A Chernoff-based approach to the estimation of transformation matrices for binary hypothesis testing

Abstract

We present a new method for improving the classificacation score in the problem of binary hypothesis testing where the classes are modeled by a Gaussian mixture. We define a cost function which is based on the Chernoff distance and from it a transformation matrix is estimated that maximizes the separation between the classes. Once defined the cost function we derive an iterative method for which we give a simplified version where one mixture component per class is previously selected to participate in the estimation. The initialization of the method is studied and we give two possibilities for this. One is based on the Bhattacharyya distance and the other is based on the average divergence measure. The experiments are carried out over a database of speech with and without pathology and show that our approach represents an improvement in classification scores over other methods also based on matrix transformation.