Using Dynamic Time Warping to Bootstrap HMM-Based Clustering of Time Series


Given a source of time series data, there is often utility in determining whether there are qualitatively different regimes in the data and in characterizing those regimes. Hidden Markov models (HMMs) have been demonstrated empirically to be capable of modeling the structure of the generative processes underlying a wide variety of real-world time series. However, existing tools for inducing HMMs from data assume that all of the data are to be fit by a single monolithic model. This paper describes an algorithm for discovering the number of distinct generative processes underlying a set of time series and fitting an HMM to the data associated with each process. An initial partitioning of the time series is created via unsupervised clustering using dynamic time warping (DTW) as a distance metric. These initial clusters serve as input to a process that trains one HMM on each cluster and iteratively moves time series between clusters based on their likelihoods given the various HMMs. A formal analysis of the behavior of the Viterbi algorithm and DTW shows that under certain conditions these algorithms are optimizing the same criterion, leading to an understanding of why the DTW/HMM combination performs well

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