A new regularized linear discriminant analysis method to solve small sample size problems

This paper presents a new regularization technique to deal with the small sample size (S3) problem in linear discriminant analysis (LDA) based face recognition. Regularization on the within-class scatter matrix S _w has been shown to be a good direction for solving the S3 problem because the solution is found in full space instead of a subspace. The main limitation in regularization is that a very high computation is required to determine the optimal parameters. In view of this limitation, this paper re-defines the three-parameter regularization on the within-class scatter matrix S _w ^αβγ, which is suitable for parameter reduction. Based on the new definition of S _w ^αβγ we derive a single parameter (t) explicit expression formula for determining the three parameters and develop a one-parameter regularization on the within-class scatter matrix. A simple and efficient method is developed to determine the value of t. It is also proven that the new regularized within-class scatter matrix S _w ^αβγ approaches the original within-class scatter matrix S _w as the single parameter tends to zero. A novel one-parameter regularization linear discriminant analysis (1PRLDA) algorithm is then developed. The proposed 1PRLDA method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. The average recognition accuracies of 50 runs for ORL and FERET databases are 96.65% and 94.00%, respectively. Comparing with existing LDA-based methods in solving the S3 problem, the proposed 1PRLDA method gives the best performance.