Exact mean computation in dynamic time warping spaces

Exact Mean Computation in Dynamic Time Warping Spaces

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 Fréchet function) is a challenging computational problem, so far solved by several heuristic, inexact strategies. We spot several inaccuracies in the literature on exact mean computation in dynamic time warp...

On the Existence of a Sample Mean in Dynamic Time Warping Spaces

Though the concept of sample mean in dynamic time warping (DTW) spaces is used in pattern recognition applications, its existence has neither been proved nor called into question. This article shows that a sample mean exists under general conditions that cover common variations of different DTW-spaces mentioned in the literature. The existence proofs are based on a Reduction Theorem that bounds...

Derivative Dynamic Time Warping

Time series are a ubiquitous form of data occurring in virtually every scientific discipline. A common task with time series data is comparing one sequence with another. In some domains a very simple distance measure, such as Euclidean distance will suffice. However, it is often the case that two sequences have the approximately the same overall component shapes, but these shapes do not line up...

shapeDTW: Shape Dynamic Time Warping

Dynamic Time Warping (DTW) is an algorithm to align temporal sequences with possible local non-linear distortions, and has been widely applied to audio, video and graphics data alignments. DTW is essentially a point-to-point matching method under some boundary and temporal consistency constraints. Although DTW obtains a global optimal solution, it does not necessarily achieve locally sensible m...

Dynamic Time Warping Algorithm Review