Elastic Time Series Motifs and Discords

The recent proposal of the Matrix Profile (MP) has brought the attention of the time series community to the usefulness and versatility of the similarity joins. This primitive has numerous applications including the discovery of time series motifs and discords. However, the original MP algorithm has two prominent limitations: the algorithm only works for Euclidean distance (ED) and it is sensitive to the subsequences length. Is this work, we extend the MP algorithm to overcome both limitations. We use a recently proposed variant of Dynamic Time Warping (DTW), the Prefix and Suffix Invariant DTW (PSI-DTW) distance. The PSI-DTW allows invariance to warp and spurious endpoints caused by segmenting subsequences and has a side-effect of supporting the match of subsequences with different lengths. Besides, we propose a suite of simple methods to speed up the MP calculation, making it more than one order of magnitude faster than a straightforward implementation and providing an anytime feature. We show that using PSI-DTW avoids false positives and false dismissals commonly observed by applying ED, improving the time series motifs and discords discovery in several application domains.