Multi-domain Features of the Non-phase-locked Component of Interest Extracted from ERP Data by Tensor Decomposition

Abstract

The waveform in the time domain, spectrum in the frequency domain, and topography in the space domain of component(s) of interest are the fundamental indices in neuroscience research. Despite the application of time-frequency analysis (TFA) to extract the temporal and spectral characteristics of non-phase-locked component (NPLC) of interest simultaneously, the statistical results are not always expectedly satisfying, in that the spatial information is not considered. Complex Morlet wavelet transform is widely applied to TFA of event-related-potential (ERP) data, and mother wavelet (which should be firstly defined by center frequency and bandwidth (CFBW) before using the method to TFA of ERP data) influences the time-frequency results. In this study, an optimal set of CFBW was firstly selected from the number sets of CFBW, to further analyze for TFA of the ERP data in a cognitive experiment paradigm of emotion (Anger and Neutral) and task (Go and Nogo). Then tensor decomposition algorithm was introduced to investigate the NPLC of interest from the fourth-order tensor. Compared with the TFA results which only revealed a significant difference between Go and Nogo task condition, the tensor-based analysis showed significant interaction effect between emotion and task. Moreover, significant differences were found in both emotion and task conditions through tensor decomposition. In addition, the statistical results of TFA would be affected by the selected region of interest (ROI), whereas those of the proposed method were not subject to ROI. Hence, this study demonstrated that tensor decomposition method was effective in extracting NPLC, by considering spatial information simultaneously as the potential to explore the brain mechanisms related to experimental design.

Objective Extraction of Evoked Event-Related Oscillation from Time-Frequency Representation of Event-Related Potentials

“…Thirdly, we have to define a mother wavelet by a set of bandwidth and frequency centre (BWCF) before we used morlet wavelet transformation to transform the time-domain signals into time-frequency signals. According to our previous study [ 20 ], different sets of BWCF could lead to different time-frequency results; thus, the experimenters have to attempt the number of BWCF for TFA and then select an optimal one from them for the TFA of ERP signals.…”

“…Sequentially, TFRs were calculated by the wavelet transform for the source, mixed, and projected signals separately. During this step, aiming at obtaining better time resolution and frequency resolution of TFRs, the centre frequency and bandwidth were set as 1, respectively, to define a mother wavelet as applied in our previous study [ 20 ]. The frequency range of interest was defined from 1 to 15 Hz with 30 frequency bins in nonlinear distribution.…”

“…For the back-projected components from the original signal , we turned this time domain signal to time-frequency domain signal using the complex morlet wavelet transform [ 20 , 38 – 44 ]. Specifically, a mother wavelet was first defined using a set of bandwidth and centre frequency.…”

Objective Extraction of Evoked Event-related Oscillations from Time-frequency Representation of Event-related Potentials

“…The TFRs were calculated via wavelet transformation for the source, mixed, and the extracted signals separately. Meanwhile, aiming at obtaining better time-resolution and frequency-resolution of TFRs, the center frequency and bandwidth were set as 1 respectively to define the mother wavelet as applied in our previous study (Zhang et al, 2020), and the frequency range of interest was from 1 to 15Hz with 40 frequency bins in nonlinear distribution. For each frequency layer, the power values were baseline corrected by subtracting the mean power of the baseline (200 ms before the stimulus onset) for each point using the subtraction approach (Benvenuti et al, 2017;Hu et al, 2014;Peng et al, 2019).…”

“…Thus, all of them should be selected to project to the electrode filed to correct their indeterminacy for further analysis. Herrmann et al, 2014; Zhang et al, 2020). Specifically, a mother wavelet was first defied using a set of bandwidth and center frequency.…”