Revisiting Inaccuracies of Time Series Averaging under Dynamic Time Warping

Brijnesh Jain

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arXiv · 1809.03371

Revisiting Inaccuracies of Time Series Averaging under Dynamic Time Warping

Brijnesh Jain

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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.

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Brijnesh Jain. 2018-09-07. Revisiting Inaccuracies of Time Series Averaging under Dynamic Time Warping. https://arxiv.org/abs/1809.03371

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