Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

Details Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

2008-04-28

arxiv.org/abs/0804.4434v1

Physics

Mathematical Physics

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

Scientific paper

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.

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