c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47
journa l homepage: www. int l .e lsev ierhea l th .com/ journa ls /cmpb
EG data classification through signal spatial redistributionnd optimized linear discriminants
avid Gutiérrez ∗, Diana I. Escalona-Vargasentro de Investigación y de Estudios Avanzados (CINVESTAV), Unidad Monterrey, Vía del Conocimiento 201, Parque de Investigación e
nnovación Tecnológica (PIIT), Autopista al Aeropuerto Km. 9.5, Lote 1, Manzana 29, Apodaca, N. L. 66600, Mexico
r t i c l e i n f o
rticle history:
eceived 23 January 2009
eceived in revised form
1 May 2009
ccepted 12 May 2009
eywords:
lectroencephalography
rain–computer interface
eamforming
patial filtering
isher’s linear discriminant
ignal classification
a b s t r a c t
This paper presents a preprocessing technique for improving the classification of elec-
troencephalographic (EEG) data in brain–computer interfaces (BCI) for the case of realistic
measuring conditions, such as low signal-to-noise ratio (SNR), reduced number of mea-
suring electrodes, and reduced amount of data used to train the classifier. The proposed
method is based on a linear minimum mean squared error (LMMSE) spatial filter specifically
designed to improve the SNR of the signals before being classified. The design parameters of
the spatial filter are obtained through an optimized version of Fisher’s linear discriminant
(FLD) whose area under the receiver operating characteristics (ROC) curve is maximized.
The combination of the spatial filter and the optimized FLD increases the SNR and changes
the spatial distribution of the measured signals. As a result, the signals can be more easily
discriminated by means of a simple sign detector or threshold-based classifier. A series of
experiments on simulated EEG data compare the performance of the proposed classification
scheme to the performance of the Mahalanobis distance-based classifier, which is widely
used in BCI systems. Numerical results show that the proposed preprocessing technique
enhances the classifier’s performance even for low SNR conditions and few measurements,
while the Mahalanobis classifier is not reliable under such realistic operating conditions.
Furthermore, real EEG data from a self-paced key typing experiment is used to demonstrate
the applicability of the preprocessing technique. The proposed method has the potential
of improving the efficiency of real-life BCI systems, as well as reducing the computational
complexity associated with their implementation.
a user from a variety of different electrophysiological sig-
. Introduction
brain–computer interface (BCI) is a real-time communi-ation system designed to allow users to voluntarily sendessages or commands without using the brain’s normal out-
ut pathways [1]. One of the main purposes of a BCI system
s to allow an individual with severe motor disabilities to haveffective control over devices such as computers, speech syn-hesizers, assistive appliances and neural prostheses. Such an
interface would increase an individual’s independence, lead-ing to an improved quality of life and reduced social cost.Over the past 20 years, productive BCI research programs haveconcentrated on developing new augmentative communica-tion and control technology based on deciding the intent of
41.
nals. A review of some of the most representative technologydeveloped and signals used in BCI research can be found in[2,3].
optimization of the method in order to achieve maximum
40 c o m p u t e r m e t h o d s a n d p r o g r a
BCI systems based on electroencephalographic (EEG) datarely on accurate classification methods in order to use thebrain’s electrical activity to control computerized devices inreal-time [4]. In the last few years, many classifiers have beenproposed in the literature, some of which report excellent per-formance in classifying different motor and cognitive tasksfor BCI applications (see [5] for a comprehensive review ofthese methods). Most studies evaluate the performance of theBCI in terms of the speed and/or accuracy of the classifica-tion. However, such performance is usually computed underad hoc conditions, and an evaluation of the BCI for those cir-cumstances may not be sufficient to predict its performanceon real-life conditions. Therefore, BCI evaluation should alsoinclude testing in circumstances like those of real-life, such aslow signal-to-noise ratio (SNR), reduced number of measure-ments, and reduced amount of data used to train the classifier.
While the number of measuring channels and the amountof training data are design variables that can be adjusted inreal-life applications to make the classifier achieve better per-formance, the SNR is hard to control as it depends on manyfactors: in addition to external noise and artifacts affecting thesignal of interest, SNR may vary as a function of user atten-tion, tiredness, and other physiological factors. For this reason,the aim of this paper is to propose a method based on spatialfiltering techniques (also known as beamforming) to increasethe SNR of the signals before they are classified. Beamformingtechniques have been used to solve various problems of ana-lyzing neuroelectric and neuromagnetic signals, such as thelocalization of brain activity sources using EEG sensor arrays,as well as source signal reconstruction and interference can-cellation [6]. Furthermore, beamforming techniques have beenshown effective in doing those tasks for low SNR and low-rankinterference [7]. Therefore, this paper proposes a linear min-imum mean squared error (LMMSE) spatial filter to improvethe SNR of single-trial EEG data.
The proposed spatial filter is designed to suit, as close aspossible, the provided data before being passed to a classifier.This is a limitation since the data, at the time of filtering,can only be assumed to belong to one of a number of differ-ent classes of data and, therefore, the design parameters ofthe spatial filter cannot be exactly calculated. A solution tothis problem is to design the filter based on average charac-teristics obtained from the training data, but this results ina suboptimal solution with high variability [8]. For this rea-son, this paper proposes to obtain the design parameters ofthe filter from an optimized version of Fisher’s linear discrimi-nant (FLD) where the best discriminating hyperplane is chosensuch that the area under the receiver operating characteris-tics (ROC) curve is maximized [9]. This type of optimal FLDshave been used in many discrimination problems in the areasof radar, sonar, and seismology [10]. Also, optimal FLDs haveshown to provide better training performance than the classi-cal Fisher discriminant, as well as a comparable classificationperformance to linear support vector machines, but for a muchlower computational burden [11].
In this paper, EEG measurements are arranged as a lin-
ear model with additive Gaussian noise and in the form ofa spatio-temporal matrix. Under this condition, the Maha-lanobis classifier [12] is introduced as a bench-mark classifier,and then the proposed LMMSE filter is developed for the case
n b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47
when its design parameters are obtained from the optimalFLD. Then, experiments with simulated and real EEG dataare used to evaluate the performance and to demonstratethe applicability of the proposed methods to a practical BCIsystem.
2. Background
The present study is part of an on-going effort to develop signalprocessing methods for the improvement of BCI systems. Asmentioned in Section 1, the scientific community in this areahas placed a big amount of effort in the classification meth-ods. However, the development of preprocessing techniquesand performance assessment have not been paid the sameamount of attention. For this reason, preliminary work of theauthors of this paper has focused in those areas.
In [13], a preprocessing technique based in thelength/energy Transforms was proposed to enhance thevariability of EEG signals corresponding to different cognitivetasks. Even though that technique showed to improve thepercentage of correct classifications achieved by the Maha-lanobis distance-based classifier, the method still had thedisadvantage of requiring large amounts of training data inorder to compute the corresponding Mahalanobis distances.Such requirement represents a limitation when developingBCI systems.
Therefore, a first attempt to use a spatial filtering approachas a preprocessing step in BCI systems was presented in [8].There, the LMMSE spatial filter was proposed as a techniqueto improve the SNR of the EEG signals before being passed toa given classifier. However, the parameters of the filter werecomputed based on the classical FLD, where the covariancematrices of each class are equally weighted. As result, thefiltering scheme had good performance only when a largenumber of measuring channels and large amounts of train-ing data were used. Furthermore, the results showed largevariability in the performance given that the filter parame-ters were obtained only from average characteristics of thedata (i.e., those obtained through the classical FLD) withoutconsidering their variance.
For this reason, the present study shows the improvementsmade to the method in [8], which in summary are:
• The parameters of the proposed spatial filter are obtainedthrough an optimized version of the FLD, where the way thecovariance matrices of each class are weighted depend onan optimization criterion.
• For the optimization criterion, the area under the ROC curveassociated to the FLD’s hyperplane was selected due to itswidespread use in different applications to evaluate theperformance in classification processes [14] and its easierimplementation compared to the estimation of the proba-bility density function used in [8].
• While the main focus in [8] was the evaluation of the classi-fication performance, the current work is interested in the
performance with the minimum requirements. Therefore,the applicability of the method in real-life conditions is thepriority.
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. Description of method
n this section, the problem of classifying EEG signals comingrom different neural events is discussed for the case whenata is provided in the form of spatio-temporal matrices anddistance-based classification scheme is used. Since the clas-
ification performance is expected to depend mainly on SNR,his section also proposes a LMMSE spatial filter specificallyesigned for a two-classes discrimination problem. However,he proposed method can be easily extended to any numberf classes.
.1. Measurement model
onsider the case of measuring the potentials over the scalpy an array of m EEG sensors. Assume that the neural sourceshange in time, but remain at the same position during theeasurement period. This assumption holds in practice for
voked responses and event-related experiments [15]. Then,EG data is collected by the array of m sensors at time samples= 1, 2, . . . , N. The m × N spatio-temporal data matrix of thisrray at the k th independent trial is given by
k = X + Ek, (1)
here X is the desired signal matrix, and Ek is the noise matrix,hich is assumed to be distributed as N(0, �2) and uncorre-
ated in time and space between samples.Finally, assume that the measurements can be classified
nto i = 1, 2, . . . , I classes, each corresponding to different neu-al events. In that case, we will have {Yk}i data sets (where theub-index indicates that the set belongs to class i).
.2. Classification
iven a measurement matrix Y containing the spatio-emporal information of an unknown neuronal event, thelassification problem consists in assigning Y to the class i forhich a classification criterion is satisfied. In many cases, the
lassification rules rely on the minimization of the distance df the measured data to a group of unique identifiers obtainedpriori for each class using K independent trials as training
ata. An example of this distance-based classification schemes the Mahalanobis classifier, which is defined in terms of the
ahalanobis distance (dM) of Y to the mean of a group of Kndependent trials as
M = ‖(Y − Y)TR−1
YY (Y − Y)‖F, (2)
here ‖ · ‖F indicates the Frobenious norm, Y is the mean mea-urement given by
¯ = 1K∑
Y , (3)
K
k=1
k
nd RYY is the covariance matrix of the data. For the case ofnknown RYY , a consistent estimate of this covariance matrix
b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47 41
can be computed as
RYY =(
1K
K∑k=1
YkYTk
)− Y YT. (4)
Hence, the discrimination of a measured matrix Y using theMahalanobis classifier is carried as follows:
1. For each of the i classes, the corresponding matrices{Y, RYY}i are calculated using training data.
2. dM of the matrix Y to each of the classes’ {Y, RYY}i is calcu-lated using (2).
3. Y is assigned to the class for which dM is minimum.
The Mahalanobis classifier has been widely used in BCIapplications given its ability to assort EEG measurements fromdifferent motor and cognitive neural processes with affordableaccuracy even when a reduced set of measuring channels isused (see, e.g., [12,13]). However, this is only true for a suffi-ciently large set of training data (K), in which case a consistentestimate of the covariance matrix is attained. Other typesof classifiers require not only a large value of K, but also alarge number of measuring sensors m, therefore the com-putational complexity is increased. In addition to K and m,classification accuracy strongly depends on SNR. For this rea-son, the next section proposes a beamforming technique toincrease SNR and, therefore, improve the performance of theclassifier.
3.3. Spatial filter
The covariance matrix of EEG measurements usually exhibitsconsiderable spatial structure. Then, recent attempts toimprove the SNR of multi-channel measurements have cen-tered on spatial filtering techniques [16]. Here, a LMMSE filteris formulated for the special case of a discrimination problemof I = 2 classes.
Consider the measurement model in (1) and define themean square error (MSE) between the signal X and the spatialfilter F applied to the data Y as
e2(F) = tr{
(X − FY)(X − FY)T}
, (5)
where tr{·} denotes the trace. The filter that minimizes (5) isgiven by [17]
FOPT = RXXR−1YY, (6)
where RXX is the signal covariance matrix. In practice, RXX isapproximated using the sample average:
RXX = Y YT. (7)
For practical applications, we can estimate the values of the
covariance matrices by using (4) and (7), and then obtain anestimated filter F, i.e.
F = RXXR−1YY, (8)
m s i
42 c o m p u t e r m e t h o d s a n d p r o g r a
such that F → FOPT for a sufficiently large value of K. However,it is not possible to apply this filtering approach to a classi-fication process because the class i to which the measuredmatrix Y belongs to it is not yet known and the corresponding{Y, RYY}i cannot be calculated. For this reason, the followingapproximation to the filter in (8) is proposed:
FAPP = CXXC−1YY, (9)
where
CYY = �{RYY}1 + (1 − �){RYY}2, (10)
and
CXX = [{Y}2 − {Y}1][{Y}2 − {Y}1]T. (11)
The filter defined by (9)–(11) is inspired in an optimized versionof the FLD, where each of the classes are projected in a direc-tion such that the ratio of the square of the Euclidean distancebetween the projected means to the sum of the projected vari-ances is maximized [18]. The best discriminating hyperplaneis then assumed to have that direction as its normal, which inthis case corresponds to
n = [�{RYY}1 + (1 − �){RYY}2]−1[{Y}2 − {Y}1]. (12)
This discriminating hyperplane is optimized through � whichstays between 0 and 1. The special case when � = 0.5 corre-sponds to the classical FLD, and its use in the design of theproposed spatial filter has been already studied in [8]. Here,the value of � that optimizes the FLD is obtained through theanalysis of the ROC curves of all the possible discriminatorsin the range 0 < � < 1. The ROC curve is a plot of the probabil-ity of correct classification of one class against the probabilityof incorrect classification of another class [14], then the bestclassification performance is achieved when the area underthe ROC curve is maximum.
Under these conditions, the calculation of FAPP starts withan extensive search for the value of � corresponding to the dis-criminator with maximum area under its ROC curve over allpossible discriminators in the range 0 < � < 1. Once the opti-mal value of � has been determined, FAPP is fully known andcan be applied to the measured data as
Y = FAPP Y, (13)
where Y is the filtered data and corresponds to a spatiallyredistributed version of the originally measured data matrixY. Usually, spatial redistribution of the data is an undesiredeffect. However, since the design of the filter is based in anoptimal discriminator, the spatial redistribution in this caseturns out to be advantageous as Y has high SNR and its new
spatial distribution can be more easily discriminated by meansof a simple sign detector or a threshold-based classifier. Thisspecial effect will be shown through a series of numericalexamples in Section 4.1.
n b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47
4. Status report
First, we show a series of numerical examples using simulatedEEG data to compute the performance of the method undervarious conditions. Then, we demonstrate the applicability ofthe method through a classification experiment performed inreal EEG data specifically suited for BCI applications.
4.1. Computer simulations
The main purpose of the following examples is to evaluatethe performance of the proposed method in assorting motoractivity EEG data coming from the left or the right hemi-sphere of the brain and compare it to the performance of theMahalanobis classifier for different number of electrodes (m),training trials (K), and SNR. Hence, realistic EEG data repre-senting activity of the left or right hemisphere were generatedusing the forward solution of the EEG spherical four-shellmodel described in [19] under the following conditions:
• The cortical activity was modeled as an equivalent currentdipole (ECD) with a magnitude changing in time to approxi-mate a typical response like the one observed in motor taskssuch as hand movements. A full description of such an ECDmodel can be found in [20].
• The position of the dipole was assumed fixed at the motorcortex area either in the left or right hemisphere of the brainduring the length of the measurements.
• The EEG measurements were acquired from arrays of m =6 and m = 16 sensors evenly distributed over the expectedactivation areas.
• Random noise distributed as N(0, �2), uncorrelated in timeand space, was added to the EEG measurements with dif-ferent values of � to achieve mean SNR values of −3, −6,and −8 dB (i.e. low, moderated, and high noise conditions).Note that the SNR is defined as the ratio (in decibels) of theFrobenious norm of the signal data matrix to that of thenoise matrix. Some examples of the EEG distribution with-out noise and with different levels of noise at the peak ofthe brain activation are shown in Fig. 1.
The process of adding noise to the simulated EEG data wasrepeated with independent noise realizations to obtain 650trials corresponding to left-side activity and 650 trials of right-side activity, where each trial had N = 100 time samples. Fromeach side, 50 trials were destined to be classified (testing data)and K trials were used as training data, where K took differentvalues in the range of K = 15–600.
The 100 trials corresponding to the testing data were clas-sified using the Mahalanobis classifier described in Section 3.2for different combinations of m, K, and SNR, and a ROC curvewas computed in each case to evaluate the classifier’s per-formance. The testing data was presented to the classifier inrandom order (left and right events uniformly distributed). Thespatial filter described in Section 3.3 was also applied to the
same data in order to generate a new data set Y.
The main effect of the proposed spatial filter on the sig-nal is to increase the SNR. However, the filter also changesthe spatial distribution of the data. An example of such spa-
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47 43
Fig. 1 – Simulated single trial EEG data of left and rightmn
tdpiat
Fig. 2 – Examples of the spatial redistribution produced bythe proposed filter in the EEG data for left and right brain
ial redistribution can be observed in Fig. 2, where single trialata for the cases of left and right hemisphere activation were
rocessed with the filter (9). As result, and in addition to the
ncrease in SNR, the spatial distribution of the data changed inway such that the positive peak of the surface potential dis-
ribution corresponds to the hemisphere of original activation.
activation. In this case, the original data has SNR = −8 dB.(a) Original testing data Y and (b) filtered data Y.
Therefore, the redistributed data Y can be easily discriminatedby identifying such a positive peak in one or some of the sen-sors over that hemisphere.
The procedure previously described was applied to the caseof m = 16, K = 250, and different values of SNR, as a specificexample of real but optimistic conditions. Then, the perfor-mance was assessed by a score corresponding to the areaunder the ROC curves, which typically lies between 0.5 for auseless classifier and 1.0 for an ideal one. Under those con-ditions, the area under the ROC curves for the case of SNR =−3 dB turned out to be 0.9948 for the spatial redistribution-based classifier, while the Mahalanobis classifier achieved anarea of only 0.3336. For the case of SNR = −6 dB, the scoreswere 0.9048 and 0.4556 for the spatial redistribution and Maha-lanobis classifiers, respectively. Finally, for SNR = −8 dB, thescores were respectively, 0.7776 and 0.4644. Clearly, the clas-sification based in the spatial redistribution improves theperformance in comparison to the Mahalanobis classifier. Infact, the Mahalanobis classifier turns out to be unreliable forthe amount of training data used in this example. It is wellknown that the Mahalanobis classifier achieves optimal per-formance when K is large. However, this condition is not easilymet in real-life applications as it requires the patient to be sub-ject of intensive and long-lasting sessions of data acquisition,which at the end tends to decrease the SNR of the measure-
ments due to tiredness and distraction.
However, the previously calculated scores only reflect theperformance of the corresponding classifiers for a given data.This is because the classification performance is a random
44 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47
Fig. 3 – Mean of the area under the ROC curves for the Mahalanobis and spatial redistribution-based classifiers as a function. (a)R =
of K. Error bars show one standard deviation from the meanm = 6, (d) SNR = −6 dB, m = 16, (e) SNR = −8 dB, m = 6, (f) SN
variable with an extreme value distribution (see [8]), whichcan be characterized by its mean and variance. Therefore, thearea under the ROC curves were calculated 100 times for ran-domly chosen data sets and for all the possible combinationsof m, K, and SNR previously defined. The mean and standarddeviation of these 100 values are shown in Fig. 3. Our resultsshow that, for the case of the spatially redistributed data,
the mean performance of the classifier stays above a scoreof 0.8 when at least K = 250 and only 6 sensors are used in themeasurements, and this is true even for the highest level ofnoise tested. Furthermore, the variability in the classification
SNR = −3 dB, m = 6, (b) SNR = −3 , m = 16, (c) SNR = −6 dB,−8 dB, m = 16.
remains low, which is an improvement in comparison to theresults previously reported in [8]. Under the same conditions,the Mahalanobis classifier fails to achieve favorable results.
The simulations also show that a good classification per-formance can be achieved using less sensors if their positionis chosen, as in this example’s case, to lie above the expectedactivation’s area. However, if this optimality condition is not
met in practice, the classification performance should notbe considerably reduced if the selected sensors remain sym-metrical to the activation areas and, therefore, symmetricallyarranged with respect to the optimal hyperplane n. Still, the
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47 45
Fig. 4 – ROC curves of the (a) spatial redistribution-based classifier and (b) Mahalanobis classifier for the case of real EEGd
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Table 1 – Area under the ROC curves in Fig. 4.
K Spatial redistribution-basedclassifier
Mahalanobisclassifier
194 0.92123 0.62879
ata and different values of K.
ptimal selection of sensors remains as an open issue whichill be addressed in future work.
.2. Real EEG data
eal EEG data from a self-paced key typing experimentas used to show the applicability of the proposedethod. The data corresponds to one of the Fraunhofer
CI competition datasets, which are freely available atttp://ida.first.fraunhofer.de/projects/bci/competitions/. Theame data was used in a previous BCI study by researchersf the Berlin Brain–Computer Interface group [21].
In the experiment, a subject was sitting in a normal chair,ith his arms resting on the table and with the fingers in the
tandard typing position at the computer keyboard. Underhese conditions, the subject performed the task of press-ng the corresponding keys in a self-chosen order and timing,ither with the left or right index and little fingers. The sub-ect typed a total of 516 keystrokes at an average speed ofne key every 2.1 s. During the experiment, the brain activ-
ty corresponding to the typing task was measured with 27lectrodes located at positions of the extended international0–20 system, from which 21 were mounted over the motornd somatosensory cortex, 5 frontal and one occipital. Theata was referenced to the nasion’s electrode and sampled at000 Hz. The timing of the keystrokes was stored along withhe EEG data. Finally, the data provided for the BCI competitionorresponded to a downsampled version of the original mea-urements, where only every 10th sample was kept to achievesampling frequency of 100 Hz without any other processing.
rom the total number of trials, 100 of them were defined ashe testing data, leaving 413 labeled trials for training data. A
ore detailed description of the data can be found in [21].In order to use the provided data, a simple line-base correc-
ion was performed by subtracting to each channel the meanoltage over the first 40 samples. Then, the data was low-passltered using a 5th order Butterworth filter with a cut-off fre-uency of 10 Hz. After that, only the last 30 samples of the data
n each channel were used for the classification experimentnd the remaining data was discarded, as only the last sam-les correspond to the negative potential (brain activation)receding the initiation of the key typing movement. Finally,
150 0.89407 0.51924100 0.73699 0.37257
80 0.60978 0.51743
for the classification experiment, only the data from six sen-sors at locations C3, C4, C5, C6, CP1, and CP2 (i.e., contra-lateraland symmetrical measuring sites) were used.
Then, the data was classified using the proposed spa-tial redistribution-based classifier, and the performance wasevaluated by computing the ROC curves for the cases whenK = 194, 150, 100, and 80 training trials. Note that K = 194 wasthe maximum number of trials such that both classes wereequally trained. The same data was used with the Maha-lanobis classifier for comparison purposes. The correspondingROC curves are shown in Fig. 4, while the areas under thoseROC curves are given in Table 1. The results show that theproposed spatial redistribution-based classifier is able to pro-vide high performance at a ROC area of 0.89407 even whena reduced number of training trials is used. Furthermore,these results show that the proposed method achieves aperformance very close to the 96.3 ± 2.6% of correct clas-sifications reported in [21] using 21 sensors, or to the 84%of correct classification using 28 sensors of the winner ofthe second BCI competition (see http://ida.first.fraunhofer.de/projects/bci/competition ii/results) using a similar datasetof self-paced key typing experiments. However, in this work,a performance at a ROC area of 0.92123 with K = 194 wasachieved using only six sensors, which is an advantage interms of the implementation of a BCI system in real-life appli-cations. Finally, Fig. 4b shows that the Mahalanobis classifieris not reliable under these conditions.
5. Conclusions
This paper proposed a classification method for EEG datawhich is based in a LMMSE beamformer that changes thespatial distribution of the signal prior to classification. The
46 c o m p u t e r m e t h o d s a n d p r o g r a
spatial redistribution results in a favorable effect since thedesign parameters of the LMMSE beamformer are obtainedfrom an optimized FLD. Therefore, by applying the proposedprocessing scheme to EEG signals, it is possible to increasetheir SNR and change their spatial distribution to makethem easier to be discriminated. The experiments performedwith simulated and real EEG data show that the proposedmethod can produce a high classification performance underrealistic conditions. Therefore, the proposed method hasthe potential of improving the performance of real-life BCIapplications even for low SNR, reduced amount of trainingdata, and few measuring sensors. Furthermore, the proposedclassifier can be used in other applications where signal dis-crimination is of interest, such as in radar, communication,or other signal processing areas where arrays of sensorsare used.
6. Future plans
Up to this point, this work has focused in processing EEG sig-nals in the time domain. However, some attention is requiredin extracting specific characteristics of the signals in orderto facilitate the computational work. One option would be touse an autoregressive (AR) model of the signal in a similarway as in [22] instead of the complete EEG time series, or touse other features like those reviewed in [23] and referencestherein.
Furthermore, the proposed method requires to be gener-alized to any number of classes, then more complex mentalprocesses could be used. An example of that kind of processesapplied to BCI systems are those studied in [13] where highermental tasks such as memory, imaging 3D objects, counting,or reading were involved. Also, the use of magnetoencephalo-graphic (MEG) data should be considered given that thesesignals are more local and easier to interpret than the cor-responding EEG signals [24]. At this moment, the cost of MEGtechnology and its immobility limits the online use of MEGmeasurements in BCI systems. Nonetheless, as technologyprogresses, we may even have portable MEG devices (see, e.g.,BabySquid, Tristan Technologies).
In terms of the computational implementation, futurework will address the issue related to the selection of the opti-mization factor �, as in this paper it was found through anintensive search within its possible range of values. Such anintensive search is computationally expensive and requires tobe optimized. Also, in terms of implementation, future workshould evaluate the classification performance as a function ofthe position of the sensors, then the optimal array of sensorscould be found for a given BCI application.
Therefore, further research in this area will focus in thoseissues and will include more extensive application to realEEG/MEG data.
Conflict of interest statement
The authors hereby stated that they have no potential conflictof interest related to any for-profit company or institution inany ways.
n b i o m e d i c i n e 9 7 ( 2 0 1 0 ) 39–47
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