On the synchrony of empirical mode decompositions with application to electroencephalography

A novel approach to measure the interdependence of time series is proposed, based on the alignment ("matching") of their Huang-Hilbert spectra. The method consists of three steps: first, empirical modes are extracted from the signals; those functions carry non-linear and non-stationary components in frequency limited bands. Second, the empirical modes are Hilbert transformed, resulting in very sharply localized ridges in the time- frequency plane; the obtained time-frequency representations are known as Huang-Hilbert spectra. At last, the latter are pairwise aligned by means of the stochastic-event synchrony method (SES), a recently proposed procedure to match pairs of multi-dimensional point processes. The level of similarity of two Huang-Hilbert spectra is quantified by three parameters: timing and frequency jitter of coincident ridges, and fraction of non-coincident ridges. The proposed method is used to detect steady-state visually evoked potentials (SSVEP) in electroencephalography (EEG) signals; numerical results indicate that the method is vastly more sensitive to SSVEP than classical synchrony measures, and therefore, it may prove to be useful in applications such as brain-computer interfaces. Although the paper mostly deals with EEG, the presented synchrony measure may also be applied to other kinds of time series.