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Extensions and relationships of some existing lower-bound functions for dynamic time warping

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Abstract

Dynamic time warping (DTW) is a state-of-the-art time series similarity measure method, which warps time axes to match the same shape between two time series with different lengths. However, its quadratic time and space complexity is an obstacle to its applications in the large time series data mining. To address this problem, some lower-bound functions for DTW, fast methods to approximately measure the distance between time series, are used to prune the dissimilar objects from time series database so as to retain the candidates for further measuring their similarity with DTW. So far, the existing lower-bound functions for DTW have been widely accepted for time series similarity search and indexing. In this paper, we propose the extensions of two existing lower-bound functions and discuss the relationships among them. The extensions are improved with high tightness and without much time cost. At the same time, we theoretically prove that these extensions satisfy lower-bound requirement and are better than their old versions respectively. The experimental results demonstrate that in most cases the quality of the proposed extensions of lower-bound functions for DTW outperforms the original versions except for a slightly higher time cost.

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Acknowledgments

This work has been partly supported by the National Natural Science Foundation of China (61300139) and the Society and Science Planning Projects in Fujian (2013C018). We also would like to acknowledge Prof. Eamonn Keogh for the datasets.

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  1. College of Business Administration, Huaqiao University, Quanzhou, 362021, China

    Hailin Li & Libin Yang

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  1. Hailin Li
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  2. Libin Yang
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Correspondence to Hailin Li.

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Li, H., Yang, L. Extensions and relationships of some existing lower-bound functions for dynamic time warping. J Intell Inf Syst 43, 59–79 (2014). https://doi.org/10.1007/s10844-014-0306-7

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