An Improved Relevance Index Method to Search Important Structures in Complex Systems

We present an improvement of a method that aims at detecting important dynamical structures in complex systems, by identifying subsets of elements that show tight and coordinated interactions among themselves, while interplaying much more loosely with the rest of the system. Such subsets are estimated by means of a Relevance Index (RI), which is normalized with respect to a homogeneous system, usually described by independent Gaussian variables, as a reference. The strategy presented herein improves the way the homogeneous system is conceived from a theoretical viewpoint. Firstly, we consider the system components as dependent and with equal pairwise correlations, which implies a non-diagonal correlation matrix of the homogeneous system. Then, we generate the components of the homogeneous system according to a multivariate Bernoulli distribution, by exploiting the NORTA method, which is able to create samples of a desired random vector, given its marginal distributions and its correlation matrix. The proposed improvement on the RI method has been applied to three different case studies, obtaining better results compared with the traditional method based on the homogeneous system with independent Gaussian variables.