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4434 K. Majumdar / Applied Soft Computing 11 (2011) 44334447

1. Introduction

In EEG analysis, most methods of analysis follow, explicitlyor not, a pattern recognition approach [1,2]. These analyses haveimportant applications in brain computer interface (BCI) [35],epilepsy research [6,7], sleep studies [810] , psychotropic drug

research and monitoring patients in critical condition in the ICUs[11,12] . However, automated analysis of EEG data is a huge chal-lenge because of the volume of the data sets and dynamic nature of thesignalswith hightemporal resolutions (inmillisecondrange).Incase of thehumanscalpEEGsignals this challenge hasbeen furtheraugmented by the introduction of high density EEG nets consist-ing of more than 300 channels [13] and with increasing samplefrequency (1000Hz or more) of digitization by means of advancedtechnologies.

HumanscalpEEGwasborn in1920s whentheGermanphysicianHansBergerrstmeasuredtracesofbrainelectricalactivitiesonthescalp [14,15] . Since then the interpretation of patterns in the scalpEEG, in the most part, has remained a challenging issue. Synapticactivity in thepyramidalneurons (85%of excitatoryhuman cortical

neurons are of this type) is the principal source of scalp EEG [16](p. 914). Modulatory dynamical actions of the neural ensembles,bothat local and global scales, give rise to patterns in the scalp EEG[17,18] . With clever quantitative methods it is possible to measure(cognitive) taskrelated integration [1921] and differentiation [22](in some sense) from even the single trial EEG signals.

The online epoch identication in human scalp EEG signalshas a long history [23] . In this classic, the vision propounded forspatio-temporal data reduction and processing by soft computingapproaches, like the Bayesian statistics, in order to bring down thecomputational loads to a manageable limit, are being largely fol-lowed even today [24] . For the sake of computational efcacy it isdesirable to keep the analysis linear as far as possible. But, thencomes the vital issue are we not overlooking the nonlinear fea-tures? It has been argued in [25] that the advantage of a nonlinearanalysis, at greater cost, of the multi-channel noisy scalp EEG datais rather marginal over the corresponding linear methods.

SincetheearlydaysoftheBCI [26] the need forrealtimeanalysisof EEG and ERP has been felt. Linear analysis and soft comput-ing techniques are the two most promising approaches in thisregard. In contrast to classical approach of exact computation ata greater cost, which may be prohibitive for the complex prob-lems like multidimensional EEG analysis, soft computingstrives toachieve tangible results at reasonable cost by allowing inexactnessand uncertainty to be part of the computational model. It includesneural networks, fuzzy logic, statistical discrimination, Bayesianinference and genetic algorithms. This list is of course not exhaus-tive, but would be sufcient for our purpose in this paper. Herewe will be reviewing various soft computing techniques that havebeen followed forhuman scalp EEG/ERP processing. Such a review,even if non-exhaustive, would hopefully be useful for the researchcommunity.

Broadly speaking, EEG processing has two parts namely, (1)decomposing the complicated signal into simpler components (byFFT, wavelet transform, ICA, PCA, etc.) and(2) bunching those com-ponents together in search of specic structures in the data (thepattern recognition part). It is in the latter part, where almostall of these approaches are to deal with uncertainty and therefore theyare soft computing approaches.

In the next two sections we will be briey presenting a physio-logical overview of scalp EEG and dimensionality reduction of thedatarespectively. In Section 4 we will be reviewing neuralnetworkapplicationson human scalp EEG, in Section 5 fuzzy systems appli-

cations, in Section 6 applications of evolutionary computation, andin Sections 79 applications of statistical discrimination, supportvectormachine (SVM) and Bayesian inference, respectively. Notall

these branches have found equal applications on human EEG. Inthis survey we have tried to be as exhaustive as we could, sacric-ing the technical details, which can be found out in the references.This, we hope, will enhance the readability and usefulness of thepaper.

2. Cortical source of scalp EEG

Excitatory postsynaptic potential (EPSP) at the apical dendritictrees of pyramidal neurons is the principal source of the scalp EEG[15,16] . When these neurons receive inputs through their apicaldendrites EPSPs are generated in the apical dendritic tree. Theapical dendritic membrane becomes transiently depolarized andconsequently extracellularly electronegative with respect to thecell soma and thebasaldendrites.This potentialdifference causesacurrent to owthrough the volume conductorfrom thenonexcitedmembrane of the soma and basal dendrites to the apical dendritictree sustaining the EPSPs [1,15].

Some of the current takes the shortest route between the sourceand the sink by traveling within the dendritic trunk (primary cur-rentin blue in Fig. 1). Conservationof electric charges imposes thatthecurrent loop be closed with extracellular currents owingeventhrough the most distant part of the volume conductor (secondarycurrent in red in Fig. 1). Intracellular currents are commonly calledprimary currents, while extracellular currents are known as sec-ondary, return, or volume currents. With the spatial arrangementandthe simultaneousactivationof a largepopulation of the cells,asshown in center of Fig. 1, contribute to the spatio-temporal super-positionof the elementalactivityof every cell, resultingin a currentow that generates detectable scalp EEG signals [15].

Both primary and secondary current contribute to scalp EEG.Macrocolumns of tens of thousands of synchronously activatedlarge pyramidal cortical neurons are thus believed to be the prin-

cipal sources of scalp EEG because of the coherent distribution of their large dendritictrunks locally oriented in parallel,and pointingperpendicularly to the cortical surface [27] . The currents associ-ated with the EPSPs generated among their dendrites are believedto be at the source of most of the signals detected in MEG andEEGbecause they typicallylast longerthan therapidly ring actionpotentials traveling along the axons of excited neurons [15,28].

3. Dimensionality reduction

Dimension of scalp EEG data at the preprocessing stage is cal-culated as number of channels number of trials (e.g., the way thedatarepresentationis made [29]). Fordensearray EEGconsistingof morethan100channels,arecordingsessionspanningthroughhun-dreds of trialseach spanningthrough several seconds or minutes oreven hours (in case of say, epilepsy monitoring) with a sample fre-quencyof 1000 Hz ormore, the amountof generateddatamay be of theorderof tens or even hundredsof gigabytes. Without some kindof data reduction it would be impossible even to load the data setinto the main memory of most modern day work stations. Dimen-sionality reduction can be done by selecting appropriate channels[30,31] or time epochs or trials [32].

Dimensionof EEGat the postprocessing stage is calculated usu-ally in terms of the dimension of the feature space. Dimensionreduction (also known as feature extraction ) is achieved either byprojection to a lower dimensional space or by selecting a subspaceof the original one [30,33] . In [22] dimensionality reduction has

been achieved by projectingEEGfrom all thechannels into a singleone dimensional time domain signal. More of it will be discussedin Section 7.


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K. Majumdar / AppliedSoft Computing 11 (2011) 44334447 4435

Fig. 1. Left: EPSPs are generatedat theapicaldendritic tree of a cortical pyramidal cell. Center: Large cortical pyramidal nerve cells areorganized in macro-assemblies withtheir dendrites normally oriented to the local cortical surface. Right: Functional networks made of these cortical cell assemblies and distributed at possibly multiple brainlocationsare themain generators of EEG signals.Adopted from [15].

4. Neural networks

This section will be organized in accordance with [34]. Low sig-nal to noise ratio (SNR) in case of scalp EEG is a good reason forusing ANN to process them [35].

4.1. Artifact removal

Eye blinks; movements of eyeballs and tongue; face, head andneck muscle contractions; cardiac rhythms; frequencyof the alter-nating current supply to the equipment (steady state 50 or 60Hz)are the major sources of artifacts in scalp EEG (for a nice overviewsee Ref. [36]). Some of these may be avoided if the subject followsappropriate guidelines. For theothers, automatedartifactdetectionand removal techniques are themost practical solutions. When thepatternsofartifactsaredifferentfromthepatternsofevokedpoten-tial ANNs cantheoreticallybe used toseparatetheartifacts outfromthe EEG. Some advancement in this direction has been reported in[3746] .

Various features of artifacts are extracted and fed into the inputof an ANN to train it. At the end of the training, success rate of aradial basis function (RBF) network has been reported to be 75% inartifact detection [43] .

4.2. Source localization

Interpretation of theclinical EEGalmost always involves specu-lationas tothe possible locationsof the sources insidethebrainthatareresponsiblefortheobservedactivityonthescalp [47].Forexcel-lent reviews see [15,48,49] . However computational cost of mostsource localization algorithms is prohibitive. An error back prop-agation NN approach was rst proposed to overcome this hurdlein case of dipole source localization [50] . In general dipole sourcelocalizationproblem is an optimization problem to nd optimumcoordinate and orientation of dipoles, and hence suitable for beingsolved by ANN. It is possible to do away with computation inten-sive head modelsif there is sufcientinputoutputdata to train thenetwork.

A general ANN system for EEG source localization is illustratedin Fig.2. Accordingto [51] , the numberof neurons in theinputlayer

is equal to the number of electrodes and the features at the inputcanbe directlythe valuesof themeasured voltage.The networkalsoconsistsofoneortwohiddenlayersof N neuronseachandanoutput

layer made up of six neurons, 3 for the coordinates and 3 for dipolecomponents. In addition each hidden layer neuron is connectedto the output layer with weights equal to one in order to permita non-zero threshold of the activation function. Weights of interconnectionsaredeterminedafterthetrainingphasewheretheneu-ral network is trained with predetermined examples from forwardmodeling simulations [49]. Localizationaccuracy has been claimedto be less than 5% by various ANN approaches [34,35,5057] andhighaccuracyincaseof [58]. Clearly ANN approach isnotveryprac-tical for distributed source models, where sources may consist of any subset of thousands of cortical mesh points [32] .

4.3. Sleep studies

K-complexes are said to be the largest events in healthy humansleep EEG [59] . Itis natural that ANN had been tried on them quiteearly with 90% success rate of identication and 8% false positive[60] , also [61]. Sleep spindle identication by ANN also started get-ting attentionat thesame time [60,62] . A simple feed forward ANNwas applied on sleep EEG even earlier [63] . 6180% accuracy wasachieved in classifying seven different sleep stages in infant EEG(wake, movement,sleepstage 1,sleepstage2, sleepstage3/4, para-doxical sleepand artifacts) [64]. Apioneering study wasundertakento distinguish sleep EEG power spectrum patterns under the inu-ence ofdifferentsleepingpills usingANN [65]. Fora detailed reviewof early ANNapplications on sleep studies see [66] (also see [34] formore references).

Use of ANN for automatic sleep stage scoring has been reportedin [67] with an average 87.5% agreement with two human experts.A dominating trend in sleep EEG analysis has been rst to extractfeatures (such as shape, frequency and power spectrum) by a suit-able wavelet transform (in some cases Fourier transform [68]) andthenusingthesefeaturesasinputtoanANN [67,69,70] . Accuracyof recognition runs from as low as 44.44% [69] to around 95% in [70] .Automatic recognition of alertness and drowsiness has been per-formedbythreedifferentANNswiththebestperformancereportedfor the learning vector quantization (LVQ) network [71], which is94.37 1.95% in agreement with the human experts.

4.4. Epilepsy

EEG analysis is an integral part of diagnosis and monitoring of epilepsy and it has a long history [72] . The effort for automatic


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Fig. 2. Block diagram for sourcelocalization by articial neural networks (ANN).Adopted from [49].

detection of epileptic activities in prolongedEEG recordings is alsoquite old [73] . Neural networks started being used for epilepticseizure detection since early nineties [74,75] followed by others[7686] . In case of neonatal seizure detection by error back propa-gation NN the average detection rate is from 79.6% to 91% [85,86].Feed forward NNand quantum NNhave been used to detectneona-tal epileptic seizure with moderate specicity (little over 79% byboth types of NN) [87] . Elman networks (ENs) have also been usedfor seizure detection [88] . These are a form of recurrent NN whichhave connections from their hidden layer back to a special copylayer. This means that the function learnt by the network can bebased on the current inputs plus a record of the previous state(s)and outputs of the network. The results that EN yields are saidto be the best with a single feature fed as the input. The over-all reported detection accuracy is about 99.6% [88]. Recurrent NNbased seizure prediction has been reported in [89] . For better per-formance of spike detection by NNs, preprocessing of the EEG hasbeen emphasized in [90] . Recurrent NN has been used for seizureEEG classication in [91]. Scalp EEG of 418 epilepsy patients wasclassiedwitha multilayer perceptron(MLP), which matched withtwo human experts in 89.2% instances [92] .

Let us conclude this subsection with a prophetic observationof Alan S. Gevins, Brain electromagnetic signals can be quite use-ful for providing corroborating evidence about the presence of aseizure disorder and also for determining the site of seizure ori-gin. Therefore, despite their limited clinical impact to date, effortsat automated epileptiform transient detection will undoubtedlycontinue [93].

4.5. Brain computer interface

BCI started with theseminal paper of Farwell andDonchin [94].Soon afterward NN was applied to classify the scalp EEG signalsduring right andleft hand movements in thehope of predicting theside of movements before they occurred [95,96]. Power spectrumof extended -band (516 Hz) had been used to train and test anhybrid of K-means and back propagation NN to achieve a classi-

cation accuracy of 8590% [97] . Cascade NN has been used for thesamepredictionpurposehasshownwidely varyingresultsdepend-ingon thepowerspectrumof EEG[98] . 91%or more classication

accuracies were achieved for mere left or right index nger move-ments discrimination by employing on ANN for each channel andselecting only the best classication results [99,100] ([100] alsoincludes right foot movements in addition to the two mentionedearlier).

The performances of a back propagation ANN with four layershave been compared in [101] with two human investigators whenboth the ANN and the humans were engaged in classifying scalpEEG of six subjects during right middle nger extension tasks. Fora cube rotation task in BCI an adaptive NN based algorithm hasachieved a 68.3% classication accuracy in [102] . Imagined handmovement in four out of seven subjects is reported to be pre-dictable with 80% accuracy in [103] . In a more recent study fastFourier transform (FFT) based amplitudes of the EEG have beenused as input to a multilayer NN with reported improved accuracyon test sets 80% or more [104]. FFTandNN based EEGclassicationof intention of right and left elbow movement has been reported in[105,106] . EEG classication of limb movement imagination by NNbased on particle swarm optimization has been reported in [107].

4.6. Other patterns

Several studies have been reported pertaining to the analysis of evokedpotential (EP) in the scalpEEGusingNN [108110] . Some of them are concerned about visual EPs [109122] , some about audi-tory EPs [100,110,118,123134] and some about somatosensoryEPs [110,135139] . For a fundamental treatment of use of NN inthe analysis of event related potential (ERP) see Ref. [140] .

Using EEG recordings several investigators have developedneural network based systems to assess the vigilance levelof the subject under investigation [141147] . In [147] aLevenbergMarquardt (LM)multilayerperceptron(MLP) was usedto classify EEG signals from 30 subjects for alertness (success rate93.6%), drowsiness (96.6%) and sleep (90%) (the LM network hasbeen reported to be performing poorer than the LVQ in [71]). Theinput to the MLP was obtained by spectral analysis of the EEGthrough a discrete wavelet transform (DWT).

Analysis of maturation level of neonatal brains (28112 weeksafter birth) has been determined using NN on the EEG [148] . NNwas used on EEG of 131 children aged between 4 and 16 years to


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detect possibleabnormality in brain [149] .NNwasappliedonaudi-tory EP of brainstem to detect hearing impairments in newborns[150] . Attention decit hyper active (ADHA) disorder is a recog-nizedproblem in child psychiatry, in whichNNshave been used onEEG to identify symptoms with good success [151,152] .

In certain neurological disorders EEGtends to be different from

the normal. Tacitly using this fact NN based classication of dis-ordered EEG with respect to the control has been achieved. Thiswas done for headache and migraine [153155] , neuroophthal-mological disorder [156], head injury [140] , multiple sclerosis[39,157] , schizophrenia [158163] , Alzheimer disease [164167] ,Parkinsons disease [167], Huntingtons disease [162,168171] ,depression [161] andalcoholics [172,173] .ProbabilisticNNhasalsobeen used forEEG classication in [174] withmoderatesuccess andslightly poorer performance than SVM, but with much better per-formance in [175] . For some clinical applications of NN on EEG seeSection 4 of [176].

MLP and EN have been used on EEG to determine the depthof anesthesia during surgery with 99% success for the EN [177](for a survey of applications of NN on EEG during anesthesia see

Ref. [178]). EN has been shown to perform better on human visualevoked potential (VEP) than the k nearest neighbor (kNN) algo-rithm [179] . Continuous monitoring of brain state by means of NNapplication on EEG of the critically ill patients in the intensive careunit (ICU) has been reported in [12,180] . Use of NN on EEG underthe effects of drugs (sedatives) in order to classify the effects dueto different drugs has been reported in [181,182] . Classication of online scalpEEG byNN during threedifferent mentaltasks hasbeenperformed with 70% accuracy, but with only 5% mis-classication[183] . Convolutional NN has been used in BCI for classifying EEGduring different activities with 95% accuracy [184] .

5. Fuzzy logic

Fuzzy logic based analysis of human scalp EEG started with thepioneering paper [8]. Fuzzyclusteringand neuro-fuzzy techniqueshave remained the most notable methodologies in this regard.

5.1. Fuzzy clustering

Cluster analysis is based on partitioning a collection of datapoints into a numberof subgroups, where the objects inside a clus-ter (a subgroup) show a certain degree of closeness or similarity.Hard clustering assigns each data point (feature vector) to one andonly one of the clusters, witha degree of membership equal to one,assumingwelldenedboundariesbetweentheclusters.Thismodeloftendoes notreect thedescription of realdata, where boundariesbetween subgroups might be fuzzy, and where a more nuanceddescription of the objects afnity to the specic cluster is required[10] . In case of human EEG this was rst utilized in [8] (before thisfuzzyclustering wasappliedon sleep EEGof chimpanzee [185] ).Anefcient human sleep EEG data classication has been reported in[10] by means of unsupervised fuzzy partition-optimal number of classes (UFP-ONC), which is a combination of fuzzy k-means (FKM)algorithm [186] and fuzzy maximum likelihood estimation. Thishas been able to decompose the sleep EEG from a single subjectinto optimum number of distinct classes, which has been treatedas a priori unknown [10,187,188] .

A different fuzzy clustering algorithm was used in [189] for EPidentication in low signal to noise ratio (SNR) EEG. In this FKMalgorithm hasbeen appliedwiththe numberof clustersdeterminedby the criterionproposed in [190] . Trialswith prominent(same) EPwere grouped together using fuzzy clustering before being aver-

aged for extraction of the EP. Single instances of EP have beenreported to be classied up to 95% accuracy. FKM clustering (alsoknown as fuzzy c-means clustering) was used in conjunction with

an ANNto classify epilepticspikes (ES) in scalp EEG [191] . Howeverthe performance is not very impressive.

Fuzzy if-then rule-based online classication of a single subjects EEG signal during pain and no pain experiences has beenreported in [192] with only 64% overall classication accuracy,which is slightly poorer than the corresponding hidden Markov

model (HMM) classication studied on the same data set. A fuzzyclassication technique for epilepsy risk level has been proposedin [193] .

5.2. Neuro-fuzzy techniques

Combination of NN and fuzzy logic gives a powerful soft com-puting methodology, which has been applied on human EEG withmixed success. In one of the rst applications auditory evokedpotential (AEP) from the EEG of a patient under anesthesia wasanalyzed by an NN. The output of the NN was utilized as input toa fuzzy if-then rule-based controller, which controlled the dosageof the anesthetic drug. The performance was graphicallycomparedwith a trained anesthetist during a real surgery [194] .

About 88.2% infant sleepwake stage classication on the testEEGdata has been achieved by ANFIS-based classier [195] (Fig. 3).The architecture is in Fig. 3. Layer 1 is the fuzzication layer. X 1 , X 2 ,and X 3 are three of the input variables, each with two associatedfuzzy concepts ( Ai and Bi). Layer 2 generatesall thepossiblerulesof theformIF X 1 is A1 and X 2 is B2 and X 3 is A3 , with a T-normoperator(), considering one fuzzy concept per input variable. The output of layer 2 is a strength parameter for each of the rules. Each node atlayer 3 performs a linear combination of the rules and uses a sig-moidal function to determine the degree of belonging of the inputpattern to each class (C 1 , C2 , C3). In another study ANFIS classierswere used on features extracted from EEG by wavelet transfor-mations (WTs) for classication pertaining to ve different classeswith a total accuracy of 98.68% [196]. WTon EEGfollowedby ANFIS

could classify normal subjects from epileptic patients with 93.7%and 94.3% respectively, which is slightly higher than that achievedby an MLP [84] . WT followed by ANFIS has been used to analyzeEEG pertaining to left and right hand movements [197] , state of alertness [198] . Neuro-fuzzy NN has been used to determine thestates of fatigue or alertness in drivers [199]. EEG feature extrac-tion by Lyapunov exponent followed by ANFIS classication wasused to detect changes in the signal [200] . A comparative study of neuro-fuzzy classiers with some other classication methods isalso available [201]. For a comprehensive treatment of the subjectsee Ref. [202].

Combining adaptedresonancetheory (ART) NNwithfuzzy logic,fuzzy ARTMAP NN was created [203] , which has found severalapplications in human EEG processing [169,204208] , often with

classication success rate of 90% or above. Very recently a fasterself-organizing fuzzy neural network has been applied in BCI withup to 70% processing time reduction [209] .

5.3. Other fuzzy systems

After extracting features from EEG by DWT fuzzy SVM(FSVM) has been applied for the classication [210] . HoweverFSVM is reported to have given poor results on classicationof schizophrenic EEG from the control subjects [211] . FeaturesextractedfromEEGusing wavelet packethavebeen sortedby fuzzylogic foroptimumperformance [212].Fuzzyif-thenruleshavebeenused on features extracted by time frequency analysis of EEG inorder to determine the depth of anesthesia on 22 patients [213] .

Fuzzy rule based detection of -band activity has been proposedin [214] . EEG based use of a fuzzy controller has been proposed toadminister anesthesia in [215] .


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Fig. 3. A simple adaptive neuro-fuzzy inference system (ANFIS) for infant sleepwake stage classication.Adopted from [195] .

6. Evolutionary computation

Signals in medicine,such as EEG, processing is subject to severalimportant constraints. First, the number of signals to be pro-cessed is high, and often tightly interdependent. Second, signalsare unique, in the sense that the circumstances under which theywere obtained are normally not repeatable. Third, given the char-acteristics of their sources, medical signals are often very noisy.Finally, in some cases information about the signals is required inreal time in order to take crucial decisions [216]. Genetic algorithm(GA) was applied on EEG during different mental tasks in order toclassify them intask specic categories. The goalwasachieved with76% accuracy [25] . Genetic programming (GP) has been appliedon human scalp EEG for epileptic pattern recognition [217] withsuccess rate of 93% or more (in intracranial EEG seizure precursorfeatures have been detected by GP in [218]). GP has been used for

normal EEG classication in [219] . Epilepsy risk assessment withGA has been done in [220,221] .

7. Statistical discrimination

Statistical discriminants are standard tools for classicationof multidimensional patterns (for a general introduction see Ref.[222] ). Their need in human scalp EEG classication has long beenfelt [23]. Usingthemon scalpEEG, classication ofdyslexiapatientswas performed in [223] . EEG of mild head injury patients wasclassied (with respect to a group of normal control subjects) bystatistical discriminants with more that 90%accuracy in [224,225] .[226] presents a review of classication of scalp EEG by discrimi-nators in case of traumatic brain injury. Discriminants have been

used to classify EEG belonging to subjects with neuropsychiatricdisorders [227] . Unfortunately, very little detail is available of thediscriminators implemented in [224227] .

Scalp EEG of normal human subjects has been classied dur-ing rapid serial visual presentation (RSVP) of interesting and

uninteresting scenes by statistical discrminants [22,228,229] . Dis-criminant analysis has been performed in single trials on theweightedsum of allthe scalp channels, where theoptimum weighthas been selected by ne tuning a logistic regression (LR) function(for a nice exposition of LR see Ref. [230]) with the help of gra-dient descent method [22] . Then normalized projection of signalfrom each channel on this average is calculated. Intensity of thisprojection is used to classify signals between interesting (91.8%classication accuracy) and uninteresting scenes (98.3% classica-tion accuracy) [228] .

Although LR is more robust, it is a less efcient classier andtakes more resources to compute compared to the normal sta-tistical discriminators [231] . A study was undertaken to compareperformance between Fishers discriminant (FD, see [232,233] for

description) and LR on the scalp EEG of three subjects (two malesand one female, mean age thirty years, all of them left handed).They did not have any known neurological or vision disorder. Thedata was collected using 256 channel Hydrocell Geodesic SensorNet (Electrical Geodesics, Inc., Eugene, OR) during a series of RSVPtasks at a rate of 3 grey level satellite images per second [234] . Theanalysis wasperformedon single trials. LR turnedout to be good inidentifying target, but poor in identifying non-target data( Table 1 ).

Table 1Average performance of LR vis--vis FD on the EEG of three subjects during RSVP(3 images persecond) of three differenttargets vs. non-target. ROC area means thearea under the receiver operator characteristic (ROC) curve.

LR FD

Target 0.9752 0.7601Non-target 0.5768 0.8770ROC area 0.9311 0.8700


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Table 2Average performance of LR vis--vis FD on the EEG of three subjects during RSVP(3 images per second) of target tank and target truck in different sessions (eachconsisting of about 300 trials) in each of which only one type of target images aremixed with non-target images roughly at 1:4 ratio.

LR FD

Tank 0.6186 0.9858Truck 0.7623 0.9751ROCarea 0.7067 0.9939

Ontheother hand FD waspoor in identifying targetdata, butmuchbetter in identifying non-target data ( Table 1 ). FD was also goodin separating various pairs of target EEG data (see Table 2 for anexample). The general conclusion was that there is no particulardiscriminator uniformly suitable for all types of EEG data. Differ-ent discriminators perform differently on different data sets [234].FD was used on EEG after feature extraction by a combination of continuous WT and student t -statistic with the best classicationaccuracyinthe2003BCIcompetition [235] .FDwas usedforrandomclassication of EEGchannels forBCI in [236] with a very moderateaccuracy of 56.66%. A comparison of FD andtwo of itsvariantswithSVM and k nearest neighbor (kNN) algorithm on EEG data beforeonsetof nger movements appears in [237]. The outcomes are pre-sented in Table 3 . Fora reviewof applicationsof lineardiscriminantanalysis in BCI research see Ref. [238] .

LR has been compared with NN on seizure EEG data [83] . Clas-sication accuracy of two different MLPs has been reported to bemore than 91% compared to 89% for the LR. Superior performanceof NNover LR has beenreported in [239,240] . Onan average LR hadperformedbetter on thesingle trial EEG than a conventional spatialpattern (CSP) based classier [241].

A statistical discriminant was used to classify EEG signalsbelonging to schizophrenic patients for negative and positive fea-tures associated with the symptoms. 78% classication accuracy

for schizophrenia wasachieved on a test data set (disjoint from thetraining data) with 85% specicity [242] . Quadratic discriminantfunctionwasapplied onEEGof 33subjects to classify amongdiffer-ent tasks with 93% accuracy for the training data and 85% accuracyfor the testing data [243] .

8. Support vector machine

Despite greater difcultyin implementation andlonger runningtime ontestdata comparedto theNN andlineardiscriminants,SVMhas become a popular classication algorithm for the EEG for itsusually higher classication accuracy compared to the former. Foranexcellenttutorialon SVMsee Ref. [244] . The primary motivationbehind SVM is to directly deal with the objective of generalizationfrom training data to testing data with minimization of error andcomplexity of the learning algorithm [25] . Table 3 shows superiorperformance of SVM on EEG data. A recent study on classication(vis--vis a human expert) of neonatal EEGof six infants hasshownthat SVM has outperformed the FD and NN ( Fig. 4) [245] .

Table 3Test set error ( std) for classication at 120ms before keystroke. mc refers to the21 channels over (sensori) motor cortex, all refersto all 27 channels. RFD and SFDstand forregularized and sparseFD respectively. ch stands forchannel.

Filter chs FD RPD SFD SVM k-NN


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Table 4The Bayesiangraphical network (BGN), neural network, Bayesian quadratic classier,Fisherlinear and hidden Markov model (HMM) are compared forclassication of binarycombinationsof ve mental tasks. Theresults in thetable are averaged over tendifferent possible binary combinationsof mental tasks.

Subject BGN Neural network Bayesian Fisher lilies HMM

1 94.07 2.2 92.48 2.9 93.78 2.8 91.15 2.7 70.18 8.83 87.43 3.9 85.04 4.3 89.22 3.5 82.77 4.1 64.10 9.1

82.48 2.8 82.61 3.0 86.58 3.4 81.79 3.1 62.43 7.86 90.31 2.7 89.39 3.1 92.49 3.2 90.38 3.1 64.61 8.3Means 88.57 .3.0 87.38 3.4 90.51 .3.2 86.63 3.3 65.33 8.5

Reproduced from [268] .

9.3. Bayesian classication

There are two standard approaches to EEG classication dis-criminative and generative . Bayesian classication falls under thegenerative class. For a nice overview see Ref. [270]. In a genera-tive approach, we dene a model for generating data V belongingto particular mental task c {1, . . . , C } in terms of a distribution p(V |c ). Here, V will correspond to a time-series of multi-channelEEG recordings, possibly preprocessed. The class c will be oneof the mental tasks. For each class c , we train a separate model p(V |c ), with associated parameters c , by maximizing the likeli-hood of the observed signals for that class. We then use Bayes ruleto assign a novel test signal V * to a certain class c according to: p(c | V ) = p(V |c ) p(c ) p(V ) . That model c with the highest posterior proba-bility p(c |V *) is designated the predicted class [270] .

Input outputHidden Markovmodel(IOHMM,see Ref. [271] ,andFig. 7(d) for the architecture) based classication of EEG, which isa special case of Bayesian classication, has been applied in BCI[270] . IOHMM has performed better than HMM, Gaussian mixturemodel(GMM)andMLP withreducedclassicationerrorrate. HMMwas applied on whole night EEG of nine subjects for sleep stageclassication with accuracy ranging from 26% (rapid eye move-ment sleep) to 86% (wake stage) [272] . To overcome the problemof nonstationarityin EEG signals HMM has been introduced, whichthen according to the scheme presented in Fig. 6 determines if themovementintention is on left or right by evaluating the expressionMAX(P P (V |HMML ), P P (V |HMMR )) [273] . The online classication

Fig.6. BCIsystemcomprising HMM L for leftmovement featureselectionand HMM R that forthe right.Adopted from [273] .

rate occurringin four healthy subjects varied between 75%and 95%[274].FortheoryandsomeapplicationsofHMM seeRefs. [275,276] .HMM on EEG was used to classify arousal and sleep states in [277] .Various HMM architectures have been shown in Fig. 7. A compar-ative study of their performances on human EEG data has beenpresented in [278] . HMM along with Principal Component Analy-sis (PCA) and SVM has been applied on EEG to classify left rightmovement in [279] .

Kernel PCA and HMM are combined to identify mental fatiguefeatures in EEG in [280] with a classication accuracy of 88%. The

Fig. 7. Various HMM architectures. The empty circles are the hidden states and the shaded ones are observation nodes, the lightly shaded ones (in d) are input nodes. (a)Standard coupled HMMs; (b) event coupled HMMs; (c) factorial HMMs; (d) inputoutput HMM.Adopted from [278] .


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