Symmetrical feature for interpreting motor imagery EEG signals in the brain–computer interface

Symmetrical feature for interpreting motor imagery EEG signals in the brain–computer interface

Accepted Manuscript Title: Symmetrical feature for Interpreting Motor Imagery EEG Signals in the Brain-Computer Interface Author: Seung-Min Park Xinya...

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Accepted Manuscript Title: Symmetrical feature for Interpreting Motor Imagery EEG Signals in the Brain-Computer Interface Author: Seung-Min Park Xinyang Yu Pharino Chum Woo-Young Lee Kwee-Bo Sim PII: DOI: Reference:

S0030-4026(16)31214-1 http://dx.doi.org/doi:10.1016/j.ijleo.2016.10.047 IJLEO 58315

To appear in: Received date: Accepted date:

13-8-2016 18-10-2016

Please cite this article as: Seung-Min Park, Xinyang Yu, Pharino Chum, Woo-Young Lee, Kwee-Bo Sim, Symmetrical feature for Interpreting Motor Imagery EEG Signals in the Brain-Computer Interface, (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.047 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Symmetrical feature for Interpreting Motor Imagery EEG Signals in the Brain-Computer Interface Seung-Min Park, Xinyang Yu, Pharino Chum, Woo-Young Lee, and Kwee-Bo Sim∗

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School of Electrical and Electronics Engineering, Seoul, Republic of Korea

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Chung-Ang University1,∗

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Abstract

Feature extraction is an important issue of Brain-Computer Interface (BCI). It determines whether the classification performance is high or low. In this

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paper, a new type of feature called Symmetrical Feature is proposed. This innovative feature extraction method is built upon the features Common Spatial Pattern (CSP) algorithm. After an electroencephalographic signal is enhanced,

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class discrimination using the CSP algorithm can be extracted using optimal

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symmetrical axis chosen by a 10-fold cross-validation technique. Simulation results from nine data sets provided by brain-computer interface competition

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III and Iva showed that, on average, the proposed Symmetrical Feature can be combined with the CSP power band feature to boost the performance of the classification in a BCI system. Keywords: Symmetrical Feature, Common Spatial Pattern, Brain-Computer Interface, Perceptron Learning Algorithm

1. Introduction

Brain-computer interface is a new technique that does not depend on normal

peripheral nerves and muscles of a communication system. This technique carI Fully

documented templates are available in the elsarticle package on CTAN. author Email address: [email protected] (Chung-Ang University) URL: alife.cau.ac.kr (Chung-Ang University)

∗ Corresponding

Preprint submitted to Journal of LATEX Templates

August 13, 2016

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ries out direct communications between the brain and external devices. People 5

can directly communicate through the brain to express ideas or control equip-

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ment. Many research studies have found that event-related synchronization (ERS) and event-related desynchronization (ERD) can describe the firing of

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a neuron population corresponding to a specific mental task with the proper selection of signals from the electrode related to that particular mental task [1, 2]. The ERD/ERS can be defined by the ratio of the power of the elec-

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troencephalography (EEG) signal between the reference periods and the active periods of the task. The reference period refers to the empty task of the subject,

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which usually is the relaxation period. Meanwhile, the active period refers to the time when the subject is required to perform the task. This feature type has 15

been proven to have a subject-dependent characteristic, which causes a major

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problem when creating a subject-independent system that could work for most human subjects [3, 4].

In this study, we proposed a method to classify EEG motor imagery for left-

proposed method can classify three kinds of motor imageries and the classifica-

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hand, right-hand and right-foot movement imaginations. We expect that the

tion performance can meet the requirements of a BCI system. First, we use the

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band pass filter to address the original EEG signal. Then, filtered EEG signals from all electrodes are transformed by a linear time-invariant system using the CSP algorithm.

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In this study, we investigated another type of feature called symmetrical

feature to interpret the EEG signal, which is built on the ERD/ERS principle. The investigated feature is analyzed by comparing it with the power band feature with several aspects where the power band feature is used in the EEG classification task.

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The outline of the paper is as follows: Section 2 describes the detailed description of the EEG dataset which is used in this experiment. Section 3 describes the proposed analysis method including the extract feature, classifier and the learning algorithm. In Section 4, the experimental results are given. In Section 5, the conclusions of the experiment and the suggestions. 2

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2. EEG data set

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In this study, we used two independent data sets. The first dataset provided by Fraunhofer FIRST. Intelligent Data Analysis Group and Campus Benjamin Franklin of the Charit - University Medicine Berlin, Department of Neurology,

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Neurophysics Group (Gabriel Curio) from BCI Competitions III data set IVa[5]. This data set was obtained from five healthy subjects. Each subject was

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asked to sit in a comfortable chair with their arms resting on the armrests. This data set contains only the data from the four initial sessions without feedback. Visual cues were shown for 3.5s in which the subject was asked to decide which

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of the following three motor imageries to perform: a. Imagination of the left-hand movements.

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b. Imagination of the right-hand movements. c. Imagination of the right-foot movements.

The presentation of the target cues was randomly alternated by a certain

in Figure 1. The data shown to the subject consisted of only two classes: imag-

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period from 1.75 to 2.25 s in which the subject was allowed to relax, as shown

ination of the right-hand and the right-foot movement. This data set included five subjects to study the variation in the BCI system named: aa, al, av, aw,

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and ay. Each subject performed 280 trials in the experiment.

Figure 1: Time scheme for BCI III competition data set IVa experimental paradigm

The second data set utilized the BCI competition IV data set I with four 55

subjects. Two subjects performed imagination of the left and right-hand movements, whereas another two subjects performed imagination of the right-hand and right-foot movements. The calibration session from the data set I of BCI competition IV provided by the Berlin BCI group was used in the experiment. 3

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In the experiment, the subject was requested to sit in an armchair in a 60

relaxed position in front of the screen. Figure 2 shows the paradigm of this

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experiment. In the initial 2s, a blank screen was shown. After a 2-s period, a cross section was shown on the screen for 2s to alert the subject of the coming

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trial. At 4s, a cue shown by a right-pointed arrow to the left or right appeared

on the screen, the subject performed the imagined task of left-hand or righthand movement. The cross section was superimposed on the cue. In total, each

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subject performed 200times imagination trials. The BCI IV subject names were

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a, b, f, and g.

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Figure 2: Time scheme for BCI IV competition data set I experimental paradigm

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3. Analysis Method

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3.1. Common Spatial Pattern 70

A common spatial pattern (CSP) is an orthogonal transformation of a seg-

ment of an EEG signal constrained with the maximization of the discriminant of spatial information (energy of the electrodes) between two patterns, for instance, the imagination of right-hand and right-foot movements [6, 7, 8]. By letting x ∈ RC×T as a segment of the EEG signal from C electrode and T time

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samples and the center, the next step of the CSP algorithm is to calculate the covariance of pattern c [9, 10] , as shown in Equation(1). (c) X

=

1 X xi xTi , (c = {+, −}) |Ic |

(1)

i∈Ic

In Equation(1), Ic is a set of trials that belongs to pattern c = {+} for imagination of the right-hand movement and c = {−} for the imagination of the

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right-foot movement. The objective of the CSP algorithm can be formulated 80

in Equation (2), where J(w) is expressed in Equation (3). Sd = Σ+ − Σ−

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is a discriminant activity of the {+} and {−} brain activity patterns. Sd = Σ+ +Σ− is the common activity of the EEG patterns. The scalability properties

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J(kw)=J(w) of the objective function reduce the complexity of this problem. For any arbitrary k, we can scale w without changing the value of the discriminant function J(w). Choosing a constraint for the denominator of J(w), the objective

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in Equation (2) can be simplified as a maximization problem with a constraint,

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as shown in Equation(4).

argmaxw J(w)

wT Sd w wT Sc w

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J(w) =

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argmaxw wT Sd w

(2)

(3)

(4)

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constraint : wT Sc w = 1

By using Lagrange multipliers to solve the maximization problem, a new

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maximization objective function can be introduced, such as Equation(5) and 90

(6), where λ is the Lagrange coefficient, and L(λ, w) is the objective function

of the maximization problem. The quadratic form of Equation(6) simplifies the problem. Values of w and λ that correspond to the maximum value of L(λ, w) are found by setting differential partial derivatives of L(λ, w) with respect to the λ and w equal to zero. Therefore, the value of w satisfies Equation(7).

argmaxw L(λ, w)

(5)

L(λ, w) = wT Sd w − λwT Sc w

(6)

wT Sd w = λwT Sc w

(7)

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Here, the solution of w can be interpreted as the generalized eigenvalue and eigenvector decomposition of the matrices Sd and Sc , respectively. w =

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[w1 , · · · , wc ] is a solution matrix whose column vector wi is the eigenvector cor-

responding to its eigenvalue λi ∈ λ. The CSP can increase the performance of a

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classifier by enhancing the spatial information of a EEG signal. By keeping only the most discriminant channel and rejecting the lesser ones, the dimension of

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the output signal from the CSP can be reduced. By reducing the spatial number from a total of C electrodes to K ≤ C, the effectiveness of a feature can be enhanced ; thus, it increases the performance of the classifier or at least main-

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tains the same level of performance while avoiding the curse-of dimensionality problem. By using the CSP as a spatial filter, the CSP acts as a linear transformation input signal x ∈ RC×T to a new signal y ∈ RK×T , where w ˆ ∈ RK×C

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is obtained by concatenating K eigenvectors wi from a pool of eigenvectors Sc .

(8)

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y=w ˆ Tx

In [1], the authors suggested selecting six out of the total pool of eigenvectors,

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where the first three are eigenvectors that corresponded to the first three largest eigenvalues, and the other three are eigenvectors that have the least eigenvalues.

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In this paper, we proposed selecting K eigenvectors that maximize the fitness function as a model selection method as follows: 1) Initial:

ˆ = [ ]: set of model transformation matrix • w

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ˆ = [w1 , · · · , wc ]: pool of eigenvectors • w

2) For i = 1, · · · C :

• If i is odd, then j = argmaxi wi ; else j = argmini wi • Add wj to w ˆ • Remove wj from w

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• Calculate the model fitness using w ˆ

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3) Select the best model

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In agreement with [1, 11], the feature extracted using the CSP algorithm can be calculated using Equation (9), where log(.) is a logarithm operator and

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var(.) is the variance. y is the filtered EEG signal from Equation (8).

z = log(var(y))

In this research, two objectives are set when using the CSP algorithm. The

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(9)

first objective is to minimize the classification error rate using a linear classifier.

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The second objective is to minimize the number of selected eigenvectors to form the transformation matrix w, ˆ which has fewer selected eigenvectors and fewer features created by the CSP. By combining these two objectives, a single fitness function can be formed as shown in Equation (10) with the minimization

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objective expressed in Equation (11) where E is the classification error rate corresponding to the input features in Equation (8) and (9). K ≤ C is the

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number of selected eigenvectors. α1 and α2 are the shrinkage coefficients.

(10)

w ˆ = argminwˆ f (w) ˆ

(11)

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α1 E + α2 K C α1 + α2

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f (w) ˆ =

3.2. Perceptron Learning Algorithm

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The perceptron learning algorithm (PLA) was used as the classifier in this

study owing to its simplicity and lack of pre-assumption over the distribution of the feature pattern. A linear model and a gradient descending rule were used as the model. The learning rule was used for the PLA. The correct classification accuracy (CCA) rate in terms of percentage was used as the fitness value in the

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model selection for the CSP algorithm. The measurement performance of the CSP cases were studied. The liner model of the PLA is given in Equation (12), where x ∈ Rm+1 is the input feature vector of the classifier with dimension

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m (x0 = 1). w = [w0 , w1 , · · · , wn ], i = 0, · · · , m is the weight of the linear

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classifier, and w0 is the bias. f (a) is a step function defined in Equation (13). y(x) = f (wT φ(x))

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a≥0

if

a<0

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if

 −1

(13)

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f (a) =

  +1

(12)

The convergence of the PLA can be observed by estimating the error of the classifier defined in Equation (14), where (xn , tn ) is a pair of training samples

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and its target classes (tn ∈ {+1, −1}). Target class (+1) is an imagination of the right-hand movement, and target class (-1) is an imagination of the right-

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foot movement. M is a set of misclassification training samples. |M | denotes the size of set M. By using the partial differential of E(w) with respect to w, the gradient values of E(w) can be found, as expressed in Equation (15). 1 X T w φ(xn )tn |M |

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E(w) =

(14)

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n∈M

1 X φ(xn )tn |M |

(15)

n∈M

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∇E(w) =

In the case when the feature space is not linearly separable, the PLA will

not find the convergence value (E(w = 0)). To avoid such a situation, the PLA with a pocket algorithm can be improved by accepting a certain error value even

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though the PLA converges. The updating rule that uses a gradient descent and the pocket algorithm can be implemented using a learning rate parameter for the PLA, as shown below. In the initial step, w(t = 0) is assumed as the weight of the linear regression. Thus, it provides a leap step that is better than selecting β = 0 or by random generation. tmax is the maximum iteration to stop

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the PLA. 1) Initialize weight w(0) and E(w(0)) 2) For t = 0, 1, · · · , tmax , do the following: 8

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• Compute the gradient ∇E(w(0))

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• Compute the error rate : E(w(t + 1))

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ˆ = w(t + 1) • If E(w(t + 1)) < E(w(t)), then set w

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• Update the weight : w(t + 1) = w(t) − η∇E(w(t))

• Iterate to the next step t = t + 1

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ˆ 3) Return the final value of weight w

The CCA rate was used as the fitness value for selecting the spatial information value K and for comparison of the study results.

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4. Method

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4.1. Pre-processing

In this study, we investigated the effects of a new feature called symmetrical feature. The symmetrical feature extraction method is built upon the CSP method, as shown in Figure 3. Initially, band pass filtering is applied to the

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EEG signal. The band pass filter is designed with an infinite impulse response (IIR) filter using the windowing technique. The filtering window is the practical

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Hamming window with a length of 1s. Then, the filtered EEG signals from all electrodes are transformed by a linear time-invariant system using the CSP

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algorithm.

After a certain number of output electrodes have been reduced, the symmet-

rical feature can be extracted and classified by the linear classification algorithm using the PLA.

4.2. Symmetrical feature

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The symmetrical feature can be understood simply as the ratio between the covered areas to the left and right of the symmetry axis. This feature can be calculated from the segmented EEG signal, as shown in Figure 4. The EEG of a selected electrode is segmented from the initial sample when a subject is exposed to the stimulus until the end of the experiment. As the symmetrical 9

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Figure 3: Flow chart for the proposed feature extraction based on the symmetrical feature

feature is based on the ratio between the areas of the EEG signal, we only need

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to obtain the positive region of the EEG sample. Therefore, the EEG signal is squared to obtain the sample power and separate them into two regions: one to the left of the symmetry axis and the other to the right, as shown in Figure 4(b). Using an appropriate symmetry axis, the left area is designated as AL , and the

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right area is designated as AR . The mathematical description for extracting the symmetrical feature is created. At the first filter signal w ∈ RT , the EEG signal from a selected electrode is squared to obtain only the positive power sample, as expressed in Equation(16). The general knowledge, a symmetrical feature extracted from signal x, is given by Equation(17), where AL and AR are the

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covered areas to the left and right sides of the symmetrical axis expressed by yi ∈ y. The area covered by the EEG power is formulated by Equation(18), where S ∈ {L, R} denotes the set of samples on the right of left side. δt is

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the sample period of the EEG signal. ymax is the maximum of the EEG power sample in the observed epoch. N is the total number of EEG samples in the

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chosen epoch.

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Figure 4: (a) Typical EEG signal in the experiment trial, where 0s is the start time when the

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stimulus is given to a subject. (b) Sample power of the EEG signal. The area to the left AL

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of the symmetrical axis is in black, and the right-side area AR is hatched.

yi = x2i

(16)

AR AL

(17)

yi ∆t y N ∆t Pmax yi = i∈S ymax N

(18)

z=

S

A =

P

i∈S

Using Equation(18), the symmetrical feature can be interpreted by Equation(19), and it can be further formalized by Equation(20), where y¯ is the average of the EEG power in the observed epoch that can be calculated using Equation (21). We note that N y¯ is the total power of the EEG signal in the 11

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observed epoch, simply known as the power band feature of signal x, as shown

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in Equation(21). P yi z = Pi∈R y i∈L i

y¯ =

−1

N 1 X yi N i=1

(20)

(21)

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4.3. Choosing the symmetry axis

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yi

i∈L

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N y¯ z= P

(19)

Choosing the right symmetry axis is the critical problem in this method. To

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select the optimal axis position, models are created by changing the size of set L. Size |L| is changed by choosing an EEG sample from 1 to N-1. The best model is selected on the basis of maximizing the criteria for the fitness function

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using the error rate of the PLA classifier in Equation(14). Using the k-fold cross validation technique (our study used a 10 folds), the classification error rate for

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each model is calculated using the validation set, as shown in Figure 5.

Figure 5: Scheme for the 10-fold cross validation. Each rectangle represents the block partitioning of the data. For each fold, the data in the unhatched blocks are used to train the model, and the data in the hatched blocks are used to validate the model. The average result of the validation set in all folds is the final result

k X ¯|L| = 1 E Ei k i=1

(22)

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¯|L| |L| = argmin|L| E

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(23)

Then, the average error rate value E¯i is calculated from all folds using Equa-

tion(22), and the best model is selected from the pool of average error rate

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values in mode Ei ,(where i = 1, · · · , N − 1) using the minimization criteria in

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Equation(23).

5. Simulation Results

The experimental data obtained from each subject were divided into training

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and test sets. The training set data were chosen randomly from 150 trials, and the remaining data from each subject were used as the test set. For the

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training set, the data were then subdivided into small blocks and underwent the cross-validation process in Figure 5. After the optimal model for the CSP 230

and the symmetry axis were found using the training set, the test set was then

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applied to the selected model, and the CCA was evaluated to determine the

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performance of each method. Each method was analyzed using EEG signals in four different bands: 7-14 Hz, 15-22 Hz, 23-30 Hz, and a 7-30 Hz broad band; these frequency bands corresponded to the most active range of frequency in the α, lower-β, upper-β, and broad bands, respectively. These frequency bands

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are recommended by many BCI-based EEG systems [1, 12, 13]. In addition, we analyzed the EEG signals with different frequency bands. We repeated the process 100 times for each method where 150 trials of training data were chosen randomly each time. This repeated method aimed to avoid results that could be

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achieved by chance during the randomized training and test data. The results presented in this paper were obtained after averaging all 100 simulations. Figure 6 shows the values of the fitness functions for the model selection by

the CSP method and the symmetry axis position for the data of the subject aa. The fitness values were obtained from averaging the 10-fold cross validation 245

data. Figure 6(a) shows the fitness values for the CSP models, and Figure 6(b) shows the fitness values for the models of the symmetrical features. Using the 13

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Figure 6: Scheme of the 10-fold cross validation. Each rectangle represents a block partitioning

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of the data. The averaged result for the validation set of all folds is the final result.

shrinkage coefficients α1 = 0.8 and α2 = 0.2, the global minimum fitness values for the CSP and the symmetrical models can be found.

eters to achieve the current CCA of the CSP feature using Equation(9), the

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Tables I-IV summarize the CCAs for all subjects and their optimal param-

Symmetrical feature using Equation(20), and the concatenating feature vector

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using the CSP and symmetrical features. Each table summarizes the results from different band widths : 7-14 Hz, 15-22 Hz, 23-30 Hz, and a 7-30 Hz. In addition, we note that the results in each table were obtained from the average

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of 100 trials. The actual value of K in each model is an integer. K is the number of eigenvectors selected by the CSP algorithm. L is the width of the left area separated by the optimal symmetrical axis. SYM is the symmetrical feature extraction method. COMB is the combination feature vector from the symmetrical feature methods.

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By averaging the CCA for all subjects, the performance of each method for different frequency bands can be compared easily. Figure 7 shows the results of the averaging. The white bars are the average CCA of the CSP method. The hatched bars are the average CCA of the symmetrical feature extraction

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Table 1: Average of all repeated evaluations of the CCA of each method with different data sets using EEG signals in the frequency band of 7-14Hz

K

L

CSP(%)

SYM(%)

COMB(%)

aa

17.9

0.79

66.15

68.15

70.15

al

7.80

1.11

92.00

90.69

93.77

av

18.70

0.80

57.46

62.85

64.23

aw

3.90

0.99

91.08

78.46

92.31

ay

8.80

0.77

84.08

78.62

86.15

a

9.50

0.71

82.00

66.40

77.40

b

10.20

1.91

62.20

59.40

59.80

f

6.50

0.80

91.00

66.60

87.60

g

5.90

0.70

86.80

81.80

88.20

Average

9.91

0.95

79.20

72.55

79.96

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Table 2: Average of all repeated evaluations of the CCA of each method with different data

K

L

CSP(%)

SYM(%)

COMB(%)

aa

14.20

1.20

51.38

51.38

52.23

14.60

0.82

76.77

70.77

82.62

13.50

0.64

60.46

53.31

58.15

aw

14.30

0.84

63.31

56.69

64.00

ay

14.40

0.53

67.31

57.23

65.69

a

15.20

0.68

68.40

60.00

70.60

b

17.70

1.87

46.80

52.40

50.80

f

16.30

0.64

64.60

52.40

59.40

g

11.60

0.66

81.20

82.20

86.40

Average

14.64

0.88

64.47

59.60

65.54

al

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av

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subject

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sets using EEG signals in the frequency band of 15-22Hz

(SYM). The black bars (COMB) are the average CCA of the combined CSP and 265

symmetrical features. This figure shows the CCA on the horizontal axis for each feature type for different band widths on the vertical axis. The combined CSP 15

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Table 3: Average of all repeated evaluations of the CCA of each method with different data

K

L

CSP(%)

SYM(%)

COMB(%)

aa

14.00

0.72

63.92

71.08

73.46

al

4.30

1.02

90.00

84.23

91.85

av

17.80

0.70

52.15

48.23

aw

15.00

1.07

70.85

64.54

ay

13.80

0.91

55.15

51.00

54.08

a

13.90

0.95

69.80

55.40

66.20

b

12.10

1.28

54.20

53.00

55.80

f

18.40

0.98

53.60

52.20

53.00

g

17.70

0.99

69.80

64.80

71.80

Average

14.11

0.96

64.39

60.50

64.94

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subject

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sets using EEG signals in the frequency band of 23-30Hz

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70.69

Table 4: Average of all repeated evaluations of the CCA of each method with different data

K

L

CSP(%)

SYM(%)

COMB(%)

aa

26.10

0.90

67.38

70.92

72.62

6.90

1.11

94.46

93.23

95.92

19.70

0.81

58.54

63.46

63.54

aw

7.50

0.96

88.15

81.54

89.85

ay

11.20

0.74

86.77

79.85

88.38

a

12.40

0.60

80.80

71.20

81.00

b

12.90

1.22

61.60

55.20

65.40

f

6.70

0.80

87.80

98.00

89.20

g

7.10

0.66

87.60

86.40

88.20

Average

12.28

0.87

79.23

74.42

81.57

al

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av

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subject

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sets using EEG signals in the frequency band of 7-30Hz

and symmetrical features exhibited a higher performance in the α and broad bands and in both lower-β and upper-β bands. On average, the symmetrical feature achieved a lower performance than the CSP feature. However, the CCA 16

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Figure 7: Average CCA for all subjects with different band widths

performance can be increased by concatenating these two feature types, and

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realized.

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stability between the performance results for different frequency bands can be

Figure 8: Average CCA trade off (CCATO) between the training and the test models for all subjects with different band widths

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Figure 8 shows the bar graph of CCATO. The white bars are the average CCATO of the CSP method. The hatched bars are the average CCATO of the symmetrical feature extraction (SYM). The black bars (COMB) are the

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average CCATO of the combined CSP and symmetrical features. CCATO was

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used to measure the robustness of the method. A good method will have a lower CCATO for the evaluation performance in the test data that are well-

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tracked with the predicted performance in the training data. Figure 8 shows that all methods have a lower CCATO in the α and broad band, whereas in the lower-β and upper-β bands. By comparing each feature type, the symmetrical

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feature has a lower CCATO than the other methods, which indicates that the symmetrical feature is more robust to varying EEG data such as in changing

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sessions or problems caused by non-stationary subjects.

6. Conclusion

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In this study, a new feature extraction method called symmetrical feature was proposed. The average results showed that the new feature type has lower

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performance in terms of power than the CSP but has a robust characteristic of invariant EEG data compared with the previous CSP power band. By combining the CSP power feature and the new symmetrical feature, the classification

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performance of a BCI system can be significantly enhanced.

Acknowledgement

(1) This research was supported by the National Research Foundation of KOREA [NRF] grant funded by the KOREA government [MEST] [2012-0008726].

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(2) This research was supported by the Chung-Ang University Research Scholarship Grants in 2016.

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