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list of spatial patterns according to the discriminative power between two populations. As a result,
the spatial pattern with the maximal variance of
post
X
would capture the minimal variance of
pre
X
, and vice versa. Typically, only a few spatial patterns were sufficient for the discrimination 130
between two populations [17]. These few spatial patterns, which can isolate stimulus-evoked EEG
responses (contained only in
post
X
) from spontaneous EEG activity (contained in
post
X
as well
as
pre
X
), worked as an effective spatial filter. In the present study, three eigenvectors
corresponding to the largest eigenvalues of
post
X
and lowest eigenvalues of
pre
X
were
selected to reconstruct spatial-filtered single-trial EEG responses of all channels (see Section 1 in 135
the Supplementary materials for the reason of selecting three CSP components).
1.2.3 Multiple linear regression
To estimate single-trial LEP features automatically and reliably, we applied a multiple linear
regression method [22] to LEP trials recorded at Cz within the post-stimulus time interval (0 to
500 ms), which were filtered using the combination of BPF, ICA, and CSP. The MLR approach 140
takes into account the variability of both N2 and P2 latency and amplitude of LEPs, and models
single-trial LEP responses as follows:
(
(
(
=+++
NN N PP P
taytl aytl
(2)
where
(
t is a modeled single-trial LEP waveform that varies as a function of time t ,
)(ty
N
and
)(ty
P
are the templates of N2 and P2 waves, which can generally be obtained as
the average of all LEP trials of each participant,
N
a
and
P
a
are the weights of N2 and P2 145
templates, and
N
l
and
P
l
are the latency shift values of the N2 and P2 templates, respectively.
Since the N2 and P2 peaks of the LEPs reflect the activity of the different neural generators [5],
and their amplitudes can be differentially modulated by several experimental factors (e.g., spatial
attention and probability of perception) [23,24], we modeled the N2 and P2 waves separately, thus
avoiding the assumption that all generators contributing to the LEP responses covary linearly [25]. 150
Using the Taylor expansion, the MLR model can be written as follows:
(
(
(
() () () ()
ββ ββ β
≈+ ++ +
=+ ++ +
NN NN N PP PP P
1N 2 N 3P 4 P 5
ft ay t lay' t ay t lay' t
yt y't yt y't
(3)
where
(
N
't
and
()
P
y' t
are the temporal derivatives of N2 and P2 templates, respectively,
and
is the residual term. Thus the single trial LEP waveform is approximated using the sum of
the weighted averages of N2 and P2 templates and their respective temporal derivatives.
Considering that these weights (
1
,
2
,
3
,
4
,
5
) captured the single-trial variability of N2 155
and P2 latency and amplitude in LEPs, these coefficients could be closely related to the subjective
intensity of pain perception. Correlations between these estimated single-trial coefficients and the
corresponding single-trial ratings of pain perception were measured using Pearson’s correlation
coefficient for each participant [25]. The obtained correlation coefficients were transformed to Z
values using the Fisher R-to-Z transformation and were finally compared against zero using a 160
one-sample t-test.
1.2.4 Performance evaluation
To quantitatively assess the performance of each analysis step (BPF, ICA, CSP, and MLR)