Optimizing dynamic time warping’s window width for time series data mining applications

Abstract

Dynamic Time Warping (DTW) is a highly competitive distance measure for most time series data mining problems. Obtaining the best performance from DTW requires setting its only parameter, the maximum amount of warping (w). In the supervised case with ample data, w is typically set by cross-validation in the training stage. However, this method is likely to yield suboptimal results for small training sets. For the unsupervised case, learning via cross-validation is not possible because we do not have access to labeled data. Many practitioners have thus resorted to assuming that "the larger the better", and they use the largest value of w permitted by the computational resources. However, as we will show, in most circumstances, this is a naïve approach that produces inferior clusterings. Moreover, the best warping window width is generally non-transferable between the two tasks, i.e., for a single dataset, practitioners cannot simply apply the best w learned for classification on clustering or vice versa. In addition, we will demonstrate that the appropriate amount of warping not only depends on the data structure, but also on the dataset size. Thus, even if a practitioner knows the best setting for a given dataset, they will likely be at a lost if they apply that setting on a bigger size version of that data. All these issues seem largely unknown or at least unappreciated in the community. In this work, we demonstrate the importance of setting DTW's warping window width correctly, and we also propose novel methods to learn this parameter in both supervised and unsupervised settings. The algorithms we propose to learn w can produce significant improvements in classification accuracy and clustering quality. We demonstrate the correctness of our novel observations and the utility of our ideas by testing them with more than one hundred publicly available datasets. Our forceful results allow us to make a perhaps unexpected claim; an underappreciated "low hanging fruit" in optimizing DTW's performance can produce improvements that make it an even stronger baseline, closing most or all the improvement gap of the more sophisticated methods proposed in recent years.

Using time-series similarity measures to compare animal movement trajectories in ecology

“…Here, we used biological insights from a previous study to set ε at a spatial scale reflecting that at which GPS-tracked gannets typically forage, but one could set ε to reflect known location error from ones tracking device for example. For DTW, LCSS and EDR one must also set a δ value and while many studies adopt an unconstrained approach as we do here adjusting this parameter can sometimes improve clustering performance (Dau et al 2018). We also note that the similarity measures covered here represent only a subset of available trajectory similarity measures (Ranacher and Tzavella 2014) and that rather than having to choose between similarity measures it may be possible to use them as an ensemble for machine learning methods of time-series classification purposes (Lines and Bagnall 2015).…”

Deep Multivariate Time Series Embedding Clustering via Attentive-Gated Autoencoder

“…Also in this case we perform zero padding to fit all the time-series lengths to the size of the longest one. -The Dynamic Time Warping measures [7] (DTW ) coupled with K-means algorithm. Such distance measure is especially tailored for time-series data with variable length-size.…”

Combining SDAE Network with Improved DTW Algorithm for Similarity Measure of Ultra-Weak FBG Vibration Responses in Underground Structures

“…The bandwidth r defines the constraint range of the matching path in the distance matrix and suppresses the influence of undesired convergence in the matching path [52]. Because there was a correlation between the defined warping offset distance and the SDTW algorithm, as well as the SDTW-based distance and the constraint bandwidth r, different r not only affected the optimal matching path of the SDTW but also led to the change of d similarity .…”

“…For case II, it can be considered that the constraint bandwidth did not affect the distance measured by the SDTW algorithm, and the first r corresponding to the minimum can be seen as the candidate. For the situation in case III that multiple candidate values within the convergence region corresponded to the same minimum value E SUM , the median of these candidate values was selected as r. Here, the general rules for determining and adjusting the preset range for r can refer to [52].…”