In recent years Dynamic Time Warping (DTW) has emerged as the distance measure of choice for virtually all time series data mining applications. For example, virtually all applications that process data from wearable devices use DTW as a core sub-routine. This is the result of significant progress in improving DTW’s efficiency, together with multiple empirical studies showing that DTW-based classifiers at least equal (and generally surpass) the accuracy of all their rivals across dozens of datasets. Thus far, most of the research has considered only the one-dimensional case, with practitioners generalizing to the multi-dimensional case in one of two ways, dependent or independent warping. In general, it appears the community believes either that the two ways are equivalent, or that the choice is irrelevant. In this work, we show that this is not the case. The two most commonly used multi-dimensional DTW methods can produce different classifications, and neither one dominates over the other. This seems to suggest that one should learn the best method for a particular application. However, we will show that this is not necessary; a simple, principled rule can be used on a case-by-case basis to predict which of the two methods we should trust at the time of classification. Our method allows us to ensure that classification results are at least as accurate as the better of the two rival methods, and, in many cases, our method is significantly more accurate. We demonstrate our ideas with the most extensive set of multi-dimensional time series classification experiments ever attempted.

中文翻译：

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将DTW泛化为多维情况需要一种自适应方法。

近年来，动态时间规整（DTW）已经成为几乎所有时间序列数据挖掘应用程序选择的距离度量。例如，几乎所有处理可穿戴设备中数据的应用程序都将DTW用作核心子例程。这是在提高DTW效率方面取得的重大进步的结果，再加上多项经验研究表明，基于DTW的分类器在数十个数据集中至少等于（并且通常超过）所有竞争对手的准确性。迄今为止，大多数研究仅考虑一维案例，而从业人员则以依赖或独立两种方式之一将其推广到多维案例。翘曲。通常，社区似乎认为这两种方法是等效的，或者选择是不相关的。在这项工作中，我们证明事实并非如此。两种最常用的多维DTW方法可以产生不同的分类，并且任何一个都不占主导。这似乎表明人们应该为特定应用学习最佳方法。但是，我们将证明这是没有必要的。一个简单的，有原则的规则可以根据具体情况使用，以预测在分类时我们应该信任两种方法中的哪一种。我们的方法使我们能够确保分类结果至少与两种竞争方法中的更好方法一样准确，并且在许多情况下，我们的方法明显更准确。