Infinitely exchangeable random graphs generated from a Poisson point process on monotone sets and applications to cluster analysis for networks
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We construct an infinitely exchangeable process on the set of subsets of the power set of the natural numbers N via a Poisson point process with mean measure Λ on the power set of N. Each E∈ has a least monotone cover in , the collection of monotone subsets of , and every monotone subset maps to an undirected graph G∈, the space of undirected graphs with vertex set N. We show a natural mapping →→ which induces an infinitely exchangeable measure on the projective system ^ of graphs under permutation and restriction mappings given an infinitely exchangeable family of measures on the projective system ^ of subsets with permutation and restriction maps. We show potential connections of this process to applications in cluster analysis, machine learning, classification and Bayesian inference.
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