Symbolic Higher-Order Analysis of Multivariate Time Series

TL;DR

This paper introduces a novel method for detecting higher-order dependencies in multivariate time series by transforming data into symbolic sequences, extracting significant motifs, and modeling them as hyperedges in a hypergraph, revealing complex interactions.

Contribution

The method combines symbolic transformation, Bayesian motif extraction, and hypergraph modeling to identify higher-order interactions in multivariate time series data, a novel approach in the field.

Findings

Reveals meaningful higher-order dependencies in neural data

Highlights complex social interactions through the hypergraph model

Demonstrates the method's effectiveness on real-world systems

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.