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Network connectivity analysis in complex systems using large-scale non-linear Granger causality (lsNGC)

We propose a method for exploring non-linear directed information transfer in complex systems, which we expect to be useful for analyzing functional MRI (fMRI) neuroimaging data. In contrast to existing approaches that attempt to analyze complex systems by simplification and subsequent analysis of a simplified system, we propose to retain the original system complexity during the analysis. To this end, we introduce largescale Non-Linear Granger Causality (lsNGC) as a method for effective connectivity network analysis in high-dimensional systems with short time-series. By introducing a dimension reduction step into a non-linear timeseries prediction approach, lsNGC aims at directed, non-linear, multivariate time-series causality analysis in large complex networks, such as brain activity in fMRI analysis. We quantitatively evaluate the performance of lsNGC in computer simulations on structural recovery of synthetic networks with known ground truth. We find that our method performs better than a widely used non-linear network analysis method (Convergent Cross Mapping – CCM) with high statistical significance (p<10−6 ). In addition, as an outlook to possible clinical application, we perform a preliminary qualitative analysis of connectivity matrices for fMRI data of Autism Spectrum Disorder (ASD) patients and typical controls, using a subset of 59 subjects of the Autism Brain Imaging Data Exchange II (ABIDE II) data repository. Our results suggest that lsNGC, by extracting sparse connectivity matrices, may be useful for network analysis in complex systems, and may be applicable to clinical fMRI analysis in future research, such as targeting disease-related classification or regression tasks on clinical data.