Dynamical networks from correlations

The extraction of relevant and meaningful information from large streams of data has become one of the major challenges for scientists working in the field of complex systems. In particular, one of the main goals is to get information about the underlying system of interactions that leads to complex collective dynamics. In this paper, we discuss how a set of relevant interactions can be extracted from the analysis of the cross-correlation matrix. We show that an active and adaptive correlation filtering procedure can be associated to the dynamics of a network which is a sort of ‘hyper-molecule’ warped on a D-dimensional unitary sphere.