Clustering algorithm based on molecular dynamics with nose-hoover thermostat. Application to Japanese candlesticks

Abstract

A hybrid pattern clustering algorithm connecting Particle Swarm Optimization with Simulated Annealing is proposed. The swarm particles are directly associated with the centroids of each cluster. They are assumed to move in the phase space associated under the influence of a potential generated by each pattern to be partitioned and interacting with each other. Thus, the problem of partitioning acquires a direct physical interpretation. The motion of swarm particles is simulated with the help of a thermal bath represented by one additional dynamical variable within the Nose-Hoover formalism. The temperature is decreased at each step in the dynamics of the swarm providing the resemblance to the Simulated Annealing. Clustering of the Japanese candlesticks which appear in the dynamics of assets in the Warsaw stock market is used as an example.