Two Dimensional Fisher Discriminant Analysis: Forget About Small Sample Size Problem

Abstract

This paper addresses the small sample size (SSS) problem in linear discriminant analysis (LDA) utilizing a so called 2D Fisher discriminant analysis (2D-FDA) algorithm. As opposed to traditional LDA-based approaches, 2D-FDA is based on 2D image matrices rather than 1D vectors so the image matrix does not need to be transformed into a vector before feature extraction. The between-class scatter and the within-class scatter is constructed using the original image matrices. The advantage arising in this way is that the SSS problem existing in traditional linear discriminant analysis does not occur any more. To test the performance of 2D-FDA with small number of training samples, a series of experiments are conducted on two public databases: ORL and Yale face database B. In both two trials, the 2D-FDA outperforms the other linear subspace methods when there are only very limited training images for each subject.