  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.
