Intrinsic multi-scale analysis: a multi-variate empirical mode decomposition framework

Abstract

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.

Financial Stress Through Complexity Science

“…The novel intrinsic phase synchrony [28] has been employed to quantify scale-wise couplings in financial indices, and has indicated pronounced and physically meaningful synchronisation in the DJIA and the S&P 500, across the scales. Higher degrees of synchrony have also been found in short-term dependencies during the periods with low market stress and low variations in the determinism.…”

“…We also examine the degree of synchrony between financial indices and establish the extent to which IPS [28] can be used to quantify synchronous behaviour -financial contagion leading to systemic risk -among multiple stock indices related to the same sector, as elaborated in Section III-E.…”

“…The intrinsic phase synchrony (IPS) was originally proposed in the so called intrinsic multiscale analysis framework in [28] and generalises standard phase synchrony by equipping it with the ability to operate at the intrinsic scale level. It employs multivariate empirical mode decomposition (MEMD) [43] to decompose a given multivariate signal into its narrowband intrinsic oscillations (IMFs), which makes it possible to quantify the temporal locking of the phase information in IMFs using the standard phase synchronisation index (PSI), as outlined in Algorithm 4.…”

Adaptive-projection intrinsically transformed multivariate empirical mode decomposition in cooperative brain–computer interface applications

“…It is also capable of alleviating mode-mixing and yields fewer IMFs for unbalanced data. This work also introduces applications of intrinsic multiscale analysis [24] using NA-APIT-MEMD to cooperative BCI applications based on steady-state visual evoked potentials (SSVEP) and P300 responses.…”

“…The MEMD can be used in conjunction with standard data-association measures such as phase synchrony, sample entropy and correlation, to quantify intra-and inter-component dependences of a complex system, within a framework referred to as intrinsic multiscale analysis [24]. Applications of MEMD include neural signal processing [25], BCIs [26], image processing [27] and artefact removal [28].…”