Sequential visibility-graph motifs

TL;DR

This paper introduces sequential visibility graph motifs as a new method for analyzing time series, providing an exact theoretical framework to distinguish different dynamics and apply to real-world data like heart-rate series.

Contribution

It develops a theory to compute motif profiles for deterministic and stochastic dynamics, enabling efficient and robust time series analysis.

Findings

Motif profiles can distinguish different types of dynamics.

Method is robust against noise contamination.

Effective in classifying relaxation states from heart-rate data.

Abstract

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of sequential visibility graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated to general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable to distinguish among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification and description of physical, biological, and financial time series.