A novel shape-based averaging algorithm for time series

Abstract

Time series averaging is one of the essential subroutines in time series analysis. DTW Barycenter Averaging (DBA) has proven to be an effective and popular DTW-based time series averaging algorithm. However, DBA lacks the ability to average time series in the time domain, making it sensitive to initialization. In this research, we propose a novel shape-based time series averaging algorithm, called Shape DTW Weighted Averaging (ShapeDWA), to address the shortcomings of DBA. The proposed ShapeDWA algorithm combines the advantages of the DBA and the Cubic-spline DTW (CDTW) averaging methods. The concepts of time index averaging and re-sampling in the CDTW algorithm are incorporated into the DBA algorithm, giving ShapeDWA the ability to average a set of time series in both the amplitude and time domains. Moreover, ShapeDWA utilizes a weighed average instead of the barycenter average in DBA, which effectively attenuate the effects of noise, outliers, and local amplitude differences between the time series. To qualitatively evaluate and compare the proposed time series averaging algorithm, two metrics have been developed: average discrepancy distance and average time distortion. Extensive experimental results on the UCR time series database illustrate the superior performance of ShapeDWA over DBA and SSG, with an average reduction of 23.42% and 24.89% for average discrepancy distance, and 18.76% and 19.81% for average time distortion. Furthermore, the template matching-based classification experiment shows that ShapeDWA combined with these two developed metrics improves the classification rate by 17.07% and 16.42% compared to DBA and SSG, respectively.