Mining Novel Multivariate Relationships in Time Series Data Using Correlation Networks

TL;DR

This paper introduces multipoles, a new method for identifying complex multivariate relationships in time series data by analyzing correlation networks, revealing novel insights in climate science and neuroscience.

Contribution

The paper proposes multipoles as a new class of linear relationships among multiple time series, identified via correlation network cliques, enabling discovery of novel domain-specific phenomena.

Findings

Identified multipoles as cliques of negative correlations in correlation networks.

Discovered reproducible multipole relationships in climate and neuroscience datasets.

Revealed new physical phenomena through multipole analysis.

Abstract

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.