K*-Means: A Parameter-free Clustering Algorithm

2025-05-17

AI Summary

Clustering typically requires pre-specifying the number of clusters $k$ or relies on user-defined thresholds, limiting its automation and robustness. To address this, we propose $k^*$-means, the first fully parameter-free variant of $k$-means that adaptively determines the optimal number of clusters $k^*$ within the $k$-means framework. Leveraging the Minimum Description Length (MDL) principle, $k^*$-means jointly optimizes both $k^*$ and clustering quality via a provably convergent split-merge mechanism that dynamically evolves the cluster structure. The algorithm is theoretically guaranteed to converge without any hyperparameters. Extensive experiments demonstrate that $k^*$-means significantly outperforms state-of-the-art methods in scenarios where $k$ is unknown: it achieves high accuracy in $k$ estimation, superior clustering quality (e.g., adjusted Rand index, normalized mutual information), and maintains favorable time efficiency and scalability on large-scale datasets.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations

Abstract

Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a novel clustering algorithm that eliminates the need to set k or any other parameters. Instead, it uses the minimum description length principle to automatically determine the optimal number of clusters, k*, by splitting and merging clusters while also optimising the standard k-means objective. We prove that k*-means is guaranteed to converge and demonstrate experimentally that it significantly outperforms existing methods in scenarios where k is unknown. We also show that it is accurate in estimating k, and that empirically its runtime is competitive with existing methods, and scales well with dataset size.

Problem

• Eliminates need to specify cluster count k
• Automatically determines optimal clusters k*
• Outperforms methods when k is unknown

Innovation

• Parameter-free clustering using MDL principle
• Automatically determines optimal cluster count
• Competitive runtime and scalability performance