Time series clustering with ARMA mixtures

Clustering problems are central to many knowledge discovery and data mining tasks. However, most existing clustering methods can only work with fixed-dimensional representations of data patterns. In this paper, we study the clustering of data patterns that are represented as sequences or time series possibly of different lengths. We propose a model-based approach to this problem using mixtures of autoregressive moving average (ARMA) models. We derive an expectation-maximization (EM) algorithm for learning the mixing coefficients as well as the parameters of the component models. To address the model selection problem, we use the Bayesian information criterion (BIC) to determine the number of clusters in the data. Experiments are conducted on a number of simulated and real datasets. Results from the experiments show that our method compares favorably with other methods proposed previously by others for similar time series clustering tasks. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.