Dually flat structure with escort probability and its application to alpha-Voronoi diagrams
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2010
- DOI:
- 10.48550/arXiv.1010.4965
- arXiv:
- arXiv:1010.4965
- Bibcode:
- 2010arXiv1010.4965O
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- Computer Science - Information Theory;
- Mathematics - Differential Geometry
- E-Print:
- Several results in this paper can be found in the conference paper [36] without complete proofs