Improved discriminate analysis for high-dimensional data and its application to face recognition

Abstract

Many pattern recognition applications involve the treatment of high-dimensional data and the small sample size problem. Principal component analysis (PCA) is a common used dimension reduction technique. Linear discriminate analysis (LDA) is often employed for classification. PCA plus LDA is a famous framework for discriminant analysis in high-dimensional space and singular cases. In this paper, we examine the theory of this framework and find out that even if there is no small sample size problem the PCA dimension reduction cannot guarantee the subsequent successful application of LDA. We thus develop an improved discriminate analysis method by introducing an inverse Fisher criterion and adding a constrain in PCA procedure so that the singularity phenomenon will not occur. Experiment results on face recognition suggest that this new approach works well and can be applied even when the number of training samples is one per class.