A novel multi-scale approach for quantifying both inter-and intra-component dependence of a complex system is introduced. This is achieved using empirical mode decomposition (EMD), which, unlike conventional scale-estimation methods, obtains a set of scales reflecting the underlying oscillations at the intrinsic scale level. This enables the datadriven operation of several standard data-association measures (intrinsic correlation, intrinsic sample entropy (SE), intrinsic phase synchrony) and, at the same time, preserves the physical meaning of the analysis. The utility of multi-variate extensions of EMD is highlighted, both in terms of robust scale alignment between system components, a pre-requisite for inter-component measures, and in the estimation of feature relevance. We also illuminate that the properties of EMD scales can be used to decouple amplitude and phase information, a necessary step in order to accurately quantify signal dynamics through correlation and SE analysis which are otherwise not possible. Finally, the proposed multi-scale framework is applied to detect directionality, and higher order features such as coupling and regularity, in both synthetic and biological systems.

One contribution of 13 to a theme issue 'Adaptive data analysis: theory and applications' . An extension to multivariate empirical mode decomposition (MEMD), termed adaptive-projection intrinsically transformed MEMD (APIT-MEMD), is proposed to cater for power imbalances and inter-channel correlations in real-world multichannel data. It is shown that the APIT-MEMD exhibits similar or better performance than MEMD for a large number of projection vectors, whereas it outperforms MEMD for the critical case of a small number of projection vectors within the sifting algorithm. We also employ the noise-assisted APIT-MEMD within our proposed intrinsic multiscale analysis framework and illustrate the advantages of such an approach in notoriously noise-dominated cooperative braincomputer interface (BCI) based on the steady-state visual evoked potentials and the P300 responses. Finally, we show that for a joint cognitive BCI task, the proposed intrinsic multiscale analysis framework improves system performance in terms of the information transfer rate.

A highly localized data-association measure, termed intrinsic synchrosqueezing transform (ISC), is proposed for the analysis of coupled nonlinear and non-stationary multivariate signals. This is achieved based on a combination of noise-assisted multivariate empirical mode decomposition and short-time Fourier transform-based univariate and multivariate synchrosqueezing transforms. It is shown that the ISC outperforms six other combinations of algorithms in estimating degrees of synchrony in synthetic linear and nonlinear bivariate signals. Its advantage is further illustrated in the precise identification of the synchronized respiratory and heart rate variability frequencies among a subset of bass singers of a professional choir, where it distinctly exhibits better performance than the continuous wavelet transform-based ISC. We also introduce an extension to the intrinsic phase synchrony (IPS) measure, referred to as nested intrinsic phase synchrony (N-IPS), for the empirical quantification of physically meaningful and straightforward-to-interpret trends in phase synchrony. The N-IPS is employed to reveal physically meaningful variations in the levels of cooperation in choir singing and performing a surgical procedure. Both the proposed techniques successfully reveal degrees of synchronization of the physiological signals in two different aspects: (i) precise localization of synchrony in time and frequency (ISC), and (ii) large-scale analysis for the empirical quantification of physically meaningful trends in synchrony (N-IPS).

Multichannel data-driven time-frequency algorithms, such as the multivariate empirical mode decomposition (MEMD), have emerged as important tools in the analysis of inter-channel dependencies that arise in multivariate data. Such methods employ uniform projection schemes on hyper spheres in order to estimate the local mean, thus requiring dense but underutilised sampling when processing unbal anced data channels. To this end, we propose a nonuniform projection scheme that adapts to the second order statistics of trivariate data; this provides the estimation of the local mean in the case of power imbalances and correlations between the channels. The algorithm is particularly useful for gener ating a low number of direction vectors within MEMD. Its performance is illustrated on synthetic and real-world data.

Radiofrequency catheter ablation is one of the commonly available therapeutic methods for patients suffering from cardiac arrhythmias. The prerequisite of successful ablation is sufficient energy delivery at the target site. However, cardiac and respiratory motion, coupled with endocardial irregularities, can cause catheter drift and dispersion of the radiofrequency energy, thus prolonging procedure time, damaging adjacent tissue, and leading to electrical reconnection of temporarily ablated regions. Therefore, positional accuracy and stability of the catheter tip during energy delivery is of great importance for the outcome of the procedure. This paper presents an analytical scheme for assessing catheter tip stability, whereby a sequence of catheter tip motion recorded at sparse locations on the endocardium is decomposed. The spatial sliding component along the endocardial wall is extracted from the recording and maximal slippage and its associated probability are computed at each mapping point. Finally, a global map is generated, allowing the assessment of potential areas that are compromised by tip slippage. The proposed framework was applied to 40 retrospective studies of congenital heart disease patients and further validated on phantom data and simulations. The results show a good correlation with other intraoperative factors, such as catheter tip contact force amplitude and orientation, and with clinically documented anatomical areas of high catheter tip instability.