Study on the Essence of Optimal Statistically Uncorrelated Discriminant Vectors and Its Application to Face Recognition

A study has been made on the essence of optimal uncorrelated discriminant vectors. A whitening transform has been constructed by means of the eigen decomposition of the population scatter matrix, which makes the population scatter matrix be an identity matrix in the transformed sample space no matter whether the population scatter matrix is singular or not. Thus, the optimal discriminant vectors solved by the conventional linear discriminant analysis (LDA) methods are statistically uncorrelated. The research indicates that the essence of the statistically uncorrelated discriminant transform is the whitening transform plus conventional linear discriminant transform. The distinguished characteristics of the proposed method is that the obtained optimal discriminant vectors are not only orthogonal but also statistically uncorrelated. The proposed method is applicable to all the problems of algebraic feature extraction. The numerical experiments on several facial databases show the effectiveness of the proposed method.