# Number of Clusters in a Dataset: A Regularized K-means Approach

arXiv: https://arxiv.org/abs/2505.22991 · HTML: https://mlsanity.com/paper/2505.22991/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 29 May 2025.

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

- [Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms](https://mlsanity.com/paper/1612.07925/) (2016)
- [Recovering the number of clusters in data sets with noise features using feature rescaling factors](https://mlsanity.com/paper/1602.06989/) (2016)
- [Estimating the number of clusters using cross-validation](https://mlsanity.com/paper/1702.02658/) (2017)

## Abstract (arXiv)

Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most common formulation of the regularization function is the additive linear term λ k, where k is the number of clusters and λ a positive coefficient. Currently, there are no principled guidelines for setting a value for the critical hyperparameter λ. In this paper, we derive rigorous bounds for λ assuming clusters are em ideal. Ideal clusters (defined as d-dimensional spheres with identical radii) are close proxies for k-means clusters (d-dimensional spherically symmetric distributions with identical standard deviations). Experiments show that the k-means algorithm with additive regularizer often yields multiple solutions. Thus, we also analyze k-means algorithm with multiplicative regularizer. The consensus among k-means solutions with additive and multiplicative regularizations reduces the ambiguity of multiple solutions in certain cases. We also present selected experiments that demonstrate performance of the regularized k-means algorithms as clusters deviate from the ideal assumption.