1

Pattern Recognition Letters
journal homepage: www.elsevier.com

Multiclass Common Spatial Pattern for EEG based Brain Computer Interface with
Adaptive Learning Classifier

arXiv:1802.09046v1 [] 25 Feb 2018

Hardik Meisheria,∗∗, Nagaraj Ramraoa , Suman K. Mitraa
a Dhirubhai

Ambani Institute of Information and Communication Technology, Indroda Circle, Gandhinagar - 382007, India

ABSTRACT
In Brain Computer Interface (BCI), data generated from Electroencephalogram (EEG) is non-stationary with low signal to noise ratio and contaminated with artifacts. Common Spatial Pattern (CSP)
algorithm has been proved to be effective in BCI for extracting features in motor imagery tasks, but it
is prone to overfitting. Many algorithms have been devised to regularize CSP for two class problem,
however they have not been effective when applied to multiclass CSP. Outliers present in data affect
extracted CSP features and reduces performance of the system. In addition to this non-stationarity
present in the features extracted from the CSP present a challenge in classification. We propose a
method to identify and remove artifact present in the data during pre-processing stage, this helps in
calculating eigenvectors which in turn generates better CSP features. To handle the non-stationarity,
Self-Regulated Interval Type-2 Neuro-Fuzzy Inference System (SRIT2NFIS) was proposed in the literature for two class EEG classification problem. This paper extends the SRIT2NFIS to multiclass
using Joint Approximate Diagonalization (JAD). The results on standard data set from BCI competition IV shows significant increase in the accuracies from the current state of the art methods for
multiclass classification.
c 2018 Elsevier Ltd. All rights reserved.

1. Introduction
There is on-going research to connect brain signals with
computers/machines in order to create a comfortable communication pathway for disabled people with external environment.
Brain Computer Interface (BCI) aims to provide non-muscular
communication between brain and computer/machine by interpreting the thoughts in the brain. BCI can be defined as: ”a
system that acquires brain signal activity and translates it into
an output that can replace, restore, enhance, supplement, or improve the existing brain signal, which can, in turn, modify or
change ongoing interactions between the brain and its internal
or external environment”. Or in simple words, it is a system that
translates brain signals into new kinds of outputs as mentioned
in Daly and Wolpaw (2008). In intelligent devices, which rely
hugely upon the user experience, BCI is used for monitoring
purposes, for example monitoring attention level of driver on a
long drive. Apart from clinical application for disabled people

∗∗

e-mail: hardik_meisheri@daiict.ac.in (Hardik Meisheri)

for controlling devices, BCI is used in virtual reality, gaming
industry and entertainment industry. It is also used for meditation and rehabilitation purposes. BCI is employed in boosting
learning abilities of children who have difficulty with this.
There are three broad categories of BCIs namely, implantable/invasive, non-invasive and partial/semi-invasive, distinguished by invasively and noninvasively acquired brain signals, respectively. Invasive BCI have a requirement of placing
the sensors inside the brain, for which operation is necessary.
Although this type of BCI provide one of the best signal-tonoise ratio (SNR), they are not preferred due to high economic
cost, short sensor duration and surgical risks. Non-invasive BCI
can be realized using brain’s electric or magnetic field, out of
which electric field is preferred choice as it is mobile and set of
apparatus needed for this is easily available and not bulky. Electroencephalography (EEG) has been used to detect the electric
signals in a non-invasive manner. BCI using EEG can be further catergorized into event related potential - P300 proposed
by Farwell and Donchin (1988), steady state visual evoked potential (SSVEP) mentioned in Vidal (1973) and event related
desynchronization/synchronization (ERD/S). In this paper, we

2
concentrate on motor imagery system based BCI which is a type
of ERD/S.
Motor Imagery based BCI were invented to help people with
disabilities to communicate with the outer world. EEG has
proven to be effective in motor imagery based BCI due to its
very light equipment, low cost and high temporal resolution
Curran and Stokes (2003). However, BCI using EEG suffers
from challenges such as extracting features which are useful
for specific task due to low specificity, vulnerable to volume
conduction effects, non-stationarity, and prone to noise Wolpaw et al. (2000). Another problem posed by EEG signals is
that they vary from person to person and session to session
Krauledat et al. (2007). Spatial filtering has been introduced
to discriminate between the motor imagery signals using multichannel EEG. The objective behind this filtering is to transform
the multichannel EEG signals into small set of channels which
are useful to distinguish between the different brain activities
Vidaurre et al. (2011); Tangwiriyasakul et al. (2013).
2. Related Work
Common spatial Pattern (CSP) has proven to be very efficient in context of motor imagery based BCI Tangermann et al.
(2012); Ramoser et al. (2000); Blankertz et al. (2008, 2004,
2006). Ideally, CSP computes the filters which maximizes the
ratio of variance between the brain activities, details of which
are explained in the subsection 3.1. However, CSP is vulnerable
to noise and problem of overfitting Reuderink and Poel (2008);
Grosse-Wentrup et al. (2009). To overcome these shortcomings, many methods have been proposed in literature Blankertz
et al. (2008); Lu et al. (2009); Kang et al. (2009); Lotte and
Guan (2010). Lotte and Guan (2011) presents detailed comparisons of these regularization techniques. Dornhege et al.
(2004a) in their pioneer work extended CSP to multiclass by
using methods such as one-versus-rest, pair-wise and simultaneous diagonalization. A major drawback in extending CSP to
multiclass is that regularization methods proposed for two class
are not effective, therefore accuracies for multiclass are substantially low. For extending original CSP algorithm to more
than two class, Naeem et al. (2006), Brunner et al. (2007),
Grosse-Wentrup and Buss (2008), Gouy-Pailler et al. (2008),
Gouy-Pailler et al. (2010), Grosse-Wentrup and Buss (2008)
and Wei et al. proposed different methods using Joint Approximate Diagonalization (JAD) . Among all these approaches
common part was that they assumed that CSP is equivalent to
finding independent common components for 2-class problem.
Naeem et al. (2006) and Brunner et al. (2007) researched on different Independent Component Analysis (ICA) algorithms for
finding features and components including Informax Bell and
Sejnowski (1995), FastICA Hyvarinen (1999) and SOBI Belouchrani et al. (1997). They presented key differences between
the performance of ICA-based methods with other CSP methods which are variants of One-versus-the- Rest and Pair-Wise
Dornhege et al. (2004b). Their findings concluded that overall,
CSP methods perform better than ICA-based methods. In addition to this they also stated that among the ICA-based methods,
Infomax achieved better performance than others. CSP is identical to ICA was proven mathematically by Grosse-Wentrup

and Buss (2008). The authors proposed that CSP by JAD is
identical to ICA and also proposed information theoretic approach for feature extraction. Gouy-Pailler in their recent work
Gouy-Pailler et al. (2008), Gouy-Pailler et al. (2010) proposed
maximum likelihood method for finding spatial filters which
is extension of JAD method. They claimed that their method
is a neurophysiologically adapted version of JAD. They validated their approach on Dataset 2a of the BCI Competition IV
which has nine subjects(they have used only 8 subjects out of
9) with four motor-imagery tasks, and reported that their newly
proposed JAD method achieved a better classification accuracy
than the CSPs method. They also claimed that CSP with JAD is
not better significantly than CSP methods which are variant of
of One-versus-the- Rest and Pair-Wise as reported in the findings of Grosse-Wentrup and Buss (2008). In a separate work,
Wei et al. used quadratic optimization to find common spatial patterns for multi-class BCI problems. However, in this
case they conducted experiments on their own dataset instead
on more widely used datasets so it is difficult to compare their
results with previously noted research results. Apart from these
two methods there is some interesting work done using subspace method by Ramoser et al. (2000), in which they propose
Union-based common principal components (UCPC) to create
a subspace for class of data from covariance matrix, and finally
the union of all the all subspaces is used as common principal
component. However, drawback of this method is that chosen
principal components may not contribute to some data classes
at all.
In summary, multi-class BCI systems can be broken down
into two main groups. The first is based on extension of two
class methods that original CSP was designed to work upon, on
the other hand other groups deals with JAD. Key point of two
class CSP- based methods is that it breaks down the multi-class
problems into various classification two-class problems. The
two popular methods are One-versus-the-Rest, and a combination of pairs of two-class classification problems (Pair-Wise).
Each of these two methods has its own weakness. In the first
method there is an assumption that covariance matrix all the
other classes are almost identical. However, this assumption
hardly stands true in real world data. In latter, there is no surety
of getting the CSPs that are optimal of different pairs of classes.
This is similar to grouping common principal components of
pairs of classes and then finding CSPs.
Non-stationarity nature of data in EEG presents major problem, which is due to the variation in intra- and inter- session in
the same task. This results in very low accuracies in the classification phase, due to poor modeling of data. Recently fuzzy
inference systems were used in EEG which has proved to be effective for classification purpose. As shown in Guler and Ubeyli
(2005); Coyle et al. (2009); Fabien et al. (2007); Subasi (2007);
Yang et al. (2014) type-1 inference systems have been employed for classification of EEG signals. However, type-1 fuzzy
sets are inefficient in handling non-stationarity of EEG signals
as pointed out by Herman et al. (2006). Type-2 fuzzy sets which
was proposed by Zadeh (1975) along with uncertainty framework can be used to handle non-stationarity as shown in Mendel
and John (2002). Type-2 sets are computationally very expen-

3
sive which limits their usage. Modification in type-2 set was
presented by Liang and Mendel (2000), where uncertainty is
represented as bounded interval is highly efficient in computation. Interval type-2 neuro fuzzy inference systems were proposed for classification as mentioned by Herman et al. (2006,
2008); Nguyen et al. (2015). Although they gave decent accuracies, fixed structure of these network have proven to be limitations in handling time varying data of EEG as pointed out by
Lughofer (2011); Lughofer et al. (2015); Pratama et al. (2015).
To handle this, evolving structure and learning algorithm was
proposed in literature. Self-Regulated Interval Type-2 NeuroFuzzy Inference System (SRIT2NFIS) proposed in Das et al.
(2016) is one such algorithm where structure is evolved based
on data. SRIT2NFIS has been used in this paper for classifying the motor imagery EEG details of which are presented in
section 4.
3. Feature Extraction
3.1. Common Spatial Pattern
CSP algorithm is widely used in BCI field and is used to find
spatial filters which can maximize variance between classes on
which it is conditioned. As mentioned in page 2, many extensions to basic algorithm has been proposed which has made
CSP base line model for feature extraction. We present CSP
algorithm for two class problem which is then extended to multiclass. We assume that frequency band and the time window
of the input EEG signal is known apriori. In addition to this we
assume that signal is jointly gaussian with zero mean. These
assumptions put no limitations to the further analysis due to following reasons. First, transformation is linear and mean can be
subtracted and added at the end. Second BCI based motor imagery systems using EEG data operates in specific frequencies,
hence there are no information present in the higher moments
and hence there is no loss of information in assuming gaussianity. Given an EEG signal extracted from single trail, E with
dimension N × T from ith class, where N is the number of channels in the recording and T is the number of time samples taken
for each channel. The corresponding covariance matrix can be
defined as

Ci =

EE 0
trace(EE 0 )

(1)

where 0 is a transpose operator and trace() is function which
calculates sum of diagonal of matrix. For each class, average
spatial covariance matrix (C̃i ) is calculated, for two class we
have C˜1 and C˜2 . Composite spatial covariance matrix is generated by adding both the averaged matrix. The Composite Matrix can be defined as
C̃ = C˜1 + C˜2

(2)

Eigen values (λ) and Eigen vectors (U) of the composite matrix are calculated, which can be represented as
C̃ = UλU 0

(3)

The eigen values are then sorted in descending order and
whitening transformation is applied to de-correlate it
√
λ−1 U

P=

(4)

C1 and C2 are then transformed as

S 1 = PC1 P0

S 2 = PC2 P0

and

(5)

and by simultaneous diagonalization,

S 1 = Bλ1 B0

and

S 2 = Bλ2 B0 ;

λ1 + λ2 = I

(6)

where B is the common eigen vector matrix, λ1 and λ2 are
the eigen values of S 1 and S 2 respectively. I denotes the identity matrix. Addition of both the eigen values ensures that the
largest eigen value in one class correspond to lowest eigen value
in other class. This helps in the classification while selecting channel which can effectively distinguish between the two
class. Spatial Filter W can be defined as W = (BP0 )0 and transformed EEG signal can be viewed as

Z = WE

(7)

CSP are the columns of W −1 , which is time invariant source
of EEG. From this, features are extracted, relatively very small
number m channels suitable for discrimination. First m and last
m rows of Z are selected for classification. Selection of m is
done using following method as proposed by Blankertz et al.
(2008)
score(W j ) =

med(1)
j
(2)
(3)
(4)
med(1)
j + med j + med j + med j

(8)

where,
0
0
med(c)
j = mediani∈ιc W j E i E i W j



(c ∈ 1, 2, 3, 4)

ι in a set of trials belonging to a particular class. Ratio of
median score near to 1 or 0 indicates good score of the corresponding spatial filter. m = 3 gives optimal discriminable
features. Features are selected using value of m as presented,




 var(Z ) 
p


f p = log 
;
 2m
P
 var(Zi ) 

where

p = 1, 2..., 2m

(9)

i=1

f1 , f2 ... f2m are the features used for classification. Log transformation projects the data into normal distribution.

4
cally as

3.2. Proposed CSP
To mitigate the effect of noisy trials on eigen values and eigen
vectors, the calculation of average covariance matrix for each
class, Frobenius norm as presented in Meyer (2000) of each covariance matrix obtain from different trials is calculated. Frobenius norm is square root of the sum of the diagonal elements
of the matrix. The covariance matrices from the same class
have a similar magnitude of the Frobenius norm. Z-score Marx
and Larsen (2006) is calculated for all trials, which transforms
Frobenius norm obtained earlier into zero mean and unity standard variance. If the Z-score is more than threshold then that
trial is termed as an outlier and is removed from the calculation
of CSP filter.
As mentioned in section 2, JAD based methods were performing better relative to other methods for extending CSP to
multi-class. The notion behind JAD is

W 0C̃i W = Di

where H(.) represents Shannon Entropy, |C| is total number of classes present in C, and G the set of all classifiers
• Upper Bound inequality :Pe ≤ 1 − 2I(c, f (~x)) − H(c).

(14)

These two inequalities helps in maximizing the mutual information and reducing the error. In context of BCI, out main
objective is to find a reduction in dimension of the input data
while simultaneously maximizing the mutual information between the features extracted and their corresponding class labels.

(10)

where C̃i is the average covariance matrix of ith class, W is
the spatial filter and Di is the corresponding diagonal matrix for
each class. The objective is to find W such that, all the classes
can be diagonalized as mentioned above. There are many ways
of obtaining spatial filters by JAD as stated in section 2. In
this paper we have used method proposed by Liyanage et al.
(2010) which uses fast Frobenius diagonalization (FFDIAG).
Instead of using log variance as measure of feature extraction
as we do in basic CSP, we will be using information theoretic
feature extraction Grosse-Wentrup and Buss (2008) for selecting the relevant spatial filters from W. Information Theoretic
Feature Extraction has recently received considerable attention
in the machine learning community, mostly in a nonparametric setting. It can be briefly explained as follows; Suppose we
have a random variable ~x ∈ χ, which is in our application EEG
data. Also we suppose that it belongs to one of the class c ∈ C,
where C is a set of all the classes present in the data. Objective of algorithm is to identify the transformation, which can be
mathematically stated as f ∗ : χ → χ̂, where χ is our input feature space and χ̂ is the discrete set. This transformation should
also preserve the information related to the class labels.

f ∗ = argmax f ∈F {I(c, f (~x))},

H(c| f (~x)) − 1
, (12)
log|C|
H(c) − I(c, f (~x)) − 1
,
(13)
=
log|C|

Pe := argming∈G {Pr {c , g( f (~x))} ≥

(11)

where this equation, calculates the I(.) in other function
space which is mutual information between c and f(.). The basic notion of this algorithm is to provide upper bounds as well
as lower bounds on the classification error. Minimum classification is taken into consideration also with respect to mutual information. This bounds are provided by two inequalities which
are as follows,
• Fano’s inequality :- This inequality provides the lower
bound for classifier g : χ → C and is shown mathemati-

4. Classification
Extracted features after CSP, are given as the input to the
classifier. Keeping in mind the non-stationarity nature of EEG
signals and small amount of training data, SRT2NFIS is used
for classification. SRIT2NFIS is Takagi-Sugeno-Kang (TSK)
type neuro-fuzzy inference system with sequential learning.
Uncertainty framework helps in modeling the non-stationarity
in the signals. Uncertainty is modeled as Gaussian membership function with uncertain mean and fixed variance. TSK
type neuro-fuzzy inference system is embedded upon neural
network, these network then can be realised in four to six layers. SRIT2NFIS is a 5 layer network as shown in Figure 1
with projection based learning algorithm. Let us assume that
we have a labeled input data, (xt , ct ), where xt is m-dimensional
input vector of tth sample and ct is its corresponding class label.
ct ∈ (1, 2, ..., n) where n is the total number of class. Output yt
is described as,



i f j == ct
 1,
t
yj = 
j = 1, 2, ..., n
(15)

 −1, otherwise
The main goal of SRIT2NFIS is to estimate the function
which can map input(xt ) to output(yt ), where xt is a m dimensional input vector and yt is the output class label.
Layer 1 - Input Layer: Input layer directly maps the input to
the layer 2, which can be represented as uti = xit for tth sample
and i = 1, 2, ..., m
Layer 2 - Fuzzification Layer: In this layer, type-2 Gaussian
membership function is used in each of the neuron to model the
non-stationarity in the input.
Layer 3 - Firing Layer: This layer calculates the firing
strength which is represented by each neuron of this layer.
Algebraic product of the membership values amounts to the
strength, output of this layer is type-1 fuzzy set.
Layer 4 - Type reduction layer: Using Nie-Tan type-reduction
approach Nie and Tan (2008), each neuron converts the input

5

Fig. 1. Structure of SRIT2NFIS Das et al. (2016)

type-1 fuzzy set to a fuzzy number for each rule. α is set to 0.5,
which is the weighted measure of uncertainty.
Layer 5 - Output layer: Normalized weighted sum of the firing strength is calculated in this layer, output of which gives the
predicted output class of each trail.
It uses a projection based algorithm Babu and Suresh (2013),
with minimization of sum of squared hinge error for avoiding
over-fitting where the regularization parameter is set to 0.01.
When a new sample arrives at the input of the network, prediction error and spherical potential Babu and Suresh (2013) are
calculated. Based on these two parameters, decision is taken either to keep the sample and modify parameter/addition of rule,
discard the sample or reserve it for the later use. The learning
algorithm parameters are discussed as follows:
Absolute maximum hinge-error: It is calculated to measure
the prediction error of the current sample.
Class-Specific Spherical potential: Knowledge content in the
sample is measured using spherical potential for that particular
class. It is calculated by averaging the distance in the hyper
dimensional space between current sample and the rules from
the same class which are contributing significantly. Higher the
potential lower is the novelty in the sample.
Rule growing criterion: If the novelty of the current sample
is high and absolute maximum hinge-error is also high, new
rule is added in the network provided the predicted class label
is incorrect or no rule has been fired for the current sample.
This is controlled by two threshold; Add threshold and novelty
threshold. Add threshold is a adaptive in nature, main objective of this is to capture global knowledge at the start and then
fine tune accordingly. It’s adaptiveness is controlled by another
parameter γ which is set to 0.99, this value has been estimated
due to small training samples. Range for add threshold is [1.01,
1.20] and that for novelty threshold is [0.01, 0.60].
Intra/Inter class overlap factor : Width of the new rule is influenced by the nearest intra/inter class rules. Intra class overlap factor should be higher as we need a higher overlap in case
of BCI, it is set to 0.95. However, Inter class overlap factor

is chosen in range [0.1, 0.4], very little overlap will hinder the
generalization capability of network.
Parameter update criterion: Adaptation of the output network weights are carried out whenever the predicted class label
is correct and absolute hinge error is greater than update threshold. Update threshold is also a adaptive parameter and it is also
controlled by γ mentioned earlier. Rule add threshold range is
[0.04, 0.2].
Rule Pruning Criterion: If for consequent number of samples greater than pruning window of the same class, contribution of the rule is not significant then that rule is removed from
the network. Pruning threshold is set to 0.01 and pruning window is set to 10.
Sample deletion criterion: If current sample contains no novelty then that sample is discarded, sample delete threshold is set
to 0.05.
Sample reserve criterion: If the sample does not meet any of
the above mentioned criteria, then it is reserved for the later use
by pushing this sample at last of the sequence.
5. Results and Discussion
5.1. Data
We have implemented proposed method on benchmark
dataset of BCI competition IV namely dataset 2a. It is a continuous Multiclass Motor Imagery EEG data of 9 subjects. It consisted of four different motor imagery class, imagination of the
left hand, right hand, both feet and tongue. Data was recorded
in two session on different days for each patient. Each sessions
consisted of 6 runs and each run comprised of 48 trials (12 for
each class). So we have 288 trial for each session. Each trail
consisted of 7.5 sec recording. At the beginning of each trail
a fixation cross appeared on the screen and also an acoustic
warning tone was also presented. After 2 sec cue was presented
on screen in the form of arrow which pointed either left, right,
down or up corresponding to each of the four class. Subjects
were asked to imagine respective movement after the cue has
been presented till sixth sec. This was followed by a 1.5 sec
break.
Figure 2 shows the graphical view of the paradigm used for
recording.

Fig. 2. Timing scheme of Data set 2 Brunner et al.

The signals were samples at 250Hz and then filtered using
a band pass filter having 0.5Hz as low and 100Hz as high frequency. Along with this it was also filtered using 50Hz notch
filter for removing the line noise. This experiment was done
using 22 electrodes. For each subject training and testing data
set was provided separately.

6
5.2. Experiment
We have used training data to train our network and results
are generated for the testing data. For evaluation metric overall
classification is used as a parameter for comparison. Accuracy
is defined as ratio of correctly classified trials in their respective
class to total number of trials for that subject.
Data is preprocessed before feeding to proposed mechanism.
Butterworth Band pass filter of order 5 used to filter signals
between 8-40Hz as proposed in Müller-Gerking et al. (1999).
Proposed CSP method was used to extract features with m =
3, as described in subsection 3.1. While using SRIT2NFIS as
classifier, parameters such as add threshold, update threshold,
novelty and inter-class overlap have to be optimized for each
patient. This was achieved by implementing particle swarm optimization (PSO) for each subject independently. Two parameters that govern the PSO are number of iteration and parameter
width. Figure 3 shows the plot of these two parameters and accuracy for subject 2. The two parameters differ from subject
to subject. Best accuracy for subject 2 was 45.48% which is
66.59% increase in accuracy reported in Grosse-Wentrup and
Buss (2008). Addition to this, it is interesting to note here that
subject 2 and subject 5 have a very noisy data as compared to
other subjects which is evident from the earlier results in the literature and also this can be seen in the two class classification
results on same data.

Fig. 3. Surf plot for Parameter Width Vs Iteration vs Accuracy

Table 1 shows the comparison of proposed approach and
Multiclass CSP (mCSP) Grosse-Wentrup and Buss (2008) and
ComplexCSP Zhang et al. (2013). Comparison of proposed approach is done with Multiclass CSP (mCSP) Grosse-Wentrup
and Buss (2008) and ComplexCSP Zhang et al. (2013), both of
these algorithms use Support vector Machine (SVM) as their
classifier. The increase in accuracy can be attributed to two major arguments; formation of generalized eigen vectors due to
removal of noisy trials which causes a better feature after CSP
and better handling of over fitting and non stationarity of EEG
data by SRIT2NFIS by its self regulating learning algorithm.
6. Conclusion
In this paper we have presented common spatial pattern algorithm for multiclass EEG classification with a pre-processing
step which can improve the generalization of CSP covariance
matrices by removing the trials which are noisy/affected with
artefact. SRIT2NFIS is used as a classifier to handle the non

stationarity present in the signal. The results were presented
on publically available data set BCI competition IV data 2a.
Results are compared with the currently state of the art algorithms for multiclass classification. It clearly shows that proposed method outperforms the in four class classification by
improving the mean accuracy 8-13%. The increase is significant in subjects which earlier had very low accuracies.
ACKNOWLEDGMENT
Authors would like to thank Prof. N. Sundararajan, Prof. S.
Suresh and Mr. Ankit Das for their immense support in this
research work.
References
Babu, G.S., Suresh, S., 2013. Parkinsons disease prediction using gene expression a projection based learning meta-cognitive neural classifier approach.
Expert Systems with Applications 40, 1519 – 1529.
Babu, G.S., Suresh, S., 2013. Sequential projection-based metacognitive learning in a radial basis function network for classification problems. IEEE
Transactions on Neural Networks and Learning Systems 24, 194–206.
Bell, A.J., Sejnowski, T.J., 1995. An information-maximization approach to
blind separation and blind deconvolution. Neural Comput. 7, 1129–1159.
Belouchrani, A., Abed-Meraim, K., Cardoso, J.F., Moulines, E., 1997. A blind
source separation technique using second-order statistics. IEEE Transactions on Signal Processing 45, 434–444.
Blankertz, B., Muller, K.R., Curio, G., Vaughan, T.M., Schalk, G., Wolpaw,
J.R., Schlogl, A., Neuper, C., Pfurtscheller, G., Hinterberger, T., Schroder,
M., Birbaumer, N., 2004. The bci competition 2003: progress and perspectives in detection and discrimination of eeg single trials. IEEE Transactions
on Biomedical Engineering 51, 1044–1051.
Blankertz, B., Muller, K.R., Krusienski, D.J., Schalk, G., Wolpaw, J.R.,
Schlogl, A., Pfurtscheller, G., Millan, J.R., Schroder, M., Birbaumer, N.,
2006. The bci competition iii: validating alternative approaches to actual
bci problems. IEEE Transactions on Neural Systems and Rehabilitation Engineering 14, 153–159.
Blankertz, B., Tomioka, R., Lemm, S., Kawanabe, M., r. Muller, K., 2008.
Optimizing spatial filters for robust eeg single-trial analysis. IEEE Signal
Processing Magazine 25, 41–56.
Brunner, C., Leeb, R., Muller-Putz, G., Schlogl, A., Pfurtscheller, G., . Data set
iv. URL: http://www.bbci.de/competition/iv/.
Brunner, C., Naeem, M., Leeb, R., Graimann, B., Pfurtscheller, G., 2007. Spatial filtering and selection of optimized components in four class motor imagery {EEG} data using independent components analysis. Pattern Recognition Letters 28, 957 – 964.
Coyle, D., Prasad, G., McGinnity, T.M., 2009. Faster self-organizing fuzzy
neural network training and a hyperparameter analysis for a brain–computer
interface. IEEE Transactions on Systems, Man, and Cybernetics, Part B
(Cybernetics) 39, 1458–1471.
Curran, E.A., Stokes, M.J., 2003. Learning to control brain activity: A review
of the production and control of EEG components for driving braincomputer
interface (bci) systems. Brain and Cognition 51, 326 – 336.
Daly, J.J., Wolpaw, J.R., 2008.
Braincomputer interfaces in neurological rehabilitation.
The Lancet Neurology 7, 1032 – 1043.
doi:http://dx.doi.org/10.1016/S1474-4422(08)70223-0.
Das, A.K., Sundaram, S., Sundararajan, N., 2016. A self-regulated interval
type-2 neuro-fuzzy inference system for handling non-stationarities in EEG
signals for BCI. IEEE Transactions on Fuzzy Systems PP, 1–1.
Dornhege, G., Blankertz, B., Curio, G., Muller, K.R., 2004a. Boosting bit
rates in noninvasive eeg single-trial classifications by feature combination
and multiclass paradigms. IEEE Transactions on Biomedical Engineering
51, 993–1002.
Dornhege, G., Blankertz, B., Curio, G., Muller, K.R., 2004b. Boosting bit
rates in noninvasive eeg single-trial classifications by feature combination
and multiclass paradigms. IEEE Transactions on Biomedical Engineering
51, 993–1002.

7
Table 1. Comparision with Other Approaches (Accuracy in %)

Subjects
1
2
3
4
5
6
7
8
9
Mean
S.D

Multiclass CSP
(mCSP)
Grosse-Wentrup and
Buss (2008)
48.1
27.3
70.6
21.4
22.7
32.4
52.3
65.8
34.2
41.64
18.34

ComplexCSP Zhang
et al. (2013)

Proposed CSP with
SVM

Proposed CSP with
SRIT2NFIS

61.5
32.1
68.6
27.1
34.3
35.3
48
65.6
41.8
46.01
15.65

68.75
41.67
66.31
37.98
25
36.62
52.97
65.55
64.58
51.04
16.15

74.65
45.48
74.31
39.58
32.99
37.9
54.17
66.32
66.31
54.63
16.27

Fabien, L., Anatole, L., Fabrice, L., Bruno, A., 2007. Studying the use of fuzzy
inference systems for motor imagery classification. IEEE transactions on
neural systems and rehabilitation engineering 15, 322–324.
Farwell, L.A., Donchin, E., 1988. Talking off the top of your head: toward a mental prosthesis utilizing event-related brain potentials. Electroencephalography and clinical Neurophysiology 70, 510–523.
Gouy-Pailler, C., Congedo, M., Brunner, C., Jutten, C., Pfurtscheller, G., 2008.
Multi-Class Independent Common Spatial Patterns: Exploiting Energy Variations of Brain Sources, in: Brain-Computer Interface Workshop and Training Course 2008, Graz, Austria. pp. 20–25.
Gouy-Pailler, C., Congedo, M., Brunner, C., Jutten, C., Pfurtscheller, G., 2010.
Nonstationary brain source separation for multiclass motor imagery. IEEE
Transactions on Biomedical Engineering 57, 469–478.
Grosse-Wentrup, M., Buss, M., 2008. Multiclass common spatial patterns and
information theoretic feature extraction. IEEE Transactions on Biomedical
Engineering 55, 1991–2000.
Grosse-Wentrup, M., Liefhold, C., Gramann, K., Buss, M., 2009. Beamforming
in noninvasive brain-computer interfaces. IEEE Transactions on Biomedical
Engineering 56, 1209–1219.
Guler, I., Ubeyli, E.D., 2005. Adaptive neuro-fuzzy inference system for classification of EEG signals using wavelet coefficients. Journal of Neuroscience
Methods 148, 113 – 121.
Herman, P., Prasad, G., McGinnity, T., 2006. Investigation of the type-2 fuzzy
logic approach to classification in an eeg-based brain-computer interface,
in: Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005.
27th Annual International Conference of the, IEEE. pp. 5354–5357.
Herman, P., Prasad, G., McGinnity, T.M., 2008. Designing a robust type-2
fuzzy logic classifier for non-stationary systems with application in braincomputer interfacing, in: Systems, Man and Cybernetics, 2008. SMC 2008.
IEEE International Conference on, IEEE. pp. 1343–1349.
Hyvarinen, A., 1999. Fast and robust fixed-point algorithms for independent
component analysis. IEEE Transactions on Neural Networks 10, 626–634.
Kang, H., Nam, Y., Choi, S., 2009. Composite common spatial pattern for
subject to subject transfer. IEEE Signal Processing Letters 16, 683–686.
Krauledat, M., Dornhege, G., Blankertz, B., Müller, K.R., 2007. Robustifying
EEG data analysis by removing outliers. Chaos and Complexity Letters 2,
259–274.
Liang, Q., Mendel, J.M., 2000. Interval type-2 fuzzy logic systems: theory and
design. IEEE Transactions on Fuzzy systems 8, 535–550.
Liyanage, S.R., Xu, J.X., Guan, C., Ang, K.K., Lee, T.H., 2010. Eeg signal separation for multi-class motor imagery using common spatial patterns based
on joint approximate diagonalization, in: Neural Networks (IJCNN), The
2010 International Joint Conference on, IEEE. pp. 1–6.
Lotte, F., Guan, C., 2010. Spatially regularized common spatial patterns for eeg
classification, in: 20th International Conference on Pattern Recognition, pp.
3712–3715.
Lotte, F., Guan, C., 2011. Regularizing common spatial patterns to improve bci
designs: Unified theory and new algorithms. IEEE Transactions on Biomed-

ical Engineering 58, 355–362.
Lu, H., Plataniotis, K.N., Venetsanopoulos, A.N., 2009. Regularized common
spatial patterns with generic learning for eeg signal classification, in: Annual
International Conference of the IEEE Engineering in Medicine and Biology
Society, pp. 6599–6602.
Lughofer, E., 2011. Evolving fuzzy systems-methodologies, advanced concepts
and applications. volume 53. Springer.
Lughofer, E., Cernuda, C., Kindermann, S., Pratama, M., 2015. Generalized
smart evolving fuzzy systems. Evolving Systems 6, 269–292.
Marx, M.L., Larsen, R.J., 2006. Introduction to mathematical statistics and
its applications. volume 31. Pearson/Prentice Hall Upper Saddle River, NJ,
USA.
Mendel, J.M., John, R.B., 2002. Type-2 fuzzy sets made simple. IEEE Transactions on fuzzy systems 10, 117–127.
Meyer, C.D., 2000. Matrix analysis and applied linear algebra. Siam.
Müller-Gerking, J., Pfurtscheller, G., Flyvbjerg, H., 1999. Designing optimal
spatial filters for single-trial eeg classification in a movement task. Clinical
neurophysiology 110, 787–798.
Naeem, M., Brunner, C., Leeb, R., Graimann, B., Pfurtscheller, G., 2006.
Seperability of four-class motor imagery data using independent components analysis. Journal of Neural Engineering 3, 208.
Nguyen, T., Khosravi, A., Creighton, D., Nahavandi, S., 2015. Eeg signal
classification for bci applications by wavelets and interval type-2 fuzzy logic
systems. Expert Systems with Applications 42, 4370–4380.
Nie, M., Tan, W.W., 2008. Towards an efficient type-reduction method for interval type-2 fuzzy logic systems, in: Fuzzy Systems, 2008. FUZZ-IEEE 2008.
(IEEE World Congress on Computational Intelligence). IEEE International
Conference on, pp. 1425–1432.
Pratama, M., Anavatti, S.G., Joo, M., Lughofer, E.D., 2015. pclass: an effective
classifier for streaming examples. IEEE Transactions on Fuzzy Systems 23,
369–386.
Ramoser, H., Muller-Gerking, J., Pfurtscheller, G., 2000. Optimal spatial filtering of single trial eeg during imagined hand movement. IEEE Transactions
on Rehabilitation Engineering 8, 441–446.
Reuderink, B., Poel, M., 2008. Robustness of the common spatial patterns
algorithm in the bci-pipeline.
Subasi, A., 2007. Application of adaptive neuro-fuzzy inference system for
epileptic seizure detection using wavelet feature extraction. Computers in
Biology and Medicine 37, 227–244.
Tangermann, M., Mller, K.R., Aertsen, A., Birbaumer, N., Braun, C., Brunner, C., Leeb, R., Mehring, C., Miller, K.J., Mueller-Putz, G., Nolte, G.,
Pfurtscheller, G., Preissl, H., Schalk, G., Schlgl, A., Vidaurre, C., Waldert,
S., Blankertz, B., 2012. Review of the BCI competition IV. Frontiers in
Neuroscience 6.
Tangwiriyasakul, C., Verhagen, R., van Putten, M.J.A.M., Rutten, W.L.C.,
2013. Importance of baseline in event-related desynchronization during a
combination task of motor imagery and motor observation. Journal of Neural Engineering 10, 026009.

8
Vidal, J.J., 1973. Toward direct brain-computer communication. Annual review
of Biophysics and Bioengineering 2, 157–180.
Vidaurre, C., Kawanabe, M., von Bnau, P., Blankertz, B., Mller, K.R., 2011. Toward unsupervised adaptation of LDA for brain computer interfaces. IEEE
Transactions on Biomedical Engineering 58, 587–597.
Wei, Q., Ma, Y., Chen, K., . Application of quadratic optimization to multiclass common spatial pattern algorithm in brain-computer interfaces.
Wolpaw, J.R., Birbaumer, N., Heetderks, W.J., McFarland, D.J., Peckham, P.H.,
Schalk, G., Donchin, E., Quatrano, L.A., Robinson, C.J., Vaughan, T.M.,
2000. Brain-computer interface technology: a review of the first international meeting. IEEE Transactions on Rehabilitation Engineering 8, 164–
173.
Yang, Z., Wang, Y., Ouyang, G., 2014. Adaptive neuro-fuzzy inference system
for classification of background eeg signals from eses patients and controls.
The Scientific World Journal 2014.
Zadeh, L.A., 1975. The concept of a linguistic variable and its application to
approximate reasoningi. Information sciences 8, 199–249.
Zhang, H., Yang, H., Guan, C., 2013. Bayesian learning for spatial filtering
in an EEG based brain-computer interface. IEEE Transactions on Neural
Networks and Learning Systems 24, 1049–1060.

