Regularized complete linear discriminant analysis

Linear discriminant analysis (LDA) searches for a linear transformation that maximizes class separability in a reduced dimensional space. Because LDA requires the within-class scatter matrix to be non-singular, it cannot be directly applied to small sample size (SSS) problems in which the number of available training samples is smaller than the dimensionality of the sample space. To solve SSS problems, this paper develops a system of regularized complete linear discriminant analysis (RCLDA). In RCLDA, two regularized criteria are used to derive discriminant vectors that include “regular” and “irregular” discriminant vectors in the range space and null space, respectively, of the within-class scatter matrix. Extensive experiments on the SSS problem of image recognition are performed to evaluate the proposed algorithm in terms of classification accuracy, and the experimental results demonstrate its effectiveness.