A discriminant analysis method for face recognition in heteroscedastic distributions

Linear discriminant analysis (LDA) is a popular method in pattern recognition and is equivalent to Bayesian method when the sample distributions of different classes are obey to the Gaussian with the same covariance matrix. However, in real world, the distribution of data is usually far more complex and the assumption of Gaussian density with the same covariance is seldom to be met which greatly affects the performance of LDA. In this paper, we propose an effective and efficient two step LDA, called LSR-LDA, to alleviate the affection of irregular distribution to improve the result of LDA. First, the samples are normalized so that the variances of variables in each class are consistent, and a pre-transformation matrix from the original data to the normalized one is learned using least squares regression (LSR); second, conventional LDA is conducted on the normalized data to find the most discriminant projective directions. The final projection matrix is obtained by multiply the pre-transformation matrix and the projective directions of LDA. Experimental results on FERET and FRGC ver 2.0 face databases show the proposed LSR-LDA method improves the recognition accuracy over the conventional LDA by using the LSR step.