Mixed dissimilarity measure for piecewise linear approximation based time series applications

In recent years, expert systems built around time series-based methods have been enthusiastically adopted in engineering applications, thanks to their ease of use and effectiveness. This effectiveness depends on how precisely the raw data can be approximated and how precisely these approximations can be compared. When performance of a time series-based system needs to be improved, it is desirable to consider other time series representations and comparison methods. The approximation, however, is often generated by a non-replaceable element and eventually the only way to find a more advanced comparison method is either by creating a new dissimilarity measure or by improving the existing one further. In this paper, it is shown how a mixture of different comparison methods can be utilized to improve the effectiveness of a system without modifying the time series representation itself. For this purpose, a novel, mixed comparison method is presented for the widely used piecewise linear approximation (PLA), called mixed dissimilarity measure for PLA (MDPLA). It combines one of the most popular dissimilarity measure that utilizes the means of PLA segments and the authors' previously presented approach that replaces the mean of a segment with its slope. On the basis of empirical studies three advantages of such combined dissimilarity measures are presented. First, it is shown that the mixture ensures that MDPLA outperforms the most popular dissimilarity measures created for PLA segments. Moreover, in many cases, MDPLA provides results that makes the application of dynamic time warping (DTW) unnecessary, yielding improvement not only in accuracy but also in speed. Finally, it is demonstrated that a mixed measure, such as MDPLA, shortens the warping path of DTW and thus helps to avoid pathological warpings, i.e. the unwanted alignments of DTW. This way, DTW can be applied without penalizing or constraining the warping path itself while the chance of the unwanted alignments are significantly lowered. (C) 2015 Elsevier Ltd. All rights reserved.