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

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-bysample 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. Key-Words: Learning algorithm, Chernoff bound, transformation matrix, cost function, Gaussian mixture models