Visibility graphs for fMRI data: multiplex temporal graphs and their modulations across resting state networks

Abstract

Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph 1 theory and network science can be used for the characterization of time series. This approach has proved a 2 convenient tool and visibility graphs have found applications across several disciplines. Recently, an approach has 3 been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective 4 dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (i) 5 this approach allows to simultaneously capture and process relevant aspects of both local and global dynamics in 6 an easy and intuitive way, and (ii) this provides a suggestive bridge between time series and network theory 7 which nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals 8 differences in the similarities of temporal networks (and thus in correlated dynamics) across resting state 9 networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be 10 picked up by this approach.

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“…Research on this methodology has been primarily theoretical, elaborating on mathematical methods [28][29][30][31] to extract rigorous results on the properties of these graphs when associated to canonical models of complex dynamics, including stochastic processes with and without correlations or chaotic processes [32][33][34][35] . In practice, this method can be used as a feature extraction procedure for constructing feature vectors for statistical learning purposes and has been widely applied across the disciplines (see, for instance, [36][37][38][39][40] for just a few examples).…”

Estimation of Dynamic Bivariate Correlation Using a Weighted Graph Algorithm

“…Building upon the mapping of multivariate time series into a multilayer graph proposed in [ 34 ], Sannino and co-authors described an approach to capture modulations across resting-state networks [ 35 ]. Sannino et al observed that the networks within the multiplex layers have a modular structure which is an indication of different temporal regimes.…”

“…Partitioning the visibility graph based on these modules provides a natural decomposition of the time series into time intervals. The approach presented in [ 35 ] is to capture the similarity between neural events using Sörensen similarity index between each pair of modules in the two time series. One difference from our approach is that we did not use a visibility criterion; another difference is that the approach in [ 35 ] is based on decomposing time series into time intervals.…”

“…The approach presented in [ 35 ] is to capture the similarity between neural events using Sörensen similarity index between each pair of modules in the two time series. One difference from our approach is that we did not use a visibility criterion; another difference is that the approach in [ 35 ] is based on decomposing time series into time intervals. As in our case, we consider the approach in [ 35 ] could also be robust towards extreme values.…”

“…One difference from our approach is that we did not use a visibility criterion; another difference is that the approach in [ 35 ] is based on decomposing time series into time intervals. As in our case, we consider the approach in [ 35 ] could also be robust towards extreme values. Systematically exploring the differences and similarities between these two approaches will be an interesting topic for future work.…”