# Consistency constraints for overlapping data clustering

arXiv: https://arxiv.org/abs/1608.04331 · HTML: https://mlsanity.com/paper/1608.04331/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2016.

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

- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [Flattening Multiparameter Hierarchical Clustering Functors](https://mlsanity.com/paper/2104.14734/) (2021)

## Abstract (arXiv)

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in the context of metric spaces with non-expansive maps, which is appropriate for modeling data processing which does not increase information content.