A Novel Two-Stage Criterion: Range Space Linear Discriminant Analysis

Linear discriminant analysis (LDA) is one of the most popular methods for feature extraction and dimensionality reduction, but it may encounter the so called small sample size (SSS) problem when applied to high dimensional data analysis such as face recognition. Many two-stage methods were proposed to solve this problem such as Fisherfaces, Direct LDA and Null space LDA, but they are suboptimal from the perspective of optimization. In this paper we propose a novel two-stage discriminant criterion named Range Space LDA, which projects all samples into the range space of between-class scatter matrix in the first stage and then performs traditional LDA. The effectiveness of our method is verified in the experiments on some benchmark face databases.