Electrical and Electronic Engineering, Imperial College London
Doi
Abstract
Established dynamical complexity analysis measures operate at a single scale and thus fail
to quantify inherent long-range correlations in real world data, a key feature of complex
systems. They are designed for scalar time series, however, multivariate observations are
common in modern real world scenarios and their simultaneous analysis is a prerequisite for
the understanding of the underlying signal generating model. To that end, this thesis first
introduces a notion of multivariate sample entropy and thus extends the current univariate
complexity analysis to the multivariate case. The proposed multivariate multiscale entropy
(MMSE) algorithm is shown to be capable of addressing the dynamical complexity of such
data directly in the domain where they reside, and at multiple temporal scales, thus
making full use of all the available information, both within and across the multiple data
channels. Next, the intrinsic multivariate scales of the input data are generated adaptively
via the multivariate empirical mode decomposition (MEMD) algorithm. This allows for
both generating comparable scales from multiple data channels, and for temporal scales
of same length as the length of input signal, thus, removing the critical limitation on
input data length in current complexity analysis methods. The resulting MEMD-enhanced
MMSE method is also shown to be suitable for non-stationary multivariate data analysis
owing to the data-driven nature of MEMD algorithm, as non-stationarity is the biggest
obstacle for meaningful complexity analysis. This thesis presents a quantum step forward
in this area, by introducing robust and physically meaningful complexity estimates of
real-world systems, which are typically multivariate, finite in duration, and of noisy and
heterogeneous natures. This also allows us to gain better understanding of the complexity
of the underlying multivariate model and more degrees of freedom and rigor in the analysis.
Simulations on both synthetic and real world multivariate data sets support the analysis
