Linear Discriminant Analysis on Brain ComputerInterface.

Jose Luis Martinez Perez, Antonio Barrientos Cruz.Grupo de Robotica y Cibernetica.Universidad Politecnica de Madrid.

Madrid, Espana.email: jlmartinez@ etsii.upm.esantonio.barrientos @upm.es

Abstract - This report analyses the application of Linear Discrimi- and more invasive electrophysiological methods, magnetoen-nant Analysis in Brain Computer Interface technology. It is aimed cephalography (MEG), positron emission tomography (PET),to obtain an objective evaluation of the discrimination capability functional magnetic resonance imaging (fMRI), and opticalachieved when different filtering windows are considered in orderto differentiate between three different cerebral activities. imaging. However, MEG, PET, fMRI, and optical imaging are

still technically demanding, some of them depend on blood flowIn this report the following issues are discussed: and have long time constants and thus are less amenable to fast

communication. At present, only EEG meets the requirements* Quantification of the discrimination capability between the of short time constant, affordable cost, and it is relatively simple

employed cerebral activities. to implement. Different approaches are considered in current* Identification of the frequency bands with the highest BCI research, they include standard scalp-recorded EEG as welldiscrimination power.* Methodology to weight the amplitude of the previous as those that use epidural, subdural, or intracortical recording.

frequency bands in order to reduce the dimensionality of the While all these BCls use electrophysiological methods, the basicfeature space and facilitate posterior analysis, without lost of principles of BCI design and operation apply also to BCls thatintrinsic characteristics of each cerebral activity. use other methods to monitor brain activity.

* Determination of the best preprocess window.In order to control an external device using thoughts it

Linear Discrimination Analysis is employed in order to reduce is necessary to associate some mental patterns to devicethe dimensionality of the input feature space; bilateral contrasts commands, so an algorithm that detects, acquires, filters andbetween features, inferred from each cerebral activity, are used to classifies the human electroencephalographic signal is requireddetermine the discrimination power. [2][5][6][7]. Usually all BCI systems are compounded from the

Keywords - Brain Computer Interface; Electroencephalography; following parts:Linear Discriminant Analysis; Pattern recognition; Spectral * Signal acquisition. Electrophysiological BCls can beAnalysis. categorized by whether they use non-invasive or invasive

methodology. They can also be categorized by whether theyuse evoked or spontaneous inputs. In the signal-acquisition

I. INTRODUCTION. part of BCI operation, the chosen input is acquired by therecording electrodes, amplified, and digitized.

Brain Computer Interface technology, BCI, is aimed to . Signal processing: feature extraction. The digitized signalcommunicate human beings with external computerized devices are then subjected to one or more of a variety of featureusing the encephalographic signal as primary source of extraction procedures, such as spatial filtering, voltagecommands [1][2][3][4]; in the first international meeting for amplitude measurements, spectral analysis, or single-BCI technology in 1999 it was established that BCI "must not neuron separation. This analysis extracts the signal featuresdepend on the brain 's normal output pathways of peripheral that encode the user's messages or commands. BCIsnerves and muscles", can use signal features that are in the time domain (e.g.A variety of methods for monitoring brain activity might evoked potential amplitudes or neuronal firing rates) or the

serve in BCI technology: electroencephalography (EEG) frequency domain (e.g. mu or beta-rhythm amplitudes)

1-4244-0830-X/07/$20.OO ©2007 IEEE.

[8]. A BCI could conceivably use both time-domain space [10]. To minimize the leakage effect seven differentand frequency-domain signal features, and might thereby types of preprocess windows has been considered: rectangular,improve performance. It is also possible for a BCI to use triangular, Blackman's, Hamming's, Hanning's, Kaiser's andsignal features, like sets of autoregressive parameters, that Tukey's [11] [12] [13]. The evidence of statistical difference incorrelate with the user's intent but not necessarily reflect the feature populations associated to different brain activities hasspecific brain events, in those cases it is necessary to ensure been previously shown [14].that the chosen features are not contaminated by EMG, To determine the discrimination power between the proposedEOG or other non-CNS artifacts. cerebral activities and the effect of filtering window, a statisticalSignal processing: the translation algorithm. It translates procedure of bilateral contrast of independent populations hasthe signal features into device commands-orders that carry been used [15], the results of each contrast is both qualitativeout the user's intent. This algorithm might use linear and quantitative, qualitative in order to accept or reject themethods (e.g. classical statistical analysis) or nonlinear null hypothesis of equality in the population of features,methods (e.g. neural networks). The algorithm changes quantitative in order to compare the discrimination powerindependent variables (i.e. signal features) into dependent through significance contrast level a = - p.variables (i.e. device control commands). This article is composed of the following sections:

* The output device. At the moment the output device is a Section II briefly describes the methodology.computer screen and the output is the selection of targets, Section III describes the LDA technique.letters, or icons presented on it. Initial studies are also Section IV explains the statistical bilateral contrasts.exploring BCI control of a neuroprothesis or orthesis that Section V and VI presents and analyzes the results.provides hand closure to people with cervical spinal cord Section VII is devoted to conclusions.injuries.

* The operating protocol. It is the protocol that guides the II. EXPERIMENTAL PROCEDURE.operation of the BCI device. It defines how the system isturned on and off, whether communication is continuous or The tests described below were carried out on five malediscontinuous, or if the message transmission is triggered healthy subjects, one of them has been trained before, but theby the system or by the user, the sequence and speed of other four were novice in the use of the system.interactions between user and system, and what feedback is In order to facilitate the mental concentration on the proposedprovided to the user. activities, the experiments were performed in a room with low

BCI devices fall into two classes: dependent and independent level of noise and under controlled environmental conditions,[9]. A dependent BCI does not use the brain's normal output all electronic equipments external to the experiment aroundpathways to carry the message, but activity in these path- subject were switched off to avoid electromagnetic artifacts.ways is needed to generate the brain activity that does carry The subjects were sat down in front of the acquisition systemit. A dependent BCI is an alternative method for detecting monitor, at 50 cm from the screen, their hands were in a visiblemessages carried in the brain's normal output pathways (e.g. position, the supervisor of the experiment controlled the correctgaze direction is detected by monitoring EEG rather than by development of it [16] [17].monitoring eye position directly). An independent BCI does notdepend in any way on the brain's normal output pathways. The A. Methodology.message is not carried by peripheral nerves and muscles (e.g.P300 evoked potential). The experimental process is shown on figure 1.

This report focus on the applicability ofLDA to BCI and how Test of system devices. Checks the correct level of battery,the windowing effect affects the discrimination capability of the and the correct state of the electrodes.brain proposed activities. System assembly. Device connections: superficial electrodes

In the experiments considered for this report a low number (Grass Au-Cu), battery, bio-amplifier (g.BSamp by g.tec), ac-of scalp-electrodes has been used to capture the endogenous quisition signal card (PCI-MIO-16/E-4 by National Instrument),electroencephalographic subject's signal. In order to facilitate computer.the use of this technology it is important to make it easy to System test. Verifies the correct operation of the wholeuse, cosmesis is often crucial; that is, how the system looks and system. To minimize noise from the electrical network the Notchhow the user looks while employing it, the number of electrodes filter (5OHz) of the bio-amplifier is switched on.employed in these devices is a global key feature, as the fewer Subject preparation for the experiment. Application ofof electrodes used, the higher the comfort [2] [4]. electrodes on subject's head. It is verified that electrode

Because the main changes in brain activity are associated impedance was lower than 4 KOhms.to changes in the power amplitude of band frequencies [4], System initialization and setup. Verification of data register.spectrograms based on FFT are used to obtain initial feature Experiment setup. The supervisor of the experiment sets-vectors. LDA technique is used to combine these initial up the number of replications, Nrep =10, and the quantityfeatures in order to reduce the dimensionality of the input of different mental activities, Nact =3. The duration of each

Activity B. Motor imagery. The subject imagines moving their'e mlimbs or hands, but without the materialization of the movement.Number of different activities N actIF ,Number of replicates: N_rep. Activity C. Relax. The subject is relaxed.

,i=i=OTest of systemdevices. C. Feature selection.

NoN rep.

The registered signal is chopped in packages of samples,3ys en Y similar to the bundles of samples obtained from and acquisitionasseml

No. by *<iN act. card in an on-line BCI application. Each package has 128les samples, because each trial has 7s of registered signal at f=tXe , Ot * |l384Hzand no overlapping has been considered, there are 21

System test, ropose e thepeld |f N cetheerd of packages per trial. A vector of features is extracted from eachmental activity

package. This vector is made up as the mean of the amplitudesGet samples Of of the frequency bands [11]. Because the frequency of normalimental activityz. _ *Xber mentai at=t7s.0 human brain is under 40-5OHz, only frequencies between 6 and

Subjecttpreparation for 38Hz have been considered.thie experiment.y

Record Relax,samples. T 7 s. TABLE I.

System FEATURE VECTOR.initialization & Notice the end of

setup. thistrial. FFT index. Frequency. Denomination.1 0 - 2 Not considered

+ ~ ~ ~~~~~~~~~~~23 -5 Not consideredFinish. 3 6-8 0.

4 9-11 al.5 12- 14 a2.

Fig. 1. DIAGRAM OF THE EXPERIMENT REALIZATION. 6 - 7 15 - 20 131.8 - 10 21 - 29 /32.11- 13 30 - 38 /33.

mental activity, a trial, is t = 7s, the acquisition frequency is 14 - 64 39 - 192 Not consideredfs = 384Hz. The system randomly suggests to the subject tothink about the proposed mental activity. A short relax is allowedat the end of each trial; between replications the relax time ist =7S. III. LINEAR DISCRIMINANT ANALYSIS PROCEDURE.

A. Introduction.B. Position of the electrodes and description of cerebral

activities. Linear Discriminant Analysis is a preprocess technique usedin machine learning, its objective is to find the best combination

Electrodes were placed in the central zone of the skull, next of features that separate two or more types of objects or events.to C3 and C4, two pair of electrodes were placed in front of The result can be used as linear classifier or as a techniqueand behind of Rolandic sulcus, this zone is one with the highest to reduce the feature space dimension before the classificationdiscriminant power, it takes signal from motor and sensory areas process. LDA try to express the dependent variable as aof the brain [17] [7]. Reference electrode was placed on the right combination of independent variables.mastoid, two more electrode are placed near to the corner of the Supposed N classes of observations x with means Ti andeyes to register blinking. covariances Si. The linear combination of features w.x will have

means w.fty and variances wTStw for i = 0, N. Fisher definedthe separation between these N distributions to be the ratio of thevariance between the classes to the variance within the classes.

The maximum separation occurs whenFig. 2. ELECTRODE PLACEMENT.

The supervisor of the experiment asks the subject to figureout the following mental activities, these activities will be the Under the assumptions of normally distributed classes andcerebral patterns to differentiate among them. equal class covariancesActivity A. Mathematical task. Recursive subtraction of a primeT i(,-number, i.e. 7, from a big quantity, i.e. 3.000.000.T=S .(i )

B. Operationalprocedure. in the degrees of freedom. These contrasts were done for eachtype of window.

The operational procedure followed to carry on the Linear . Bilateral contrast to the variance ratio.Discriminant Analysis is described afterwards. The equality of variances is obtained with R = 1.

1. Samples from each mental tasks are obtained. n, = sample size of the first population.Xa Mathematical Activity. n2 = sample size of the second population.Xbl/b2 Movement imagination / realization. S1 = standard deviation of the first population.Xc Relax. S2 = standard deviation of the second population.

2. Statistical definition of each population. F = Fisher distribution.Mean: Covariance matrix Null hypothesis Ho vs. alternative hypothesis H1.

Xa Ha COVa = (Xa Ia)(Xa-Ia)T 2 2

Xb Ilb COVb = (Xb -Pb) (Xb - 1b)T*HT: (U1)2 2 R vs. H1: (Ui)2, R

Xc hc COVc =(a - (Xc - AC)T Considering that:3. Statistical definition of all populations.

Mean: Covariance matrix (1)S2 2 (1). 2 2XT PT COVT =(X-T)(X-,PT)T. I 2X-1i 1

4. Within and Between covariance matrices calculation.1(nl -1)S12

Witthin: S, = EjpjCOVj 1 2 2 F l,n2-1C1jvPT-\j- PTT n21 (-17S2 1S2Between: Sb = YjPj (jP9T) jIT) n2-1 < 2

In which the probability of each population is pj. Therefore under the fulfillment of the null hypothesis:5. The optimizing criterion in LDA is the ratio of between- ^ 2

class to the within-class covariance matrices. The solution FEXP R R22 "n -l,n2-obtained by maximizing this criterion defines the axes of

the transformedspace. ~~~~~The zone of HO acceptance is:the transformed space.

C = St,, xSb ateo = F(ni- l,n2 -,1i) y bteo = F(n- l,n2 1,12

6. By definition, an eigen-vector represents a 1-D invariant ateo . FEXP . bteosubspace of vector space in which the transformation is . Bilateral contrast of two independent normal and homo-applied. A set of these eigen-vectors with non-zero eigen- cedastic populations. Null hypothesis HO vs. alternativevalues are linearly independent and invariant under the hypothesis H1.transformation. Thus any vector space can be representedin terms of linear combinations of the eigen-vectors. HO Il1-2 A VS. Hi:l1-2 A

7. Once the transformation matrices have been obtained, The variances of the both population are equal butthe data sets are transformed using LDA transform. Thedecision region in the transformed space is a hyperplane oflower dimension than the feature space. TEXPJ= (Xi-X2)-(ii-/2)Xa X>= T.Xa. s n 72Xb Xb = T.Xb. 2 2Xc X>T.XC. In which S2 is the pseudo-variance of S1 and S2

8. Once the transformations are completed using LDA t2 (nl-l1)*l12+(n2 1)*S22transforms, Euclidean or Mahalanobis distance can be used S =+n2-2to classify new vectors.

9. The smallest value among the n distances classifies thenew vector as belonging to class n. TTeo=t(nl+n2-2,1-

IV. STATISTICAL ANALYSIS PROCEDURE. If TTExpp < TTeo then HO is accepted, on the contrary H1is accepted and HO is rejected.

Bilateral contrasts between two population are used to . Bilateral contrast of two independent normal and he-determine if there is statistical evidence of difference between terocedastic populations. The null hypothesis HO andthe population of features obtained from each mental activity. alternative hypothesis are similar to the previous ones, theEach component of the vector is considered to determine its statistical measure is:significance and separability power. Bilateral contrast makes T_(x -x2 ) -(/11 42) >- tfuse of population variance, if the equality of both population EX- /^2±+22variances is rejected it is necessary to apply a correction factor V1n 2

In which f is the number of degrees of freedom calculated 1000 10 10 1 0 1 0 10 10 1 0with the Welch's formula: -0'0 9995 0T9990 ±

I(i±!~ S22) 0,29

n1+1 nj n2+1 n2

In this case the zone of H0 acceptance is: 0990 0 0 0 l98

If |TExp < TTeo then Ho is accepted, on the contrary is 0.985 C3'- C3assumed that the populations are different.

C

0,9800

V. RESULTS.

The next figures show for the LDA transformed coordinates 0,975of both channels: C3'-C3 and C4'-C4", and for each type Rectangular Triangular Blackman Ham ming Hanning Kaiser Tukeyof filtering window the associated probability results p of thebilateral contrast tests between the former mental tasks. In orderto represent the dispersion of the results the mode value and bars 1,0 00 0,999 1,0 0999 1,0 1.0 10 101,0 1,01,0 1.0 ,0 1,0 1,0from 15th to 85th percentile have been used. T Il lt

1 01 0 1,0 0 1 0 0 1, 0 10 0 1 00 0l951,000 1

0,997 0,997 0,9897 0,897 0,997 069909I9I

0,995 - I_ l_ l_ lJ0.990 C~~~~~~~~096 3'-C3"~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0.980

,9

*CY- 03

C404-4" 0,975 ---------0,9 00- Rectangular Triangular Blackman Ham m ing Hanning Kaiser Tuk ey

Fig. 5. MOTOR IMAGERY vs. RELAX. COORDINATE XI.0,975-

Rectangular Triangular Blackman Hamming Hanning Kaiser Tukey the mode values and lower dispersion, are obtained for Xl with

Fig. 3. MATH TASK VS. MOTOR IMAGERY. COORDINATE XI. Tukey's and Kaiser's filtering windows, the worst results areobtained with Blackman's, Hamming's and Hanning's windows.

VI. DISCUSSION. It is observed that as higher the eigen-value magnitude, case

of Xl, the higher the value of one component of the eigen-In all cases only two eigen-values have got significant vector, normally in Q frequency band, by the contrary, as lower

magnitudes, so only two eigen-vectors have been considered the eigen-value more the contribution of the rest of eigen-vectorin the transformation matrix. This causes that LDA technique components.had projected the original six dimensional feature space over a The highest contrast power is obtained in the comparison ofbidimensional space, maintaining the intrinsic characteristics of Motor imagery vs. Relax, it is followed by Mathematical taskeach cerebral activity. vs. Relax, and the lowest is for Mathematical task vs. Motor

The analysis of the results for the transformed coordinate X1, imagery.shows that with a significance level of a = 2.5%, a = 1-p,in almost all cases the null hypothesis Ho, which maintains the VII. CONCLUSIONS.equality in the populations of the features associated to mentaltasks, should be rejected. On the other hand, the same analysis This report shows a methodology, based on LDA technique,for X2 shows that the difference appears only in some cases. It is which weight the power amplitude of frequency bands, and at thealso shown that channel C4'-C4" performs better than C3'-C3". same time, allow to reduce the feature input space maintaining

On average all filtering windows show statistical difference the particularities of the considered cerebral activities. On thebetween mental tasks; the best results, with higher quantities for other hand, eigen-vector analysis shows that the discrimination

09870 0,98051,0 _ 1 ,000 _ 870

0 ,5 0,.,9,0,005 05 05 05 , , , , 06 0505 05 , , , ,

0,7405P P 0,74400.7 400 0.7380

0.7 ---0.7 00___

0,5 _ i 0.500j0,0 0,0 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0.5 0,5 0,5 0,5 0,5 0,8 0,80,5

0I4 ICT C03 03 '4 C4'4 *I C3'T- 03 4 C4'- 04"0,4- - IIl 0,4001Rectangular Triangular Blackm an Ham m ing Hanning K aiaer Tuk ey Rectangular Triangular Blackm an H am m ing Hanning Kainer Tuk ey

Fig. 6. MATH TASK VS. MOTOR IMAGERY. COORDINATE X2. Fig. 8. MOTOR IMAGERY vs. RELAX. COORDINATE X2

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