An extended formula for divergence measures using invariance

The f-divergence, which is defined by using a class of convex functions, is used as a generalized phenotype of discriminant measures between two probability distributions. In this paper, we derive a new class of discriminant measures defined on the set of all positive finite measures using the invariance of the f-divergence. This is a class of discriminant measures different from ones which have often been used. We mention some aspects of its effectiveness concerning the extension of discriminant measures by showing that the proposed class includes measures that facilitate statistical data processing and are suitable for the explicit formulation and analysis of the ensemble learning method.