Local sparse discriminant analysis for robust face recognition

The Linear Discriminant Analysis (LDA) algorithm plays an important role in pattern recognition. A common practice is that LDA and many of its variants generally learn dense bases, which are not robust to local image distortions and partial occlusions. Recently, the LASSO penalty has been incorporated into LDA to learn sparse bases. However, since the learned sparse coefficients are globally distributed all over the basis image, the solution is still not robust to partial occlusions. In this paper, we propose a Local Sparse Discriminant Analysis (LoSDA) method, which aims at learning discriminant bases that consist of local object parts. In this way, it is more robust than dense or global basis based LDA algorithms for visual classification. The proposed model is formulated as a constrained least square regression problem with a group sparse regularization. Furthermore, we derive a weighted LoSDA (WLoSDA) approach to learn localized basis images, which also enables multi subspace learning and fusion. Finally, we develop an algorithm based on the Accelerated Proximal Gradient (APG) technique to solve the resulting weighted group sparse optimization problem. Experimental results on the FRGC v2.0 and the AR face databases show that the proposed LoSDA and WLoSDA algorithms both outperform the other state-of-the-art discriminant subspace learning algorithms under illumination variations and occlusions.