On the Non-Trivial Generalization of Dynamic Time Warping to the Multi-Dimensional Case

Abstract

In the last decade, Dynamic Time Warping (DTW) has emerged as the distance measure of choice for virtually all time series data mining applications. This is the result of significant progress in improving DTW's efficiency, and multiple empirical studies showing that DTW-based classifiers at least equal the accuracy of all their rivals across dozens of datasets. Thus far, most of the research has considered only the one-dimensional case, with practitioners generalizing to the multi-dimensional case in one of two ways. In general, it appears the community believes either that the two ways are equivalent, or that the choice is irrelevant. In this work, we show that this is not the case. The two most commonly used multidimensional DTW methods can produce different classifications, and neither one dominates over the other. This seems to suggest that one should learn the best method for a particular application. However, we will show that this is not necessary; a simple, principled rule can be used on a case-by-case basis to predict which of the two methods we should give credence to. Our method allows us to ensure that classification results are at least as accurate as the better of the two rival methods, and in many cases, our method is strictly more accurate. We demonstrate our ideas with the most extensive set of multi-dimensional time series classification experiments ever attempted.

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“…To address the two technical challenges, background noise and multi-dimensional data (with different length in each dimension), we adopted an extended DTW algorithm [58], which extends the original DTW algorithm to multi-dimensional time series. The multi-dimensional DTW, denoted DTW_I, calculates DTW distance for each feature separately, and sums up each DTW distance after normalization.…”

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“…Energies 2016, 9, 561 6 of 11 DTW utilizes dynamic programming to find the optimal mapping of points in two sequences and compute the distance between them. Detailed steps for computing the DTW distance can be found in several papers [20,21], and efficient algorithms can be found in [17].…”

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“…Note that for the remainder of this article, we use the terms distance and similarity interchangeably, as the former is simply the inverse of the latter. We have chosen the Dynamic Time Warping (DTW) algorithm 6,7 to measure the distance between two time-series of a given WITI factor. DTW is an algorithm for computing the distance between two time-series that can be tuned to overlook slight differences in the rates or speeds at which the time-series evolve.…”