Epilepsy is a common neurological disorder characterized by abnormal excessive or synchronous neural activity in brain. In this study, we develop an unsupervised learning for seizure prediction. Extracting wavelet features of brain electroencephalogram (EEG), we propose a Hidden Markov Model (HMM) with a mixture of Gaussian observation model as an unsupervised learning setting for seizure prediction, where the seizure predictions are derived from the posterior distributions over the hidden states in the HMM. By using the Variational Bayesian (VB) method instead of the Maximum Likelihood estimation, which is the method commonly used for training HMMs, we overcome data overfitting and make it possible to compare models with different model orders by means of the variational free energy. VB learning also improves results in terms of convergence speed and achieved performance. The proposed method was evaluated using 20h of labeled EEG recordings from 7 epileptic rats with total number of 350 seizures. Our method obtained a high sensitivity of 90.7% and a specificity of 88.9% with early detection of 1.3s, which makes it more reliable than ML estimation with a sensitivity of 82.1% and a specificity of 86.2% and late detection of 4s. Keywords-Electroencephalogram (EEG); Epilepcy; seizure prediction; hidden Markov model (HMM); variational Bayesian . I. , {π θ K J J J J
In many multidimensional data such as radar recordings and astrophotography images, the receiver sensors record a linear mixture of signals propagated by a few activities, and the signal of each activity is repetition of a specific waveform at different times and with different amplitudes. The goal of multichannel blind deconvolution problem is retrieving the characteristics of the mentioned activities from the recorded signals. This problem is ill-posed without additional constraints, hence, different constraints are considered for this problem depending on the considered application. In this study, we propose a maximum likelihood framework for solving multichannel blind deconvolution problem when (1) the waveforms of the activities are time-limited signals, (2) the waveforms occur only a few times in the signal of each activity, or in other words, the occurrence times of the activities are sparse signals, and (3) there is no overlap between two consecutive occurrences of the waveform in the signal of each activity. The considered scenario can be adapted to several applications especially to neural recordings. We verify the efficiency of the proposed framework using simulations. Moreover, we apply the proposed framework on a real neural data set, and show how the obtained results can be employed to analyze the data from signal processing point of view.
Joint diagonalisation (JD) of a set of target matrices is a common approach to solve the blind source separation (BSS) problem. In fact, the separating matrix (the inverse of the mixing matrix) of the sources is the joint diagonaliser of the target matrices. In this study, the authors show that each row of the separating matrix maps the target matrices using a linear mapping into the new vectors which are located on a direct line along the corresponding column of the mixing matrix. Based on this geometrical interpretation, the authors propose a method for solving JD problem, which let us estimate the rows of the separating matrix and the columns of the mixing matrix, (i) independently and in parallel, (ii) consecutively or (iii) simultaneously. Simulation results in different scenarios such as additive noise, ill-posed mixing matrix, and high-dimensional data demonstrate the effectiveness of the proposed method relative to state-of-the-art JD methods. The authors also propose an approach to omit the effect of outlier data, which severely degrades parameters estimation. The proposed approach can be used in JD algorithms to improve their performance in the presence of outlier data.
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