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A Polarity Alignment Method for Group-Averaging of Event-Related Neural Signals at Source Level in MEG Beamforming Applications

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Abstract

Brain waveforms reconstructed at source level, like in beamforming, suffer polarity indeterminacy, which precludes direct group averaging of associated waveforms. We describe a polarity alignment method as an alternative of averaging rectified (i.e. absolute value) waveforms. Using MEG from an auditory localisation task, we compare the ability of the two approaches to enable signal detection in the primary auditory cortex over increasing sample size. The two methods are comparable in signal detection sensitivity, but the alignment method preserves group-average polarity alternation.
Abstract
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&' !"!!"
(
1. Introduction
)!!" !"*
 +,,- . 
)/0+,1-
//+,,2

3 . 
3
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#
#%:0+
(
;
=8:0+
%

2. Methods
:; 
!"+5

(>?@A>?@$
+?6;
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;B0 ///+,,2
4<56++
###9
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#
%#C69$(
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$+?E3
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##(
$#+?6
%#(($(
%HI
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:8

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;+,,?:0+%

%)(
:0+#$3
:0+J


:0+G:0+.0
)K6L+?6M(
%
.0#
4K(+666M(


%:; 
(()GN$
5+584n+5
$
<$
L

3. Results and Discussion
%+)GNL#
$LO
O


%:; 

%


4. Conflict of Interest Statement
OJ
5. Acknowledgment
%.<0 !"
N0")LG)!N0L;#
"OG)!N0
0;.
6. References
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accompanying voluntary movements using an eventPrelated beamforming
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Jobst, C., Ferrari, P., Isabella, S., Cheyne, D. (2018). BrainWave: A Matlab Toolbox for
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Makeig S, Bell AJ, Jung TP, Sejnowski TJ. (1996) Independent component analysis of
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Scherg, M., Von Cramon, D. (1986) Evoked dipole source potentials of the human
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Oostenveld, R., Fries, P., Maris, E., Schoffelen, J. M. (2011). FieldTrip: Open source
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data. Computational Intelligence and Neuroscience, 2011: article ID 156869.
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Van Veen, B. D., Van Drongelen, W., Yuchtman, M., Suzuki, A. (1997). Localization of
brain electrical activity via linearly constrained minimum variance spatial
filtering. IEEE Transactions on Biomedical Engineering, 44: 867-880.
Figure 1: Aligned waveforms displayed for the group of 12 subjects for the condition
Heschl Left – Auditory Right. Thicker curve is group average.
Table 1: Averaged p values (in bold when <.05) obtained from PC1 signal detection for
group sizes 2 to 12 under the PAM and Rectifying methods. Legend: HL (Heschl Left);
HR (Heschl Right) AL (Auditory Left stimulation); AR (Auditory Right stimulation).
HL - AL HR - AL HR - AR HL - AR
:; N!0% :; N!0% :; N!0% :; N!0%
Q
565?> 65>C 65CC 6+1- 65,? 65>5 6+-6 656,
Q
C6+15 6+-2 6+C> 6++5 65CC 6+?1 66-> 6+5+
Q
>6+C5 6+5+ 6616 66-- 6+1> 6611 0.025 6625
Q
?66,6 661, 0.04
8
0.04
16+>> 0.04
90.010 0.04
4
Q
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0
0.02
66+++ 0.02
70.005 0.02
8
Q
2
0.03
8
0.05
0
0.01
8
0.01
6661? 0.01
50.002 0.01
8
Q
1
0.02
4
0.03
6
0.01
1
0.01
066-> 0.00
90.001 0.01
2
Q
,
0.01
5
0.02
6
0.00
7
0.00
6
0.04
7
0.00
5
0.000
5
0.00
8
Q
+6
0.00
9
0.01
8
0.00
5
0.00
4
0.03
4
0.00
3
0.000
2
0.00
5
Q
++
0.00
6
0.01
2
0.00
3
0.00
2
0.02
4
0.00
2
0.000
1
0.00
4
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+5
0.00
4
0.00
8
0.00
2
0.00
1
0.01
7
0.00
1
0.000
06
0.00
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... Thus, based on the calculation, polarities of both ERPs and the scalp topographies are flipped together such that covariance of ERPs is maximized for each IC cluster. The similar idea was recently published from the same journal in a context beamforming for magnetoencephalography (MEG) analysis (Doualot and Achim 2021). In the current study, we demonstrate the usefulness of the covariance maximization in the context of ICA-decomposed ERP analysis and discuss potential advantages over the EEGLAB's default correlation maximization. ...
... We propose a covariance maximization method that uses the sign vector of the first eigenvector to maximize linear sum of the vectors to define eigenpolarities, similar to adapted from the 'polarity alignment method' (PAM) reported previously (Doualot and Achim 2021). However, we propose more descriptive names for the two methods compared in this study, iterative correlation maximization and covariance maximization, because both methods compared in this study are 'polarity alignment methods' which cannot be sensibly distinguished. ...
... Then the coefficient ŵ i for polarity alignment is defined as (4) is now identical as principal component analysis (PCA). Therefore, the polarities of ICs in a cluster may be aligned by taking the sign of its first principal component, which has also been applied as a polarity alignment method for different applications in previous studies (Doualot and Achim 2021). Group-level IC polarities can be aligned in two domains, spatial and temporal. ...
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