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1 Introduction Time series are a ubiquitous form of data occurring in virtually every scientific discipline and business application. There has been much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time series 7. Debregeas and Hebrail 8 demonstrate a technique for scaling up time series clustering algorithms to massive datasets. Keogh and Pazzani introduced a new, scalable time series classification algorithm 16. Almost all algorithms that operate on time series data need to compute the similarity between them. Euclidean distance, or some extension or modification thereof, is typically used. However as we will demonstrate in Section 2.1, Euclidean distance can be an extremely brittle distance measure.
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