On the Generalization of the Mahalanobis Distance

Gabriel Martos, Alberto Muñoz, Javier González

Abstract: The Mahalanobis distance (MD) is a widely used measure in Statistics and Pattern Recognition. Interestingly, assuming that the data are generated from a Gaussian distribution, it considers the covariance matrix to evaluate the distance between a data point and the distribution mean. In this work, we generalize MD for distributions in the exponential family, providing both, a definition in terms of the data density function and a computable version. We show its performance on several artificial and real data scenarios.