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Making clustering in delay-vector space meaningful

机译：使延迟向量空间中的聚类有意义

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摘要

Sequential time series clustering is a technique used to extract important features from time series data. The method can be shown to be the process of clustering in the delay-vector space formalism used in the Dynamical Systems literature. Recently, the startling claim was made that sequential time series clustering is meaningless. This has important consequences for a significant amount of work in the literature, since such a claim invalidates these work's contribution. In this paper, we show that sequential time series clustering is not meaningless, and that the problem highlighted in these works stem from their use of the Euclidean distance metric as the distance measure in the delay-vector space. As a solution, we consider quite a general class of time series, and propose a regime based on two types of similarity that can exist between delay vectors, giving rise naturally to an alternative distance measure to Euclidean distance in the delay-vector space. We show that, using this alternative distance measure, sequential time series clustering can indeed be meaningful. We repeat a key experiment in the work on which the "meaningless" claim was based, and show that our method leads to a successful clustering outcome.
机译：顺序时间序列聚类是一种用于从时间序列数据中提取重要特征的技术。该方法可以证明是动态系统文献中使用的延迟向量空间形式主义中的聚类过程。最近，令人吃惊的说法是顺序时间序列聚类是没有意义的。这对文献中的大量工作具有重要的影响，因为这样的主张使这些工作的贡献无效。在本文中，我们表明顺序时间序列聚类不是没有意义的，并且这些工作中突出的问题源于他们使用欧几里得距离度量作为延迟向量空间中的距离度量。作为解决方案，我们考虑了相当通用的时间序列类别，并提出了一种基于可能在延迟向量之间存在的两种相似性的机制，自然地为延迟向量空间中的欧几里得距离提供了一种替代距离度量。我们表明，使用这种替代的距离度量，顺序时间序列聚类确实是有意义的。我们在“无意义”声明所基于的工作中重复了一个关键实验，并证明了我们的方法成功实现了聚类结果。

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