Adaptive signal decomposition methods are widespread in the field of nonstationary signal analysis. One such method is the Swarm Decomposition (SwD), which relies on the collective dynamics of a virtual swarm-prey model, in order to analyze a given univariate signal into a set of oscillatory components (OCs). In this paper, we present the generalization of the SwD method for the multivariate or multi-channel case, namely, the multivariate swarm decomposition (MSwD). Instead of performing channel-wise operations, we treat the signal in the N-dimensional space, utilizing a reformulated swarm filtering model, which is able to extract multivariate OCs. The frequencies of these dominant OCs are estimated based on a generalized cross-spectrum measure, which permits the analysis of signals with an arbitrary number of channels. Using synthetic signals, we study the mode alignment, quasi-orthogonality, filterbank properties, and robustness of the proposed approach. Particular emphasis is given to the robustness investigation, which is conducted in the systematic context of sensitivity analysis and Monte Carlo simulations, thus forming a generalized benchmark framework. The obtained results are compared to other well–known multivariate decomposition methods, such as the multivariate empirical mode decomposition and the multivariate variational mode decomposition, showcasing the efficiency of MSwD against them. Finally, we showcase the applicability and potential of the proposed MSwD in real-life signals, such as electroencephalography and subsurface oceanographic float signals, exemplifying its efficiency and contribution to accurately reveal their multi-component character.
