A Novel Distance Matric: Generalized Relative Entropy

Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We presented the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy is presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric.