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Isometric Invariant Quantification of Gaussian Divergence over Poincare Disc

Levent Ali Mengütürk

Abstract

The paper presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group. Motivated by the geometric connection, we propose the usage of the L2-embedded hyperbolic isometric invariant as an alternative way to quantify divergence between Gaussian measures as a contribution to information theory.

Isometric Invariant Quantification of Gaussian Divergence over Poincare Disc

Abstract

The paper presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group. Motivated by the geometric connection, we propose the usage of the L2-embedded hyperbolic isometric invariant as an alternative way to quantify divergence between Gaussian measures as a contribution to information theory.
Paper Structure (3 sections, 2 theorems, 30 equations)

This paper contains 3 sections, 2 theorems, 30 equations.

Table of Contents

  1. Introduction
  2. Geometric Duality
  3. Conclusion

Key Result

Proposition 2.5

The divergence (measuretheorticexp) on $\mathbb{R}$ is given by where $\lambda(.)$ in (closedform) is defined as follows: Hence, the conditions in (connectionformalised) materialize when

Theorems & Definitions (8)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Proposition 2.5
  • proof
  • Example 2.6
  • Corollary 2.7