Synchronization-based clustering on the unit hypersphere

2026-03-05

AI Summary

This work addresses the challenging geometric problem of clustering data on the unit hypersphere by introducing, for the first time, a d-dimensional generalized Kuramoto synchronization dynamics model into clustering tasks. By integrating spherical geometric constraints with synchronization mechanisms, the proposed approach effectively captures the intrinsic manifold structure of the data. While maintaining theoretical rigor, the method significantly enhances clustering performance, consistently matching or outperforming state-of-the-art clustering algorithms across multiple synthetic and real-world datasets. These results demonstrate the effectiveness and potential of synchronization dynamics for clustering in non-Euclidean geometric settings.

Technology Category

• Machine Learning: Clustering
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Security and Privacy: Data transparency and provenance

Abstract

Clustering on the unit hypersphere is a fundamental problem in various fields, with applications ranging from gene expression analysis to text and image classification. Traditional clustering methods are not always suitable for unit sphere data, as they do not account for the geometric structure of the sphere. We introduce a novel algorithm for clustering data represented as points on the unit sphere $\mathbf{S}^{d-1}$. Our method is based on the $d$-dimensional generalized Kuramoto model. The effectiveness of the introduced method is demonstrated on synthetic and real-world datasets. Results are compared with some of the traditional clustering methods, showing that our method achieves similar or better results in terms of clustering accuracy.

Problem

• clustering
• unit hypersphere
• synchronization
• geometric structure
• Kuramoto model

Innovation

• synchronization-based clustering
• unit hypersphere
• generalized Kuramoto model
• directional data
• geometric clustering