Any symmetric affinity function w: V × V → 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 2D lattice. © 2009 Taylor & Francis.

Original language English Pages (from-to) 259-268 Journal Stochastics State Published - Nov 26 2009

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Affine transformation

Metric space

Adjacency Matrix

Vision

Polyhedron

Undirected Graph

Locus

Topological space

Euclidean space

Chain

Metric

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title = "Probabilistic embedding of discrete sets as continuous metric spaces",

abstract = "Any symmetric affinity function w: V × V → 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 2D lattice. {\textcopyright} 2009 Taylor & Francis.",

author = "Ph Blanchard and Dimitri Volchenkov",

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N2 - Any symmetric affinity function w: V × V → 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 2D lattice. © 2009 Taylor & Francis.

AB - Any symmetric affinity function w: V × V → 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 2D lattice. © 2009 Taylor & Francis.

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EP - 268

JO - Stochastics

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