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Mathematical Problems in Engineering
Volume 2014, Article ID 572124, 12 pages
http://dx.doi.org/10.1155/2014/572124
Research Article

Generalized Framework for Similarity Measure of Time Series

1China University of Mining and Technology, Xuzhou 221116, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
4Synopsys Inc., Mountain View, CA 94043, USA
5Portland State University, Portland, OR 97207, USA

Received 9 July 2014; Revised 10 October 2014; Accepted 13 October 2014; Published 3 November 2014

Academic Editor: Yan Liang

Copyright © 2014 Hongsheng Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Currently, there is no definitive and uniform description for the similarity of time series, which results in difficulties for relevant research on this topic. In this paper, we propose a generalized framework to measure the similarity of time series. In this generalized framework, whether the time series is univariable or multivariable, and linear transformed or nonlinear transformed, the similarity of time series is uniformly defined using norms of vectors or matrices. The definitions of the similarity of time series in the original space and the transformed space are proved to be equivalent. Furthermore, we also extend the theory on similarity of univariable time series to multivariable time series. We present some experimental results on published time series datasets tested with the proposed similarity measure function of time series. Through the proofs and experiments, it can be claimed that the similarity measure functions of linear multivariable time series based on the norm distance of covariance matrix and nonlinear multivariable time series based on kernel function are reasonable and practical.