Using differential evolution to set weights to segments with different information content in the piecewise aggregate approximation

Time series mining handles several tasks such as classification, clustering and similarity search. These data are high-dimensional in nature so time series representation methods are widely used to reduce the dimensionality of these data so that they can be handled efficiently and effectively. One of the side effects of using representation methods is the loss of information which results from the dimensionality reduction implied in the representation methods. Several representation methods have pointed out that some regions in the times series may contain more information than others so a faithful representation method should be able to reflect the different information contents in different regions of a time series. One of the techniques that can be utilized for this purpose is to set different weights to different regions according to the information they contain, but the challenge is to find an objective scheme to set the weights. Differential evolution is an efficient optimizer that has been successfully used to solve many optimization problems, mainly continuous ones. In this paper we show how differential evolution can be used to set weights to different segments of time series according to their information content. Although our scheme establishes a fully functional time series representation method, with lower bounding distance and a dimensionality reduction technique, we consider this as a by-product of our work and our main aim is to show how the information contents of different time series segments can be reflected using unconventional methods such as the differential evolution. We compare the new scheme with the piecewise aggregate approximation as a method that completely lacks the ability to distinguish regions with high information from others with low information. We show how the new scheme can recover the loss of information caused by dimensionality reduction. We validate our scheme by experiments on different datasets.