Ranking and significance of variable-length similarity-based time series motifs

TL;DR

This paper investigates the challenges in comparing variable-length time series motifs based on dissimilarity measures, revealing intrinsic dependencies on motif length, and proposes a beta distribution-based model to rank and assess their significance.

Contribution

It demonstrates the non-linear dependencies of motif dissimilarities on length and introduces a beta distribution model to enable meaningful ranking and significance measurement.

Findings

Normalized dissimilarities are affected by motif length.

Dependencies on length are non-linear and dataset-dependent.

The proposed model accurately ranks motifs by significance.

Abstract

The detection of very similar patterns in a time series, commonly called motifs, has received continuous and increasing attention from diverse scientific communities. In particular, recent approaches for discovering similar motifs of different lengths have been proposed. In this work, we show that such variable-length similarity-based motifs cannot be directly compared, and hence ranked, by their normalized dissimilarities. Specifically, we find that length-normalized motif dissimilarities still have intrinsic dependencies on the motif length, and that lowest dissimilarities are particularly affected by this dependency. Moreover, we find that such dependencies are generally non-linear and change with the considered data set and dissimilarity measure. Based on these findings, we propose a solution to rank those motifs and measure their significance. This solution relies on a compact but accurate model of the dissimilarity space, using a beta distribution with three parameters that depend on the motif length in a non-linear way. We believe the incomparability of variable-length dissimilarities could go beyond the field of time series, and that similar modeling strategies as the one used here could be of help in a more broad context.