# Dendrogram of mixing measures: Hierarchical clustering and model selection for finite mixture models

arXiv: https://arxiv.org/abs/2403.01684 · HTML: https://mlsanity.com/paper/2403.01684/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Builds on (most cited first, 3 of 3)

- [Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Models](https://mlsanity.com/paper/2202.08786/) (2022)
- [Finite mixture models do not reliably learn the number of components](https://mlsanity.com/paper/2007.04470/) (2020)
- [Bayesian Clustering via Fusing of Localized Densities](https://mlsanity.com/paper/2304.00074/) (2023)

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

- [Model Selection for Gaussian-gated Gaussian Mixture of Experts Using Dendrograms of Mixing Measures](https://mlsanity.com/paper/2505.13052/) (2025)

## Abstract (arXiv)

We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and mixture modeling. The dendrogram's construction is derived from the theory of convergence of the mixing measures, and as a result, we can both consistently select the true number of mixing components and obtain the pointwise optimal convergence rate for parameter estimation from the tree, even when the model parameters are only weakly identifiable. In theory, it explicates the choice of the optimal number of clusters in hierarchical clustering. In practice, the dendrogram reveals more information on the hierarchy of subpopulations compared to traditional ways of summarizing mixture models. Several simulation studies are carried out to support our theory. We also illustrate the methodology with an application to single-cell RNA sequence analysis.