Flattening Multiparameter Hierarchical Clustering Functors

2021/04/30 by Dan Shiebler, Shiebler, Dan · 1 citation
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #cs.AI #cs.LG

paper · pdf · doi:10.48550/arxiv.2104.14734

arxiv created 2021/04/30 · arxiv updated 2021/05/03

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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