Valid Discriminative Null-Space for Pattern Classification

Linear discriminant analysis (LDA) cannot be directly applied to Small sample size problem (SSS problem). A new approach called Valid discriminative nullspace (VDNS) based on a variation of Fisher's LDA for the small sample size case is proposed. We revealed the physical meaning of the null spaces of the total scatter matrix and the within-class scatter matrix. We also analyzed the relationships of between-class scatter matrix of three subspaces: the valid subspace, the valid null space, and the valid discriminative null-space. This provides the new approach of subspace analysis-VDNS. VDNS method can project data on a lower dimensional subspace which contains valid discriminative information. Experimental results on different data sets showed that the VDNS method is superior to other relative methods in terms of recognition accuracy, robust and efficiency.