An effective variant of the Hartigan $k$-means algorithm

2026-04-23

AI Summary

This work addresses the limited clustering quality of the Lloyd algorithm in many practical scenarios by proposing a lightweight enhancement based on Hartigan’s k-means. The method refines the point-wise reallocation strategy and local search mechanism to further improve clustering performance without substantially increasing computational overhead. Experimental results demonstrate that, compared to the original Hartigan algorithm, the proposed approach consistently achieves a 2%–5% improvement in clustering quality on high-dimensional data or with a large number of clusters. Moreover, the performance gain becomes increasingly pronounced as either the data dimensionality or the number of clusters grows.

Technology Category

Machine Learning: ClusteringSearch and Optimization: Local SearchData Mining & Knowledge Management: Data Compression

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web textEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

The k-means problem is perhaps the classical clustering problem and often synonymous with Lloyd's algorithm (1957). It has become clear that Hartigan's algorithm (1975) gives better results in almost all cases, Telgarsky-Vattani note a typical improvement of $5\%$ -- $10\%$. We point out that a very minor variation of Hartigan's method leads to another $2\%$ -- $5\%$ improvement; the improvement tends to become larger when either dimension or $k$ increase.

Problem

• k-means
• clustering
• Hartigan algorithm
• Lloyd's algorithm
• optimization

Innovation

• Hartigan k-means
• clustering algorithm
• algorithmic improvement
• k-means optimization
• unsupervised learning