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. 2015 Mar;27(3):615-27.
doi: 10.1162/NECO_a_00656. Epub 2014 Aug 22.

Delay differential analysis of electroencephalographic data

Claudia Lainscsek  1 , Manuel E Hernandez, Howard Poizner, Terrence J Sejnowski
Affiliations

Delay differential analysis of electroencephalographic data

Claudia Lainscsek et al. Neural Comput. 2015 Mar.

Abstract

We propose a time-domain approach to detect frequencies, frequency couplings, and phases using nonlinear correlation functions. For frequency analysis, this approach is a multivariate extension of discrete Fourier transform, and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short and sparse time series and can be extended to cross-trial and cross-channel spectra (CTS) for electroencephalography data where multiple short data segments from multiple trials of the same experiment are available. There are two versions of CTS. The first one assumes some phase coherency across the trials, while the second one is independent of phase coherency. We demonstrate that the phase-dependent version is more consistent with event-related spectral perturbation analysis and traditional Morlet wavelet analysis. We show that CTS can be applied to short data windows and yields higher temporal resolution than traditional Morlet wavelet analysis. Furthermore, the CTS can be used to reconstruct the event-related potential using all linear components of the CTS.

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Figures

Figure 1
Figure 1
Realignment of data for the computation of a cross-trial spectrogram (CTS) that assumes some phase coherence in the data. First, the data are realigned around the stimulus S. Then for each data window, the data are concatenated and a new time vector is generated. The concatenated data are then the signal 𝒮 in equation 1.1, and the new time vector is the time in the probing signal.
Figure 2
Figure 2
Frequency spectra time-locked to a stimuli onset (dashed white line) in the Cz electrode for the (a) Morlet wavelet spectrogram, (b) phase-dependent cross-trial spectrogram (CTS), (c) phase-independent CTS, and (d) cross-trial bispectrum (CTB), based on 50 randomly selected trials.
Figure 3
Figure 3
Frequency spectra of raw, unprocessed EEG data from the previously selected trials in Figure 2 time-locked to a stimuli onset (dashed white line) in the Cz electrode, for the (a) Morlet wavelet spectrogram, (b) phase-dependent cross-trial spectrogram (CTS), (c) phase-independent CTS, and (d) cross-trial bispectrum (CTB).
Figure 4
Figure 4
Coherence analysis before and after the stimulus (S) in raw and clean EEG data in theta (3–8 Hz), alpha (8–12 Hz), and low (12–20 Hz) and high (20–30 Hz) beta frequency bands using the cross-correlation between the phase-dependent and phase-independent CTS.
Figure 5
Figure 5
Event-related potentials (ERP) and event-related spectral perturbations (ERSPs) on (a, b) raw and (c, d) clean data, demonstrating low-frequency activity after the stimuli (S) in both raw and clean EEG data.
Figure 6
Figure 6
Event-related potential (ERP) time-locked to stimuli (top) and representative ERP reconstructions using 50, 100, 150, and 200 ms data windows. As the data windows increase, more of the lower-frequency characteristics of the ERP such as the negative drift prior to the tone onset are recovered, as measured by the increased cross-correlation between the original and the reconstructed ERP.
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