Trajectory clustering with mixtures of regression models

Abstract

In this paper we address the problem of clustering trajectories, namely sets of short sequences of data measured as a function of a dependent variable such as time.Examples include storm path trajectories, longitudinal data such as drug therapy response, functional expression data in computational biology, and movements of objects or individuals in video sequences.Our clustering algorithm is based on a principled method for probabilistic modelhng of a set of trajectories as individual sequences of points generated from a finite mixture model consisting of regression model components.Unsupervised learning is carried out using maximum likelihood principles.Specifically, the EM algorithm is used to cope with the hidden data problem (i.e., the cluster memberships).We also develop generalizations of the method to handle non-parametric (kernel) regression components as well as multi-dimensional outputs.Simulation results comparing our method with other clustering methods such as K-means and Gaussian mixtures are presented as well as experimental results on real data sets.