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The problems of mathematical modelling, feature extraction and classification of electroencephalogram (EEG) signals have been considered in this chapter. They play a vital role in medical diagnosis and in developing information systems for brain-computer interface technologies. The chapter introduces a mathematical framework for EEG signal representation, utilizing the theory of linear random processes and conditional linear random processes. The mathematical model of EEG signal has been justified using biophysical nature of EEG generation as the sum of large number of random postsynaptic potentials occurring at Poisson time moments. The properties of multivariate characteristic function, expectation and covariance function of the model have been analyzed. The estimations of autocorrelation functions and power spectrum density of EEG signal of different brain states have been represented and analyzed. The new set of diagnostic features has been extracted as a set of samples of the kernel of the EEG signal model in the form of discrete time linear random process. A comparative examination of binary classification machine learning methods is conducted, focusing on autoregressive coefficients and the newly extracted features. The improvement of classification metrics has been shown.

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EEG Signal Classification Using Linear Process Model-Based Feature Extraction and Supervised Learning

  • 章节

  • 发表日期：

    2025年

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  • Artur Zaporozhets,
  • Yurii Kuts,
  • Bogdana Mlynko,
  • Mykhailo Fryz,
  • Leonid Scherbak

摘要

The problems of mathematical modelling, feature extraction and classification of electroencephalogram (EEG) signals have been considered in this chapter. They play a vital role in medical diagnosis and in developing information systems for brain-computer interface technologies. The chapter introduces a mathematical framework for EEG signal representation, utilizing the theory of linear random processes and conditional linear random processes. The mathematical model of EEG signal has been justified using biophysical nature of EEG generation as the sum of large number of random postsynaptic potentials occurring at Poisson time moments. The properties of multivariate characteristic function, expectation and covariance function of the model have been analyzed. The estimations of autocorrelation functions and power spectrum density of EEG signal of different brain states have been represented and analyzed. The new set of diagnostic features has been extracted as a set of samples of the kernel of the EEG signal model in the form of discrete time linear random process. A comparative examination of binary classification machine learning methods is conducted, focusing on autoregressive coefficients and the newly extracted features. The improvement of classification metrics has been shown.