Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition
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 matr...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/871565 |
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| author | Yujian Zhou Liang Bao Yiqin Lin |
| author_facet | Yujian Zhou Liang Bao Yiqin Lin |
| author_sort | Yujian Zhou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8a1f287526de417884450955c2767726 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8a1f287526de417884450955c27677262025-02-03T05:44:58ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/871565871565Fast Second-Order Orthogonal Tensor Subspace Analysis for Face RecognitionYujian Zhou0Liang Bao1Yiqin Lin2Department of Mathematics and Computational Science, Institute of Computational Mathematics, Hunan University of Science and Engineering, Yongzhou 425100, ChinaDepartment of Mathematics, East China University of Science and Technology, Shanghai 200237, ChinaDepartment of Mathematics and Computational Science, Institute of Computational Mathematics, Hunan University of Science and Engineering, Yongzhou 425100, ChinaTensor 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.http://dx.doi.org/10.1155/2014/871565 |
| spellingShingle | Yujian Zhou Liang Bao Yiqin Lin Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition Journal of Applied Mathematics |
| title | Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition |
| title_full | Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition |
| title_fullStr | Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition |
| title_full_unstemmed | Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition |
| title_short | Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition |
| title_sort | fast second order orthogonal tensor subspace analysis for face recognition |
| url | http://dx.doi.org/10.1155/2014/871565 |
| work_keys_str_mv | AT yujianzhou fastsecondorderorthogonaltensorsubspaceanalysisforfacerecognition AT liangbao fastsecondorderorthogonaltensorsubspaceanalysisforfacerecognition AT yiqinlin fastsecondorderorthogonaltensorsubspaceanalysisforfacerecognition |