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Journal of Applied Mathematics
Volume 2014, Article ID 871565, 11 pages
Research Article

Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition

1Department of Mathematics and Computational Science, Institute of Computational Mathematics, Hunan University of Science and Engineering, Yongzhou 425100, China
2Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received 21 August 2013; Accepted 5 December 2013; Published 2 January 2014

Academic Editor: Jen-Tzung Chien

Copyright © 2014 Yujian Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Tensor subspace analysis (TSA) and discriminant TSA (DTSA) are two effective two-sided projection methods for dimensionality reduction and feature extraction of face image matrices. However, they have two serious drawbacks. Firstly, TSA and DTSA iteratively compute the left and right projection matrices. At each iteration, two generalized eigenvalue problems are required to solve, which makes them inapplicable for high dimensional image data. Secondly, the metric structure of the facial image space cannot be preserved since the left and right projection matrices are not usually orthonormal. In this paper, we propose the orthogonal TSA (OTSA) and orthogonal DTSA (ODTSA). In contrast to TSA and DTSA, two trace ratio optimization problems are required to be solved at each iteration. Thus, OTSA and ODTSA have much less computational cost than their nonorthogonal counterparts since the trace ratio optimization problem can be solved by the inexpensive Newton-Lanczos method. Experimental results show that the proposed methods achieve much higher recognition accuracy and have much lower training cost.