State-space model estimation of EEG time series for classifying active brain sources

Electroencephalography (EEG) signals are known to be generated from the current source signals occurring inside human brains and these sources may or may not be active concurrently at a certain time. This paper aims to classify active and inactive sources from the information that can be inferred from parameters of a dynamical model that captures characteristics of EEG time series. We propose a state-space model for explaining coupled dynamics of the source and EEG signals where EEG is a linear combination of sources according to the characteristics of volume conduction. Our model has a structure that the sparsity pattern of the model output matrix can indicate the position of active and inactive sources. With this assumption, the proposed estimation method consists of two steps. Firstly, a subspace identification method is performed to estimate the dynamic matrix of the model and the mapping matrix from the state variable to EEG output. Secondly, the estimation of the output matrix in the state-space model from the mapping matrix is solved by a group lasso problem to promote a sparsity pattern. As a result, nonzero rows of the output matrix represent active source that corresponding to EEG data. We verify the performance of our method on randomly generated data sets that represent realistic human brain activities in a fair setting. An acceptable accuracy of 95 - 98% is obtained with a suitable selection of a problem parameter and a thresholding process to discard small magnitudes of the output matrix.