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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 636928, 9 pages
Research Article

Face Recognition Using Double Sparse Local Fisher Discriminant Analysis

Zhan Wang,1,2 Qiuqi Ruan,1,2 and Gaoyun An1,2

1Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China
2Beijing Key Laboratory of Advanced Information Science and Network Technology, Beijing 100044, China

Received 17 October 2014; Revised 4 March 2015; Accepted 9 March 2015

Academic Editor: Zhan Shu

Copyright © 2015 Zhan Wang 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.


Local Fisher discriminant analysis (LFDA) was proposed for dealing with the multimodal problem. It not only combines the idea of locality preserving projections (LPP) for preserving the local structure of the high-dimensional data but also combines the idea of Fisher discriminant analysis (FDA) for obtaining the discriminant power. However, LFDA also suffers from the undersampled problem as well as many dimensionality reduction methods. Meanwhile, the projection matrix is not sparse. In this paper, we propose double sparse local Fisher discriminant analysis (DSLFDA) for face recognition. The proposed method firstly constructs a sparse and data-adaptive graph with nonnegative constraint. Then, DSLFDA reformulates the objective function as a regression-type optimization problem. The undersampled problem is avoided naturally and the sparse solution can be obtained by adding the regression-type problem to a penalty. Experiments on Yale, ORL, and CMU PIE face databases are implemented to demonstrate the effectiveness of the proposed method.