This paper investigates the interaction phenomena of the coupled axons while the mutual coupling factor is presented as a pairwise description. Based on the Hodgkin-Huxley model and the coupling factor matrix, the membrane potentials of the coupled myelinated/unmyelinated axons are quantified which implies that the neural coupling can be characterised by the presented coupling factor. Meanwhile the equivalent electric circuit is supplied to illustrate the physical meaning of this extended model. In order to estimate the coupling factor, a data-based iterative learning identification algorithm is presented where the Rényi entropy of the estimation error has been minimised. The convergence of the presented algorithm is analysed and the learning rate is designed. To verified the presented model and the algorithm, the numerical simulation results indicate the correctness and the effectiveness. Furthermore, the statistical description of the neural coupling, the approximation using ordinary differential equation, the measurement and the conduction of the nerve signals are discussed respectively as advanced topics. The novelties can be summarised as follows: 1) the Hodgkin-Huxley model has been extended considering the mutual interaction between the neural axon membranes, 2) the iterative learning approach has been developed for factor identification using entropy criterion, and 3) the theoretical framework has been established for this class of system identification problems with convergence analysis.
Extreme learning machine (ELM) is an effective machine learning technique with simple theory and fast implementation, which has gained increasing interest from various research fields recently. A new method that combines ELM with probabilistic model method is proposed in this paper to classify the electroencephalography (EEG) signals in synchronous brain-computer interface (BCI) system. In the proposed method, the softmax function is used to convert the ELM output to classification probability. The Chernoff error bound, deduced from the Bayesian probabilistic model in the training process, is adopted as the weight to take the discriminant process. Since the proposed method makes use of the knowledge from all preceding training datasets, its discriminating performance improves accumulatively. In the test experiments based on the datasets from BCI competitions, the proposed method is compared with other classification methods, including the linear discriminant analysis, support vector machine, ELM and weighted probabilistic model methods. For comparison, the mutual information, classification accuracy and information transfer rate are considered as the evaluation indicators for these classifiers. The results demonstrate that our method shows competitive performance against other methods.
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