Bayesian contiguity constrained clustering, spanning trees and dendrograms

Etienne Côme

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arXiv · 2302.12546

Bayesian contiguity constrained clustering, spanning trees and dendrograms

Etienne Côme

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Abstract

Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints i.e. clusters must form connected subgraphs of this graph. This paper discusses the interest of such a setting and proposes a new way to formalise it in a Bayesian setting, using results on spanning trees to compute exactly a posteriori probabilities of candidate partitions. An algorithmic solution is then investigated to find a maximum a posteriori (MAP) partition and extract a Bayesian dendrogram from it. The interest of this last tool, which is reminiscent of the classical output of a simple hierarchical clustering algorithm, is analysed. Finally, the proposed approach is demonstrated with real applications. A reference implementation of this work is available in the R package gtclust that accompanies the paper (available at http://github.com/comeetie/gtclust)

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Etienne Côme. 2023-02-24. Bayesian contiguity constrained clustering, spanning trees and dendrograms. https://arxiv.org/abs/2302.12546

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