Degree-Pruning Dynamic Programming Approaches to Central Time Series Minimizing Dynamic Time Warping Distance

The central time series crystallizes the common patterns of the set it represents. In this paper, we propose a global constrained degree-pruning dynamic programming (g(dp)2) approach to obtain the central time series through minimizing dynamic time warping (DTW) distance between two time series. The DTW matching path theory with global constraints is proved theoretically for our degree-pruning strategy, which is helpful to reduce the time complexity and computational cost. Our approach can achieve the optimal solution between two time series. An approximate method to the central time series of multiple time series [called as m_g(dp)2] is presented based on DTW barycenter averaging and our g(dp)2 approach by considering hierarchically merging strategy. As illustrated by the experimental results, our approaches provide better within-group sum of squares and robustness than other relevant algorithms.