Generalizing DTW to the multi-dimensional case requires an adaptive approach

Abstract

In recent years Dynamic Time Warping (DTW) has emerged as the distance measure of choice for virtually all time series data mining applications. For example, virtually all applications that process data from wearable devices use DTW as a core sub-routine. This is the result of significant progress in improving DTW’s efficiency, together with multiple empirical studies showing that DTW-based classifiers at least equal (and generally surpass) 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, dependent or independent warping. 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 multi-dimensional 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 trust at the time of classification. 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 significantly more accurate. We demonstrate our ideas with the most extensive set of multi-dimensional time series classification experiments ever attempted.

Using electromagnetic articulography with a tongue lateral sensor to discriminate manner of articulation

“…DTW is widely accepted as the best distance measure among time-series signals. 15 DTW has been successfully used in many domains, including speech kinematics. 15 The standard DTW algorithm calculates the summed distances between data points of two time-series signals, after aligning the peaks.…”

“…15 DTW has been successfully used in many domains, including speech kinematics. 15 The standard DTW algorithm calculates the summed distances between data points of two time-series signals, after aligning the peaks. Thus, DTW is particularly useful in signals that have temporal variations (e.g., speech).…”

“…In this paper, DTW was used as a classifier to distinguish different sounds from articulatory time-series data (i.e., the spatial coordinates of sensors attached on the tongue). The procedure of using DTW for classification includes three steps: 15 First, the training process generates a "representative" or "reference" signal based on multiple training samples for each sound. Second, the distances between the test sample and each reference signal for each sound (here, for each consonant) are calculated.…”

Towards semantic‐aware multiple‐aspect trajectory similarity measuring

“…Shokoohi‐Yekta, Hu, Jin, Wang, and Keogh () proposed an adaptive DTW‐based approach for multidimensional time series classification, namely DTW A . DTW A runs both an independent and a dependent version of DTW (DTW I and DTW D , respectively), and then chooses the best approach according to a scoring function and a threshold.…”

“…Both DTW and MD-DTW consider a single distance function for all dimensions, and deal with numerical attributes only, so are not applicable to multiple-aspect trajectories. -Yekta, Hu, Jin, Wang, and Keogh (2017) proposed an adaptive DTW-based approach for multidimensional time series classification, namely DTW A . DTW A runs both an independent and a dependent version of DTW (DTW I and DTW D , respectively), and then chooses the best approach according to a scoring function and a threshold.…”