General Averaged Divergence Analysis

Subspace selection is a powerful tool in data mining. An important subspace method is the Fisher-Rao linear discriminant analysis (LDA), which has been successfully applied in many fields such as biometrics, bioinformatics, and multimedia retrieval. However, LDA has a critical drawback: the projection to a subspace tends to merge those classes that are close together in the original feature space. If the separated classes are sampled from Gaussian distributions, all with identical covariance matrices, then LDA maximizes the mean value of the Kullback-Leibler (KL) divergences between the different classes. We generalize this point of view to obtain a framework for choosing a subspace by 1) generalizing the KL divergence to the Bregman divergence and 2) generalizing the arithmetic mean to a general mean. The framework is named the general averaged divergence analysis (GADA). Under this GADA framework, a geometric mean divergence analysis (GMDA) method based on the geometric mean is studied. A large number of experiments based on synthetic data show that our method significantly outperforms LDA and several representative LDA extensions.