Geometry and clustering with metrics derived from separable Bregman divergences

TL;DR

This paper explores the geometric properties of separable Bregman divergences, demonstrating their Euclidean isometry after embeddings, and evaluates clustering algorithms based on these Riemann-Bregman distances through experiments.

Contribution

It introduces the geometric framework of Riemann-Bregman distances and assesses clustering methods using these metrics, highlighting their practical performance.

Findings

Riemann-Bregman spaces are isometric to Euclidean space after embeddings

Partition-based, hierarchical, and soft clustering algorithms perform effectively with these distances

Experimental results show competitive clustering performance using Riemann-Bregman metrics

Abstract

Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental performances of partition-based, hierarchical, and soft clustering algorithms with respect to these Riemann-Bregman distances.