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Mathematical Problems in Engineering
Volume 2015, Article ID 105128, 13 pages
http://dx.doi.org/10.1155/2015/105128
Research Article

Chebyshev Similarity Match between Uncertain Time Series

1School of Information Science and Technology, Donghua University, Shanghai 201620, China
2School of Computer Science and Technology, Donghua University, Shanghai 201620, China
3School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China

Received 27 April 2015; Revised 11 June 2015; Accepted 25 June 2015

Academic Editor: Hamed O. Ghaffari

Copyright © 2015 Wei Wang 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

In real application scenarios, the inherent impreciseness of sensor readings, the intentional perturbation of privacy-preserving transformations, and error-prone mining algorithms cause much uncertainty of time series data. The uncertainty brings serious challenges for the similarity measurement of time series. In this paper, we first propose a model of uncertain time series inspired by Chebyshev inequality. It estimates possible sample value range and central tendency range in terms of sample estimation interval and central tendency estimation interval, respectively, at each time slot. In comparison with traditional models adopting repeated measurements and random variable, Chebyshev model reduces overall computational cost and requires no prior knowledge. We convert Chebyshev uncertain time series into certain time series matrix; therefore noise reduction and dimensionality reduction are available for uncertain time series. Secondly, we propose a new similarity matching method based on Chebyshev model. It depends on overlaps between two sample estimation intervals and overlaps between central tendency estimation intervals from different uncertain time series. At the end of this paper, we conduct an extensive experiment and analyze the results by comparing with prior works.