Making the dynamic time warping distance warping-invariant

Abstract

The literature postulates that the dynamic time warping (dtw) distance can cope with temporal variations but stores and processes time series in a form as if the dtw-distance cannot cope with such variations. To address this inconsistency, we first show that the dtw-distance is not warping-invariant. The lack of warping-invariance contributes to the inconsistency mentioned above and to a strange behavior. To eliminate these peculiarities, we convert the dtw-distance to a warping-invariant semi-metric, called time-warp-invariant (twi) distance. Empirical results suggest that the error rates of the twi and dtw nearest-neighbor classifier are practically equivalent in a Bayesian sense. However, the twi-distance requires less storage and computation time than the dtw-distance for a broad range of problems. These results challenge the current practice of applying the dtw-distance in nearest-neighbor classification and suggest the proposed twi-distance as a more efficient and consistent option.

Shape Pattern Recognition of Building Footprints Using t-SNE Dimensionality Reduction Visualization

“…where P a i is the coordinate sequence that starts at the i th vertex in A. Subsequently, the canonical warping distance between the sequences in CodeSet a and P b , denoted as the minimum, serves as the ultimate distance between A and B, as depicted by Equation (7).…”

“…Pattern recognition, a cornerstone of computer vision, has seen various methodologies proposed, including Dynamic Programming (DP), Dynamic Time Warping (DTW), and Canonical Time Warping (CTW) [6][7][8]. DP techniques leverage contour point sequences to establish local correspondences between shapes for measuring shape dissimilarity.…”

Object Detection of Ground-Penetrating Radar Signals Using Empirical Mode Decomposition and Dynamic Time Warping

“…Meanwhile, the required computation time and storage of TWI-distance sometimes were less than the DTW-distance. They suggested that the proposed TWI-distance was a more efficient and consistent option [26].…”

A Data-Driven Approach for Estimating the Effects of Station Closures in Metro Systems

“…Specifically, SAX ignores the pattern of a shift in the value of the segment, which in some cases can lead to an incorrect classification, because it is not capable of distinguishing different time series with different patterns from the same average value symbol. Dynamic Time Warping (DTW) [15], [16] is used to calculate the value change trend in the passenger flow segment, the value change trend during each passenger flow data segment is further calculated using SAX, and a new weight equivalent distance is created taking into account the mean value and trend information of the passenger flow data.…”