# Flattening Multiparameter Hierarchical Clustering Functors

arXiv: https://arxiv.org/abs/2104.14734 · HTML: https://mlsanity.com/paper/2104.14734/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 2 of 2)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Consistency constraints for overlapping data clustering](https://mlsanity.com/paper/1608.04331/) (2016)

## Built on by (most cited first, 2 of 2)

- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2512.03899/) (2025)

## Abstract (arXiv)

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.