Abstract
In this paper, we propose an efficient algorithm for reducing the computational complexity of dynamic time warping (DTW) for obtaining similarity measures between time series. The DTW technique exhibits superior classification accuracy compared to other algorithms but has a limitation of high computational complexity. To reduce the computational complexity of standard DTW, constrained DTW and fast DTW techniques have been proposed. The constrained DTW technique reduces the computational complexity of standard DTW by only considering limited alignments and prevent excessive alignments between two time series, which can reduce the overall classification accuracy. However, since the searching window for limited alignments is fixed, the computational complexity is still high when the length of time series is long. In contrast, fast DTW has a lower classification accuracy than the constrained DTW technique. However, fast DTW estimates the optimal alignment while considering only the alignments within an adaptive window; as two time series increase in length, the fast DTW technique more strongly reduces the computational complexity. Therefore, we propose a fast constrained DTW approach that applies the optimal alignment estimation of fast DTW within the limited alignments of constrained DTW. As the proposed fast constrained DTW operates within a fixed window area of the constrained DTW, which prevents excessive alignments, it has a classification accuracy similar to that of the constrained DTW. Also, in the fast constrained DTW, when the length of the time series is long, a low computational complexity is maintained by the influence of the adaptive window of the fast DTW. Experimental results on 19 UCR time series datasets show that the proposed fast constrained DTW method achieves computational complexity reductions of approximately 52.2% and 22.3% compared to the existing fast DTW and constrained DTW, while maintaining almost the same classification accuracy as the constrained DTW.
Highlights
T IME series data mining is utilized in numerous applications such as clustering, classification [1]–[3] fault detection [4], [5], pattern recognition [6], and prediction [7]
Unlike the existing fast dynamic time warping (DTW), which finds the optimal warping path while considering all areas of the accumulated cost matrix, the proposed fast Sakoe–Chiba DTW (SC-DTW) finds the optimal warping path only within the window area of the SC-DTW. Despite this difference, when the optimal warping path is located near index points that match on the time axis between the two time series, the fast SC-DTW has a computational complexity similar to that of the fast DTW
When the optimal warping path is located far from index points that match on the time axis between the two time series, the fast SC-DTW forms the optimal warping path at the boundary regions of the SC-DTW window
Summary
T IME series data mining is utilized in numerous applications such as clustering, classification [1]–[3] fault detection [4], [5], pattern recognition [6], and prediction [7]. As indicated by the red line, when the optimal warping path lies in the regions in which the index points of the two time series match in the lower resolution,the alignments within the dark and light window regions in Fig. 7(b) are performed for the higher resolution. In this case, we have the worst-case scenario for performing calculations for the largest number of cells. In this paper, we propose a fast constrained DTW method in which the optimal warping path estimation technique of fast DTW is applied within the limited window area of the constrained DTW
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