Systems, Man & Cybernetics - October 2017 - 22

letters were nontargets. All stimuli
Causality Analysis for
were presented at a frequency of
Assessing Brain Connectivity
The determined
5 Hz (200 ms/letter). The interval
The feature extraction is crucial
between two sequential targets is
to the system performance of the
parameters in the
20-25 nontarget stimuli, such that
BCI. Rather than extract the brain
training stage were
the occurrence rate of target is
activity from a single brain
approximately 5%. Subjects were
region, the brain network that
further exploited to
instructed to use their right index
characterizes some coordinated
optimize the proposed
finger to press the response button
activity within a network of funcDR-DBFN and
while they detected the target on
tionally distinct regions can prothe screen. In each session, the
vide a more detailed description
enhance the system
experiment would end when the
of complex behaviors. Graph theperformance.
ory [36], the dynamic causal
subjects de--tected 80 targets.
model [37], and GC [38] are the
The EEG data were recorded
most widely used measures for
using a dry EEG device at a samstudying effective connectivity.
pling rate of 250 Hz. A low-pass filFor example, GC refers to the fact that signal X 1 can
ter with a cutoff frequency of 30 Hz and high-pass filter
with a cutoff frequency of 0.5 Hz were applied to remove
lead to another signal X 2 if the information in the past
the line noise and dc drift, respectively. Each EEG epoch
of X 1 helps predict the future of X 2 . We can represent
of 900 ms began 100 ms before and ended 800 ms after
the multivariate -process at time t as a stationary autorethe stimulus onsets were selected from the continuous
gressive -process of order p . Consider, for example, two
EEG recordings. Baseline wander was removed by sub-signals ^ n = 2 h:
tracting the mean of the data before stimulus onset.
p
p
Then, the target-evoked P3 wave estimated by the DRX 1 ^ t h = |A 11 ^ i h X 1 ^t - i h + |A 12 ^ i h X 2 ^t - i h + p 1 ^ t h
i=1
i=1
RBFN [23] was compared with that estimated by ensemp
p
^
h
^
h
^
h
=
X
t
A
i
X
t
i
+
A 22 ^ i h X 2 ^t - i h + p 2 ^ t h,
2
21
1
|
|
ble averaging (EA), a conventional approach to assess the
i=1
i=1
ERP. In the DR-RBFN, the number of reused data was set
(6)
to 3, and the number of hidden nodes was set to 50. The
learning rate and positive constant were set to 0.1 and
where t ! " p + 1, p + 2, f, T , is the current time point
0.001, respectively. We used a grid search for the parameand T is the length of the signal. The model order p is
ter learning in this study. The DR-LMS algorithm is
typically obtained by minimizing information criteria,
exploited for real-time implementation of the DR-RBFN.
such as the Akaike information criterion or Bayesian
The DR-LMS algorithm reuses data pairs from previous
information criterion, to accurately model the data. The
iterations to generate the new gradient estimates that are
parameters A and p model the coefficient matrix
in turn used to update the adaptive weight vector. This
and prediction error, respectively, which can be estialgorithm operates in real time and has a fast convermated using an ordinary least-squares approach [39].
gence rate and can thus track signal variations across triTo determine the causal effect of X 2 on X 1, the predicals. The determined parameters in the training stage
tion error is re-estimated using a submodel that excludes
were further exploited to optimize the proposed DRsignal X 2 . Then, the error pr 1 ^ t h is estimated and comDBFN and enhance the system performance.
pared with p 1 ^ t h obtained in the full model:
The red trace shown in Figure 6(c) is the average
p
ERP of 80 target epochs in the Pz site estimated by EA.
X 1 ^ t h = |Ar 11 ^ i h X 1 ^t - i h + pr 1 ^ t h .(7)

Compared with the average ERP of nontarget epochs
i=1
(blue trace), the P3 elicited by the targets can be easily
detected at approximately 400 m. The green, black, blue,
The strength of the effect of X 2 on X 1 (i.e., causal magand red traces shown in Figure 6(d) represent the avernitude) was determined as GC ^2 " 1 h = ln R 11 /R 11, where
age ERPs of 20, 40, 60, and 80 target epochs, respectiveR 11 and R 11 are the variances of p 1 and pr 1, respectively.
ly, in the Pz site estimated by the DR-RBFN. Increasing
Here, we applied GC to independent EEG processes
the number of epochs used leads to a higher SNR and
that were collected from a simulated driving experiment
more stable ERP. The average ERP of 40 target epochs
in which participants performed a sustained-attention
approximated the results obtained by EA, indicating that
driving task [40]. The asymmetric ratio of the causal
the DR-RBFN led to a considerably higher convergence
flow [Figure 7(a)] and the significant connectivity of the
rate. This property of the DR-RBFN is advantageous for
brain network [Figure 7(b)] varied with changes in
real-time BCI applications, because it helps reduce the
behavioral performance, which were measured by the
number of trials required for an accurate estimation and
reaction time in response to unexpected events. During
to precisely track potentials.
the transition from optimal to poor task performance,
22

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Oc tob e r 2017

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