587 research outputs found
Empirical Characterization of the Temporal Dynamics of EEG Spectral Components
The properties of time-domain electroencephalographic data have been studied extensively. There has however been no attempt to characterize the temporal evolution of resulting spectral components when successive segments of electroencephalographic data are decomposed. We analyzed resting-state scalp electroencephalographic data from 23 subjects, acquired at 256 Hz, and transformed using 64-point Fast Fourier Transform with a Hamming window. KPSS and Nason tests were administered to study the trend- and wide sense stationarity respectively of the spectral components. Thereafter, the Rosenstein algorithm for dynamic evolution was applied to determine the largest Lyapunov exponents of each component’s temporal evolution. We found that the evolutions were wide sense stationary for time scales up to 8 s, and had significant interactions, especially between spectral series in the frequency ranges 0–4 Hz, 12–24 Hz, and 32-128 Hz. The spectral series were generally non-chaotic, with average largest Lyapunov exponent of 0. The results show that significant information is contained in all frequency bands, and that the interactions between bands are complicated and time-varying
Fractal Fluctuations and Quantum-Like Chaos in the Brain by Analysis of Variability of Brain Waves: A New Method Based on a Fractal Variance Function and Random Matrix Theory
We developed a new method for analysis of fundamental brain waves as recorded
by EEG. To this purpose we introduce a Fractal Variance Function that is based
on the calculation of the variogram. The method is completed by using Random
Matrix Theory. Some examples are given
Feature-based time-series analysis
This work presents an introduction to feature-based time-series analysis. The
time series as a data type is first described, along with an overview of the
interdisciplinary time-series analysis literature. I then summarize the range
of feature-based representations for time series that have been developed to
aid interpretable insights into time-series structure. Particular emphasis is
given to emerging research that facilitates wide comparison of feature-based
representations that allow us to understand the properties of a time-series
dataset that make it suited to a particular feature-based representation or
analysis algorithm. The future of time-series analysis is likely to embrace
approaches that exploit machine learning methods to partially automate human
learning to aid understanding of the complex dynamical patterns in the time
series we measure from the world.Comment: 28 pages, 9 figure
Wavelet Lifting over Information-Based EEG Graphs for Motor Imagery Data Classification
The imagination of limb movements offers an intuitive paradigm for the control of electronic devices via brain computer interfacing (BCI). The analysis of electroencephalographic (EEG) data related to motor imagery potentials has proved to be a difficult task. EEG readings are noisy, and the elicited patterns occur in different parts of the scalp, at different instants and at different frequencies. Wavelet transform has been widely used in the BCI field as it offers temporal and spectral capabilities, although it lacks spatial information. In this study we propose a tailored second generation wavelet to extract features from these three domains. This transform is applied over a graph representation of motor imaginary trials, which encodes temporal and spatial information. This graph is enhanced using per-subject knowledge in order to optimise the spatial relationships among the electrodes, and to improve the filter design. This method improves the performance of classifying different imaginary limb movements maintaining the low computational resources required by the lifting transform over graphs. By using an online dataset we were able to positively assess the feasibility of using the novel method in an online BCI context
Detection of time reversibility in time series by ordinal patterns analysis
Time irreversibility is a common signature of nonlinear processes, and a
fundamental property of non-equilibrium systems driven by non-conservative
forces. A time series is said to be reversible if its statistical properties
are invariant regardless of the direction of time. Here we propose the Time
Reversibility from Ordinal Patterns method (TiROP) to assess time-reversibility
from an observed finite time series. TiROP captures the information of scalar
observations in time forward, as well as its time-reversed counterpart by means
of ordinal patterns. The method compares both underlying information contents
by quantifying its (dis)-similarity via Jensen-Shannon divergence. The
statistic is contrasted with a population of divergences coming from a set of
surrogates to unveil the temporal nature and its involved time scales. We
tested TiROP in different synthetic and real, linear and non linear time
series, juxtaposed with results from the classical Ramsey's time reversibility
test. Our results depict a novel, fast-computation, and fully data-driven
methodology to assess time-reversibility at different time scales with no
further assumptions over data. This approach adds new insights about the
current non-linear analysis techniques, and also could shed light on
determining new physiological biomarkers of high reliability and computational
efficiency.Comment: 8 pages, 5 figures, 1 tabl
Change Point Methods on a Sequence of Graphs
Given a finite sequence of graphs, e.g., coming from technological,
biological, and social networks, the paper proposes a methodology to identify
possible changes in stationarity in the stochastic process generating the
graphs. In order to cover a large class of applications, we consider the
general family of attributed graphs where both topology (number of vertexes and
edge configuration) and related attributes are allowed to change also in the
stationary case. Novel Change Point Methods (CPMs) are proposed, that (i) map
graphs into a vector domain; (ii) apply a suitable statistical test in the
vector space; (iii) detect the change --if any-- according to a confidence
level and provide an estimate for its time occurrence. Two specific
multivariate CPMs have been designed: one that detects shifts in the
distribution mean, the other addressing generic changes affecting the
distribution. We ground our proposal with theoretical results showing how to
relate the inference attained in the numerical vector space to the graph
domain, and vice versa. We also show how to extend the methodology for handling
multiple change points in the same sequence. Finally, the proposed CPMs have
been validated on real data sets coming from epileptic-seizure detection
problems and on labeled data sets for graph classification. Results show the
effectiveness of what proposed in relevant application scenarios
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