Diogo C. Soriano

Comparative analysis of strategies for feature extraction and classification in SSVEP BCIs.

Abstract Brain–computer interface (BCI) systems based on electroencephalography have been increasingly used in different contexts, engendering applications from entertainment to rehabilitation in a non-invasive framework. In this study, we perform a comparative analysis of different signal processing techniques for each BCI system stage concerning steady state visually evoked potentials (SSVEP), which includes: (1) feature extraction performed by different spectral methods (bank of filters, Welchs method and the magnitude of the short-time Fourier transform); (2) feature selection by means of an incremental wrapper, a filter using Pearsons method and a cluster measure based on the Davies–Bouldin index, in addition to a scenario with no selection strategy; (3) classification schemes using linear discriminant analysis (LDA), support vector machines (SVM) and extreme learning machines (ELM). The combination of such methodologies leads to a representative and helpful comparative overview of robustness and efficiency of classical strategies, in addition to the characterization of a relatively new classification approach (defined by ELM) applied to the BCI-SSVEP systems.

Do chaos-based communication systems really transmit chaotic signals?

Many communication systems based on the synchronism of chaotic systems have been proposed as an alternative spread spectrum modulation that improves the level of privacy in data transmission. However, depending on the map and on the encoding function, the transmitted signal may cease to be chaotic. Therefore, the sensitive dependence on initial conditions, which is one of the most interesting properties for employing chaos in telecommunications, may disappear. In this paper, we numerically analyze the chaotic nature of signals modulated using a system that employs the Ikeda map. Additionally, we propose changes in the communication system in order to guarantee that the modulated signals are in fact chaotic. HighlightsWe analyze a chaos-based communication system to verify if the signals are chaotic.An analysis concerning the presence of co-existing attractors in the Ikeda map is performed.We compute Lyapunov exponents of the orbits of the Ikeda map, including an encoded message.We propose a strategy to guarantee a truly chaos-based system.

Performance analysis of nonlinear echo state network readouts in signal processing tasks

Echo state networks (ESNs) characterize an attractive alternative to conventional recurrent neural network (RNN) approaches as they offer the possibility of preserving, to a certain extent, the processing capability of a recurrent architecture and, at the same time, of simplifying the training process. However, the original ESN architecture cannot fully explore the potential of the RNN, given that only the second-order statistics of the signals are effectively used. In order to overcome this constraint, distinct proposals promote the use of a nonlinear readout aiming to explore higher-order available information though still maintaining a closed-form solution in the least-squares sense. In this work, we review two proposals of nonlinear readouts - a Volterra filter structure and an extreme learning machine - and analyze the performance of these architectures in the context of two relevant signal processing tasks: supervised channel equalization and chaotic time series prediction. The obtained results reveal that the nonlinear readout can be decisive in the process of aproximating the desired signal. Additionally, we discuss the possibility of combining both ideas of nonlinear readouts and preliminary results indicate that a performance improvement can be attained.

Unorganized Machines: From Turing’s Ideas to Modern Connectionist Approaches

This work presents a discussion about the relationship between the contributions of Alan Turing – the centenary of whose birth is celebrated in 2012 – to the field of artificial neural networks and modern unorganized machines: reservoir computing (RC) approaches and extreme learning machines (ELMs). Firstly, the authors review Turing’s connectionist proposals and also expose the fundamentals of the main RC paradigms – echo state networks and liquid state machines, - as well as of the design and training of ELMs. Throughout this exposition, the main points of contact between Turing’s ideas and these modern perspectives are outlined, being, then, duly summarized in the second and final part of the work. This paper is useful in offering a distinct appreciation of Turing’s pioneering contributions to the field of neural networks and also in indicating some perspectives for the future development of the field that may arise from the synergy between these views.

Characterization of multiscroll attractors using Lyapunov exponents and Lagrangian coherent structures.

The present work aims to apply a recently proposed method for estimating Lyapunov exponents to characterize-with the aid of the metric entropy and the fractal dimension-the degree of information and the topological structure associated with multiscroll attractors. In particular, the employed methodology offers the possibility of obtaining the whole Lyapunov spectrum directly from the state equations without employing any linearization procedure or time series-based analysis. As a main result, the predictability and the complexity associated with the phase trajectory were quantified as the number of scrolls are progressively increased for a particular piecewise linear model. In general, it is shown here that the trajectory tends to increase its complexity and unpredictability following an exponential behaviour with the addition of scrolls towards to an upper bound limit, except for some degenerated situations where a non-uniform grid of scrolls is attained. Moreover, the approach employed here also provides an easy way for estimating the finite time Lyapunov exponents of the dynamics and, consequently, the Lagrangian coherent structures for the vector field. These structures are particularly important to understand the stretching/folding behaviour underlying the chaotic multiscroll structure and can provide a better insight of phase space partition and exploration as new scrolls are progressively added to the attractor.

Blind extraction of chaotic sources from mixtures with stochastic signals based on recurrence quantification analysis

This work aims to present a new method to perform blind extraction of chaotic deterministic sources mixed with stochastic signals. This technique employs the recurrence quantification analysis (RQA), a tool commonly used to study dynamical systems, to obtain the separating system that recovers the deterministic source. The method is applied to invertible and underdetermined mixture models considering different stochastic sources and different RQA measures. A brief discussion about the influence of recurrence plot parameters on the robustness of the proposal is also provided and illustrated by a set of representative simulations.

SEARCHING FOR SPECIFIC PERIODIC AND CHAOTIC OSCILLATIONS IN A PERIODICALLY-EXCITED HODGKIN-HUXLEY MODEL

This work has a twofold aim: to present a numerical analysis of the Hodgkin–Huxley model in a nonsmooth excitation scenario — which is both challenging and theoretically relevant — and to use the established framework as a basis for testing a method to search for specific oscillating patterns in dynamical systems. The analysis is founded on classical qualitative methods — bifurcation diagrams, phase space and spectral analysis — and on the calculation of the system Lyapunov spectrum. This calculation is carried out by means of an algorithm particularly suited to deal with nonsmooth excitation and the complexity of the state equations. The obtained Lyapunov exponents are then used to build a robust cost function (invariant with respect to the initial conditions or specific trajectories in a given basin of attraction) for seeking predefined dynamical patterns that are optimized using the particle swarm optimization algorithm. This bioinspired method possesses two desirable features: it has a significant global search potential and does not demand cost function manipulation. The proposed approach, which was tested here in different representative scenarios for the Hodgkin–Huxley model, has a promising application potential in general dynamical contexts and can also be a valuable tool in the planning of drug administration and electrical stimulation of neuronal and cardiac cells.

White Gaussian Chaos

A discrete-time white Gaussian noise (WGN) is a random process with impulsive autocorrelation function. Also, the random variables obtained by sampling the process at any time instants are jointly Gaussian. WGN is widely used to model noise in engineering and physics. In this letter, we propose a way to generate chaotic signals that behave like WGN, due to the features of its autocorrelation function and its invariant density. From the tent map and by using as conjugacy map transformations commonly employed to random variables, we obtain a white Gaussian chaos (WGC) map. Numerical simulations are shown to illustrate the technique. WGC can be an interesting choice for chaos generator in chaos-based communication systems.

Effect of the combination of different numbers of flickering frequencies in an SSVEP-BCI for healthy volunteers and stroke patients

The steady-state visually evoked potential (SSVEP) is a particular response of the brain observed as an oscillating wave induced by repetitive visual stimulation. This paper focuses on the use of this paradigm for the construction of a brain-computer interface (BCI) system using different numbers of visual stimuli in different frequencies. The responses were analyzed for healthy subjects and stroke patients and show that a suitable choice of stimulation frequencies can be of paramount importance insofar as the system performance is concerned.

Music versus motor imagery for BCI systems a study using fMRI and EEG: Preliminary results

The development of brain-computer interfaces (BCIs) for disabled patients is currently a growing field of research. Most BCI systems are based on electroencephalography (EEG) signals, and within this group, systems using motor imagery (MI) are amongst the most flexible. However, for stroke patients, the motor areas of the brain are not always available for use in these types of devices. The aim of this work was to evaluate a set of imagery-based cognitive tasks (right-hand MI versus music imagery, with rest or “blank” periods in between), using functional Magnetic Resonance Imaging (fMRI) and EEG. Eleven healthy subjects (control group) and four stroke patients were evaluated with fMRI, and nine of the healthy subjects also underwent an EEG test. The fMRI results for the control group showed specific and statistically differentiable activation patterns for motor versus music imagery (t-test, p <; 0.001). For stroke patients the fMRI results showed a very large variability, with no common activation pattern for either of the imagery tasks. Corroborating this fact, EEG results concerning feature selection for minimizing the classification error (using the Davies-Bouldin index) have also found no common activation pattern, although a well-defined set of meaningful electrodes and frequencies was found for some subjects. In terms of classification performance using EEG data, this work has detected a group of subjects with classifier rate of success up to 60%, which is promising in view of the cognitive complexity of the adopted tasks.