Flattening Multiparameter Hierarchical Clustering Functors

• URL: http://arxiv.org/abs/2104.14734v1
• Date: Fri, 30 Apr 2021 03:10:20 GMT
• Title: Flattening Multiparameter Hierarchical Clustering Functors
• Authors: Dan Shiebler
• Abstract summary: We introduce a procedure for flattening multiparameter hierarchical clusterings. We then introduce a Bayesian update algorithm for learning clustering parameters from data. We demonstrate that the composition of this algorithm with our flattening procedure satisfies a consistency property.
• Score: 1.52292571922932
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We bring together topological data analysis, applied category theory, and machine learning to study multiparameter hierarchical clustering. We begin by introducing a procedure for flattening multiparameter hierarchical clusterings. We demonstrate that this procedure is a functor from a category of multiparameter hierarchical partitions to a category of binary integer programs. We also include empirical results demonstrating its effectiveness. Next, we introduce a Bayesian update algorithm for learning clustering parameters from data. We demonstrate that the composition of this algorithm with our flattening procedure satisfies a consistency property.

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