Adaptive Global Time Sequence Averaging Method Using Dynamic Time Warping

Time sequence averaging under dynamic time warping (DTW) is a non-trivial problem, and its exact solution requires unrealistic computational complexity in practice. The DTW barycenter averaging (DBA) method is one of the most effective iterative approximation solutions to date. However, there are still a few drawbacks in the DBA method. First, the length of the resulting average sequence depends on the selected initial average sequence; second, the discrepancy distance between the resulting average sequence and target sequence set is highly sensitive to the initialization, as we have demonstrated through the experiments described here. In this study, we propose an adaptive DBA (ADBA) algorithm to address these drawbacks. We define a scaling coefficient based on the DTW alignments such that the temporal aberrations between the average sequence and target sequence set can be qualitatively captured. The algorithm is realized by an iterative process. For each iteration, the temporary average sequence and target sequence set are partitioned into several aligned subsequence sets according to the variation in the signs of the scaling coefficients. Then, these partitioned average subsequences are adaptively compressed or stretched such that the average discrepancy distance and overall temporal aberration can be locally minimized. The comparison experiments carried out on the standard datasets illustrate that the proposed algorithm achieves lower average discrepancy distance, overall temporal aberration, and higher robustness than the available methods. Additionally, the proposed algorithm is verified by an accelerometer-based hand gesture recognition system, where ADBA produces more effective gesture templates.