Exact Mean Computation in Dynamic Time Warping Spaces

TL;DR

This paper introduces an exact dynamic programming method for computing the mean of time series in dynamic time warping spaces, providing a benchmark and revealing limitations of existing heuristics.

Contribution

It presents the first exact dynamic program for mean computation in DTW spaces and analyzes properties and heuristic performance.

Findings

Exact dynamic program outperforms heuristics in quality

Identifies issues with existing heuristic methods

Provides polynomial-time algorithm for binary time series

Abstract

Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fr\'echet function) is a challenging computational problem, so far solved by several heuristic and inexact strategies. We spot some inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Our contributions comprise an exact dynamic program computing a mean (useful for benchmarking and evaluating known heuristics). Based on this dynamic program, we empirically study properties like uniqueness and length of a mean. Moreover, experimental evaluations reveal substantial deficits of state-of-the-art heuristics in terms of their output quality. We also give an exact polynomial-time algorithm for the special case of binary time series.