  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.
