Revisiting Inaccuracies of Time Series Averaging under Dynamic Time Warping

TL;DR

This paper critically re-evaluates the accuracy of time series averaging under dynamic time warping, challenging previous criteria and demonstrating that state-of-the-art methods often produce incoherent approximations.

Contribution

It clarifies the concept of drift-out, shows that sample means are always coherent, and reveals limitations of current averaging methods in time series analysis.

Findings

Sample means as Fréchet minimizers never drift out.

State-of-the-art methods SSG and DBA often produce incoherent averages.

Rectified correctness criteria are unsatisfiable.

Abstract

This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters. They claimed that averages are inaccurate if they are incorrect or drift-outs. Furthermore, they conjectured that such inaccuracies are caused by the lack of triangle inequality. We show that a rectified version of the correctness-criterion is unsatisfiable and that the concept of drift-out is geometrically and operationally inconclusive. Satisfying the triangle inequality is insufficient to achieve correctness and unnecessary to overcome the drift-out phenomenon. We place the concept of drift-out on a principled basis and show that sample means as global minimizers of a Fr\'echet function never drift out. The adjusted drift-out is a way to test to which extent an approximation is coherent. Empirical results show that solutions obtained by the state-of-the-art methods SSG and DBA are incoherent approximations of a sample mean in over a third of all trials.