To estimate the robustness of different ERSP models to noise, for both the artificial and the real EEG data described above, we added noise to a given percentage of data trials. To model noise in single-trials, an independent Gaussian noise with SD of five times the SD of the EEG data — computed over all time points and all data trials — was added to a random set of trials in Figure 5 , we varied this coefficient from 1 to 5.
In order to evaluate the accuracy of the two different baseline correction methods, we first used the artificial EEG dataset containing the controlled spectral perturbation and computed confusion matrices for each ERSP method and for each percentage of noisy trials. We considered True Positives TP, i. Similarly, the maximum FP is reached when all the time—frequency estimates outside of the spectral perturbation area are significant. These measures allow evaluating the quality of each ERSP method through different metrics basically defined by signal detection theory and used in evaluation of classifiers or subject performances in categorization tasks Green and Swets, ; Fawcett, We computed sensitivity, i.
Both metrics can be formalized as follows:. Figure 2 shows that when computing single-trial baseline, post-baseline spectral estimates tend to be biased toward positive values. This effect occurs because spectral estimates are skewed toward positive values. Therefore performing single-trial baseline correction is sensitive to post-stimulus outliers and large positive post-baseline values are dominating the ERSP. One hypothesis is that pre-stimulus outliers affect the post-stimulus results as if the pre-stimulus data were stable, then the results would not be so sensitive to how the baseline subtraction is handled.
However, the fact that this bias is observed with Gaussian noise disproves this hypothesis.
The bias is a result of non-stationary of both the EEG signal and the computation method Figure 3. Figure 2.
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Single-trial baseline correction. Figure 3. Comparison of different baseline approaches.
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This figure shows spectral power at 5. The thick black line represents the average of all trials. Figure 3 shows the apparent superiority of full-epoch length single-trial correction. For the classical baseline methods, outliers with large power values are clearly visible Figure 3 A. The middle panel Figure 3 B shows the single-trial pre-stimulus baseline approach where data is well normalized in the baseline period.
However in the post-stimulus period positive outliers are clearly visible and bias the average spectral estimate toward positive values. This is the same effect we were observing in the bottom row of Figure 2. In the last panel Figure 3 C , we use the single-trials full-epoch length correction method see Materials and Methods , and observe that all single-trial corrected spectral estimates are within the same range of z -score values.
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In the rest of this manuscript, we focus on comparing classical ERSP methods versus ERSP methods based on single-trial full-epoch length correction methods. We then compared the performance of classical ERSP methods versus single-trial full-epoch length correction methods on artificial data using the baseline permutation statistical methods Figure 4.
However, using other ERSP methods return similar results.
The bootstrap random polarity inversion method for significant testing returned qualitatively similar results. Figure 4. B Sensitivity and specificity of the two methods. Significance of ERSP results is computed using baseline permutation statistical method. Table 1. It may be argued that low sensitivity to noisy trials of the classical ERSP method depends on the level of the noise introduced. We thus used the same two ERSP methods on noisy trials with different amplitudes of noise. We used different coefficient values ranging from 1 to 5.
Results are presented on Figure 5 , which shows that for all values of coefficient greater than 1, the ERSP method using single-trial correction clearly outperforms the classical ERSP method with a higher TP rate of significant values and a comparable rate of FN responses. This performance improves as the coefficient increases. Figure 5. All methods show similar ERSP images with interesting nuances. Region 1 circled in Figure 6 shows a significant feature at high frequency that appears only when classical baseline correction methods are used.
Since it is not present for the single-trial baseline correction, this region most likely represents activity from a few noisy data trials. After visual inspection of the raw data, 6 of the data trials proved to contain high frequency noise. Upon removal of these data trials, region 1 is not any more significant and visible in classical method results. In addition, region 1 did not prove to be significant in any of the other 13 subjects of the same study. Region 3 indicates a post-stimulus power decrease centered at about 13 Hz and spanning over the 10 to Hz frequency band for the ERSP z method.
For all single-trial correction solutions, one additional significant region appears region 4. This region corresponds to an early post-stimulus power increase in the 5 to 7-Hz frequency band. Note that the positive peak in the last panel of Figure 3 at about ms corresponds to region 4 in Figure 6. To test if significance in this region was driven by noise, we applied a band-pass filter to single-trials between 5 and 7 Hz and showed that the filtered signal exceeded the SE of the average signal in the to ms time region.
The presence of this additional region, although anecdotal, argues in favor of using single-trial baseline methods, which renders visible finer grained spectral changes. Note that the subject selected for Figure 6 was chosen for didactic purposes. When spectral activity is more homogenous across trials, the six types of ERSP are more similar. Figure 6. The top row shows results from classical baseline ERSP methods. The bottom row shows ERSP using full-epoch length single-trial correction.
Circled regions of interest are discussed in the text. We attempted to determine if regions of significance differed across ERSP methods. We also tried two methods for assessing significance: baseline permutation and bootstrap random polarity inversion see Materials and Methods.
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Table 2 summarizes the mean over 14 subjects of the number of significant pixels for different ERSP methods. Classical baseline and single-trial correction methods also differed significantly although the method returning more significant pixel was contingent on the statistical method used to assess significance. Table 2. Mean percentage of significant time—frequency points pixels for different ERSP methods for electrode Iz.
In Figure 7 , we test the hypothesis that full-epoch length single-trial baseline approaches are less sensitive to outlier trials in real EEG. To test this hypothesis, we first added noisy trials to real EEG see Materials and Methods and estimated the number of significant time—frequency points pixels for different ERSP time—frequency decomposition.
We also used two independent methods to estimate significance: either the baseline permutation method or the bootstrap random polarity inversion method see Materials and Methods. It shows that if the percentage of noisy trials is greater than 2, the single-trial method gives more significant pixels than the classical method, although this difference decreases monotonically as the number of trials increases. Note that the percentage of significant pixels is not a true measure of sensitivity as the ones presented in Figure 4. However, given that we do not have access to the TP pixel measure, it is not possible to compute the more rigorous measures we used for artificial data.
Figure 7. Two different statistical methods are tested: the baseline permutation method on the left column, and the bootstrap random polarity inversion method on the right column see Materials and Methods. Classical ERSP baseline correction methods are represented in red and single-trial correction methods are represented in blue.
Single-trial correction methods always outperform classical baseline methods when the number of noisy trials increases.
A percentage of overlap between two ERSP methods was computed for each subject by taking the ratio between the intersection of significant regions and the union of these regions. This percentage of overlap was then averaged across subjects:.