An extension of the Chernoff-based transformation matrix estimation method for on-line learning in Bayesian binary hypothesis tests

Abstract

In a previous paper [8] we have proposed a method to improve the classification between two classes in a new transformed space using the Chernoff similarity measure. The key idea is to estimate a transformation matrix such that the overlap between the pdf associated to the competing classes is minimum thus leading to a minimization of the classification error. Starting from a surrogate cost function we review the previous method from the consideration that in many practical applications the (online) learning examples come in a sample-by-sample manner instead of a batch manner. Then we propose a new formulation of the learning algorithm in online mode and we derive the corresponding formulation. We arrive to iterative formulations of the estimation processes. The classes are modeled by a Gaussian mixture model with a varying number of components and we investigate the new method for several dimensionalities of the transformed subspace. The experiments are carried out over a database of speech with and without pathology and we show that the performance of the online approach compares favorably with respect to the batch mode and outperforms some reference methods.