A critical issue of applying Linear (or Fisher) Discriminant Analysis (LDA) is the singularity and instability of the within-class scatter matrix. In practice, particularly in image recognition applications such as face recognition, there are often a large number of pixels or pre-processed features available, but the total number of training patterns is limited and commonly less than the dimension of the feature space. Hence, a considerable amount of effort has been devoted to the design of Fisher-based methods, for targeting limited sample and high dimensional problems. In this paper, a new Fisher-based method is proposed. It is based on a novel regularisation approach for the within-class scatter matrix. In order to evaluate its effectiveness, experiments on face recognition using the well-known ORL and FERET face databases were carried out and compared with similar methods, such as Fisherfaces, Chen et al.'s, Yu and Yang's, and Yang and Yang's LDA-based methods. In both databases, our method improved the LDA classification performance without a PCA intermediate step and using less discriminant features.
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