Institute of Technology (HIT), Harbin, P. R. China in 2002 and 2004, respectively. He is currently working toward the Ph.D. degree in the Measurement Technology and Instrument, in HIT, Harbin, P. R. China. His research interests are mainly in pattern recognition and image processing.

Jeng-Shyang Pan received the B. S. degree in Electronic Engineering from the National Taiwan University of Science and Technology, Taiwan in 1986, the M. S. degree in Communication Engineering from the National Chiao Tung University, Taiwan in 1988, and the Ph.D. degree in Electrical Engineering from the University of Edinburgh, U.K. in 1996. Currently, he is a Professor in the Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, Taiwan. Professor Pan has published more than 50 journal papers and 120 conference papers. He joints the editorial board for LNCS Transactions on Data Hiding and Multimedia Security, Springer, International Journal of Knowledge-Based Intelligent Engineering Systems, IOS Press, and International Journal of Hybrid Intelligent System, Advanced Knowledge International. He is the Co-Editors-in-Chief for International Journal of Innovative Computing, Information and Control. His current research interests include data mining, information security and image processing.