Cross-correlations between signal’s components

Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with other elements, and the environment. It is subsequently composed of many components, only some of which take part in the couplings. In this paper we present a framework to detect the component correlation pattern. Firstly, the interested trajectories are decomposed into components by using decomposing methods such as the Fourier expansion and the Wavelet transformation. Secondly, the cross-correlations between the components are calculated, resulting into a component cross-correlation matrix (network). Finally, the dominant structure in the network is identified to characterize the coupling pattern in the system. Several deterministic dynamical models turn out to be characterized with rich structures such as the clustering of the components. The pattern of correlation between respiratory (RESP) and ECG signals is composed of five sub-clusters that are mainly formed by the components in ECG signal. Interestingly, only 7 components from RESP (scattered in four sub-clusters) take part in the realization of coupling between the two signals.