Synchronization-based clustering on the unit hypersphere

TL;DR

A novel algorithm for clustering data represented as points on the unit sphere $d$-dimensional generalized Kuramoto model is introduced, based on the $d$-dimensional generalized Kuramoto model.

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.

Figures (2)

• Figure 1: Simulation results for the dataset Dat_1 with clusters obtained at time $T=1.27$. The algorithm identified five clusters, including two (Cluster 4 and 5) corresponding to outliers.
• Figure 2: Order parameter during the synchronization process for the dataset Dat_2