Extracting the optimal dimensionality for discriminant analysis

For classification task, supervised dimensionality reduction is a very important method when facing with high-dimensional data. Linear Discriminant Analysis(LDA) is one of the most popular method for supervised dimensionality reduction. However, LDA suffers from the singularity problem, which makes it hard to work. Another problem is the determination of optimal dimensionality for discriminant analysis, which is an important issue but often been neglected previously. In this paper, we propose a new algorithm to address these two problems. Experiments show the effectiveness of our method and demonstrate much higher performance in comparison to LDA.