Systems, Man & Cybernetics - October 2017 - 21

	

(

C -xx1 C xy C -xy1 C yx w x = t 2 w x
,(2)
C -yy1 C yx C -xx1 C xy w y = t 2 w y

where w x and w y are eigenvectors, and the canonical
autocorrelation coefficient t 2 is the eigenvalue.
Figure 5(b) shows a 2-s EEG recording contaminated with eye blinks and muscle noises. Figure 5(c) displays the extracted time series of CCA components,
which are ordered in terms of auto-correlation coefficients from high to low in Figure 5(d). Compared with
the brain-activity components, the components with
lower autocorrelation coefficients, i.e., the 15th and
16th CCA components, correspond to muscle artifacts
because the broad frequency spectrum of the muscle
noise in EEG recordings resembles temporally white
noises. By contrast, the first CCA component with a
relatively higher autocorrelation coefficient corresponds to eye artifacts because eye movements and
eye blinks ty pically produce low-frequency, high--
amplitude signals that are highly autocorrelated with
time. An artifact-free EEG Xl ^ t h is reconstructed by
remov i ng t he se a r t i fa c t component s by set t i ng
6s 1 ^ t h, s 15 ^ t h, s 16 ^ t h@ = 0 and operating Xl ^ t h = A $ S ^ t h,
as shown in Figure 5(e).

RSVP
Paradigm

ERP-Based
BCI

Rapid ERP
Detection

(a)
E
H
I

...

G
1s

L

...

Amplitude (µV)

RBFN for Tracking Evoked Potentials
As shown in Figure 6(a), many ERP-based BCI applications are designed based on a rapid serial visual
presentation paradigm (RSVP), such as image search
[34] and auto typing [35]. However, due to the nonstationarity of brain activity, an accurate estimation of
the ERP requires the system to average over a large
number of trials. In [23], a nonlinear adaptive algorithm

referred to as a data-reusing RBFN (DR-RBFN) was
proposed to not only estimate the latency and amplitude of brain dynamics but also increase the convergence rate -c onsiderably.
Given K previous epochs " d ^ k h ! R M | k = 1, 2, f, K ,,
the output of the RBFN, denoted as y ^ k h , can be calculated as follows:
N

y ^ k h = |w j ^ k h h j ^ x h
j=1

	

h j ^ x h = exp d -

x - c j2 n
,
vj


(3)

where N is the number of hidden units, w is the
weight between the hidden layer and output layer, and
v j = b ^ M - 1/N - 1 h . In this study, b is set to 0.8. In
the kernel function h , the kernel center c can be calculated as follows:
M-1
c j = ^ j - 1 h N - 1 + 1. (4)

	

w ^ k h can be updated by the least-mean-squares (LMS)
algorithm as follows:
w j ^ k + 1 h = w j ^ k h + nH T ^ HH T + fI h-1 $ e ^ k h,
where e ^ k h = d ^ k h - y ^ k h is the error signal, n is the
learning rate, e is a positive constant, and
R h ^ x h g h ^ x hV
1
N
S 1 1
W
H=S h
j
h W .(5)
Sh ^ x h g h ^ x hW
1
M
N
M
T
X

	

Six subjects with normal or correct-to-normal vision
participated in the RSVP experiment. As shown in Figure  6(b), uppercase letters were used as visual stimuli.
The letter "G" was predefined as the target, and the other

10

Amplitude (µV)

optimal problem of (1) is equivalent to the following eigenvalue problem:

5
0
-5

0

200 400 600 800
Time (ms)
Target
Nontarget

10
5
0
-5

0

200 400 600 800
Time (ms)

20 Epochs
40 Epochs

60 Epochs
80 Epochs

DR-RBFN
(b)

(c)

(d)

Figure 6. Rapid ERP detection. (a) RBFN applied to ERP-based BCIs. (b) The RSVP paradigm. Uppercase

letters were randomly presented to subjects, who were instructed to respond to the target, i.e., the letter "G."
A comparison of the ERPs estimated by the EA and DR-RBFN algorithms. (c) ERP estimated by applying EA to
80 epochs. The red and blue traces represent the target- and nontarget-evoked ERPs, respectively. (d) Targetevoked ERP estimated by applying the DR-RBFN to 20 (green), 40 (black), 60 (blue), and 80 (red) epochs.

	

O c tob e r 2017

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE	

21



Table of Contents for the Digital Edition of Systems, Man & Cybernetics - October 2017

Systems, Man & Cybernetics - October 2017 - Cover1
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