动态时间弯曲下时间序列平均的不准确性
Revisiting Inaccuracies of Time Series Averaging under Dynamic Time Warping
摘要：
本文回顾了\cite{Niennattrakul2007}对动态时间弯曲下时间序列平均误差的分析。作者提出了一个正确的标准，并介绍了漂移的平均值从集群。他们声称，如果平均值不正确或漂移，那么平均值就是不准确的。此外，他们还指出，这种不准确性是由于缺乏三角不等式造成的。我们表明，纠正版本的正确性标准是不可满足的，漂移的概念是几何和操作不确定的。满足三角不等式不足以达到正确性，也不需要克服漂移现象。我们将漂移的概念置于原则性的基础上，并表明作为Fréchet函数的全局最小值的样本均值永远不会漂移。调整后的漂移是一种测试近似一致程度的方法。实证结果表明，解决方案获得的国家的最先进的方法SSG和DBA是不相干的近似样本均值在超过三分之一的所有试验。
英文摘要：
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.
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