Efficient Classification of Long Time Series by 3-D Dynamic Time Warping

Throughout recent years, dynamic time warping (DTW) has remained as a robust similarity measure in time series classification (TSC). 1-nearest neighbor (1-NN) algorithm with DTW is the most widely used classification method on time series serving as a benchmark. With the increasing demand for TSC on low-resource devices and the widespread of wearable devices, the need for a efficient and accurate time series classifier has never been higher. Although 1-NN DTW attains accurate results, it highly falls back on efficiency due to its quadratic complexity in the length of time series. In this paper, we propose a new approximation method for reducing the length of the time series as the input of DTW. We call it control chart approximation (CCA), after a similar concept used in statistical quality control processing. CCA representation approximates raw time series by transforming them into a set of segments with aggregated values and durations forming a reduced 3-D vector. We also propose an adaptation of DTW in 3-D space as a distance measure for 1-NN classifier, and denote the method as 1-NN 3-D DTW. Our experiments on 85 datasets from UCR archive—including 28 long-length (>500 points) time series datasets—show up to two orders of magnitude performance gain in running time compared to the state-of-the-art 1-NN DTW implementation. Moreover, it shows similar or better accuracy on the long time series in the experiment.