Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

Abstract

Any symmetric affinity function $w:V\times V\to {\mathbb{R}}_{+}$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron, and a finite 2-dimensional lattice.

13 pages, 7 figures, conference "Stochastic Analysis and Applications", 5-10 November 2007 Hammamet, Tunis