10 Computational EEG Analysis for Hyperscanning …
219
R i j X i · X
T
j .
(10.3)
The above spatial filters w can be obtained via a generalized eigenvalue decomposition based on solving the following optimization problem [17, 44]:
λ · (R 11 + R 22 ) · w R 12 · w .
(10.4)
Although the above formula is originally designed for two multivariate datasets,
Dmochowski and colleagues proposed to construct two datasets that include all
unique combination of pairs of participants [9]. A three-participant version is shown
below
X 1 [X P1 X P1 X P2 ],
X 2 [X P2 X P3 X P3 ],
(10.5)
where X Pi represents multi-channel EEG data (channel by sample) from the i-th
participant. By employing such a multivariate construct, the CoCA method hereby
can obtain the spatial filters that maximize the ‘correlation’ among EEG data from
all participants. It is worthwhile to note that the number of extracted CoCA components (each corresponding to a specific spatial filter) are normally substantially
reduced compared to the number of original EEG channels, therefore the manual
efforts needed for further data analysis can be greatly reduced. More importantly, as
the optimization problem is defined based on a relatively simple and straightforward
assumption about reliability across participants, the obtained spatial filters find neurophysiologically plausible components representing shared neural activities. Indeed,
the extracted components have been reported to be specifically responsive to certain
social stimuli, including face, hand, or high-level social emotions such as surprise,
tension, anticipation, etc. [10, 30, 69].
Beside the exploration in the spatial domain, inter-brain hyperlink has also been
investigated in the spectral and temporal domains as well, but to a less extent. Neural
oscillations at different frequency bands such as alpha, theta, delta, etc., have long
been known to have important functional roles for human cognition [52, 56]. It
is hereby reasonable to assume that inter-brain hyperlink may rely on oscillatory
brain activities. Although exploration in this direction are just beginning, it has been
reported that hyperlink in the delta band had primary contribution to behaviorally
measured audience preference [3]. In the time domain, the most critical question is
the optimal time window length for calculating hyperlink. Due to the non-stationarity
of EEG signals, calculating temporal correlation with a long time window may lead
to unstable results. To date, the reported studies have used time windows ranging
from 200 ms (e.g. [4] up to several minutes (e.g. [3, 10]. Although time window as
short as 200 ms has been demonstrated to be capable of capturing neural reliability,
hyperlinks based on different time window lengths may have different functional
implications, which can be considered as the counterpart for the spectral domain
analysis. In addition, dissociation of EEG temporal signals into phase and amplitude
may worth further exploration, as they have long been postulated to have distinct
219
R i j X i · X
T
j .
(10.3)
The above spatial filters w can be obtained via a generalized eigenvalue decomposition based on solving the following optimization problem [17, 44]:
λ · (R 11 + R 22 ) · w R 12 · w .
(10.4)
Although the above formula is originally designed for two multivariate datasets,
Dmochowski and colleagues proposed to construct two datasets that include all
unique combination of pairs of participants [9]. A three-participant version is shown
below
X 1 [X P1 X P1 X P2 ],
X 2 [X P2 X P3 X P3 ],
(10.5)
where X Pi represents multi-channel EEG data (channel by sample) from the i-th
participant. By employing such a multivariate construct, the CoCA method hereby
can obtain the spatial filters that maximize the ‘correlation’ among EEG data from
all participants. It is worthwhile to note that the number of extracted CoCA components (each corresponding to a specific spatial filter) are normally substantially
reduced compared to the number of original EEG channels, therefore the manual
efforts needed for further data analysis can be greatly reduced. More importantly, as
the optimization problem is defined based on a relatively simple and straightforward
assumption about reliability across participants, the obtained spatial filters find neurophysiologically plausible components representing shared neural activities. Indeed,
the extracted components have been reported to be specifically responsive to certain
social stimuli, including face, hand, or high-level social emotions such as surprise,
tension, anticipation, etc. [10, 30, 69].
Beside the exploration in the spatial domain, inter-brain hyperlink has also been
investigated in the spectral and temporal domains as well, but to a less extent. Neural
oscillations at different frequency bands such as alpha, theta, delta, etc., have long
been known to have important functional roles for human cognition [52, 56]. It
is hereby reasonable to assume that inter-brain hyperlink may rely on oscillatory
brain activities. Although exploration in this direction are just beginning, it has been
reported that hyperlink in the delta band had primary contribution to behaviorally
measured audience preference [3]. In the time domain, the most critical question is
the optimal time window length for calculating hyperlink. Due to the non-stationarity
of EEG signals, calculating temporal correlation with a long time window may lead
to unstable results. To date, the reported studies have used time windows ranging
from 200 ms (e.g. [4] up to several minutes (e.g. [3, 10]. Although time window as
short as 200 ms has been demonstrated to be capable of capturing neural reliability,
hyperlinks based on different time window lengths may have different functional
implications, which can be considered as the counterpart for the spectral domain
analysis. In addition, dissociation of EEG temporal signals into phase and amplitude
may worth further exploration, as they have long been postulated to have distinct