# Hierarchical clustering with maximum density paths and mixture models

arXiv: https://arxiv.org/abs/2503.15582 · HTML: https://mlsanity.com/paper/2503.15582/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 63 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Are Cluster Validity Measures (In)valid?](https://mlsanity.com/paper/2208.01261/) (2022)
- [Merging K-means with hierarchical clustering for identifying general-shaped groups](https://mlsanity.com/paper/1712.08786/) (2017)
- [Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm](https://mlsanity.com/paper/2302.07045/) (2023)
- [Git: Clustering Based on Graph of Intensity Topology](https://mlsanity.com/paper/2110.01274/) (2021)
- [A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections](https://mlsanity.com/paper/2311.16614/) (2023)
- [UniForCE: The Unimodality Forest Method for Clustering and Estimation of the Number of Clusters](https://mlsanity.com/paper/2312.11323/) (2023)
- [MNIST-Nd: a set of naturalistic datasets to benchmark clustering across dimensions](https://mlsanity.com/paper/2410.16124/) (2024)

## Built on by (most cited first, 1 of 1)

- [On Hamming-Lipschitz Type Stability of the Subdominant (Minmax) Ultrametric: Theory and Simple Proofs](https://mlsanity.com/paper/2608.04014/) (2026)

## Abstract (arXiv)

Hierarchical clustering is an effective, interpretable method for analyzing structure in data. It reveals insights at multiple scales without requiring a predefined number of clusters and captures nested patterns and subtle relationships, which are often missed by flat clustering approaches. However, existing hierarchical clustering methods struggle with high-dimensional data, especially when there are no clear density gaps between modes. In this work, we introduce t-NEB, a probabilistically grounded hierarchical clustering method, which yields state-of-the-art clustering performance on naturalistic high-dimensional data. t-NEB consists of three steps: (1) density estimation via overclustering; (2) finding maximum density paths between clusters; (3) creating a hierarchical structure via bottom-up cluster merging. t-NEB uses a probabilistic parametric density model for both overclustering and cluster merging, which yields both high clustering performance and a meaningful hierarchy, making it a valuable tool for exploratory data analysis. Code is available at https://github.com/ecker-lab/tneb clustering.