# Interpretable Clustering with the Distinguishability Criterion

arXiv: https://arxiv.org/abs/2404.15967 · HTML: https://mlsanity.com/paper/2404.15967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 48 references that are in the map.
- First posted on arXiv 24 Apr 2024.

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

- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Statistical Significance for Hierarchical Clustering](https://mlsanity.com/paper/1411.5259/) (2014)

## Abstract (arXiv)

Cluster analysis is a popular unsupervised learning tool used in many disciplines to identify heterogeneous sub-populations within a sample. However, validating cluster analysis results and determining the number of clusters in a data set remains an outstanding problem. In this work, we present a global criterion called the Distinguishability criterion to quantify the separability of identified clusters and validate inferred cluster configurations. Our computational implementation of the Distinguishability criterion corresponds to the Bayes risk of a randomized classifier under the 0-1 loss. We propose a combined loss function-based computational framework that integrates the Distinguishability criterion with many commonly used clustering procedures, such as hierarchical clustering, k-means, and finite mixture models. We present these new algorithms as well as the results from comprehensive data analysis based on simulation studies and real data applications.