Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 22, Issue 10, Pages 3904-3915Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2013.2264678
Keywords
Linear discriminant analysis; feature extraction; sparse projections; face recognition
Funding
- Natural Science Foundation of China [61203376, 60973098, 61005005, 61071179, 61125305, 61173104]
- Central Fund from the Hong Kong Polytechnic University
- Fundamental Research Funds for the Central Universities [HIT.NSRIF. 2009130]
- China Postdoctoral Science Foundation [2012M510958]
- Guangdong Natural Science Foundation [S2012040007289]
- Shenzhen Council for Scientific and Technological Innovation [JCYJ20120613134843060]
- Program for New Century Excellent Talents in University [NCET-12-0632]
- Natural Science Foundation of Jiangsu Province [BK2012033, BK2011700]
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The classical linear discriminant analysis has undergone great development and has recently been extended to different cases. In this paper, a novel discriminant subspace learning method called sparse tensor discriminant analysis (STDA) is proposed, which further extends the recently presented multilinear discriminant analysis to a sparse case. Through introducing the L1 and L2 norms into the objective function of STDA, we can obtain multiple interrelated sparse discriminant subspaces for feature extraction. As there are no closed-form solutions, k-mode optimization technique and the L1 norm sparse regression are combined to iteratively learn the optimal sparse discriminant subspace along different modes of the tensors. Moreover, each non-zero element in each subspace is selected from the most important variables/factors, and thus STDA has the potential to perform better than other discriminant subspace methods. Extensive experiments on face databases (Yale, FERET, and CMU PIE face databases) and the Weizmann action database show that the proposed STDA algorithm demonstrates the most competitive performance against the compared tensor-based methods, particularly in small sample sizes.
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