Affine and Regional Dynamic Time Warping

Abstract

Pointwise matches between two time series are of great importance in time series analysis, and dynamic time warping (DTW) is known to provide generally reasonable matches. There are situations where time series alignment should be invariant to scaling and offset in amplitude or where local regions of the considered time series should be strongly reflected in pointwise matches. Two different variants of DTW, affine DTW (ADTW) and regional DTW (RDTW), are proposed to handle scaling and offset in amplitude and provide regional emphasis respectively. Furthermore, ADTW and RDTW can be combined in two different ways to generate alignments that incorporate advantages from both methods, where the affine model can be applied either globally to the entire time series or locally to each region. The proposed alignment methods outperform DTW on specific simulated datasets, and one-nearest-neighbor classifiers using their associated difference measures are competitive with the difference measures associated with state-of-the-art alignment methods on real datasets.

Toward Detection and Monitoring of Gait Pathology using Inertial Sensors under Rotation, Scale, and Offset Invariant Dynamic Time Warping

“…DTW has been used successfully for activity recognition [10] and biometric gait recognition [4] [9][11] [13], and several variants have been proposed. Scale and offset invariant DTW, in which one sequence can be scaled or shifted to improve similarity, has been developed by several authors, notably Chen et al, who evaluated an iterative algorithm similar to ours on a number of time series data sets [2]. When analyzing gait, scale and offset invariance may mitigate variability due to walking surface, shoe type, attachment method, and moderate changes in speed.…”

“…This algorithm can be restricted for a particular use case by limiting f to a subset of the RSO transformations. If rotation is not a concern, R may be held to I, the identity matrix, reducing RSOI-DTW to scale and offset invariant DTW, as developed in [2]. Similarly, if scaling is not a concern, s may be held to 1.…”

Adaptive Algorithms for Personalized Health Monitoring

“…Algorithms for combinations of rotation, scale, and/or offset invariance have also been proposed, though our iterative algorithm for three dimensional inertial data appears to be new. Affine DTW achieves scale and offset invariance [123], and a rotation invariant…”

“…This algorithm can be restricted for a particular use case by limiting f to a subset of the RSO transformations. If rotation is not a concern, R may be held to I, the identity matrix, reducing RSOI-DTW to scale and offset invariant DTW, as developed in [123]. Similarly, if scaling is not a concern, s may be held to 1.…”

“…The goal is not to determine whether the signals are the same when distortion is removed, but rather to quantify the degree of distortion. Further work is needed to clarify the difference in meaning between these measures and to study the Warp Scores value in other health monitoring applications.4.2.3 Rotation, Scale, and Offset Invariant DTWScale and offset invariant DTW, in which one sequence can be scaled or shifted to improve similarity, has been developed by several authors, notably Chen et al, who evaluated an iterative algorithm similar to ours on a number of time series data sets[123]. When analyzing gait, scale and offset invariance may mitigate variability due to walking surface, shoe type, attachment method, and moderate changes in speed.Rotation, scale, and offset-invariant DTW (RSOI-DTW) takes the next step by incorporating rotation invariance.…”