Chebyshev Similarity Match between Uncertain Time Series

Wei Wang,Dingjia Liu,Guohua Liu

doi:10.1155/2015/105128

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.

Highlights

Over the past decade, a large amount of continuous sensor data was collected in many applications, such as logistics management, traffic flow management, astronomy, and remote sensing
Unlike traditional similarity matching methods of uncertain time series based on the measurement of distance, we adopt the overlap between sample estimation intervals and that between central tendency estimation intervals to evaluate similarity
We list our contributions as follows: (i) We propose a new model of uncertain time series based on sample estimation interval and central tendency estimation interval derived from Chebyshev inequality and convert Chebyshev uncertain time series into certain time series matrix for dimensionality reduction and noise reduction

Summary

Introduction

A large amount of continuous sensor data was collected in many applications, such as logistics management, traffic flow management, astronomy, and remote sensing. We propose a new model for uncertain time series by combining the two methods above and use descriptive statistics (i.e., central tendency) to resolve the Mathematical Problems in Engineering uncertainty. On this basis, we present an effective matching method to measure the similarity between two uncertain time series, which is adaptive to distinct error distributions. Unlike traditional similarity matching methods of uncertain time series based on the measurement of distance, we adopt the overlap between sample estimation intervals and that between central tendency estimation intervals to evaluate similarity. (iii) We conduct extensive experiments and demonstrate the effectiveness and efficiency of our new method in similarity matching between two uncertain time series

Related Work

Chebyshev Uncertain Time Series Modeling

Uncertain Time Series Preprocessing

Similarity Match Processing

Experimental Validation

Findings

Conclusion