Finding Novel Multivariate Relationships in Time Series Data: Applications to Climate and Neuroscience

Abstract

In many domains, there is significant interest in capturing novel relationships between timeseries that represent activities recorded at different nodes of a highly complex system. In thispaper, we introduce multipoles, a novel class of linear relationships between more than twotime series. A multipole is a set of time series that have strong linear dependence amongthemselves, with the requirement that each time series makes a significant contribution to thelinear dependence. We demonstrate that most interesting multipoles can be identified as cliquesof 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