Facial expression recognition using sparse local Fisher discriminant analysis

In this paper, a novel sparse learning method, called sparse local Fisher discriminant analysis (SLFDA) is proposed for facial expression recognition. The SLFDA method is derived from the original local Fisher discriminant analysis (LFDA) and exploits its sparse property. Because the null space of the local mixture scatter matrix of LFDA has no discriminant information, we find the solutions of LFDA in the range space of the local mixture scatter matrix. The sparse solution is obtained by finding the minimum ℓ1ℓ1-norm solution from the LFDA solutions. This problem is then formulated as an ℓ1ℓ1-minimization problem and solved by linearized Bregman iteration, which guarantees convergence and is easily implemented. The proposed SLFDA can deal with multi-modal problems as well as LFDA; in addition, it has more discriminant power than LFDA because the non-zero elements in the basis images are selected from the most important factors or regions. Experiments on several benchmark databases are performed to test and evaluate the proposed algorithm. The results show the effectiveness of SLFDA.