The problem of time series anomaly detection has attracted a lot of attention due to its usefulness in various application domains. However, most of the methods proposed so far used Euclidean distance to deal with this problem. Dynamic Time Warping (DTW) distance is more suitable than Euclidean distance because of its capability in shape-based similarity checking in many practical fields, for example those with multimedia data. In this paper, we propose two efficient anomaly detection methods, EP-Leader-DTW and SEP-Leader-DTW, for static and streaming time series under DTW, respectively. Our methods are based on time series segmentation, subsequence clustering, and anomaly scoring. For segmentation, the major extrema method is used to obtain subsequences. For clustering, we apply Leader algorithm to cluster the subsequences along with a lower bounding technique to accelerate DTW distance computation. Experimental results on several benchmark time series datasets reveal that our method for anomaly detection in static time series under DTW can perform very fast and accurately on large time series datasets. For streaming time series, our method can meet the instantaneous requirement with high accuracy. As a result, our anomaly detection methods are applicable to both static and streaming time series in practice.

中文翻译：

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动态时间扭曲下静态和流式时间序列异常检测的高效基于分割的方法

时间序列异常检测问题因其在各种应用领域中的有用性而引起了很多关注。然而，迄今为止提出的大多数方法都使用欧几里德距离来处理这个问题。动态时间规整 (DTW) 距离比欧几里得距离更合适，因为它具有在许多实际领域（例如多媒体数据）中基于形状的相似性检查的能力。在本文中，我们分别针对 DTW 下的静态和流式时间序列提出了两种有效的异常检测方法，EP-Leader-DTW 和 SEP-Leader-DTW。我们的方法基于时间序列分割、子序列聚类和异常评分。对于分割，主要极值方法用于获得子序列。对于聚类，我们应用Leader 算法对子序列进行聚类，并使用下限技术来加速DTW 距离计算。在几个基准时间序列数据集上的实验结果表明，我们在 DTW 下静态时间序列异常检测的方法可以在大型时间序列数据集上非常快速和准确地执行。对于流式时间序列，我们的方法可以以高精度满足瞬时要求。因此，我们的异常检测方法在实践中适用于静态和流式时间序列。我们的方法可以满足高精度的瞬时要求。因此，我们的异常检测方法在实践中适用于静态和流式时间序列。我们的方法可以满足高精度的瞬时要求。因此，我们的异常检测方法在实践中适用于静态和流式时间序列。