Quantitative Evaluation of Motif Sets in Time Series

Time Series Motif Discovery (TSMD), which aims at finding recurring patterns in time series, is an important task in numerous application domains, and many methods for this task exist. These methods are usually evaluated qualitatively. A few metrics for quantitative evaluation, where discovered motifs are compared to some ground truth, have been proposed, but they typically make implicit assumptions that limit their applicability. This paper introduces PROM, a broadly applicable metric that overcomes those limitations, and TSMD-Bench, a benchmark for quantitative evaluation of time series motif discovery. Experiments with PROM and TSMD-Bench show that PROM provides a more comprehensive evaluation than existing metrics, that TSMD-Bench is a more challenging benchmark than earlier ones, and that the combination can help understand the relative performance of TSMD methods. More generally, the proposed approach enables large-scale, systematic performance comparisons in this field.

LoCoMotif: Discovering time-warped motifs in time series

Time Series Motif Discovery (TSMD) refers to the task of identifying patterns that occur multiple times (possibly with minor variations) in a time series. All existing methods for TSMD have one or more of the following limitations: they only look for the two most similar occurrences of a pattern; they only look for patterns of a pre-specified, fixed length; they cannot handle variability along the time axis; and they only handle univariate time series. In this paper, we present a new method, LoCoMotif, that has none of these limitations. The method is motivated by a concrete use case from physiotherapy. We demonstrate the value of the proposed method on this use case. We also introduce a new quantitative evaluation metric for motif discovery, and benchmark data for comparing TSMD methods. LoCoMotif substantially outperforms the existing methods, on top of being more broadly applicable.