document: Translation-invariant mixture models for curve clustering In this paper we present a family of algorithms that can simultaneously align and cluster sets of multidimensional curves defined on a discrete time grid . Our approach uses the Expectation-Maximization ( EM ) algorithm to recover both the mean curve shapes for each cluster , and the most likely shifts , offsets , and cluster memberships for each curve . We demonstrate how Bayesian estimation methods can improve the results for small sample sizes by enforcing smoothness in the cluster mean curves . We evaluate the methodology on two real-world data sets , time-course gene expression data and storm trajectory data . Experimental results show that models that incorporate curve alignment systematically provide improvements in predictive power and within-cluster variance on test data sets . The proposed approach provides a non-parametric , computationally efficient , and robust methodology for clustering broad classes of curve data .
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