Revisiting Inaccuracies of Time Series Averaging under Dynamic Time Warping
This work addresses foundational issues in time series analysis for researchers, clarifying misconceptions about averaging accuracy and providing a principled basis for evaluating methods, though it is incremental in refining existing theory.
The paper revisits prior claims about inaccuracies in time series averaging under dynamic time warping, showing that the original correctness-criterion is unsatisfiable and drift-out is inconclusive, and it demonstrates that sample means as Fréchet function minimizers never drift out, with empirical results indicating state-of-the-art methods produce incoherent approximations in over a third of trials.
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 Fréchet 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.