Synchronization-based clustering on the unit hypersphere

TL;DR

This paper introduces a new clustering algorithm for data on the unit hypersphere based on the generalized Kuramoto model, demonstrating improved accuracy over traditional methods on synthetic and real datasets.

Contribution

A novel hypersphere clustering algorithm leveraging the generalized Kuramoto model, tailored for geometric structure, with demonstrated effectiveness on various datasets.

Findings

Achieves comparable or better accuracy than traditional methods

Effective on both synthetic and real-world datasets

Utilizes geometric structure of the hypersphere

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.