Mining Naturally Smooth Evolution of Clusters from Dynamic Data

Many clustering algorithms have been proposed to partition a set of static data points into groups. In this paper, we consider an evolutionary clustering problem where the input data points may move, disappeare, and emerge. Generally, these changes should result in a smooth evolution of the clusters. Mining this naturally smooth evolution is valuable for providing an aggregated view of the numerous individual behaviors. We solve this novel and generalized form of clustering problem by converting it into a Bayesian learning problem. Analogous to that the EM clustering algorithm clusters static data points by learning a Gaussian mixture model, our method mines the evolution of clusters from dynamic data points by learning a hidden semi-Markov model (HSMM). By utilizing characteristics of the evolutionary clustering problem, we derive a new unsupervised learning algorithm which is much more efficient than the algorithms used to learn traditional variable-duration HSMMs. Because the HSMM models the probabilistic relationship between the dynamic data set and corresponding evolving clusters, we can interpret the learned parameters as the evolving clusters intuitively using the Viterbi filtering technique. Because learning an HSMM is in fact learning an optimal Viterbi filter, the learned cluster evolutions are smooth and fit well with the data. We demonstrate the effectiveness of this method by experiments on both synthetic data and real data.