MOMENTI: Scalable Motif Mining in Multidimensional Time Series

TL;DR

MOMENTI introduces a scalable, probabilistic algorithm for motif mining in multidimensional time series that is significantly faster than existing methods and adapts to input data.

Contribution

The paper presents a novel subquadratic, probabilistic algorithm for top-k motif discovery in multidimensional time series with theoretical guarantees and adaptive parameter tuning.

Findings

Runs orders of magnitude faster than state-of-the-art methods.

Provides probabilistic guarantees on the quality of motifs found.

Adapts to input data distribution and respects memory constraints.

Abstract

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least $1-\delta$, where $\delta$ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.