Generalized synchronization between coupled dynamical systems is a phenomenon of relevance in applications that range from secure communications to physiological modelling. Here, we test the capabilities of reservoir computing and, in particular, echo state networks for the detection of generalized synchronization. A nonlinear dynamical system consisting of two coupled Rössler chaotic attractors is used to generate temporal series consisting of time-locked generalized synchronized sequences interleaved with unsynchronized ones. Correctly tuned, echo state networks are able to efficiently discriminate between unsynchronized and synchronized sequences even in the presence of relatively high levels of noise. Compared to other state-of-the-art techniques of synchronization detection, the online capabilities of the proposed Echo State Network based methodology make it a promising choice for real-time applications aiming to monitor dynamical synchronization changes in continuous signals.
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State Visual Evoked Potentials (SSVEPs) arise from a resonance phenomenon in the visual cortex that is produced by a repetitive visual stimulus. SSVEPs have long been considered a steady-state response resulting from purely oscillatory components phase locked with the stimulation source, matching the stimulation frequency and its harmonics. Here we explore the dynamical character of the SSVEP response by proposing a novel non-stationary methodology for SSVEP detection based on an ensemble of Echo State Networks (ESN). The performance of this dynamical approach is compared to stationary canonical correlation analysis (CCA) for the detection of 6 visual stimulation frequencies ranging from 12 to 22 Hz. ESN-based methodology outperformed CCA, achieving an average information transfer rate of 47 bits/minute when simulating a BCI system of 6 degrees of freedom. However, for some subjects and stimulation frequencies the detection accuracy of CCA exceeds that of ESN. The comparison suggests that each methodology captures different features of the SSVEP response: while CCA captures purely stationary patterns, the ESN-based approach presented here is capable of detecting the non-stationary nature of the SSVEP.
BackgroundRecent years have witnessed an increased interest in the use of steady state visual evoked potentials (SSVEPs) in brain computer interfaces (BCI), SSVEP is considered a stationary brain process that appears when gazing at a stimulation light source.New MethodsThe complex nature of brain processes advocates for non-linear EEG analysis techniques. In this work we explore the use of an Echo State Networks (ESN) based architecture for dynamical SSVEP detection.ResultsWhen simulating a 6-degrees of freedom BCI system, an information transfer rate of 49bits/min was achieved. Detection accuracy proved to be similar for observation windows ranging from 0.5 to 4 seconds.Comparison with existing methodsSSVEP detection performance has been compared to standard canonical correlation analysis (CCA). CCA achieved a maximum information transfer rate of 21 bits/minute. In this case detection accuracy increased along with the observation window lengthConclusionsAccording to here presented results ESN outperforms standard canonical correlation and has proved to require shorter observation time windows. However ESN and CCA approaches delivered diverse classification accuracies at subject level for various stimulation frequencies, proving to be complementary methods. A possible explanation of these results may be the occurrence of evoked responses of different nature, which are then detected by different approaches. While reservoir computing methods are able to detect complex dynamical patterns and/or complex synchronization among EEG channels, CCA exclusively captures stationary patterns. Therefore, the ESN-based approach may be used to extend the definition of steady-state response, considered so far a stationary process.HighlightsWe present a novel SSVEP dynamical detection approach based on ESN.This is the first time ESNs are applied to SSVEP based BCI systems.We provide experimental validation of proposed methodology.Experimental results indicate non-stationarity in SSVEP patterns.
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