# Estimating the number of clusters using cross-validation

arXiv: https://arxiv.org/abs/1702.02658 · HTML: https://mlsanity.com/paper/1702.02658/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2017.

## Built on by (most cited first, 6 of 6)

- [Data thinning for convolution-closed distributions](https://mlsanity.com/paper/2301.07276/) (2023)
- [The cluster structure function](https://mlsanity.com/paper/2201.01222/) (2022)
- [LOBSTUR: A Local Bootstrap Framework for Tuning Unsupervised Representations in Graph Neural Networks](https://mlsanity.com/paper/2505.14867/) (2025)
- [Selecting the number of clusters, clustering models, and algorithms. A unifying approach based on the quadratic discriminant score](https://mlsanity.com/paper/2111.02302/) (2021)
- [Interpretable Outlier Summarization](https://mlsanity.com/paper/2303.06261/) (2023)
- [Number of Clusters in a Dataset: A Regularized K-means Approach](https://mlsanity.com/paper/2505.22991/) (2025)

## Abstract (arXiv)

Many clustering methods, including k-means, require the user to specify the number of clusters as an input parameter. A variety of methods have been devised to choose the number of clusters automatically, but they often rely on strong modeling assumptions. This paper proposes a data-driven approach to estimate the number of clusters based on a novel form of cross-validation. The proposed method differs from ordinary cross-validation, because clustering is fundamentally an unsupervised learning problem. Simulation and real data analysis results show that the proposed method outperforms existing methods, especially in high-dimensional settings with heterogeneous or heavy-tailed noise. In a yeast cell cycle dataset, the proposed method finds a parsimonious clustering with interpretable gene groupings.