Re-weighting Linear Discrimination Analysis under ranking loss

Linear discrimination analysis (LDA) is one of the most popular feature extraction and classifier design techniques. It maximizes the Fisher-ratio between between-class scatter matrix and within-class scatter matrix under a linear transformation, and the transformation is composed of the generalized eigenvectors of them. However, Fisher criterion itself can not decide the optimum norm of transformation vectors for classification. In this paper, we show that actually the norm of the transformation vectors has strong influence on classification performance, and we propose a novel method to estimate the optimum norm of LDA under the ranking loss, re-weighting LDA. On artificial data and real databases, the experiments demonstrate the proposed method can effectively improve the performance of LDA classifiers. And the algorithm can also be applied to other LDA variants such as non parametric discriminant analysis (NDA) to improve theirs performance further.