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Abstract
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One of the most important issues in analyzing the time series is to find a method that is highly capable and at the same time be stable with respect to irregular stochastic variations (noise). A lot of efforts have been made in this direction and many methods have been introduced, but many of them are based on restrictive assumptions such as normal and linearity, which may not be hold in practice. Singular spectral analysis is a powerful nonparametric method for analyzing time series data that is used to reduce noise disturbances and modeling. In principle, this method reconstructs a signal into components that are interpretable, such as trends, seasonal component, and noise terms and are not based on limiting assumptions such as being normal and linearity. Although classical singular spectral analysis has many good features in practice, it does not require performance in the analysis of nonstationary series as this method works with the covariance matrix. Many of the actual signals, especially physiological signals such as the EEG, are not stationary. A tensor based singular spectral analysis method is a good way to solve this problem, which improves the performance of the ordinary singular spectral analysis algorithm significantly in nonstationary series by applying tensor decomposition instead of singular value decomposition. In this thesis, the mentioned methods are used as a filter to feature extraction of the EEG signal, and then the extracted features are used by an artificial neural network to predict the sleep stages. Finally, by working on real data and simulation studies, we will compare the performance of considered approach to the typical singular spectral analysis method in nonstationary series.
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