Single Trial Classification for Mobile BCI
A Multiway Kernel Approach
Lieven Billiet
1,2
, Borb´ala Hunyadi
1,2
, Vladimir Matic
1,2
, Sabine Van Huffel
1,2
, Michel Verleysen
3
and Maarten De Vos
4,5
1
STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, Department of Electrical Engineering,
KU Leuven, Kasteelpark Arenberg 10, 3001, Leuven, Belgium
2
Medical IT, iMinds, 3001, Leuven, Belgium
3
Institute for Information and Communication Technologies, Electronics and Applied Mathematics,
Universit´e Catholique de Louvain, Place du levant 3, 1348, Louvain-La-Neuve, Belgium
4
Methods in Neurocognitive Psychology Lab, Department of Psychology, Cluster of excellence Hearing4all,
Carl von Ossietzky University, Oldenburg, Germany
5
Research Center Neurosensory Science, Carl von Ossietzky University, Oldenburg, Germany
Keywords:
Single-trial ERP BCI, Mobile BCI, Tensors, Subspaces.
Abstract:
Subspace methods have been applied in various application fields to obtain robust results. Using multilinear
algebra, they can also be applied on structured tensorial data. This work combines this principle with the power
of non-linear kernels to investigate its merits in single trial classification for a mobile BCI ERP classification
task. The accuracy difference with regard to more conventional vector kernels is evaluated for sitting and
walking condition, increasing training data set and averaging over multiple trials. The study concludes that in
general, the tensorial approach does not yield any advantage, though it might for specific subjects.
1 INTRODUCTION
BCI is a multidisciplinary field aiming at using brain
activity to drive applications. It has various possi-
ble uses, particularly as assistive technology (e.g. for
people suffering from neural or muscle degradation,
locked-in syndrome). It led to the development of
brain spellers, robot, wheelchair or prosthesis con-
trol and even coma detection (Jackson and Mappus,
2010). One way to steer such systems is a syn-
chronised reactive approach: the user is presented
with stimuli and his selective attention for a partic-
ular stimulus can be discovered as a positive Event
Related Potential (ERP) approx. 300ms after stimu-
lus onset (P300).
Brain activity can be measured in various ways:
using cortical electrodes, with fMRI etc. However,
many systems aim at non-invasiveness and mobility.
Therefore, wireless EEG is a suitable method. Mo-
bile EEG systems are already available commercially,
several of which offer wireless communication. Some
have been shown to perform as good as more classi-
cal systems. The system of Debener et al., used in this
work, has been subject to several tests for ERP detec-
tion (De Vos et al., 2013). This study aims to confirm
the system’s practical usefulness.
The brain response on a single stimulus is called a
single trial. Most systems average over several trials
to obtain a higher signal-to-noise ratio. Yet, when sin-
gle trials can be classified accurately, the system can
be controlled faster, an advantage for real-time use.
For this purpose, mostly relatively simple features are
extracted from EEG data and concatenatedin a vector,
after which a classifier can be trained. However, these
features often disregard structural information of the
data. Representing EEG data as tensors allows a mul-
tilinear comparison based on signal subspaces rather
than classical feature values. For example, Onishi et
al. use a tensorial expansion and dimensionality re-
duction to extract an informative feature vector (On-
ishi et al., 2012). Other studies focus on regulariza-
tion using the nuclearnorm of a tensor (Hunyadiet al.,
2013). Tensor discriminant analysis has been used to
obtain informative subspaces from wavelets (Li and
Zhang, 2010) and with Gabor features on motor im-
agery tasks and EEG seizure detection (Nasehi and
Pourghassem, 2011).
Tensorial approaches can be combined with SVM
classification by kernels for structured informa-
tion (Zhao et al., 2013). Signoretto et al. (Signoretto,
5
Billiet L., Hunyadi B., Matic V., Van Huffel S., Verleysen M. and De Vos M..
Single Trial Classification for Mobile BCI - A Multiway Kernel Approach.
DOI: 10.5220/0005163000050011
In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2015), pages 5-11
ISBN: 978-989-758-069-7
Copyright
c
2015 SCITEPRESS (Science and Technology Publications, Lda.)
2011) developed a tensorial kernel. They apply it
among others for classification of MEG signals in a
BCI task.
In this work, several vectorial and tensorial rep-
resentations for single-trial BCI data are compared,
with a focus on the influence of training set size and
the interference of motor activity when walking. Fi-
nally, though the main focus is on single trials, av-
eraging over multiple trials is studied as well, since
the effectiveness of a BCI system is often a trade-off
between fast classification (less averaging) and high
accuracy (more averaging). This trade-off is expected
to be different for different methods.
2 DATA AND METHODS
2.1 Data
The dataset for this study was acquired for the study
of De Vos et al. (De Vos et al., 2013). 20 subjects
were asked to participate in a three stimulus auditory
oddball paradigm (Halder et al., 2010). Subjects were
presented with a train of standard tones (900Hz) inter-
spersed with rare target and distractor (deviant) tones
(600Hz and 1200Hz, randomly assigned) of 62ms du-
ration with a mean interstimulus interval of 1000ms.
A focus on the target tone leads to a more pronounced
P300 compared to the deviant, which allows to detect
binary choices. The recordings were performed in
two conditions, walking and sitting, both outdoor, to
estimate the impact of motor activity. Subjects were
equipped with the wireless EEG system developed by
Debener et al. (Debener et al., 2012). It combines a 14
channel sintered Ag-AgCl electrode cap based on the
international 10-20 system with a light-weight ampli-
fier. The system is presented in Figure 1. It has a
sample frequency of 128Hz.
Figure 1: Acquisition system (De Vos et al., 2013) (A) with
electrode positions (B).
2.2 Data Processing
The data processing steps are shown in Figure 2.
First, eye blinks were removed semi-automatically
with ICA. Since the P300 response is time-locked to
a stimulus, epochs could subsequently be extracted
from the resulting signal. Each recorded trial (epoch)
starts at 200ms before stimulus onset and ends at
800ms after it. The leading 200ms was used for base-
line correction. Furthermore, high frequency noise
was removed with a 20Hz low-pass filter. Next, the
P300 response was be made more prominent by re-
referencing using the average of the Tp9 and Tp10
channel. One last additional data-driven FIR filter-
ing step was performed by truncation of the SVD of
a channel’s hankel matrix to its three most prominent
components (Hansen and Jensen, 1998). The result-
ing data set consists of 94 target and 94 deviant 12-
channel single trials for each subject.
2.3 Classification Methods
The data is classified with Least Squares SVM (LS-
SVM), an SVM variant solving the training optimiza-
tion as a system of linear equations(Suykens and Van-
dewalle, 1999). Three types of kernel functions were
used: a linear kernel, an RBF kernel and a tenso-
rial kernel (Signoretto, 2011). The tensorial kernel
is a factor kernel with a factor for each dimension
(‘mode’) of the tensorial inputs, given as:
K(X , Y ) =
∏
i
e
d(X
(i)
,Y
(i)
)
2
2σ
2
(1)
d(X
(i)
, Y
(i)
) is a distance function between the mode-
i tensors unfoldings (De Lathauwer et al., 2000). The
kernel is equivalent to an RBF kernel with the eu-
clidean distance replaced by a sum of distances d()
2
,
one for each mode. The distance function is a sub-
space measure which can be calculated using the SVD
as:
d(X
(i)
, Y
(i)
) = kV
X
(i)
· V
T
X
(i)
− V
Y
(i)
· V
T
Y
(i)
k (2)
V are the right singular vectors of the tensor unfold-
ing. The distance is called a projection Frobenius
norm (or chordal distance). The procedure is sum-
marized in Figure 3
2.4 Data Representations
2.4.1 Vector Representations
A fast way to obtain robust and informative features
is by averaging over the informative part (0-800ms)
BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing
6
Figure 2: Data acquisition steps for a single trial: after ICA (A), filtered and baseline corrected (B), re-referenced and SVD
truncated (C).
of the time signals. For this study, each channel has
been divided in 23 bins of 31ms. The binned data can
be presented as a channel-time matrix, as in the left
part of Figure 4. For the linear and RBF kernels, the
data is vectorized. The dimensionality of the prob-
lem is reduced to 60 subject-dependent features using
reliefF (Liu and Motoda, 2008). In Figure 4, the im-
portance of selected features is given as a gray value.
Note the most important lie around t = 300ms (bin
9-11). These binning values are used with both the
linear (BINLIN) and RBF (BINRBF) kernel.
As another type of features, the right side of
Figure 4 displays examples of Gabor atoms (Ga-
bor, 1946), defined as gaussian windowed cosines
(for real signals), with a certain frequency f, time
shift t
0
and window parameter σ. A vectorial Ga-
bor atom approach starts from a dictionary of gen-
erated atoms. Here, 5696 atoms have been used with
t
0
∈ {1+ 2·i|i = 1..63} [samples], f ∈ {
π
8
i|i = 0..26}
[Hz] and σ ∈ {2· i|i = 1 : 6}. The dictionary is used to
approximate signals as linear combinations of atoms
by means of orthogonal matching pursuit (Mallat and
Zhang, 1993). The combination coefficients form the
feature vector. A channel can be approximated almost
perfectly with 4 or 5 atoms. Feature vectors are there-
fore sparse and, additionally, non-consistent across
Figure 3: Graphical representation of the tensorial ker-
nel (Signoretto, 2011).
trials. One way to cope with that is to select repre-
sentative atoms based on the grand average (the aver-
age across all single trials). For each channel, atoms
are selected for both target and non-target grand aver-
ages. These sets can be unified, leading to one repre-
sentative atom set for each channel. Eventually, single
trial channels are fitted to these sets in a least-squares
sense and concatenated to form a single trial vector.
A last optimization is a further feature selection with
reliefF, yielding a final vector of 30 features. The
use of these features with RBF will be referred to as
GABRBF.
2.4.2 Tensor Representations
Three kinds of three-way tensor representations are
tested for use with the tensorial kernel. Example
slices of these tensors for the grand average differ-
ences of target and deviant can be seen in Figure 5.
The Hankel tensor consists of channel hankel ma-
trices, stacked together to form a third dimension. As
Figure 5A shows, a hankel matrix is an anti-diagonal
matrix whose entries can be defined by a signal laid
out over the first column and last row. Its use is mo-
tivated by subspace identification for linear time in-
variant systems, closely linked to (damped) harmonic
retrieval (Kung et al., 1983). Since the 23 bins are
used to construct square matrices, the eventual ten-
sors have dimensions 12× 12 × 12, two time and one
Figure 4: The bin-channel map with features 1-10 in white,
11-25 in gray and 26-60 in dark grey (A) example of Gabor
atoms (B).
SingleTrialClassificationforMobileBCI-AMultiwayKernelApproach
7
Figure 5: Hankel Pz slice (A) Topographic slice around 300ms (B) Pz Time-frequency map (C).
channel dimension. Using the hankel tensor with the
tensorial kernel is denoted by HANK.
A second data representation is topographic
(TOPO). For each of the 23 time bins, a square topo-
graphic map of the brain is generated. Such a map is a
2D gaussian mixture model based on the electrode po-
sitions and their voltages for the given time bin. The
maps are stacked to form a 23× 23 × 23 tensor, two
spatial and one time dimension.
Finally, a time-frequency tensor is constructed. It
is closely related to the Gabor transform (Wexler and
Raz, 1990), which will here be considered as a win-
dowed STFT. For each channel, a 12 × 12 matrix is
constructed, corresponding to an equal division of
time (0-800ms) and frequency (0-11Hz). The width
of the gaussian window is optimized for each subject.
Similar data representations have been used in BCI,
though mostly for motion imagery. Using this repre-
sentation for classification is indicated with GABT.
2.5 Experiments
Three kinds of experiments will be discussed, high-
lighting the influence of condition (sitting vs walk-
ing), the training set size and averaging.
3 RESULTS
3.1 Influence of Condition
As mentioned before, data was recorded in sitting and
walking condition to estimate the influence of mo-
tor activity. A general comparison of the methods
across all subjects and their accuracy changes due to
the recording condition is given in Figure 6. Based
on these average results, the influence of condition is
clear: there is a significant decrease in accuracy from
sitting to walking (p < 0.01, paired t-test). For indi-
vidual subjects, 18 out of 20 have all methods non-
increasing (either significantly decreasing or no sig-
nificance).
Conclusions about a comparison between the
methods can be drawn as well. In sitting condition,
the following order can be established (p < 0.05):
BINLIN > BINRBF > TOPO > HANK, GABT
> GABRBF. The difference between HANK and
GABT is not significant. BINLIN and GABRBF are
least affected by the condition change (-4%), whereas
GABRBF, HANK and TOPO lose around 6% and
GABT even 8%. The ordering of the methodsremains
almost the same, only GABRBF and GABT switch
place (p < 0.05). BINLIN strengthens its position.
3.2 Influence of Training Set Size
Figure 7 sketches the influence of the training set size
for two subjects. Although there is a big difference
in the actual values for the two subjects, all methods
increase in performance with a growing set, which is
only logical: a better model can be derived. It should
be remarked that the linear method proves superior in
all cases, followed by BINRBF. For the second sub-
ject however, TOPO is seen to be better for increasing
size of the data set.
3.3 Influence of Averaging
The average over all subjects (left part of Figure 8)
shows that BINLIN and BINRBF have an almost
parallel increase of accuracy when averaging. They
increase more than all other methods. TOPO and
HANK also follow this, though less clearly. All
methods except for GABRBF show an eventual de-
crease when using more trials for averaging, partic-
ularly clear for GABT. This will probably be due to
the decrease in training set size, a direct result of the
Figure 6: Accuracies for all methods for sitting and walking
condition.
BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing
8
Figure 8: Influence of averaging over 1-5 trials: across subjects (left), for one specific subject (right).
averaging process. Yet, this is not true for GABRBF.
Since it is built using a model derived from the grand
average, trials can be more accurately modelled when
averaging is applied as it yields a lower variance.
The right part of Figure 8 shows an interesting in-
sight. TOPO is the only tensorial method which fre-
quently can keep pace with or outperforms BINLIN
and/or BINRBF. In the given example, HANK per-
forms better than BINLIN as well. This is an example
where it is already the case for single trials, averaging
is therefore not more beneficial to vectorial methods.
On the other hand, in most cases where TOPO be-
comes competitive, it performs worse on single trials.
Therefore, for some subjects, the benefit of averaging
is higher for TOPO than for the vectorial methods,
which cannot be derived from the left part of the Fig-
ure.
Figure 7: Influence of training set size for two subjects.
4 DISCUSSION
The idea of using subspace methods was to obtain a
more robust measure of class discrimination. It ap-
pears that this is not the case. Particularly, the ex-
pectations that such methods would better withstand
noise (represented here by additional brain activity
when walking) and capture essential discriminative
information with smaller data sets do not hold. Sev-
eral possible reasons and influences should be men-
tioned. First of all, the vector methods use an ad-
ditional feature selection, which allow them to focus
on essential local features. The subspace methods, as
they are applied here, do not have such an optimiza-
tion. An additional bin-channel selection could im-
prove the discrimination. This theory is confirmed by
the performance of GABRBF, which is significantly
lower than BINRBF. One the one hand, the features
are based on loose approximations of the trials based
on the grand average, but more importantly, the fea-
tures are global and cannot exploit feature selection
as the binning methods.
A second reason is the possibility of generaliza-
tion, essential for a good classification. The linear
method mostly outperforms the others due to its nec-
essary approximation of the decision boundary. The
other methods are all RBF-based (even the tenso-
rial), thus having the universal approximation prop-
erty. Despite the regularization of (LS-)SVM, overfit-
ting seems to occur. This becomes clear when com-
paring the high training accuracy with the signifi-
cantly lower test accuracy. The gap shrinks with a
larger training set, as was indeed observed in the sec-
ond experiment. Yet, the total data set remains small
for accurate learning, which cannot be overcome.
Thirdly, the tensorial kernel presupposes an un-
derlying structure of the data. Each class is supposed
to correspond to a congruence set; that is, to be gener-
ated from a multilinear basis which characterizes the
class. Most tensor representations do not completely
SingleTrialClassificationforMobileBCI-AMultiwayKernelApproach
9
Table 1: Number of times the method mentioned in the row
outperforms the method in the column (p < 0.05) for the
single trial case in sitting condition.
BL BR GR HNK TOP GT
BINLIN 0 5 16 13 13 13
BINRBF 2 0 14 9 8 11
GABRBF 0 0 0 1 1 2
HANK 2 1 7 0 4 6
TOPO 3 2 12 8 0 10
GABT 1 1 8 4 5 0
fulfil this condition e.g. due to noise. The extent to
which they do can e.g. be estimated from kernel-
target alignment (Cristianini et al., 2002), calculated
for the tensorial kernel.
It is hard to draw general conclusions with regard
to the future of subspace methodsfrom this study. The
subspace structure implied by the tensorial kernel is
just one way of measuring the similarity between tri-
als. Furthermore, one could consider other data rep-
resentations.
Finally, it should be noted that there are large dif-
ferences among the subjects. In the best performing
subject, the results as presented abovehold. Yet, other
subjects have comparable results for vector and tensor
methods, or even better results with tensors, particu-
larly for TOPO. As already mentioned, this is particu-
larly true when averaging, but Figure 7 (bottom) gives
an example for single trials as well. Table 1 is an ad-
ditional illustration. It gives the number of subjects
for which the method on the row significantly outper-
forms the method in the column (p < 0.05). The table
supports the conclusion of BINLIN and BINRBF be-
ing the superior methods, while TOPO dominates the
tensorial methods. Even apart from these rather nega-
tive results, tensor methods are computationally more
expensive as well.
Further study could involve additional data sets,
other dimensions or other types of tensors and ker-
nels. Furthermore, instead of creating data represen-
tations to directly measure similarities, tensors could
also be used for regularization or to extract structural
features for use in a vector classifier.
5 CONCLUSIONS
Subspace discrimination of tensorial data has been
combined with kernels for BCI ERP classification.
Three tensorial data representations were introduced:
one based on Hankel matrices, one on topographic
maps and one on time-frequency matrices. By means
of analyses on the influence of condition, training set
size and averaging, they were evaluated against more
conventionallocal (time-channel bins) and global (ga-
bor atom matching) feature vector methods with lin-
ear or RBF kernels. By and large, the tensorial ap-
proach does not yield any advantage, although it is at
least competitive for some subjects, particularly the
topographic method.
ACKNOWLEDGEMENTS
• Research Council KUL: GOA/10/09 MaNet, CoE
PFV/10/002 (OPTEC);
PhD/Postdoc grants
• Flemish Government:
– FWO: projects: G.0427.10N (Integrated
EEG-fMRI), G.0108.11 (Compressed Sensing)
G.0869.12N (Tumor imaging) G.0A5513N
(Deep brain stimulation); PhD/Postdoc grants
– IWT: projects: TBM 080658-MRI (EEG-
fMRI), TBM 110697-NeoGuard; PhD/Postdoc
grants
– iMinds Medical Information Technologies
SBO 2014, ICON: NXT
Sleep Flanders Care:
Demonstratieproject Tele-Rehab III (2012-
2014)
• Belgian Federal Science Policy Office: IUAP
P7/19/ (DYSCO, ‘Dynamical systems, control
and optimization’, 2012-2017)
• Belgian Foreign Affairs-Development Coopera-
tion: VLIR UOS programs
• EU:
– EU: The research leading to these results has
received funding from the European Research
Council under the European Union’s Sev-
enth Framework Programme (FP7/2007-2013)
/ ERC Advanced Grant: BIOTENSORS (n
339804).This paper reflects only the authors’
views and the Union is not liable for any use
that may be made of the contained information.
• other EU funding: RECAP 209G within IN-
TERREG IVB NWE programme, EU MC ITN
TRANSACT 2012 (n 316679), ERASMUS EQR:
Community service engineer (n 539642-LLP-1-
2013)
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