A new class of entropic information measures, formal group theory and information geometry. (6th February 2019)

• Record Type: Journal Article
• Authors: Rodríguez, Miguel Á.; Romaniega, Álvaro; Tempesta, Piergiulio
• Is Part Of: Proceedings. Volume 475:Number 2222(2019)
• Publication Date: 2019-02-06
• Subjects: entropic measures -- formal groups -- information geometry -- divergences; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2018.0633
• Languages: English
• ISSNs: 1364-5021

Abstract

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.