  We propose a geometric model-free causality measurebased on multivariate
delay embedding that can efficiently detect linear and nonlinear causal
interactions between time series with no prior information. We then exploit the
proposed causal interaction measure in real MEG data analysis. The results are
used to construct effective connectivity maps of brain activity to decode
different categories of visual stimuli. Moreover, we discovered that the
MEG-based effective connectivity maps as a response to structured images
exhibit more geometric patterns, as disclosed by analyzing the evolution of
toplogical structures of the underlying networks using persistent homology.
Extensive simulation and experimental result have been carried out to
substantiate the capabilities of the proposed approach.
