Weighted pairwise scatter to improve linear discriminant analysis

Linear Discriminant Analysis (LDA) aims to transform an original feature space to a lower dimensional space with as little loss in discrimination as possible. We introduce a novel LDA matrix computation that incorporates confusability information between classes into the transform. Our goal is to improve discrimination in LDA. In conventional LDA, a between class covariance matrix that is based on the scatter of class means around the global mean is used. By rewriting the between class covariance expression in a more revealing way, we unveil that each class pair is considered equally confusable in the conventional LDA. We introduce a weighting factor for each pairwise scatter that enables to integrate the confusability information into the between class covariance matrix. There are many possibilities to choose the weighting factors. We consider few of them that depend on Euclidean and Kullback-Leibler distances between classes when a single Gaussian approximation is used for each class. The method combined with speaker cluster based transformation decreases the error rate by about relative 10% on a large vocabulary speech recognition task using IBM's speech recognition engine.