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Regularized least square discriminant projection and feature selection

[+] Author Affiliations
Jun Shi

Beijing University of Aeronautics and Astronautics, School of Astronautics, Image Processing Center, Beijing Key Laboratory of Digital Media, Beijing 100191, China

Zhiguo Jiang

Beijing University of Aeronautics and Astronautics, School of Astronautics, Image Processing Center, Beijing Key Laboratory of Digital Media, Beijing 100191, China

Danpei Zhao

Beijing University of Aeronautics and Astronautics, School of Astronautics, Image Processing Center, Beijing Key Laboratory of Digital Media, Beijing 100191, China

Hao Feng

Beijing University of Aeronautics and Astronautics, School of Astronautics, Image Processing Center, Beijing Key Laboratory of Digital Media, Beijing 100191, China

Chao Gao

Beijing University of Aeronautics and Astronautics, School of Astronautics, Image Processing Center, Beijing Key Laboratory of Digital Media, Beijing 100191, China

J. Electron. Imaging. 23(1), 013003 (Jan 10, 2014). doi:10.1117/1.JEI.23.1.013003
History: Received April 10, 2013; Revised November 14, 2013; Accepted December 13, 2013
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Abstract.  Conventional graph embedding framework uses the Euclidean distance to determine the similarities of neighbor samples, which causes the graph structure to be sensitive to outliers and lack physical interpretation. Moreover, the graph construction suffers from the difficulty of neighbor parameter selection. Although sparse representation (SR) based graph embedding methods can automatically select the neighbor parameter, the computational cost of SR is expensive. On the other hand, most discriminant projection methods fail to perform feature selection. In this paper, we present a novel joint discriminant analysis and feature selection method that employs regularized least square for graph construction and l2,1-norm minimization on projection matrix for feature selection. Specifically, our method first uses the regularized least square coefficients to measure the intraclass and interclass similarities from the viewpoint of reconstruction. Based on this graph structure, we formulate an object function with scatter difference criterion for learning the discriminant projections, which can avoid the small sample size problem. Simultaneously, the l2,1-norm minimization on projection matrix is applied to gain row-sparsity for selecting useful features. Experiments on two face databases (ORL and AR) and COIL-20 object database demonstrate that our method not only achieves better classification performance, but also has lower computational cost than SR.

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Citation

Jun Shi ; Zhiguo Jiang ; Danpei Zhao ; Hao Feng and Chao Gao
"Regularized least square discriminant projection and feature selection", J. Electron. Imaging. 23(1), 013003 (Jan 10, 2014). ; http://dx.doi.org/10.1117/1.JEI.23.1.013003


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