Chebyshev Similarity Match between Uncertain Time Series

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.