TS-mIoU: A Time Series Similarity Metric Without Mapping

Abstract

Quantifying the similarity or distance between time series, processes, signals, and trajectories is a task-specific problem and remains a challenge for many applications. The simplest measure, meaning the Euclidean distance, is often dismissed because of its sensitivity to noise and the curse of dimensionality. Therefore, elastic mappings (such as DTW, LCSS, ED) are often utilized instead. However, these measures are not metric functions, and more importantly, they must deal with the challenges intrinsic to point-to-point mappings, such as pathological alignment. In this paper, we adopt an object-similarity measure, namely Multiscale Intersection over Union (MIoU), for measuring the distance/similarity between time series. We call the new measure TS-MIoU. Unlike the most popular time series similarity measures, TS-MIoU does not rely on a point-to-point mapping, and therefore, circumvents all respective challenges. We show that TS-MIoU is indeed a metric function, especially that it holds the triangle inequality axiom, and therefore can take advantage of indexing algorithms without a lower bounding. We further show that its sensitivity to noise is adjustable, which makes it a strong alternative to the Euclidean distance while not suffering from the curse of dimensionality. Our proof-of-concept experiments on over 100 UCR datasets show that TS-MIoU can fill the gap between the unforgiving strictness of the $\ell _p$ ℓ p -norm measures, and the mapping challenges of elastic measures.