Study and analysis of temporal data using Hidden Markov models

In this paper we have developed a method for dividing a set of temporal data into clusters by using Hidden Markov Models. Given a number of clusters, each cluster is represented by one Hidden Markov Model. In order to determine the optimal number of clusters and the consistency of their structures, this approach defines an objective function based on the calculation of likelihood. The algorithm is presented in terms of four nested levels of searches: (1) the search for the optimal number of clusters in a partition, (2) the search for the optimal structure for a given partition, (3) the search for the optimal HMM structure for each cluster, and (4) the search for the optimal HMM parameters for each HMM. Preliminary results are given to support the proposed methodology.