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Semilocal properties of canonical divergences in dually flat spaces

  • Atsuya KumagaiEmail author
Original Paper Area 1

Abstract

The properties of divergences in dually flat spaces are investigated beyond the local perspective. First, an approximative representation of divergence is shown on the basis of the expansion with respect to relative coordinates. A consideration concerning triangular relation is done from similar perspective and an equation which extends classical multidimensional scaling to incorporate Riemannian metric and affine connection coefficients is obtained. Furthermore, a consideration from a viewpoint of probability distribution is done. The representation of divergence can be regarded as Kullback–Leibler divergence between normal distributions with a common covariance matrix. Especially, it is shown that the asymmetry of divergence arises from the spatial change in differential entropy in those distributions.

Keywords

Information geometry Divergence Dually flat space 

Mathematics Subject Classification

51K05 91C15 94A17 

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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2016

Authors and Affiliations

  1. 1.College of CommerceNihon UniversityTokyoJapan

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