Multivariate synchronization curve: A measure of synchronization in different multivariate signals

As a method to measure the synchronization between two different sets of signals, the multivariate synchronization index (MSI) has played an irreplaceable role in the field of frequency recognition of brain-computer interface since it was proposed. On this basis, we make a generalization of MSI by using the escort distribution to replace the original distribution. In this way, MSI can be converted from a determined value to the multivariate synchronization curve, which will vary as the parameter q of the escort distribution changes. Numerical experiments are carried out on both simulated and real-world data to confirm the effectiveness of this new method. Compared with the case of MSI (i.e., q = 1), the extended form of MSI proposed in this article can obviously capture the relationship between signals more comprehensively, implying that it is a more perfect method to describe the synchronization between them. The results reveal that this method can not only effectively extract the important information contained in different signals, but also has the potential to become a practical synchronization measurement method of multivariate signals.