Exact multi-length scale and mean invariant motif discovery

Abstract

Discovering approximately recurrent motifs (ARMs) in timeseries is an active area of research in data mining. Exact motif discovery is defined as the problem of efficiently finding the most similar pairs of timeseries subsequences and can be used as a basis for discovering ARMs. The most efficient algorithm for solving this problem is the MK algorithm which was designed to find a single pair of timeseries subsequences with maximum similarity at a known length. This paper provides three extensions of the MK algorithm that allow it to find the top K similar subsequences at multiple lengths using both the Euclidean distance metric and scale invariant normalized version of it. The proposed algorithms are then applied to both synthetic data and real-world data with a focus on discovery of ARMs in human motion trajectories.