Mapping Time Series to Networks: a Brief Overview of Visibility Algorithms

In the last years a new approach for making time series analysis has appeared. This new approach considers the mapping of time series to networks, in order to characterize the structure of time series (and therefore the dynamics that generated the series) via characterization of the associated network. It makes use of several metrics recently developed in the so called Complex Network theory, and makes a bridge between this latter discipline and the more general aspects of time series analysis and nonlinear dynamics. While several possibilities have been proposed, here we focus on the so called visibility algorithm, which has received much attention in the last two years. This method has been shown to be well defined as time series correlations are inherited in the associated visibility graphs, opening the possibility of characterizing complex signals from a brand new viewpoint. We will make an overview of the method, addressing two different possible mapping criteria (i.e. the visibility algorithm and the horizontal visibility algorithm) for mapping series into graphs. This method captures the correlations of a time series and encodes it in the topology of the associated graph. After presenting the mapping properties, we will address within the visibility algorithms three fundamental problems in nonlinear time series analysis, namely (i) the network characterization of fractional Brownian motion, (ii) the characterization of uncorrelated processes, and (iii) the discrimination between randomness and chaos through the visibility algorithm. ∗E-mail address: [email protected], [email protected] 2 Lucas Lacasa, Bartolo Luque