Flattening Multiparameter Hierarchical Clustering Functors
This work addresses clustering challenges in topological data analysis and machine learning, but appears incremental as it builds on existing methods in applied category theory.
The paper tackles the problem of multiparameter hierarchical clustering by introducing a flattening procedure that maps hierarchical partitions to binary integer programs and a Bayesian update algorithm for learning parameters, with empirical results showing its effectiveness.
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.