Event-related components are structurally represented by intrinsic event-related potentials

Figure 1. iERP analysis of EEG/MEG signals. (a) Flowchart of iERP analysis. The iERP method involves using the improved CEEMDAN method to obtain IMFs for EEG/MEG data of each trial at each channel for each condition and participant. The IMFs and their various partial sums are then averaged over trials within each condition for each channel and each participant to form iERP modes. The statistical effects were obtained by incorporating a special definition of neighbors for each mode in existing cluster-based statistical tests. (b) Illustration of the signal decomposition with the CEEMDAN method and IF distributions of the IMFs.

Figure 2. iERP analysis on EEG data of the face perception task. (a) Illustration of the face perception task in the first example, the IF distributions of the IMFs of the 200-Hz EEG data, and the representative right temporoparietal EEG channel (EEG065). (b) iERP results for the EEG signals from the EEG065 channel and TFCE repeated-measures ANOVA of the three conditions within the 2D [mode, time (50–700 ms)] domain. Time windows in yellow indicate P < 0.005 for TFCE. (c) Conventional ERP results corresponding to the iERP results in (b). (d) Statistical contrast of the iERPs between unscrambled faces (famous + unfamiliar) and scrambled faces (indicated by T values). Regions with completely opaque colors indicate P < 0.025 for TFCE. (e) Statistical contrast of the iERP results between famous and unfamiliar faces. Conventions are the same as those in (d). (f) Conventional ERP contrast between unscrambled and scrambled faces. (g) Conventional ERP contrast between famous and unfamiliar faces.

Figure 3. Topographical iERP results. (a) Topographical contrast between the iERP results for unscrambled faces (famous + unfamiliar) and scrambled faces. Statistical effects were identified using the standard CBnPP test in the 3D [channel, mode, time] domain. White circles denote the regions of “cluster P” < 0.025 in the testing domain. (b) Topographical contrast between the conventional ERP method results for unscrambled and scrambled faces. (c) Topographical contrast between the iERP results for famous and unfamiliar faces. Conventions are the same as in (a). (d) Topographical contrast between the conventional ERP method results for famous and unfamiliar faces.

Figure 4. Compact representation of the iERP results, where the y-axis and x-axis denote the initial and end IMFs of a mode, respectively. (a,b) For the contrast between unscrambled and scrambled faces, the right temporoparietal electrode cluster demonstrated clear P100 and N170 effects at 80–140 and 140–200 ms, respectively. However, the P100 effect was pronounced only if IMF 6+ was not included, whereas the N170 effect exhibited increased statistical effects in modes involving IMF 6+. (c) Compared with unfamiliar faces, famous faces exhibited more negative iERP amplitudes in the right temporoparietal cluster at 200–260 ms. (d) A more negative deflection of the iERP at the right prefrontal electrode cluster (EEG026, EEG027, EEG037, and EEG038) was observed for famous faces than for unfamiliar faces at 260–320 ms if a mode included IMF 4 but not IMF 6+.

Figure 5. iERP analysis on EEG data of the VWM task. (a) Illustration of the VWM task in the second example, IF distributions of the IMFs of the 1000-Hz EEG data, and parietal electrodes for determining the mean difference between the contralateral and ipsilateral amplitudes of the iERPs. (b) Statistical contrast of the iERPs between the contralateral and ipsilateral parietal electrodes, with the corresponding conventional ERP results shown below for comparison. The statistical results were obtained using a one-sample CBnPP test on the differences between the contralateral and ipsilateral amplitudes of the iERPs within the 2D [mode, time (0–600 ms)] iERP domain [for conventional ERP, the 1D (time) domain]. (c) Statistical contrast of the topographical iERPs between the hit-left and hit-right conditions (first graph), which revealed a pronounced negative effect across all iERP modes on the right parietal electrodes (trough T = − 5.15, cluster P = 0.0016, α = 0.05, N = 20) but not a positive effect on the left parietal electrodes. The results in (c) are partially consistent with the expected pattern. Pearson correlation analysis revealed a pronounced positive correlation between the…

Figure 6. Time scale consistency in the order of IMFs investigated through the box-and-whisker plots (the box depicting the median and the 25th and 75th quartiles and the whisker showing the 5th and 95th percentile) of instantaneous frequencies of IMFs of EEG data in the first example. (a) Between-subjects analysis: interchannel and intersubject time scale consistency in the order of IMFs. Each box-and-whisker plot represents the distribution of subjects’ representative frequencies of a specific IMF order at a given channel. For each subject, the representative frequency of a specific IMF order at a given channel is the frequency with the maximum occurrence probability in the instantaneous frequency distribution of IMFs of the order at the given channel. (b) Within-subject analysis (only for subject 10): interchannel and intertrial time scale consistency in the order of IMFs. Each box-and-whisker plot represents the distribution of instantaneous frequencies of IMFs of a specific order at a given channel from all trials.