Null Space Approach of Fisher Discriminant Analysis for Face Recognition

The null space of the within-class scatter matrix is found to express most discriminative information for the small sample size problem (SSSP). The null space-based LDA takes full advantage of the null space while the other methods remove the null space. It proves to be optimal in performance. From the theoretical analysis, we present the NLDA algorithm and the most suitable situation for NLDA. Our method is simpler than all other null space approaches, it saves the computational cost and maintains the performance simultaneously. Furthermore, kernel technique is incorporated into discriminant analysis in the null space. Firstly, all samples are mapped to the kernel space through a better kernel function, called Cosine kernel, which is proposed to increase the discriminating capability of the original polynomial kernel function. Secondly, a truncated NLDA is employed. The novel approach only requires one eigenvalue analysis and is also applicable to the large sample size problem. Experiments are carried out on different face data sets to demonstrate the effectiveness of the proposed methods.