# Rethinking Divisive Hierarchical Clustering from a Distributional Perspective

arXiv: https://arxiv.org/abs/2601.19718 · HTML: https://mlsanity.com/paper/2601.19718/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [Hierarchical Clustering via Spreading Metrics](https://mlsanity.com/paper/1610.09269/) (2016)
- [Scalable Hierarchical Agglomerative Clustering](https://mlsanity.com/paper/2010.11821/) (2020)
- [Objective-Based Hierarchical Clustering of Deep Embedding Vectors](https://mlsanity.com/paper/2012.08466/) (2020)
- [Foundations of Comparison-Based Hierarchical Clustering](https://mlsanity.com/paper/1811.00928/) (2018)
- [Nearly-Optimal Hierarchical Clustering for Well-Clustered Graphs](https://mlsanity.com/paper/2306.09950/) (2023)
- [Point-Set Kernel Clustering](https://mlsanity.com/paper/2002.05815/) (2020)
- [An Objective for Hierarchical Clustering in Euclidean Space and its Connection to Bisecting K-means](https://mlsanity.com/paper/2008.13235/) (2020)
- [A novel brain partition highlights the modular skeleton shared by structure and function](https://mlsanity.com/paper/1410.7959/) (2014)
- [Hierarchical clustering that takes advantage of both density-peak and density-connectivity](https://mlsanity.com/paper/1810.03393/) (2018)

## Abstract (arXiv)

We uncover that current objective-based Divisive Hierarchical Clustering (DHC) methods produce a dendrogram that does not have three desired properties i.e., no unwarranted splitting, group similar clusters into a same subset, ground-truth correspondence. This shortcoming has their root cause in using a set-oriented bisecting assessment criterion. We show that this shortcoming can be addressed by using a distributional kernel, instead of the set-oriented criterion; and the resultant clusters achieve a new distribution-oriented objective to maximize the total similarity of all clusters (TSC). Our theoretical analysis shows that the resultant dendrogram guarantees a lower bound of TSC. The empirical evaluation shows the effectiveness of our proposed method on artificial and Spatial Transcriptomics (bioinformatics) datasets. Our proposed method successfully creates a dendrogram that is consistent with the biological regions in a Spatial Transcriptomics dataset, whereas other contenders fail.