ISSN 1000-1239 CN 11-1777/TP

Journal of Computer Research and Development ›› 2014, Vol. 51 ›› Issue (10): 2295-2301.doi: 10.7544/issn1000-1239.2014.20130188

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Structured Sparse Linear Discriminant Analysis

Cui Zhen1,2,3, Shan Shiguang2, Chen Xilin2   

  1. 1(School of Computer Science and Technology, Huaqiao University, Xiamen, Fujian 361021); 2(Key Laboratory of Intelligent Information Processing (Institute of Computing Technology, Chinese Academy of Sciences), Beijing 100190); 3(University of Chinese Academy of Sciences, Beijing 100049)
  • Online:2014-10-01

Abstract: Linear discriminant analysis (LDA) is a very efficient image feature extraction technique in the supervised scenario. However, LDA often leads to over-fitting when using small scale training samples, and simultaneously might not show an intuitive explanation for the learnt projections from the view of human cognition. To handle these problems, especially for the discovery of those interpretability structures, a called structured sparse LDA (SSLDA) method is proposed by employing the linear regression model of LDA and the structured sparse L\-{2,1} mixed norm. Furthermore, to remove the correlations of the learnt linear transforms, the orthogonalized SSLDA (OSSLDA) is also proposed to learn more subtle textural structure information from face images. To solve both two proposed models: SSLDA and OSSLDA, we further introduce a simply and efficient half-quadratic optimization algorithm, which incorporates an auxiliary variable into the objective function and then alternately optimizes between the projecting variable and the auxiliary variable. To evaluate our proposed method, SSLDA and OSSLDA, we conduct extensive experiments on three public face datasets, AR, Extended Yale B and MultiPIE, for the face recognition task by comparing LDA and its several classical variants. The experimental results show the benefits of the proposed methods on both classification accuracy and interpretability.

Key words: linear discriminant analysis (LDA), orthogonalization, face recognition, least squares, structured sparse

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