Swarms on the 3-sphere for online clustering of multivariate time series and data streams

Abstract

We propose a novel algorithm named SwarmStream for real-time clustering of multivariate time series and data streams. The algorithm is inspired by phenomena of self-organization in complex systems. The data are processed by a swarm whose motions are governed by the system of matrix ordinary differential equations (ODEs) on the matrix group SU(2) with the group manifold S3. Such systems of matrix ODEs are referred to as non-Abelian Kuramoto models in Physics. With each object we associate one generalized oscillator and encode its attributes into the corresponding frequency matrix. The underlying idea is that oscillators with similar frequencies will synchronize their motions due to the internal communication within the swarm. The method is illustrated in several short videos, demonstrating evolution of clusters in some sets of evolving multivariate data.