Time series representation: A random shifting perspective

Abstract

A long standing challenge for time series analysis is to develop representation techniques for dimension reduction while still preserving their fundamental features. As an effective representation technique, Symbolic Aggregate Approximation (SAX) has been widely used for dimension reduction in time series analysis. However, SAX always maps time series data into symbols by definite breakpoints. As a result, the similar points close to the breakpoints cannot be well represented, and thus lead to poor Tightness of Lower Bounds (TLB). To fill this crucial void, in this paper, we develop a time series representation method, named Random Shifting based SAX (rSAX), which has the ability in significantly improving the TLB of representations without increasing the corresponding granularity of representations. Specifically, the key idea of rSAX is to generate a group of breakpoints by random shifting rather than definite breakpoints. Therefore, the points close to each other will have higher probabilities to be mapped into the same symbols, while the points far away from each other will have higher probabilities to be mapped into different symbols. In addition, we also theoretically prove that rSAX can achieve better mapping performances and TLB than SAX. Finally, extensive experiments on several real-world data sets clearly validate the effectiveness and efficiency of the rSAX approach. © 2013 Springer-Verlag Berlin Heidelberg.