# Temporal Hierarchical Clustering

arXiv: https://arxiv.org/abs/1707.09904 · HTML: https://mlsanity.com/paper/1707.09904/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2017.

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

- [Temporal Panel Selection in Ongoing Citizens' Assemblies](https://mlsanity.com/paper/2602.16194/) (2026)
- [On Hamming-Lipschitz Type Stability of the Subdominant (Minmax) Ultrametric: Theory and Simple Proofs](https://mlsanity.com/paper/2608.04014/) (2026)

## Abstract (arXiv)

We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent sequence of hierarchical clusterings from a sequence of unlabeled point sets. We encode the clustering objective by embedding each point set into an ultrametric space, which naturally induces a hierarchical clustering of the set of points. We enforce temporal coherence among the embeddings by finding correspondences between successive pairs of ultrametric spaces which exhibit small distortion in the Gromov-Hausdorff sense. We present both upper and lower bounds on the approximability of the resulting optimization problems.