Symbolic Higher-Order Analysis of Multivariate Time Series

Abstract

Identifying patterns of relations among the units of a complex system from measurements of their activities in time is a fundamental problem with many practical applications. Here, we introduce a method that detects dependencies of any order in multivariate time series data. The method first transforms a multivariate time series into a symbolic sequence, and then extract statistically significant strings of symbols through a Bayesian approach. Such motifs are finally modelled as the hyperedges of a hypergraph, allowing us to use network theory to study higher-order interactions in the original data. When applied to neural and social systems, our method reveals meaningful higher-order dependencies, highlighting their importance in both brain function and social behaviour.