Sponsor
This work is partly supported by the National Natural Science Foundation of China 61379100 and 61472388
Published In
Mathematical Problems in Engineering
Document Type
Article
Publication Date
12-3-2014
Subjects
Data analysis, Time series analysis
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.
DOI
10.1155/2014/572124
Persistent Identifier
http://archives.pdx.edu/ds/psu/13098
Citation Details
Yin, H., Qi, H., Xu, J., Hung, W. N., & Song, X. (2014). Generalized Framework for Similarity Measure of Time Series. Mathematical Problems in Engineering, 2014.
Description
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.