Journal of Robotics, Networking and Artificial Life, Vol. 2, No. 4 (March 2016), 217-220

An Optimization of Spatio-Spectral Filter Bank Design for EEG Classification
Masanao Obayashi1, Takuya Geshi2, Takashi Kuremoto3 and Shingo Mabu4

Information Science and Design Engineering, Yamaguchi University,Tokiwadai 2-16-1
E-mail: {1m.obayas,2t015vk, 3wu,4mabu}@yamaguchi-u.ac.jp

Abstract
How to select the appropriate frequency band to classify EEG signal by motor imagery is discussed in this paper.
Our proposal is an improvement of the conventional Bayesian Spatio-Spectral Filter Optimization (BSSFO). Defectof BSSFO is on the way to generate the renewal particle of the filter bank, such a random number generation. To
avoid a local optimum, an evolutional update method of particles is introduced. It is shown that performance of theEEG classification ability is improved.
Keywords: spatio-spectral filter, EEG, classification, .optimization, mutual information, common spatial filter

1. Introduction

2.1 Preprocessing

Recently, researches using brain computer interface(BCI) have been actively studied. To precisely identify
EEG signal, it is necessary to remove the artifact andnoise by using appropriate spatial and spectral filter,Refs. 1-2. Furthermore, the best frequency bands
identifying EEG signals depend on individuals andmeasurement environment, Ref. 3. Bayesian SpatioSpectral Filter Optimization (BSSFO) is known as a
powerful method to solve these problems, Ref. 4.
However, BSSFO has also drawbacks that the obtained
solution by it falls into sub-optimum. To overcome thisdrawback, we propose improvements of thepreprocessing and update method of the filter bank inRef. 4, to result in confirming effectiveness of ourproposal.

Laplacian smoothing is applied to all the EEG signals to
reduce artifacts and noise as follows. The weight of thedata in attention electrode surrounded by a green circle is
4 and that of each of four surrounding electrodes
surrounded by red circles is -1. (See Fig.1) These
weights are changed to optimal values in Section 3 by us(Improvement 1).

2. Classification System
The classification system of EEG signals proposed by K.
Suk, et al. Ref. 1 that is improved in this paper by us isshown in Fig.2. According to the flow of Fig.1, thecontents are described in the following subsections.

Fig. 1 Explanation of the weights of the EEG electrodesin smoothing of the EEG signal in the extended
international 10/20 system used in this study

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Masanao Obayashi, Takuya Geshi, Takashi Kuremoto, Shingo Mabu

Spectral Filtering(filter bank)z = h⊗x

BSSFOPreprocessing

Single-trial EEGsx

Feature Extraction(filter bank)f = log(var(y))

Spatial Filtering(filter bank)y = W+z

Prior knowledgeSVMs

classifier

Posterior Estimation
Filter bank
UpdateFig. 2 Whole structure of the EEG classification system proposed by K. Suk, et al. Ref. 1
2.2 Spectral Filtering

The filter used in this paper is a fifth-order Butterworth
bandpass-filter. The EEG signals of all the data sets are
bandpass-filtered between 4 Hz and 40 Hz covering boththe m − rhythm(8 − 14Hz ) and β − rhythm(14 − 30Hz ) .

2.4 Bayesian Spatio Spectral Filter Optimization(BSSFO)
Algorithm : BSSFO filter optimization algorithm
Input Data: {X, Ω} , K, m,X = {x i }i =1 : Set of EEG signal, D: amount of trial,DΩ = {ω i }i =1 : Set of class labels, where ω i ∈ {+ 1,−1} ,D

2.3 Common Spatial Pattern
Common Spatial Pattern (CSP) proposed by H. Ramoser,
et al. in Ref. 2 is used in this paper. CSP is applied to thesignals after bandpass filtering. CSP algorithm is forsearching for the spatial weight to multiply to the EEG
signals. The spatial weight W is gotten by solving theoptimization problem of following a generalized
eigenvalue problem:arg maxWTW Σ 1W ,W T Σ 2W

(1)

where Σ 1 and Σ 2 are covariance matrices of each class.
Σ 1 and Σ 2 are calculated as follows:Σ1, 2 = XXT trace ( XXT ) ,(2)where X means EEG signal matrix, and following: x1N x
 1, 1 , X = 
xx

C,
1C,
N



(3)

K : The number of particles,
m: The half number of spatial patterns to be
determined in a spatial pattern learning algorithm
Output Data：
η: Set of optimal particles,
Bˆ = bˆ , πˆ{j{ }j}j =1Wˆ = Wˆ j j =1 : Set of optimal spatio filters,

h : the number of particles
Optimization:--------------------------------------------------------------------------Initialization：
ˆ old = b old , π old K•B{-boldk}= {b , b }kksk

k =1ek- π kold = K1 : Weight of kth particle
while stopping criterion not satisfied doif the first iteration thenB new = B oldelse
B old = B newψ ( k ) = 0, ∀k ∈ {1,  , K }for k = 1 to K do
Generate a random number r ∈ { 0, 1} ,uniformly distributed.
Find the largest j for which r ≥ ∑ nj =1π n ,where N is the number of signal samples, C means thenumber of electrodes. The first and last row vectors aretaken as spatial patterns for class 1 and class 2,respectively.

ψ ( j) = ψ ( j) + 1 ,Improvement 2end

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if ,ψ ( j ) > 1j + N (0, R )=b new oldkotherwise
b jendAn Optimization of Spatio-Spectralfor k=1 to K doZ k = h new⊗Xk/* Perform a bandpass filter */Solve Wk (∑ ( + ) + ∑ ( + ) ) Wk = I/* Perform a CSP algorithm */ˆ = the first m and the last m column vectors in WW
kk
for i = 1 to D doˆ + z i )] /* F = f i D */f i = log [ var ( Wkkkk{}

k i =1end
I (Fk ; Ω) = H (Fk ) − {H (Fk | ω = +1) } + H (Fk | ω = −1)}

p (Fk , Ω | B k ) ≡ exp{I (Fk ; Ω)}/* Update the weight of particles */
end{}

Kend
S =  k (π k > τ ), k ∈ {1,2,  , K }}

ˆ = b new , πˆ newˆ }B, Wˆ = {Wjjj j∈Sj∈S--------------------------------------------------------------------------

After spectral and spatial filtering, we get the feature
vector Fk of kth particle as follows:{}

Dˆ + z i )] .
f ki = log [ var ( Wkk(4)Using Fk , mutual information I (Fk ; Ω) between Fk andclass label Ω is calculated as follows:
I (Fk ; Ω) = H (Fk ) − {H (Fk | ω = +1) } + H (Fk | ω = −1)} ,(5)where H ( Fk ) and H ( Fk | ω = c) are defined as followingequations.
H ( Fk ) ≅ −H ( Fk | ω = c) ≅ −1 D1∑ log  ∑ pˆ (f k ) ,j=1
D i =1
D


(6)

 1

1ij
∑ log ∑ pˆ (f k − f k ,ν ) , (7)Dc i s.s.tωi = c  Dc j s.t . ω j = c1
1 Di
∑ ϕ (f k − f k , ν ) ,D i =1
 a + Σ −1a 1,exp −ϕ (a,ν ) =d 2 d122 (2π ) ν | Σ | 2ν pˆ (f k ) =(8)(9)

where D and Dc are the total number and class c oftrials and Σ is the covariance matrix. The weight π k ofthe classification result weight of particle k is calculated
as follows:
pk =exp[I (Fk ; Ω)] .
∑ exp I (F j ; Ω)j[S =  k (π k > τ ),(11)where k ∈ {1,2,  , K } and τ denotes a thresholdparameter that is determined empirically. The class label
is determined by the following rule:

EEG x i ∗ , and Φ ck (f k∗ ) is the result of a SVM whichclassifies the EEG into the class c, in the kth frequency
band.
3. Improvement of the method

2.5 Feature Extraction

Fk = f ki i =1 ,A Gaussian kernel-based SVM is used in this paper. An
optimal filter bank S with the set of class-discrimination
frequency bands selected by the following rule:|S |∗ ccˆ = arg max (12) ∑ π k ⋅ Φ k (f k ) ,=k1c∈{+ , −} 
where |S| denotes the size of the optimal filter bank S,f k∗ denotes the feature vector from the input signal-trial

ˆ new k =1
B new = b newk ,πk{

2.6 Classifier](10)

We propose two improvements of the method
mentioned above.
3.1 Improvement 1
The first is that in the Laplacian smoothing, the weightvalue 4 of the data in attention electrode surrounded by agreen circle in Fig. 1 is changed to 5 to enhance thesignal of the attention electrode. .
3.2 Improvement 2
The second is that the improvement as to the update
method of the particles which are for band start and end
positions of bandpass filter. Use of the update method of
the conventional method results in that particles withsemi higher amount of information are remained, as aresult, particles would be biased. For improvement,remove the half of all particles from the lower amount ofinformation. Then, two particles with higher amount ofinformation are selected stochastically, crossing them,new particles are generated. After that, particles between
1/4 and half from highest amount of information are reinitialized shown in Fig. 3.
Re-initializing of particles is to generate particles byuse of following probability density function:p (B ) =11
Ν( μ, Σ μ ) + Ν( β, Σ μ )22(13)

The crossing method of two particles is as follows:(bks , bke ) new = α 1 (bks , bke ) old 1 + α 2 (bks , bke ) old 2 ,Published by Atlantis Press
Copyright: the authors
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Masanao Obayashi, Takuya Geshi, Takashi Kuremoto, Shingo Mabuwhere the weights α 1 , α 2 are set to 0.9 and 0.1,
respectively, in next simulation to avoid generation ofparticles that both particles become far away.

Table 3 Simulation results of both update methods ofparticles with conventional preprocessing

Amount of information

update method
highCrossing

EEG data
200

sampling rate

100 [Hz]used time of EEG data

0.5[s]~2.5[s]the number of electrodes

118

aw

ay

40.29

87.5

56.68

64.06

49.6

61.
43

Improvement 2average

53.57

91.61

53.67

65.54

50.36

63.
95

Table 4 Simulation results of both update methods ofparticles with preprocessing with improvement 1
update method

subjects
aaalav

aw

ayave
rage

conve
ntional

avera
ge

72.23

98.75

60.51

677.1

55.36

72.
79

Improvement 2

avera
ge

73.3

99.64

61.99

74.91

69.88

75.
9

5. Conclusion

References

BSSFO
the number of particles

15

width of frequency band
The number of loop
algorithm

4 ~ 40 {Hz]10

Table 2 Simulation results of both update methods ofparticles without preprocessing
update methodav

In this paper, we intended to improve the update methodof particles of the conventional method “BSFFO” thatmean improvement of frequency bandpass filters andalso to improve the preprocessing method. As a result, it
is verified that our method is useful.

Table 1 Simulation condition
the number of samplingalaverage

4. Computer simulation
4.1 Data set, simulation condition and results
EEG data set used in this simulation is Data set Iva inthe BCI Competition III, in Ref. 5. The conditions totake these data is shown in Table 1. Table 2 , 3, and 4
show the simulation results that update method ofparticles of both conventional and improvement 2 arecommon, but without preprocessing, with conventional
preprocessing, and with preprocessing improvement 1,respectively. In all cases, our proposed method issuperior to conventional one.

aa

ave
rag
e

conve
ntionalRe-initiali
zationFig. 3 Our proposed update method of particles

subjects

aa

alav

aw

ay

av
era
ge

subjects

conve
ntional

aver
age

70.5
4

99.8
2

60.5
6

76.2
5

56.6
7

72.
77

Improv
ement
2

aver
age

72.8
6

99.6
4

63.2
170.5
8

69.1
375.
08

1.

H. Ramoser, J. Muller-Gerking, and G. Pfurtscheller,“Optimal Spatial Filtering of Single Trial EEG during
Imagined Hand Movement”, IEEE Trans. Rehabilitation
Eng., vol. 8, no. 4, pp.441-446, Dec. 2000.

2.

Fikri Goksu, Nuri F. Ince, Ahmed H. Tewfik, “Greedy
solutions for the construction of sparse spatial and spatiospectral filters in brain computer interface applications”,
Neurocomputing, vol. 108, no. 2, pp.69-78, May. 2013.

3.

H. Ramoser, J. Muller-Gerking, and G. Pfurtscheller,“Optimal Spatial Filtering of Single Trial EEG during
Imagined Hand Movement”, IEEE Trans. Rehabilitation
Eng., vol. 8, no. 4, pp.441-446, Dec. 2000.

4.

Heung-Il Suk, Seong-Whan Lee, “A Novel Bayesian
Framework for Discriminative Feature Extraction in
Brain-Computer Interfaces”, IEEE Transactions. PatternAnalysis and Machine Intelligence, vol. 35, no. 2, pp.286299, Feb. 2013.

5.

http://bbci.de/competition/iii/desc_IVa.html

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