Complete local Fisher discriminant analysis with Laplacian score ranking for face recognition

In this paper, we propose a novel manifold learning method, called complete local Fisher discriminant analysis (CLFDA), for face recognition. LFDA often suffers from the small sample size problem, which makes the local within-class scatter matrix singular. In practice, principal component analysis is applied as a preprocessing step to solve this problem. However, this strategy may discard dimensions that contain important discriminative information. The aim of CLFDA is to make full use of two kinds of discriminant information, regular and irregular. At first, CLFDA removes the null space of local within-class scatter to extract the regular discriminant features in the range space of local within-class scatter. Then, the irregular discriminant features are extracted in the null space of local between-class scatter. In addition, we impose Laplacian score to rank the regular and irregular features to achieve the best performance more quickly. Experiments on AT&T, YaleB and CMU PIE face databases are performed to demonstrate the effectiveness of the proposed method.