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A new class of entropic information measures, formal group theory and information geometry.

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Rodríguez González, Miguel Ángel and Romaniega, Álvaro and Tempesta, Piergiulio (2019) A new class of entropic information measures, formal group theory and information geometry. Proceedings of the Royal Society A: Mathematical physical and engineering sciences, 475 (2222). ISSN 1364-5021

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Official URL: http://dx.doi.org/10.1098/rspa.2018.0633




Abstract

In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for a large class of entropies. In addition, a method for defining new entropies, using previously known ones with some desired group-theoretical properties is proposed. In the second part of this work, the information geometrical counterpart of the previous construction is examined and a general class of divergences are proposed and studied. Finally, a method of constructing new divergences from known ones is discussed; in particular, some results concerning the Riemannian structure associated with the class of divergences under investigation are formulated.


Item Type:Article
Additional Information:

© 2019 Royal society.
M.A.R. has been partly supported by the research project no. FIS2015-63966, MINECO, Spain. P.T. has been partly supported by the research project FIS2015-63966, MINECO, Spain, by the ICMAT Severo Ochoa grant no. SEV-2015-0554 and by the GNFM, Italy.

Uncontrolled Keywords:Renyi; Sharma
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:55558
Deposited On:07 Jun 2019 16:02
Last Modified:07 Jun 2019 16:02

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