Decomposition of Neurological Multivariate Time Series by State Space Modelling |
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Authors: | Andreas Galka Kin Foon Kevin Wong Tohru Ozaki Hiltrud Muhle Ulrich Stephani Michael Siniatchkin |
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Institution: | (1) Department of Neurology, University of Kiel, Kiel, Germany;(2) Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany;(3) Institute of Statistical Mathematics (ISM), Minami-Azabu 4-6-7, Tokyo 106-8569, Japan;(4) Department of Neuropediatrics, University of Kiel, 24098 Kiel, Germany |
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Abstract: | Decomposition of multivariate time series data into independent source components forms an important part of preprocessing
and analysis of time-resolved data in neuroscience. We briefly review the available tools for this purpose, such as Factor
Analysis (FA) and Independent Component Analysis (ICA), then we show how linear state space modelling, a methodology from
statistical time series analysis, can be employed for the same purpose. State space modelling, a generalization of classical
ARMA modelling, is well suited for exploiting the dynamical information encoded in the temporal ordering of time series data,
while this information remains inaccessible to FA and most ICA algorithms. As a result, much more detailed decompositions
become possible, and both components with sharp power spectrum, such as alpha components, sinusoidal artifacts, or sleep spindles,
and with broad power spectrum, such as FMRI scanner artifacts or epileptic spiking components, can be separated, even in the
absence of prior information. In addition, three generalizations are discussed, the first relaxing the independence assumption,
the second introducing non-stationarity of the covariance of the noise driving the dynamics, and the third allowing for non-Gaussianity
of the data through a non-linear observation function. Three application examples are presented, one electrocardigram time
series and two electroencephalogram (EEG) time series. The two EEG examples, both from epilepsy patients, demonstrate the
separation and removal of various artifacts, including hum noise and FMRI scanner artifacts, and the identification of sleep
spindles, epileptic foci, and spiking components. Decompositions obtained by two ICA algorithms are shown for comparison. |
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