Information Geometry and Its Applications: An Overview

Critchley, Frank and Marriott, Paul (2016). Information Geometry and Its Applications: An Overview. In: Nielsen, Frank; Critchley, Frank and Dodson, Christopher T. J. eds. Computational Information Geometry: For Image and Signal Processing. Signals and Communication Technology. Cham: Springer, pp. 1–31.

DOI: https://doi.org/10.1007/978-3-319-47058-0_1

Abstract

We give a personal view of what Information Geometry is, and what it is becoming, by exploring a number of key topics: dual affine families, boundaries, divergences, tensorial structures, and dimensionality. For each, we start with a graphical illustrative example (Sect. 1.1), give an overview of the relevant theory and key references (Sect. 1.2), and finish with a number of applications of the theory (Sect. 1.3). We treat ‘Information Geometry’ as an evolutionary term, deliberately not attempting a comprehensive definition. Rather, we illustrate how both the geometries used and application areas are rapidly developing.

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