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 l1 penalty. Experiments on Yale, ORL, and CMU PIE face databases are implemented to demonstrate the effectiveness of the proposed method.
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