Dually flat structure with escort probability and its application to alpha-Voronoi diagrams

This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which well characterizes nonadditive statistics on the space. As a result escort probabilities are proved to be flat coordinates of the usual probabilities for the derived dually flat structure. Finally, we demonstrate that escort probabilities with the new structure admits a simple algorithm to compute Voronoi diagrams and centroids with respect to alpha-divergences. PACS numbers: 05.90.+m, 89.70.Cf, 02.40.Hw ‡ Several results in this paper can be found in the conference paper [36] without complete proofs. Escort Probability and Its Applications via Conformal Transformation 2