Particle Clustering Machine: A Dynamical System Based Approach

TL;DR

This paper introduces a deterministic clustering method based on dynamical systems theory that identifies clusters without predefining their number, offering stable and theoretically grounded results.

Contribution

A novel dynamical systems approach to clustering that is deterministic, does not require specifying the number of clusters, and is grounded in interaction potential theory.

Findings

Deterministic clustering results consistent across multiple runs

No need to predefine the number of clusters

Outperforms some existing methods in simulations

Abstract

Identification of the clusters from an unlabeled data set is one of the most important problems in Unsupervised Machine Learning. The state of the art clustering algorithms are based on either the statistical properties or the geometric properties of the data set. In this work, we propose a novel method to cluster the data points using dynamical systems theory. After constructing a gradient dynamical system using interaction potential, we prove that the asymptotic dynamics of this system will determine the cluster centers, when the dynamical system is initialized at the data points. Most of the existing heuristic-based clustering techniques suffer from a disadvantage, namely the stochastic nature of the solution. Whereas, the proposed algorithm is deterministic, and the outcome would not change over multiple runs of the proposed algorithm with the same input data. Another advantage of the proposed method is that the number of clusters, which is difficult to determine in practice, does not have to be specified in advance. Simulation results with are presented, and comparisons are made with the existing methods.