A cooperation index based on correlation matrix spectrum and Renyi entropy

Indices based on correlation or more subtle strategies are among the standard ways to infer dependencies (i.e., exchange of information or coupling) in aggregations of different systems observed in the time domain. We propose a new index based on Renyi entropy and confront it with other indices, studying if some of these techniques can recognize when we are observing the same system twice, even when the observation conditions are bad. It turns out that our index gives better results than the other examined ones. Moreover, we notice that those indices based on data processed with state space reconstruction and filtered with Principal Component Analysis are, generally, less sensitive to bad observations. However, state space reconstruction by itself is not enough to obtain good performances when the data are very noisy, and a Principal Component Analysis filter is needed to improve the results.