An Average-Compress Algorithm for the Sample Mean Problem under Dynamic Time Warping

Computing a sample mean of time series under dynamic time warping (DTW) is NP-hard. Consequently, there is an ongoing research effort to devise efficient heuristics. The majority of heuristics have been developed for the constrained sample mean problem that assumes a solution of predefined length. In contrast, research on the unconstrained sample mean problem is underdeveloped. In this article, we propose a generic average-compress (AC) algorithm for solving the unconstrained problem. The algorithm alternates between averaging (A-step) and compression (C-step). The A-step takes an initial guess as input and returns an approximation of a sample mean. Then the C-step reduces the length of the approximate solution. The compressed approximation serves as initial guess of the A-step in the next iteration. The purpose of the C-step is to direct the algorithm to more promising solutions of shorter length. The proposed algorithm is generic in the sense that any averaging and any compression method can be used. Experimental results show that the AC algorithm substantially outperforms current state-of-the-art algorithms for time series averaging.