BRAIN COMPUTER INTERFACE
Feedback Effect Analysis by Comparison of Discrimination Capability of On-line
and Off-line Experimental Procedures based on LDA
Jos´e Luis Mart´ınez P´erez and Antonio Barrientos Cruz
Grupo de Rob´otica y Cibern´etica, Universidad Polit´ecnica de Madrid, C/Jos´e Gutierrez Abascal 2, Madrid, Spain
Keywords:
Electroencephalography, Brain Computer Interface, Linear Discriminant Analysis, Spectral Analysis,
Biomedical signal detection, Pattern recognition.
Abstract:
This paper analyses the user’s feedback influence in the mental task discrimination capability through the
comparison of results obtained from Off-line and On-line Brain Computer Interface experimental procedures.
Experiments performed under these two paradigms were carried out by five male volunteers. In order
to develop a wearable BCI device only two electrodes in C3 and C4 zones have been used for electro-
encephalographic signal acquisition. These procedures apply seven different types of preprocessing windows
and Linear Discrimination Analysis technique to reduce the dimension of the feature space before the quan-
tification of the discrimination capability between the proposed mental activities.The discrimination capability
is quantified through statistical analysis, based on bilateral contrast test, between the population of the LDA
transformed feature vectors.
1 INTRODUCTION
The objective of Brain Computer Interface technol-
ogy is the direct communication of user’s mind with
external devices, it uses the encephalographic signal
as primary source of commands for the external de-
vices (Wolpaw et al. 2000), (Birbaumer, N. et al.,
2000), (Wolpaw, 2007). A variety of methods for
monitoring brain activity might serve in BCI tech-
nology: electroencephalography (EEG), magnetoen-
cephalography (MEG), positron emission tomogra-
phy (PET), functional magnetic resonance imaging
(fMRI), and optical imaging. At present, only EEG
meets the requirements of short time constant, afford-
able cost, and it is relatively simple to implement.
In order to control an external device using
thoughts, it is necessary to associate some mental pat-
terns to device commands, so an algorithm that de-
tects, acquires, filters and classifies the human elec-
troencephalographic signal is required (Wolpaw et
al., 2002), (Vidal, 1973), (Kostov and Polak, 2000),
(Pfurtscheller et al. 2000b). Usually all BCI systems
are compounded of the following blocks:
• Signal Acquisition. In this block the signal is ac-
quired by the recording electrodes, amplified, and
digitalised. BCI devices can be categorised by
the different approaches they use for the signal
acquisition: non-invasive recordings with stan-
dard scalp electrodes, and invasive recording with
epidural, subdural, or intracortical electrodes.
• Signal Processing: Feature Extraction. The dig-
italised signals are subjected to feature extrac-
tion procedures, such as spatial filtering, volt-
age amplitude measurements, spectral analysis, or
single-neuron separation (Lopes da Silva, 1999).
• Signal Processing: The Translation Algorithm.
It translates the signal features into device
commands-orders that carry out the user’s intent.
• The Output Device. Generally the output device
is a computer screen and the output is the selec-
tion of targets, letters, or icons presented on it.
Initial studies are exploring BCI control of a neu-
roprothesis that provides hand closure to people
with cervical spinal cord injuries(Pfurtscheller et
al., 2000a).
• The Operating Protocol. It is the protocol that
guides the operation of the BCI device.
BCI devices fall into two classes: dependent and
independent (Chiappa, 2006). A dependent BCI does
not use the brain’s normal output pathways to carry
the message, but activity in these path-ways is needed
to generate the brain activity that does carry it. An
186
Martínez Pérez J. and Barrientos Cruz A. (2009).
BRAIN COMPUTER INTERFACE - Feedback Effect Analysis by Comparison of Discrimination Capability of On-line and Off-line Experimental
Procedures based on LDA.
In Proceedings of the International Conference on Biomedical Electronics and Devices, pages 186-191
DOI: 10.5220/0001512801860191
Copyright
c
 SciTePress

independent BCI does not depend in any way on the
brain’s normal output pathways.
This paper focus on the user’s feedback influ-
ence in the discrimination capability of three different
mental activities, it analyses the applicability of LDA
to BCI and how the windowing effect affects the dis-
crimination capability of the brain proposedactivities.
Section 2 describes the Off-line and On-line ex-
perimental procedures applied to evaluate the user’s
feedback influence (Martinez and Barrientos, 2007);
because the main changes in brain activity are associ-
ated to changes in the power amplitude of frequency
bands, spectrograms based on FFT are used to obtain
initial feature vectors. To minimise the leakage effect
seven types of preprocessing windows has been con-
sidered: rectangular, triangular, Blackman’s, Ham-
ming’s, Hanning’s, Kaiser’s and Tukey’s (Proakis and
Manolakis, 1997), (Allen and Rabiner, 1977). The
evidence of statistical difference in the feature popu-
lations associated to different brain activities has been
previously shown (Martinez and Barrientos, 2006). In
the experiments considered for this report a low num-
ber of scalp-electrodes has been used to capture the
electroencephalographic signal, in order to facilitate
the use of this technology it is important to make it
easy to use, as the fewer of electrodes used, the higher
the comfort, (Wolpaw, 2007).
Section 3 describes the LDA technique used to
combine these initial features in order to reduce the
dimensionality of the input space (Ripley, 2000).
Section 4 explains the bilateral contrast test used
to determine the discrimination power between the
proposed cerebral activities and the effect of the pre-
processing windows, the results of each contrast is
both qualitative and quantitative, qualitative in or-
der to accept or reject the null hypothesis of equal-
ity in the population of features, quantitative in order
to compare the discrimination power through signifi-
cance contrast level α = 1− p = 2.5%.
Sections 5 and 6 present and analyse the results.
Section 7 is devoted to conclusions.
2 EXPERIMENTAL
PROCEDURES
Off-line and On-line tests were carried out on five
healthy male subjects, one of them has been trained
before, but the other four were novice in the use of
the system. The Off-line tests have been carried out
before On-line tests in order to have data to allow the
training procedure of a simple classifier. The subjects
were sat down in front of the acquisition system mon-
itor, at 50 cm from the screen, their hands were in
Figure 1: Diagram of the Off-line experiment realization.
a visible position, the supervisor of the experiments
controlled the correct development of them (Neuper,
2001), (Penny et al., 2000).
2.1 Procedure for Off-line Experiments
The experimental Off-line process is shown on fig.1.
Test of system devices. Checks the correct level of
battery, and the correct state of the electrodes.
System assembly. Device connections: superfi-
cial electrodes (Grass Au-Cu), battery, bio-amplifier
(g.BSamp by g.tec), acquisition signal card (PCI-
MIO-16/E-4 by National Instrument), computer.
System test. Verifies the correct operation of the
whole system.
Subject preparation for the experiment. Applica-
tion of electrodes on subject’s head. It is verified that
electrode impedance was lower than 4 KOhms.
System initialisation and Experiment setup. Ver-
ification of data register. The supervisor sets-up the
number of replications, N
rep
= 10, and the quantity
of different mental activities, N
act
= 3. The duration
of each mental activity, a trial, is t = 7s, the acquisi-
tion frequency is f
s
= 384Hz. The system randomly
suggests the mental activity to think about.
2.2 Procedure for On-line Experiments
In these tests, a cursor in the centre of the screen and
a square goal are shown to the subject, the square goal
appears half the trials on the left of the screen and the
other half on the right. The subject shall try to move
the cursor towardsthe goal thinking in the cerebralac-
BRAIN COMPUTER INTERFACE - Feedback Effect Analysis by Comparison of Discrimination Capability of On-line
and Off-line Experimental Procedures based on LDA
187

Figure 2: Diagram of the On-line experiment realization.
tivities proposed in the Off-line experiments.The ex-
perimental On-line process is shown on fig.2.
Experiment set-up. In this phase it is determined
which cerebral activities are used to move the cursor
to the left and to the right, the number of trials and the
time for each trial.
Display initialisation. It initialises the display, for
even trials the goal is on the right, for odds on the left.
Data acquisition. In this phase 128 samples per
channel are acquired at fs = 384Hz.
Record samples. The previous samples are recorded
for a posterior analysis.
Feature extraction. A vector of features is extracted
from the acquired samples.
Classification. The vector of features is classified as
belonging to one of the previous cerebral activities,
and the associated movement is performed.
Figure 3: Electrode placement.
2.3 Position of the Electrodes and
Description of Cerebral Activities
For both types of experimental procedures, the elec-
trodes were placed in the central zone of the skull,
next to C3 and C4, two pair of electrodes were placed
in front of and behind of Rolandic sulcus, this zone is
one with the highest discriminant power, it takes sig-
nal from motor and sensory areas of the brain (Penny
et al., 2000),(Pfurtscheller et al. 2000b). Reference
electrode was placed on the right mastoid, two more
electrode are placed near to the corner of the eyes to
register blinking.
The supervisor of the experiment asks the subject
to figure out the following mental activities, these ac-
tivities will be the tasks to differentiate among them.
Activity A. Mathematical task. Recursive subtraction
of a prime number from a big quantity.
Activity B. Motor imagery. The subject imagines
moving their limbs or hands, but without the mate-
rialisation of the movement.
Activity C. Relax. The subject is relaxed.
2.4 Feature Selection
For Off-line experiments the registered signal is
chopped in packages of samples, similar to the bun-
dles of samples obtained from the acquisition card in
the On-line cases. Each package has 128 samples,
acquired at f
s
= 384Hz. A vector of six features is
extracted from each package, see table 1, this vector
is made up as the mean of the amplitudes of the fre-
quency bands (Proakis and Manolakis, 1997), (Neu-
per, 2001).
Because the frequency of normal human brain is
under 40-50Hz, only frequencies between 6 and 38Hz
have been considered.
Table 1: Feature vector.
Index Denomination. Frequency (Hz).
1 θ. 6 - 8
2 α
1
. 9 - 11
3 α2. 12 - 14
4 β
1
. 15 - 20
5 β
2
. 21 - 29
6 β
3
. 30 - 38
BIODEVICES 2009 - International Conference on Biomedical Electronics and Devices
188

3 LINEAR DISCRIMINANT
ANALYSIS PROCEDURE
3.1 Introduction
Supposed C classes of observations, Linear Discrimi-
nant Analysis is a preprocess technique that finds the
transformation matrix W which separates in an opti-
mal way two or more classes. It is used in machine
learning as linear classifier or as a technique to re-
duce the feature space dimension before the classifi-
cation process. LDA considers maximising the fol-
lowing objective:
J(W) =
W
T
S
B
W
W
T
S
W
W
(1)
where S
B
is the between classes scatter matrix and S
w
is the within classes scatter matrix, the definitions of
the both matrices are:
S
B
=
∑
c
N
c
(µ
c
− ¯x)(µ
c
− ¯x)
T
(2)
S
W
=
∑
c
∑
i∈c
(x
i
− µ
c
)(x
i
− µ
c
)
T
(3)
µ
c
=
1
N
c
∑
i∈c
x
i
(4)
¯x =
1
N
∑
i
x
i
=
1
N
∑
c
N
c
µ
c
(5)
and N
c
is the number of samples in class c.
Because J is invariant to rescaling of the vectors
W → αW, hence it is possible to choose W such that
the denominator is W
T
S
W
W = 1. So the problem
of maximising J can be transformed to the following
constrained optimisation problem,
min
W
−
1
2
W
T
S
B
W (6)
s.t. W
T
S
W
W = 1 (7)
corresponding to the Lagrangian,
L
P
= −
1
2
W
T
S
B
W +
1
2
λ(W
T
S
W
W − 1) (8)
With solution (the halves are added for convenience):
S
B
W = λS
W
W ⇒ S
−1
W
S
B
W = λW (9)
This is a generalised eigen-problem, and using the
fact that S
B
is symmetric positive definite and can
hence be written as S
1
2
B
S
1
2
B
, where S
1
2
B
is constructed
from its eigenvalue decomposition as S
B
= UΛU
T
→
S
1
2
B
= UΛ
1
2
U
T
. Defining V = S
1
2
B
W it is get
S
1
2
B
S
−1
W
S
1
2
B
V = λV (10)
this is a regular eigenvalue problem for a symmetric
positive definite matrix, with solutions λ
k
as eigen-
values and V
k
as eigen-vectors, which leads to solu-
tion:
W = S
−
1
2
B
V (11)
Plugging the solution back into the objective J(W), it
is found that the desired solution which maximise the
objective is the one with largest eigenvalues.
3.2 Operational Procedure
1. Samples from each mental tasks are obtained.
X
a
Mathematical Activity.
X
b
Movement imagination.
X
c
Relax.
2. Population statistical definitions: (i = a, b, c).
¯µ
i
= E[x
i
] S
i
= E[(x
i
− ¯µ
i
)(x
i
− ¯µ
i
)
T
] (12)
3. Calculation of the scattering matrices (eq.2 & 3).
4. Application of LDA optimising criterion (eq.10).
5. Calculation of the transformation matrix, W
(eq.11), formed by the eigen-vectors, V
k
, which
eigen-values are bigger than 1∗10
−4
ordered form
high to low magnitudes.
6. Transformation of the data sets: (i = a, b, c).
X
i
⇒ X
′
i
= W
T
∗ X
i
(13)
4 STATISTICAL ANALYSIS
PROCEDURE
Bilateral contrasts between two population are used
to determine if there is statistical evidence of dif-
ference between the population of features obtained
from each mental activity. Each component of the
vector is considered to determine its significance and
separability power. Bilateral contrast makes use of
population variance, if the equality of both population
variances is rejected it is necessary to apply a correc-
tion factor in the degrees of freedom. These contrasts
were done for each type of filtering window.
• Bilateral contrast of two independent normal and
homocedastic populations.
Null hypothesis H
o
vs. alternative hypothesis H
1
.
n
1
: sample size of the first population.
n
2
: sample size of the second population.
ˆ
S
1
: variance estimation of the first population.
ˆ
S
2
: variance estimation of the second population.
T = Student distribution.
H
o
: µ
1
− µ
2
= ∆ vs. H
1
: µ
1
− µ
2
6= ∆ (14)
The variances of the both population are equal
BRAIN COMPUTER INTERFACE - Feedback Effect Analysis by Comparison of Discrimination Capability of On-line
and Off-line Experimental Procedures based on LDA
189

but unknown.
T
Exp
=
(
¯
X
1
−
¯
X
2
) − (µ
1
− µ
2
)
q
ˆ
S(
1
n
1
+
1
n
2
)
(15)
In which
ˆ
S is the pseudo-variance of
ˆ
S
1
and
ˆ
S
2
ˆ
S =
(n
1
− 1) ∗
ˆ
S
1
+ (n
2
− 1) ∗
ˆ
S
2
n
1
+ n
2
− 2
(16)
The zone of H
o
acceptance is:
T
Teo
= t
(n
1
+n
2
−2,1−
α
2
)
(17)
If |T
Exp
| ≤ T
Teo
then H
o
is accepted, on the con-
trary H
1
is accepted and H
o
is rejected.
5 RESULTS
In figures 4 to 9 are represented the results of the
bilateral contrast test for the transformed coordinate
X
1
considering the Off-line and On-line experiments.
The figures show for each channel (C3’-C3” and C4’-
C4”), and for each type of preprocessing window, the
results p of the associated probability of the bilateral
contrast tests between the mental tasks. In order to
represent the dispersion of the results the mode value
and bars from 15th to 85th percentile have been used.
6 DISCUSSION
The comparisons between the discrimination capabil-
ities of On-line and Off-line experiments are shown
in the figures 4 to 9. From the bilateral contrast
test carried out with a significant level of α = 2.5%,
α = 1− p, it is obtained that in almost all cases the
null hypothesis H
o
, which maintains the equality in
the populations of the features associated to the men-
tal tasks, shall be rejected for both types of experi-
ments; in the comparison of mathematical task versus
motor imagery, p values are lower for the On-line case
in both channels and with all types of preprocessing
windows than the ones obtained for the Off-line case;
the dispersion of the results is similar in both experi-
ments. It is also shown that for X
1
, channel C4’-C4”
performs better than C3’-C3”. The best results are
obtained for X
1
with Tukey’s and Kaiser’s windows.
The highest contrast power is obtained in the com-
parison of Motor imagery vs. Relax, it is followed by
Mathematical task vs. Relax, and the lowest is for
Mathematical task vs. Motor imagery.
In all cases only two eigen-values have got sig-
nificant magnitudes, so only two eigen-vectors have
been considered in the transformation matrix. This
causes that LDA technique had projected the orig-
inal six dimensional feature space over a bidimen-
sional space, weighting the power amplitude of the
frequencybands and maintaining the intrinsic charac-
teristics of each cerebral activity.
7 CONCLUSIONS
In this paper has been estudied the user’s feedback in-
fluence in BCI technology by analyzing the discrimi-
nation capability obtained under the Off-line and On-
line experimentscarried out with five male volunteers,
the results indicate that it is possible to differentiate
between the proposed mental tasks under the On-line
paradigm, but also that the discrimation capability is
a bit lower (< 0.3%) than the one obtained under the
BCI Off-line case, (Pineda et al., 2003).
Because the experiments have been carried out
only with five volunteers these preliminary conclus-
sions have to be corroborated with more tests.
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APPENDIX
Figure 4: Off-line. Math task vs. Motor imagery. Coordi-
nate X1.
Figure 5: Off-line. Math task vs. Relax. Coordinate X1.
Figure 6: Off-line. Motor imagery vs. Relax. Coordinate
X1.
Figure 7: On-line. Math task vs. Motor imagery. Coordi-
nate X1.
Figure 8: On-line. Math task vs. Relax. Coordinate X1.
Figure 9: On-line. Motor imagery vs. Relax. Coordinate
X1.
BRAIN COMPUTER INTERFACE - Feedback Effect Analysis by Comparison of Discrimination Capability of On-line
and Off-line Experimental Procedures based on LDA
191