Separability measures for error estimation of two normally distributed classes

In pattern classification and remote sensing, the Gaussian ML classifier is most widely used because of its speed and robustness. In this paper, we propose to use two separability measures, Bhattacharyya distance and divergence to estimate the classification error of the Gaussian ML classifier. In the proposed method, we try to find empirical relationship between the separability measures and the classification error. In order to find such relationship, we generate two classes with normal distribution and compute the separability measures and classification error between the classes. Although there are infinite number of possibilities that two classes can have, we systematically search the whole mean-covariance space. From this exhaustive search, we are able to estimate the classification error accurately using the Bhattacharyya distance and divergence. It is observed that the error estimation using both the Bhattacharyya distance and divergence does not give a significant improvement over the error estimation using the Bhattacharyya distance only.