Uncorrelated trace ratio linear discriminant analysis for undersampled problems

Abstract

For linear discriminant analysis (LDA), the ratio trace and trace ratio are two basic criteria generalized from the classical Fisher criterion function, while the orthogonal and uncorrelated constraints are two common conditions imposed on the optimal linear transformation. The ratio trace criterion with both the orthogonal and uncorrelated constraints have been extensively studied in the literature, whereas the trace ratio criterion receives less interest mainly due to the lack of a closed-form solution and efficient algorithms. In this paper, we make an extensive study on the uncorrelated trace ratio linear discriminant analysis, with particular emphasis on the application on the undersampled problem. Two regularization uncorrelated trace ratio LDA models are discussed for which the global solutions are characterized and efficient algorithms are established. Experimental comparison on several LDA approaches are conducted on several real world datasets, and the results show that the uncorrelated trace ratio LDA is competitive with the orthogonal trace ratio LDA, but is better than the results based on ratio trace criteria in terms of the classification performance.