Optimal Dimensionality Discriminant Analysis and Its Application to Image Recognition

Dimensionality reduction is an important issue when facing high-dimensional data. For supervised dimensionality reduction, linear discriminant analysis (LDA) is one of the most popular methods and has been successfully applied in many classification problems. However, there are several drawbacks in LDA. First, it suffers from the singularity problem, which makes it hard to preform. Second, LDA has the distribution assumption which may make it fail in applications where the distribution is more complex than Gaussian. Third, LDA can not determine the optimal dimensionality for discriminant analysis, which is an important issue but has often been neglected previously. In this paper, we propose a new algorithm and endeavor to solve all these three problems. Furthermore, we present that our method can be extended to the two-dimensional case, in which the optimal dimensionalities of the two projection matrices can be determined simultaneously. Experimental results show that our methods are effective and demonstrate much higher performance in comparison to LDA.