Kaniadakis's Information Geometry of Compositional Data

Giovanni Pistone; Muhammad Shoaib

doi:10.3390/e25071107

Kaniadakis's Information Geometry of Compositional Data

Entropy (Basel). 2023 Jul 24;25(7):1107. doi: 10.3390/e25071107.

Authors

Giovanni Pistone¹, Muhammad Shoaib²

Affiliations

¹ De Castro Statistics, Collegio Carlo Alberto, 10122 Torino, Italy.
² Department of Mathematics, University of Genoa, 16144 Genova, Italy.

Abstract

We propose to use a particular case of Kaniadakis' logarithm for the exploratory analysis of compositional data following the Aitchison approach. The affine information geometry derived from Kaniadakis' logarithm provides a consistent setup for the geometric analysis of compositional data. Moreover, the affine setup suggests a rationale for choosing a specific divergence, which we name the Kaniadakis divergence.

Keywords: Kaniadakis divergence; Kaniadakis logarithm; affine displacement; affine statistical bundle; barycenter; compositional data; information geometry.

Grants and funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie GA No. 101034449.