Sequential visibility-graph motifs
This work provides a method for automatic classification and description of time series in fields like physics, biology, and finance, but it is incremental as it builds on existing visibility graph techniques.
The authors tackled the problem of distinguishing different dynamics in time series by introducing sequential visibility graph motifs, which are smaller substructures that appear with characteristic frequencies, and found that this property is highly informative, computationally efficient, and robust against noise, enabling unsupervised classification such as disentangling meditative from relaxation states in heart-rate data.
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.