Modeling and Clustering of Human Sleep Time Series Using Dynamic Time Warping: Sequential and Distributed Implementations

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We present a new modified dynamic time warping approach for comparing discrete time series that reduces over-warping and maintains the efficiency of global path constraint approaches, without relying on domain-specific heuristics. In a first version, global weighted dynamic time warping, a penalty term for the deviation between the warping path and the path of constant slope is added in a post-processing step, after a standard dynamic time warping computation. A second version, stepwise deviation-based dynamic time warping, incorporates the penalty term into the dynamic programming optimization itself, yielding modified optimal warping paths. Both versions yield modified similarity metrics that we use for time series clustering within the Combined Dynamical Modeling Clustering (CDMC) framework. Additionally, we present a distributed computing implementation of dynamic time warping-based modeling and clustering using CDMC. Experiments over synthetic data, as well as over human sleep data, demonstrate significantly improved accuracy and generative log likelihood as compared with standard dynamic time warping. The distributed computing implementation achieves a reduction in processing time.