Affiliations: [a] School of Information Engineering, Zhengzhou University, Zhengzhou 450001, Henan, China | [b] Deparment of Computer Science, University of Maryland, Baltimore County, MD 21250, USA | [c] School of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450046, Henan, China
Correspondence:
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Corresponding author: Wei Song, School of Information Engineering, Zhengzhou University, Zhengzhou 450001, Henan, China. E-mail:iewsong@zzu.edu.cn
Note: [1] These authors contribute equally.
Abstract: Symbolic Aggregate approximation (SAX) has been the de facto standard representation methods for knowledge
discovery in time series on a number of tasks and applications. So far, very little work has been done in empirically investigating the intrinsic properties and statistical mechanics in SAX words. In this paper, we applied several statistical measurements and proposed a new statistical measurement, i.e. information embedding cost (IEC) to analyze the statistical behaviors of the symbolic dynamics. Our experiments on the benchmark datasets and the clinical signals demonstrate that SAX can always reduce the complexity while preserving the core information embedded in the original time series with significant embedding efficiency, as well as robust to missing values and noise. Our proposed IEC score provide a priori to determine if SAX is adequate for specific dataset, which can be generalized to evaluate other symbolic representations. Our work provides an analytical framework with several statistical tools to analyze, evaluate and further improve the symbolic dynamics for knowledge discovery in time series.
Keywords: SAX, knowledge discovery in time series, information embedding cost, permutation entropy, symbolic complexity
