Group Invariance of Information Geometry on q-Gaussian Distributions Induced by Beta-Divergence

Entropy

Atsumi Ohara¹ 

[1] Department of Electrical and Electronics Engineering, University of Fukui, Fukui 910-8507, Japan

关键词: multivariate q-Gaussian family;    β-divergence;    information geometry;    GL(n;    R);    V-potential;   

DOI  :  10.3390/e15114732

来源: mdpi

【 摘 要 】

We demonstrate that the q-exponential family particularly admits natural geometrical structures among deformed exponential families. The property is the invariance of structures with respect to a general linear group, which transitively acts on the space of positive definite matrices. We prove this property via the correspondence between information geometry induced by a deformed potential on the space and the one induced by what we call β-divergence defined on the q-exponential family with . The results are fundamental in robust multivariate analysis using the q-Gaussian family.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.