Research ArticleFast Enhanced Exemplar-Based Clustering for IncompleteEEG Signals

Anqi Bi Wenhao Ying and Lu Zhao

School of Computer Science and Engineering Changshu Institute of Technology Changshu Jiangsu China

Correspondence should be addressed to Lu Zhao constancecslgeducn

Received 16 January 2020 Accepted 27 February 2020 Published 8 May 2020

Guest Editor Chenxi Huang

Copyright copy 2020 Anqi Bi et alis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e diagnosis and treatment of epilepsy is a significant direction for both machine learning and brain science is paper newlyproposes a fast enhanced exemplar-based clustering (FEEC) method for incomplete EEG signal e algorithm first compressesthe potential exemplar list and reduces the pairwise similaritymatrix By processing themost complete data in the first stage FEECthen extends the few incomplete data into the exemplar list A new compressed similarity matrix will be constructed and the scaleof this matrix is greatly reduced Finally FEEC optimizes the new target function by the enhanced α-expansion move method Onthe other hand due to the pairwise relationship FEEC also improves the generalization of this algorithm In contrast to otherexemplar-based models the performance of the proposed clustering algorithm is comprehensively verified by the experiments ontwo datasets

1 Introduction

Epilepsy is a common disease of nervous system which ischaracterized by sudden brain dysfunction Although thereare many other neuroimaging modalities for the recognitionof brain activity EEG signals have a high temporal reso-lution which is up to themillisecond level and its acquisitionequipment is inexpensive portable and noninvasiveNowadays most diagnoses of epilepsy are based on clinicalexperience and the analysis of electroencephalogram (EEG)signals Compared withmanual diagnostic method machinelearning methods are less time-consuming and more con-sistent [1ndash6] Specifically many machine learning methodssuch as support vector learning [7 8] TakagindashSugenondashKang(TSK) fuzzy system [9 10] and Naıve Bayes [11] have beenapplied

As we know that brain activity is a nonlinear unstablecomplex network system EEG signals we usually get arecomplicated at is to say some EEG signals are completewhile others may miss some features namely incompleteerefore recognition of epilepsy based on machinelearning models will be more promising compared withclinical diagnosis depending on experience Moreover EEG

signals have the characteristics of high dimension andstochasticity which limit the performance of most existingclustering models such as k-means [11] and fuzzy c mean(fcm) [12] K-means and fcm clustering models need topreset the number of clusters in advance More specificallythe performance of the k-means model relies on the ini-tialization of data while the fcm model requires high in-terpretability us we focus on the exemplar-basedclustering model [13] which is proposed by Frey in thispaper e exemplar-based clustering model has the ad-vantages of automatically obtaining the cluster number highefficiency and not relying on the initialization of data

In conclusion we consider the scenario of EEG signalsconsisting of most complete data and few incomplete data inthis paper as shown in Figure 1 Based on the previous workabout the recognition of epileptic signals we propose a novelfast enhanced exemplar-based clustering (FEEC) model forincomplete EEG signals As shown in Figure 1 differentfrom existing exemplar-based clustering models FEECcompresses the exemplar list and reduces the pairwisesimilarity matrix and then FEEC optimizes the target modelby the enhanced α-expansion move framework Moreoverthe contributions of this paper can be highlighted as follows

HindawiComputational and Mathematical Methods in MedicineVolume 2020 Article ID 4147807 11 pageshttpsdoiorg10115520204147807

(1) We extend the existing exemplar-based clusteringalgorithm into a fast version by compressing thepotential exemplar lists in this study FEEC com-presses the number of potential exemplars by pro-cessing the most complete data in the first stage andextends the few incomplete data into the exemplarlist So the complexity of FEEC is reduced as well

(2) Along with most existing exemplar-based clusteringmodels FEEC is built on the pairwise similaritymatrix of dataus after compression FEEC wouldconstruct a new reduced similarity matrix and thegeneralization of this algorithm is improved

(3) Moreover this paper also considers the fact that thegraph cuts [14] based optimization performs betterthan those loopy belief propagation (LBP) [15] basedstructure So the proposed FEEC algorithm opti-mizes the target model by the enhanced α-expansionmove framework [16 17]

(4) Experimental results of both synthetic and real-world datasets indicate the promising efficiency ofthe proposed FEEC algorithm

e rest of this paper is listed as follows In Section 2 weintroduce some static exemplar-based clustering modelsSection 3 discusses the proposed FEEC algorithm step by

step In Section 4 we analyze the experimental results andthe comparison of FEEC and other existingmethods Section5 concludes this whole paper

2 Background

Since EEG signal feature extraction methods and exemplar-based clustering models are two important supportingtheories for the FEEC model in this study we will brieflyintroduce several feature extraction methods and exemplar-based clustering models in this section

21 Feature Extraction Methods Original EEG signals havethe characteristics of high dimensionality stochasticity andnonlinearity It would be computationally very expensive toextract features from raw EEG signals nowadays manyfeature extraction methods have been proposed to handlethis problem In sum there are three categories ie time-domain features frequency-domain features and time-frequency features

More specifically in time-domain analysis statisticscomponent features of the raw EEG signals will be analyzed[18] In frequency-domain analysis power spectrum analysisand short-time Fourier transform (STFT) [19 20] arecommonly used In time-frequency analysis time and

Few incomplete data

Most complete data

Potential exemplarsmarked as the dark ones

Obtained exemplars

Cluster result

Figure 1 Clustering procedure of FEEC algorithm

2 Computational and Mathematical Methods in Medicine

frequency domain are simultaneously extracted from non-stationary EEG signals Wavelet and other improved ver-sions [21 22] are widely used in EEG signal processing Weutilize KPCA to extract feature in this paper

22 Exemplar-Based Clustering Models Exemplar-basedclustering models select cluster centers namely exemplarsfrom existing actual data We focus on exemplar-basedclustering models in this paper and briefly introduce affinitypropagation (AP) [13] and enhanced α-expansion move(EEM) [17] in this section And several extended versions fordifferent scenarios are shown in Table 1 e target fucntiondefined by exemplar-based clustering model equals to theminimization problem of energy function of Markov ran-dom field(MRF) Two existing optimization startegies havebeen utilized and evolved into AP and EEM frameworksaccordingly Moreover loopy belief propagation (LBP) [23]is used in AP while graph cuts technique [15] is used inEEM respectively

221 Affinity Propagation AP is based on message passingamong data points and its target function is defined asfollows

maxE

1113944

N

p1S(i k) minus 1113944

N

p1δp(E) (1)

where

δp(E) infin if E xp1113872 1113873nep butexistxq E xp1113872 1113873 p

0 otherwise

⎧⎨

⎩ (2)

where X x1 x2 xN1113864 1113865 isin RNlowastD is an input dataset andN is the total number ofD-dimensional data points SE is theoutput of this framework and the element E(xp) is referredto the exemplar for each xp

According to AP each point receives availability mes-sage A(i k) and sends responsibility R(i k) message si-multaneously which are defined as follows

R(i k) S(i k) minus maxjst jnek

A(i j) + S(i j)1113864 1113865 (3)

A(i k)

min1113864 0R(k k) + 1113944jstjne ik

max(0R(j k))1113864 1113865 ine k

1113944jst jne ik

max(0R(j k))1113864 1113865 i k

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(4)

where S is the similarity matrix of data points and is definedas S(i j) minus xi minus xj

2 Meanwhile S(k k) p where p isnamed as preferences in this framework Moreover its valueshould be independent and can be set to a constant

AP does not require presetting the number of the clusterand the performance is stable Considering these advantagesmany extended versions of AP have been proposed [24 25]Specifically AP defines fading factor to adjust the iterationspeed adAP [24] is proposed to determine this fading factoradaptively Moreover several extended versions of APmethodshave been proposed to deal with large data and link constraintsFor instance IAPKM IAPNA and IAPC [26 27] employincremental strategy and semisupervised AP and SSAP [28]concentrate on instance-level constraints A two-stage fastversion of AP (FAP) [29] is also proposed to improve theefficiency However although AP has been obtaining its success

in various applications whenwe attempt to directly apply AP toincomplete EEG signals the performance is unsatisfactory

222 Enhanced α-Expansion Move In 2014 Zheng andChen [17] utilized enhanced α-expansion move frame-work to optimize the object function of exemplar-basedclustering models and accordingly proposed the EEMclustering model In line with the mathematical sym-bols above the target function of EEM is defined asfollows

maxE

1113944

N

p1s xp x

E xp( 11138571113874 1113875 minus 1113944N

p11113944

N

qgtp

θpq E xp1113872 1113873 E xq1113872 11138731113872 1113873 (5)

where

θpq E xp1113872 1113873 E xq1113872 11138731113872 1113873 M E xp1113872 1113873 q E xq1113872 1113873ne q orE xq1113872 1113873 p E xp1113872 1113873nep

0 otherwise

⎧⎨

⎩ (6)

θpq E xp1113872 1113873 E xq1113872 11138731113872 1113873 + θpq(α α)le θpq E xp1113872 1113873 α1113872 1113873 + θpq α E xq1113872 11138731113872 1113873 (7)

In terms of [17] α-expansion move algorithm has beenproved to be effective in the optimization of the target

function equation (5) Specifically whenforallp q E(xp) E(xq) α isin 1 2 N equation (7) is verified

Computational and Mathematical Methods in Medicine 3

Furthermore according to graph theory in the fast α-ex-pansion move algorithm the expansion range is limited in aone exemplar To break this limit the EEM model enlargesthe range to the whole exemplar set E when optimizing anddefines a second exemplar S(i) for each point xi as follows

S(i) argmaxsisin(El)

d xi xs( 1113857 forallxi isin Xl (8)

where Xl xi | E(xi l)1113864 1113865 is the dataset among which theexemplar is l and s isin (El) represents other exemplars in E

except for le EEM clustering model is a state-of-the-art

achievement of exemplar-based clustering model and hasbeen proved to be efficient and effective for numerousscenarios [16 17 30] IEEM [30] is proposed to deal withlink constraints by embedding a bound term in the targetfunction For dynamic data stream Bi and Wang [16] alsoproposed an incremental EEM version DSC which processesdata chunk by chunk However for incomplete EEG signalsthese methods would not recognize epilepsy well

3 Fast Enhanced Exemplar-BasedClustering Model

In this section the proposed FEEC model will be stated andtheoretically analyzed in detail We first compress the ex-emplar list and reduce the pairwise similarity matrix andthen the target model is optimized by the enhanced α-ex-pansion move framework

31 Framework As mentioned in the introduction sectionwe focus on the incomplete EEG signals which consist ofmost complete data and few incomplete data To improve theefficiency of the EEM clustering model for these incompleteEEG signals the proposed FEEC framework includes twostages namely compression stage and optimization stageAs shown in Figure 2 the compression stage compresses thepotential exemplar list and the optimization stage deter-mines the optimal exemplars from the potential exemplarlist Accordingly the target function can be defined asfollows

maxE

1113944

N

i1s xi xE xi( )1113874 1113875 minus 1113944

N

i1ηi(E) (9)

where X [XcXl] is the input dataset consisting of mostcomplete data Xc xc1 xc2 xcNc

1113966 1113967 and few incompletedata Xl xl1 xl2 xlNl

1113966 1113967 e total number of data is

defined as N Nc + Nl where Nc and Nl are the number ofcomplete and incomplete data respectively Remember thatwe only consider the scenario that Nc≫Nl in this studyesecond term in equation (9) guarantees the validity of theexemplar list its definition is similar to that of δ in equation(2) In the end E E(x1) E(x2) E(xN)1113864 1113865 represents theexemplar set in question

In the compression stage the number of potential ex-emplar list will be reduced by exemplar-based selectionalgorithm namely EEMmethod in this study To be specificwe apply the EEM model on the most complete data toobtain the potential exemplars for these data FEEC alsopulls the few incomplete data into this potential exemplar listand then constructs compressed similarity matrix ere-fore after compression only the pairwise similarities be-tween data and potential exemplars would be preservedConsidering that the FEEC method is built on the pairwisesimilarity matrix the following clustering procedure wouldbe applied on this compressed similarity matrix Further-more the scale of similarity matrix is reduced from N2 toNc where N and c are the number of data and potentialexemplars respectively

In the optimization stage only the similarity relationshipbetween data and potential exemplars is considerede newtarget function after compression is similar to that of otherexemplar-based clustering model like equations (1) and (5)so we take graph cuts and LBP into account Neverthelessgraph cuts based optimization framework outperforms LBPstructure [31] So the proposed FEEC utilizes the α-ex-pansion move method to optimize the new target functionMoreover along with EEM FEEC also expands the ex-pansion move space from a single data to the second optimalexemplar

32 Compression Stage In the compression stage the targetfunction of complete data can be defined as follows

minEc

1113944

Nc

i1d xci xEc xci( )1113874 1113875 + 1113944

Nc

i11113944

Nc

jgt i

θij Ec xci1113872 1113873 Ec xcj1113872 11138731113872 1113873

(10)

where Xc xc1 xc2 xcNc1113966 1113967 isin RNc lowastD is the complete D-

dimensional data and Nc is the number of these data Ec isthe potential exemplar list for most complete data and theelement among E(xci) is referred to the potential exemplarfor each xci e optimization framework of other exemplar-based clustering models like EEM can be utilized to solve

Table 1 Descriptions of several state-of-the-art exemplar-based algorithms

Optimization Extended version Descriptions

AP Message-passing

adAP Determine fading factor adaptivelyIAPKM IAPNA IAPC Incremental version for data stream

SAPSSAP Deal with instance-level constraintsFAP Two-stage fast version

EEM Graph cutsDSC Dynamic data stream clusterIEEM Deal with link constraints

FEEC (newly proposed) Two-stage fast version

4 Computational and Mathematical Methods in Medicine

equation (10) In this paper we select the graph cuts al-gorithm instead of message-passing algorithm to compressthe potential exemplar list us the potential exemplar listfor complete data Ec can be determined and the number ofpotential exemplars is defined as cc

e potential exemplar list after compression stagewould be

Enew Ec El1113858 1113859 (11)

where El is the exemplar set for the few incomplete datawhich is the incomplete data itself actually at is to sayEl(xli) i

In this stage we reduced the number of potential ex-emplars from Nc to cc In terms of the analysis in [13 17 30]the time complexity of this stage will be O(N2

c) Comparedwith the time complexity O(N2) if we apply exemplar-basedclustering model directly considering the fact that NltNcthe time complexity of this compression algorithm would beacceptable

erefore on the basis of the new exemplar list aftercompression we can construct the new similarity matrixSnew isin RNtimesc the element relates to the distance namelySnew(i j) minus xi minus xEnew(j)

2 e scale of the similaritymatrix reduces from N2 to Nc where c cc + Nl representsthe number of potential exemplars

33 Optimization Stage After compression we define thenew target function as follows

maxE

1113944

N

i11113944

c

j1Snew(i j) minus 1113944

N

i1ηi(E) (12)

where Snew is the new similarity matrix constructed aftercompression

In this section we construct an optimization frameworkfor equation (12) e second term of equation (12) is set toguarantee the validity of the exemplar list in order to utilizethe graph cuts based method this term should be pairwise[17] So ηi(E) is modified as ηij(E) Furthermore similar toequation (5) we define ηij(E) as follows

ηij(E) M E xi( 1113857 j E xj1113872 1113873ne j orE xj1113872 1113873 i E xi( 1113857ne i

0 otherwise

⎧⎨

⎩

(13)

It has been proved that with the definition of ηij(E)equation (12) can be optimized by the enhanced α-expansionmethod [30] To improve the efficiency of framework thismethod enlarges the expansion move to the second optimalexemplar

Before optimization we explain several symbols in-volved First we defineXe as those data with exemplar xe andxα as the current potential exemplar en the enhancedα-expansion move method considers the second optimalexemplar which is defined as

S xi( 1113857 argmaxsisin(Eα)

Snew xi xs( 1113857 forallxi isin Xα (14)

where (Eα) is the potential exemplar list except for αApparently this optimization method should consider

two cases namely xe is among exemplar list or not asshown in Figures 3 and 4 To be specific Figure 3 illus-trates the case when xα is an exemplar while Figure 4shows the case when xα is not an exemplar Rememberthat only when xα is a potential exemplar S(xi) works Weutilize the concepts of ldquoenergy reductionrdquo because thismethod was first used to optimize the Markov randomfield (MRF) energy function

In the situation shown in Figure 3 either forallxi isin Xαchanges its exemplar to S(xi) or nothing is changederefore the energy reduction R1 would be defined as

R1 max 0 R1α( 1113857 (15)

where R1α is the energy reduction when forallxi isin Xα changes itsexemplar to S(xi) and is defined as

R1α 1113944xiisinXα

Snew xi S xi( 1113857( 1113857 minus Snew xi xα( 1113857( 1113857 (16)

On the other hand as shown in Figure 4 a new exemplarxα should be considered Whether to accept the new ex-emplar is decided by the energy reduction R2 which will bediscussed next First we assume a new exemplar xα is ac-cepted In fact the following procedure is similar to thatshown in Figure 3 Specially the remaining data wouldchange its exemplar to either xα or S(xi) For data in clustere isin E theoretical analysis proves that only when the ex-emplar xe changes its exemplar forallxi isin Xe would change itsexemplar as S(xi) In this case the energy reduction isdefined as follows

R2e 1113944xiisinXe

Snew xi S xi( 1113857( 1113857 minus Snew xi xe( 1113857( 1113857 (17)

Otherwise some data in cluster e may change theirexemplar as xα we define these data as Xe

eα and the cor-responding energy reduction R2e is defined in the followingequation

R2α 1113944

xiisinXeeα

Snew xi xα( 1113857 minus Snew xi xe( 1113857( 1113857(18)

en the energy reduction R2 is defined as follows

Compression Optimization

Exemplar list Potential exemplar list Exemplar

Figure 2 Framework of FEEC algorithm compression stage and optimization stage

Computational and Mathematical Methods in Medicine 5

R2 Snew xα xα( 1113857 minus Snew xα xEnew(α)1113872 1113873 + max 1113944eisinE

R2e R2α1113864 1113865

(19)

In sum the new target function equation (12) is opti-mized and the optimal exemplar list for the EEG signals isgenerated

34 Time Complexity and Description e similarity rela-tionship can be measured by Euclidean distance betweendata defined as d(xi xj) in this study e proposed algo-rithm FEEC consists of two stages namely compressionstage and optimization stage After compression the scale ofsimilarity matrix reduces from N2 to Nc so the optimizationstage has the time complexity of O(c2) erefore thecomplexity of FEEC is considerably promising

Based on the theoretical analysis above the proposedFEEC for incomplete data can be summarized asAlgorithm 1

4 Experimental Study

To comprehensively evaluate the proposed algorithm FEECwe have conducted several experiments based on bothsynthetic and real datasets We also compare our new modelwith basic exemplar-based clusteringmodel namely AP andEEM to show these experimental results we choose fourperformance indices in this section In our experiments allthe algorithms were implemented using 2010a Matlab on aPCwith 64 bit MicrosoftWindows 10 an Intel(R) Core(TM)i7-4712MQ and 8GB memory

41 Data Preparation We choose Aggregation [32] as shownin Figure 5 and the BonnEEG signal datasets in this sectioneBonn dataset [9 10] is from the University of Bonn Germany(httpepileptologie-bonndecmsuploadworkgrouplehnertzeegdatahtml)e EEG dataset contains five groups (A to E andeach group contains 100 single channel EEG segments of 236sduration e sampling rate of all the datasets was 1736HzFigure6 shows five healthy and epileptic EEG signals and Ta-ble 2 lists detailed descriptions of these signals Table 3 shows abrief description of these datasets To construct the incompletedata scenario we randomly choose 80 data as complete dataand the remaining 20 as the incomplete dataWe utilize KPCAto extract features from EEG signals in this section

42 Performance Indices Here we give the definitions of thethree adopted performance indices ENERGY NMI andaccuracy Along with the description in [12 16 30 33 34]we call the result outputted by these involved models ascluster and the true labels as class

421 ENERGY Since all the mentioned clustering algo-rithms are optimized respectively by the energy functionsof the same type we can compare them in terms of theirenergy values defined as follows

ENERGY 1113944k

1113944i

d xk xki1113872 1113873 (20)

where xk denotes the kth exemplar xki is the ith data point inkth cluster and d(xk xki) is the Euclidean distance between xk

and xki which can be seen as a measurement of energy

Enhanced optimizationmethod

Figure 3 Case (i) xα is an exemplar

Enhanced optimizationmethod

Figure 4 Case (ii) xα is not an exemplar

6 Computational and Mathematical Methods in Medicine

frequency domain are simultaneously extracted from non-stationary EEG signals Wavelet and other improved ver-sions [21 22] are widely used in EEG signal processing Weutilize KPCA to extract feature in this paper

22 Exemplar-Based Clustering Models Exemplar-basedclustering models select cluster centers namely exemplarsfrom existing actual data We focus on exemplar-basedclustering models in this paper and briefly introduce affinitypropagation (AP) [13] and enhanced α-expansion move(EEM) [17] in this section And several extended versions fordifferent scenarios are shown in Table 1 e target fucntiondefined by exemplar-based clustering model equals to theminimization problem of energy function of Markov ran-dom field(MRF) Two existing optimization startegies havebeen utilized and evolved into AP and EEM frameworksaccordingly Moreover loopy belief propagation (LBP) [23]is used in AP while graph cuts technique [15] is used inEEM respectively

221 Affinity Propagation AP is based on message passingamong data points and its target function is defined asfollows

maxE

1113944

N

p1S(i k) minus 1113944

N

p1δp(E) (1)

where

δp(E) infin if E xp1113872 1113873nep butexistxq E xp1113872 1113873 p

0 otherwise

⎧⎨

⎩ (2)

where X x1 x2 xN1113864 1113865 isin RNlowastD is an input dataset andN is the total number ofD-dimensional data points SE is theoutput of this framework and the element E(xp) is referredto the exemplar for each xp

According to AP each point receives availability mes-sage A(i k) and sends responsibility R(i k) message si-multaneously which are defined as follows

R(i k) S(i k) minus maxjst jnek

A(i j) + S(i j)1113864 1113865 (3)

A(i k)

min1113864 0R(k k) + 1113944jstjne ik

max(0R(j k))1113864 1113865 ine k

1113944jst jne ik

max(0R(j k))1113864 1113865 i k

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(4)

where S is the similarity matrix of data points and is definedas S(i j) minus xi minus xj

2 Meanwhile S(k k) p where p isnamed as preferences in this framework Moreover its valueshould be independent and can be set to a constant

AP does not require presetting the number of the clusterand the performance is stable Considering these advantagesmany extended versions of AP have been proposed [24 25]Specifically AP defines fading factor to adjust the iterationspeed adAP [24] is proposed to determine this fading factoradaptively Moreover several extended versions of APmethodshave been proposed to deal with large data and link constraintsFor instance IAPKM IAPNA and IAPC [26 27] employincremental strategy and semisupervised AP and SSAP [28]concentrate on instance-level constraints A two-stage fastversion of AP (FAP) [29] is also proposed to improve theefficiency However although AP has been obtaining its success

in various applications whenwe attempt to directly apply AP toincomplete EEG signals the performance is unsatisfactory

222 Enhanced α-Expansion Move In 2014 Zheng andChen [17] utilized enhanced α-expansion move frame-work to optimize the object function of exemplar-basedclustering models and accordingly proposed the EEMclustering model In line with the mathematical sym-bols above the target function of EEM is defined asfollows

maxE

1113944

N

p1s xp x

E xp( 11138571113874 1113875 minus 1113944N

p11113944

N

qgtp

θpq E xp1113872 1113873 E xq1113872 11138731113872 1113873 (5)

where

θpq E xp1113872 1113873 E xq1113872 11138731113872 1113873 M E xp1113872 1113873 q E xq1113872 1113873ne q orE xq1113872 1113873 p E xp1113872 1113873nep

0 otherwise

⎧⎨

⎩ (6)

θpq E xp1113872 1113873 E xq1113872 11138731113872 1113873 + θpq(α α)le θpq E xp1113872 1113873 α1113872 1113873 + θpq α E xq1113872 11138731113872 1113873 (7)

In terms of [17] α-expansion move algorithm has beenproved to be effective in the optimization of the target

function equation (5) Specifically whenforallp q E(xp) E(xq) α isin 1 2 N equation (7) is verified

Computational and Mathematical Methods in Medicine 3

Furthermore according to graph theory in the fast α-ex-pansion move algorithm the expansion range is limited in aone exemplar To break this limit the EEM model enlargesthe range to the whole exemplar set E when optimizing anddefines a second exemplar S(i) for each point xi as follows

S(i) argmaxsisin(El)

d xi xs( 1113857 forallxi isin Xl (8)

where Xl xi | E(xi l)1113864 1113865 is the dataset among which theexemplar is l and s isin (El) represents other exemplars in E

except for le EEM clustering model is a state-of-the-art

achievement of exemplar-based clustering model and hasbeen proved to be efficient and effective for numerousscenarios [16 17 30] IEEM [30] is proposed to deal withlink constraints by embedding a bound term in the targetfunction For dynamic data stream Bi and Wang [16] alsoproposed an incremental EEM version DSC which processesdata chunk by chunk However for incomplete EEG signalsthese methods would not recognize epilepsy well

3 Fast Enhanced Exemplar-BasedClustering Model

In this section the proposed FEEC model will be stated andtheoretically analyzed in detail We first compress the ex-emplar list and reduce the pairwise similarity matrix andthen the target model is optimized by the enhanced α-ex-pansion move framework

31 Framework As mentioned in the introduction sectionwe focus on the incomplete EEG signals which consist ofmost complete data and few incomplete data To improve theefficiency of the EEM clustering model for these incompleteEEG signals the proposed FEEC framework includes twostages namely compression stage and optimization stageAs shown in Figure 2 the compression stage compresses thepotential exemplar list and the optimization stage deter-mines the optimal exemplars from the potential exemplarlist Accordingly the target function can be defined asfollows

maxE

1113944

N

i1s xi xE xi( )1113874 1113875 minus 1113944

N

i1ηi(E) (9)

where X [XcXl] is the input dataset consisting of mostcomplete data Xc xc1 xc2 xcNc

1113966 1113967 and few incompletedata Xl xl1 xl2 xlNl

1113966 1113967 e total number of data is

defined as N Nc + Nl where Nc and Nl are the number ofcomplete and incomplete data respectively Remember thatwe only consider the scenario that Nc≫Nl in this studyesecond term in equation (9) guarantees the validity of theexemplar list its definition is similar to that of δ in equation(2) In the end E E(x1) E(x2) E(xN)1113864 1113865 represents theexemplar set in question

In the compression stage the number of potential ex-emplar list will be reduced by exemplar-based selectionalgorithm namely EEMmethod in this study To be specificwe apply the EEM model on the most complete data toobtain the potential exemplars for these data FEEC alsopulls the few incomplete data into this potential exemplar listand then constructs compressed similarity matrix ere-fore after compression only the pairwise similarities be-tween data and potential exemplars would be preservedConsidering that the FEEC method is built on the pairwisesimilarity matrix the following clustering procedure wouldbe applied on this compressed similarity matrix Further-more the scale of similarity matrix is reduced from N2 toNc where N and c are the number of data and potentialexemplars respectively

In the optimization stage only the similarity relationshipbetween data and potential exemplars is considerede newtarget function after compression is similar to that of otherexemplar-based clustering model like equations (1) and (5)so we take graph cuts and LBP into account Neverthelessgraph cuts based optimization framework outperforms LBPstructure [31] So the proposed FEEC utilizes the α-ex-pansion move method to optimize the new target functionMoreover along with EEM FEEC also expands the ex-pansion move space from a single data to the second optimalexemplar

32 Compression Stage In the compression stage the targetfunction of complete data can be defined as follows

minEc

1113944

Nc

i1d xci xEc xci( )1113874 1113875 + 1113944

Nc

i11113944

Nc

jgt i

θij Ec xci1113872 1113873 Ec xcj1113872 11138731113872 1113873

(10)

where Xc xc1 xc2 xcNc1113966 1113967 isin RNc lowastD is the complete D-

dimensional data and Nc is the number of these data Ec isthe potential exemplar list for most complete data and theelement among E(xci) is referred to the potential exemplarfor each xci e optimization framework of other exemplar-based clustering models like EEM can be utilized to solve

Table 1 Descriptions of several state-of-the-art exemplar-based algorithms

Optimization Extended version Descriptions

AP Message-passing

adAP Determine fading factor adaptivelyIAPKM IAPNA IAPC Incremental version for data stream

SAPSSAP Deal with instance-level constraintsFAP Two-stage fast version

EEM Graph cutsDSC Dynamic data stream clusterIEEM Deal with link constraints

FEEC (newly proposed) Two-stage fast version

4 Computational and Mathematical Methods in Medicine

equation (10) In this paper we select the graph cuts al-gorithm instead of message-passing algorithm to compressthe potential exemplar list us the potential exemplar listfor complete data Ec can be determined and the number ofpotential exemplars is defined as cc

e potential exemplar list after compression stagewould be

Enew Ec El1113858 1113859 (11)

where El is the exemplar set for the few incomplete datawhich is the incomplete data itself actually at is to sayEl(xli) i

In this stage we reduced the number of potential ex-emplars from Nc to cc In terms of the analysis in [13 17 30]the time complexity of this stage will be O(N2

c) Comparedwith the time complexity O(N2) if we apply exemplar-basedclustering model directly considering the fact that NltNcthe time complexity of this compression algorithm would beacceptable

erefore on the basis of the new exemplar list aftercompression we can construct the new similarity matrixSnew isin RNtimesc the element relates to the distance namelySnew(i j) minus xi minus xEnew(j)

2 e scale of the similaritymatrix reduces from N2 to Nc where c cc + Nl representsthe number of potential exemplars

33 Optimization Stage After compression we define thenew target function as follows

maxE

1113944

N

i11113944

c

j1Snew(i j) minus 1113944

N

i1ηi(E) (12)

where Snew is the new similarity matrix constructed aftercompression

In this section we construct an optimization frameworkfor equation (12) e second term of equation (12) is set toguarantee the validity of the exemplar list in order to utilizethe graph cuts based method this term should be pairwise[17] So ηi(E) is modified as ηij(E) Furthermore similar toequation (5) we define ηij(E) as follows

ηij(E) M E xi( 1113857 j E xj1113872 1113873ne j orE xj1113872 1113873 i E xi( 1113857ne i

0 otherwise

⎧⎨

⎩

(13)

It has been proved that with the definition of ηij(E)equation (12) can be optimized by the enhanced α-expansionmethod [30] To improve the efficiency of framework thismethod enlarges the expansion move to the second optimalexemplar

Before optimization we explain several symbols in-volved First we defineXe as those data with exemplar xe andxα as the current potential exemplar en the enhancedα-expansion move method considers the second optimalexemplar which is defined as

S xi( 1113857 argmaxsisin(Eα)

Snew xi xs( 1113857 forallxi isin Xα (14)

where (Eα) is the potential exemplar list except for αApparently this optimization method should consider

two cases namely xe is among exemplar list or not asshown in Figures 3 and 4 To be specific Figure 3 illus-trates the case when xα is an exemplar while Figure 4shows the case when xα is not an exemplar Rememberthat only when xα is a potential exemplar S(xi) works Weutilize the concepts of ldquoenergy reductionrdquo because thismethod was first used to optimize the Markov randomfield (MRF) energy function

In the situation shown in Figure 3 either forallxi isin Xαchanges its exemplar to S(xi) or nothing is changederefore the energy reduction R1 would be defined as

R1 max 0 R1α( 1113857 (15)

where R1α is the energy reduction when forallxi isin Xα changes itsexemplar to S(xi) and is defined as

R1α 1113944xiisinXα

Snew xi S xi( 1113857( 1113857 minus Snew xi xα( 1113857( 1113857 (16)

On the other hand as shown in Figure 4 a new exemplarxα should be considered Whether to accept the new ex-emplar is decided by the energy reduction R2 which will bediscussed next First we assume a new exemplar xα is ac-cepted In fact the following procedure is similar to thatshown in Figure 3 Specially the remaining data wouldchange its exemplar to either xα or S(xi) For data in clustere isin E theoretical analysis proves that only when the ex-emplar xe changes its exemplar forallxi isin Xe would change itsexemplar as S(xi) In this case the energy reduction isdefined as follows

R2e 1113944xiisinXe

Snew xi S xi( 1113857( 1113857 minus Snew xi xe( 1113857( 1113857 (17)

Otherwise some data in cluster e may change theirexemplar as xα we define these data as Xe

eα and the cor-responding energy reduction R2e is defined in the followingequation

R2α 1113944

xiisinXeeα

Snew xi xα( 1113857 minus Snew xi xe( 1113857( 1113857(18)

en the energy reduction R2 is defined as follows

Compression Optimization

Exemplar list Potential exemplar list Exemplar

Figure 2 Framework of FEEC algorithm compression stage and optimization stage

Computational and Mathematical Methods in Medicine 5

R2 Snew xα xα( 1113857 minus Snew xα xEnew(α)1113872 1113873 + max 1113944eisinE

R2e R2α1113864 1113865

(19)

In sum the new target function equation (12) is opti-mized and the optimal exemplar list for the EEG signals isgenerated

34 Time Complexity and Description e similarity rela-tionship can be measured by Euclidean distance betweendata defined as d(xi xj) in this study e proposed algo-rithm FEEC consists of two stages namely compressionstage and optimization stage After compression the scale ofsimilarity matrix reduces from N2 to Nc so the optimizationstage has the time complexity of O(c2) erefore thecomplexity of FEEC is considerably promising

Based on the theoretical analysis above the proposedFEEC for incomplete data can be summarized asAlgorithm 1

4 Experimental Study

To comprehensively evaluate the proposed algorithm FEECwe have conducted several experiments based on bothsynthetic and real datasets We also compare our new modelwith basic exemplar-based clusteringmodel namely AP andEEM to show these experimental results we choose fourperformance indices in this section In our experiments allthe algorithms were implemented using 2010a Matlab on aPCwith 64 bit MicrosoftWindows 10 an Intel(R) Core(TM)i7-4712MQ and 8GB memory

41 Data Preparation We choose Aggregation [32] as shownin Figure 5 and the BonnEEG signal datasets in this sectioneBonn dataset [9 10] is from the University of Bonn Germany(httpepileptologie-bonndecmsuploadworkgrouplehnertzeegdatahtml)e EEG dataset contains five groups (A to E andeach group contains 100 single channel EEG segments of 236sduration e sampling rate of all the datasets was 1736HzFigure6 shows five healthy and epileptic EEG signals and Ta-ble 2 lists detailed descriptions of these signals Table 3 shows abrief description of these datasets To construct the incompletedata scenario we randomly choose 80 data as complete dataand the remaining 20 as the incomplete dataWe utilize KPCAto extract features from EEG signals in this section

42 Performance Indices Here we give the definitions of thethree adopted performance indices ENERGY NMI andaccuracy Along with the description in [12 16 30 33 34]we call the result outputted by these involved models ascluster and the true labels as class

421 ENERGY Since all the mentioned clustering algo-rithms are optimized respectively by the energy functionsof the same type we can compare them in terms of theirenergy values defined as follows

ENERGY 1113944k

1113944i

d xk xki1113872 1113873 (20)

where xk denotes the kth exemplar xki is the ith data point inkth cluster and d(xk xki) is the Euclidean distance between xk

and xki which can be seen as a measurement of energy

Enhanced optimizationmethod

Figure 3 Case (i) xα is an exemplar

Enhanced optimizationmethod

Figure 4 Case (ii) xα is not an exemplar

6 Computational and Mathematical Methods in Medicine

Furthermore according to graph theory in the fast α-ex-pansion move algorithm the expansion range is limited in aone exemplar To break this limit the EEM model enlargesthe range to the whole exemplar set E when optimizing anddefines a second exemplar S(i) for each point xi as follows

S(i) argmaxsisin(El)

d xi xs( 1113857 forallxi isin Xl (8)

where Xl xi | E(xi l)1113864 1113865 is the dataset among which theexemplar is l and s isin (El) represents other exemplars in E

except for le EEM clustering model is a state-of-the-art

achievement of exemplar-based clustering model and hasbeen proved to be efficient and effective for numerousscenarios [16 17 30] IEEM [30] is proposed to deal withlink constraints by embedding a bound term in the targetfunction For dynamic data stream Bi and Wang [16] alsoproposed an incremental EEM version DSC which processesdata chunk by chunk However for incomplete EEG signalsthese methods would not recognize epilepsy well

3 Fast Enhanced Exemplar-BasedClustering Model

In this section the proposed FEEC model will be stated andtheoretically analyzed in detail We first compress the ex-emplar list and reduce the pairwise similarity matrix andthen the target model is optimized by the enhanced α-ex-pansion move framework

31 Framework As mentioned in the introduction sectionwe focus on the incomplete EEG signals which consist ofmost complete data and few incomplete data To improve theefficiency of the EEM clustering model for these incompleteEEG signals the proposed FEEC framework includes twostages namely compression stage and optimization stageAs shown in Figure 2 the compression stage compresses thepotential exemplar list and the optimization stage deter-mines the optimal exemplars from the potential exemplarlist Accordingly the target function can be defined asfollows

maxE

1113944

N

i1s xi xE xi( )1113874 1113875 minus 1113944

N

i1ηi(E) (9)

where X [XcXl] is the input dataset consisting of mostcomplete data Xc xc1 xc2 xcNc

1113966 1113967 and few incompletedata Xl xl1 xl2 xlNl

1113966 1113967 e total number of data is

defined as N Nc + Nl where Nc and Nl are the number ofcomplete and incomplete data respectively Remember thatwe only consider the scenario that Nc≫Nl in this studyesecond term in equation (9) guarantees the validity of theexemplar list its definition is similar to that of δ in equation(2) In the end E E(x1) E(x2) E(xN)1113864 1113865 represents theexemplar set in question

In the compression stage the number of potential ex-emplar list will be reduced by exemplar-based selectionalgorithm namely EEMmethod in this study To be specificwe apply the EEM model on the most complete data toobtain the potential exemplars for these data FEEC alsopulls the few incomplete data into this potential exemplar listand then constructs compressed similarity matrix ere-fore after compression only the pairwise similarities be-tween data and potential exemplars would be preservedConsidering that the FEEC method is built on the pairwisesimilarity matrix the following clustering procedure wouldbe applied on this compressed similarity matrix Further-more the scale of similarity matrix is reduced from N2 toNc where N and c are the number of data and potentialexemplars respectively

In the optimization stage only the similarity relationshipbetween data and potential exemplars is considerede newtarget function after compression is similar to that of otherexemplar-based clustering model like equations (1) and (5)so we take graph cuts and LBP into account Neverthelessgraph cuts based optimization framework outperforms LBPstructure [31] So the proposed FEEC utilizes the α-ex-pansion move method to optimize the new target functionMoreover along with EEM FEEC also expands the ex-pansion move space from a single data to the second optimalexemplar

32 Compression Stage In the compression stage the targetfunction of complete data can be defined as follows

minEc

1113944

Nc

i1d xci xEc xci( )1113874 1113875 + 1113944

Nc

i11113944

Nc

jgt i

θij Ec xci1113872 1113873 Ec xcj1113872 11138731113872 1113873

(10)

where Xc xc1 xc2 xcNc1113966 1113967 isin RNc lowastD is the complete D-

dimensional data and Nc is the number of these data Ec isthe potential exemplar list for most complete data and theelement among E(xci) is referred to the potential exemplarfor each xci e optimization framework of other exemplar-based clustering models like EEM can be utilized to solve

Table 1 Descriptions of several state-of-the-art exemplar-based algorithms

Optimization Extended version Descriptions

AP Message-passing

adAP Determine fading factor adaptivelyIAPKM IAPNA IAPC Incremental version for data stream

SAPSSAP Deal with instance-level constraintsFAP Two-stage fast version

EEM Graph cutsDSC Dynamic data stream clusterIEEM Deal with link constraints

FEEC (newly proposed) Two-stage fast version

4 Computational and Mathematical Methods in Medicine

equation (10) In this paper we select the graph cuts al-gorithm instead of message-passing algorithm to compressthe potential exemplar list us the potential exemplar listfor complete data Ec can be determined and the number ofpotential exemplars is defined as cc

e potential exemplar list after compression stagewould be

Enew Ec El1113858 1113859 (11)

where El is the exemplar set for the few incomplete datawhich is the incomplete data itself actually at is to sayEl(xli) i

In this stage we reduced the number of potential ex-emplars from Nc to cc In terms of the analysis in [13 17 30]the time complexity of this stage will be O(N2

c) Comparedwith the time complexity O(N2) if we apply exemplar-basedclustering model directly considering the fact that NltNcthe time complexity of this compression algorithm would beacceptable

erefore on the basis of the new exemplar list aftercompression we can construct the new similarity matrixSnew isin RNtimesc the element relates to the distance namelySnew(i j) minus xi minus xEnew(j)

2 e scale of the similaritymatrix reduces from N2 to Nc where c cc + Nl representsthe number of potential exemplars

33 Optimization Stage After compression we define thenew target function as follows

maxE

1113944

N

i11113944

c

j1Snew(i j) minus 1113944

N

i1ηi(E) (12)

where Snew is the new similarity matrix constructed aftercompression

In this section we construct an optimization frameworkfor equation (12) e second term of equation (12) is set toguarantee the validity of the exemplar list in order to utilizethe graph cuts based method this term should be pairwise[17] So ηi(E) is modified as ηij(E) Furthermore similar toequation (5) we define ηij(E) as follows

ηij(E) M E xi( 1113857 j E xj1113872 1113873ne j orE xj1113872 1113873 i E xi( 1113857ne i

0 otherwise

⎧⎨

⎩

(13)

It has been proved that with the definition of ηij(E)equation (12) can be optimized by the enhanced α-expansionmethod [30] To improve the efficiency of framework thismethod enlarges the expansion move to the second optimalexemplar

Before optimization we explain several symbols in-volved First we defineXe as those data with exemplar xe andxα as the current potential exemplar en the enhancedα-expansion move method considers the second optimalexemplar which is defined as

S xi( 1113857 argmaxsisin(Eα)

Snew xi xs( 1113857 forallxi isin Xα (14)

where (Eα) is the potential exemplar list except for αApparently this optimization method should consider

two cases namely xe is among exemplar list or not asshown in Figures 3 and 4 To be specific Figure 3 illus-trates the case when xα is an exemplar while Figure 4shows the case when xα is not an exemplar Rememberthat only when xα is a potential exemplar S(xi) works Weutilize the concepts of ldquoenergy reductionrdquo because thismethod was first used to optimize the Markov randomfield (MRF) energy function

In the situation shown in Figure 3 either forallxi isin Xαchanges its exemplar to S(xi) or nothing is changederefore the energy reduction R1 would be defined as

R1 max 0 R1α( 1113857 (15)

where R1α is the energy reduction when forallxi isin Xα changes itsexemplar to S(xi) and is defined as

R1α 1113944xiisinXα

Snew xi S xi( 1113857( 1113857 minus Snew xi xα( 1113857( 1113857 (16)

On the other hand as shown in Figure 4 a new exemplarxα should be considered Whether to accept the new ex-emplar is decided by the energy reduction R2 which will bediscussed next First we assume a new exemplar xα is ac-cepted In fact the following procedure is similar to thatshown in Figure 3 Specially the remaining data wouldchange its exemplar to either xα or S(xi) For data in clustere isin E theoretical analysis proves that only when the ex-emplar xe changes its exemplar forallxi isin Xe would change itsexemplar as S(xi) In this case the energy reduction isdefined as follows

R2e 1113944xiisinXe

Snew xi S xi( 1113857( 1113857 minus Snew xi xe( 1113857( 1113857 (17)

Otherwise some data in cluster e may change theirexemplar as xα we define these data as Xe

eα and the cor-responding energy reduction R2e is defined in the followingequation

R2α 1113944

xiisinXeeα

Snew xi xα( 1113857 minus Snew xi xe( 1113857( 1113857(18)

en the energy reduction R2 is defined as follows

Compression Optimization

Exemplar list Potential exemplar list Exemplar

Figure 2 Framework of FEEC algorithm compression stage and optimization stage

Computational and Mathematical Methods in Medicine 5

R2 Snew xα xα( 1113857 minus Snew xα xEnew(α)1113872 1113873 + max 1113944eisinE

R2e R2α1113864 1113865

(19)

In sum the new target function equation (12) is opti-mized and the optimal exemplar list for the EEG signals isgenerated

34 Time Complexity and Description e similarity rela-tionship can be measured by Euclidean distance betweendata defined as d(xi xj) in this study e proposed algo-rithm FEEC consists of two stages namely compressionstage and optimization stage After compression the scale ofsimilarity matrix reduces from N2 to Nc so the optimizationstage has the time complexity of O(c2) erefore thecomplexity of FEEC is considerably promising

Based on the theoretical analysis above the proposedFEEC for incomplete data can be summarized asAlgorithm 1

4 Experimental Study

To comprehensively evaluate the proposed algorithm FEECwe have conducted several experiments based on bothsynthetic and real datasets We also compare our new modelwith basic exemplar-based clusteringmodel namely AP andEEM to show these experimental results we choose fourperformance indices in this section In our experiments allthe algorithms were implemented using 2010a Matlab on aPCwith 64 bit MicrosoftWindows 10 an Intel(R) Core(TM)i7-4712MQ and 8GB memory

41 Data Preparation We choose Aggregation [32] as shownin Figure 5 and the BonnEEG signal datasets in this sectioneBonn dataset [9 10] is from the University of Bonn Germany(httpepileptologie-bonndecmsuploadworkgrouplehnertzeegdatahtml)e EEG dataset contains five groups (A to E andeach group contains 100 single channel EEG segments of 236sduration e sampling rate of all the datasets was 1736HzFigure6 shows five healthy and epileptic EEG signals and Ta-ble 2 lists detailed descriptions of these signals Table 3 shows abrief description of these datasets To construct the incompletedata scenario we randomly choose 80 data as complete dataand the remaining 20 as the incomplete dataWe utilize KPCAto extract features from EEG signals in this section

42 Performance Indices Here we give the definitions of thethree adopted performance indices ENERGY NMI andaccuracy Along with the description in [12 16 30 33 34]we call the result outputted by these involved models ascluster and the true labels as class

421 ENERGY Since all the mentioned clustering algo-rithms are optimized respectively by the energy functionsof the same type we can compare them in terms of theirenergy values defined as follows

ENERGY 1113944k

1113944i

d xk xki1113872 1113873 (20)

where xk denotes the kth exemplar xki is the ith data point inkth cluster and d(xk xki) is the Euclidean distance between xk

and xki which can be seen as a measurement of energy

Enhanced optimizationmethod

Figure 3 Case (i) xα is an exemplar

Enhanced optimizationmethod

Figure 4 Case (ii) xα is not an exemplar

6 Computational and Mathematical Methods in Medicine

equation (10) In this paper we select the graph cuts al-gorithm instead of message-passing algorithm to compressthe potential exemplar list us the potential exemplar listfor complete data Ec can be determined and the number ofpotential exemplars is defined as cc

e potential exemplar list after compression stagewould be

Enew Ec El1113858 1113859 (11)

where El is the exemplar set for the few incomplete datawhich is the incomplete data itself actually at is to sayEl(xli) i

In this stage we reduced the number of potential ex-emplars from Nc to cc In terms of the analysis in [13 17 30]the time complexity of this stage will be O(N2

c) Comparedwith the time complexity O(N2) if we apply exemplar-basedclustering model directly considering the fact that NltNcthe time complexity of this compression algorithm would beacceptable

erefore on the basis of the new exemplar list aftercompression we can construct the new similarity matrixSnew isin RNtimesc the element relates to the distance namelySnew(i j) minus xi minus xEnew(j)

2 e scale of the similaritymatrix reduces from N2 to Nc where c cc + Nl representsthe number of potential exemplars

33 Optimization Stage After compression we define thenew target function as follows

maxE

1113944

N

i11113944

c

j1Snew(i j) minus 1113944

N

i1ηi(E) (12)

where Snew is the new similarity matrix constructed aftercompression

In this section we construct an optimization frameworkfor equation (12) e second term of equation (12) is set toguarantee the validity of the exemplar list in order to utilizethe graph cuts based method this term should be pairwise[17] So ηi(E) is modified as ηij(E) Furthermore similar toequation (5) we define ηij(E) as follows

ηij(E) M E xi( 1113857 j E xj1113872 1113873ne j orE xj1113872 1113873 i E xi( 1113857ne i

0 otherwise

⎧⎨

⎩

(13)

It has been proved that with the definition of ηij(E)equation (12) can be optimized by the enhanced α-expansionmethod [30] To improve the efficiency of framework thismethod enlarges the expansion move to the second optimalexemplar

Before optimization we explain several symbols in-volved First we defineXe as those data with exemplar xe andxα as the current potential exemplar en the enhancedα-expansion move method considers the second optimalexemplar which is defined as

S xi( 1113857 argmaxsisin(Eα)

Snew xi xs( 1113857 forallxi isin Xα (14)

where (Eα) is the potential exemplar list except for αApparently this optimization method should consider

two cases namely xe is among exemplar list or not asshown in Figures 3 and 4 To be specific Figure 3 illus-trates the case when xα is an exemplar while Figure 4shows the case when xα is not an exemplar Rememberthat only when xα is a potential exemplar S(xi) works Weutilize the concepts of ldquoenergy reductionrdquo because thismethod was first used to optimize the Markov randomfield (MRF) energy function

In the situation shown in Figure 3 either forallxi isin Xαchanges its exemplar to S(xi) or nothing is changederefore the energy reduction R1 would be defined as

R1 max 0 R1α( 1113857 (15)

where R1α is the energy reduction when forallxi isin Xα changes itsexemplar to S(xi) and is defined as

R1α 1113944xiisinXα

Snew xi S xi( 1113857( 1113857 minus Snew xi xα( 1113857( 1113857 (16)

On the other hand as shown in Figure 4 a new exemplarxα should be considered Whether to accept the new ex-emplar is decided by the energy reduction R2 which will bediscussed next First we assume a new exemplar xα is ac-cepted In fact the following procedure is similar to thatshown in Figure 3 Specially the remaining data wouldchange its exemplar to either xα or S(xi) For data in clustere isin E theoretical analysis proves that only when the ex-emplar xe changes its exemplar forallxi isin Xe would change itsexemplar as S(xi) In this case the energy reduction isdefined as follows

R2e 1113944xiisinXe

Snew xi S xi( 1113857( 1113857 minus Snew xi xe( 1113857( 1113857 (17)

Otherwise some data in cluster e may change theirexemplar as xα we define these data as Xe

eα and the cor-responding energy reduction R2e is defined in the followingequation

R2α 1113944

xiisinXeeα

Snew xi xα( 1113857 minus Snew xi xe( 1113857( 1113857(18)

en the energy reduction R2 is defined as follows

Compression Optimization

Exemplar list Potential exemplar list Exemplar

Figure 2 Framework of FEEC algorithm compression stage and optimization stage

Computational and Mathematical Methods in Medicine 5

R2 Snew xα xα( 1113857 minus Snew xα xEnew(α)1113872 1113873 + max 1113944eisinE

R2e R2α1113864 1113865

(19)

In sum the new target function equation (12) is opti-mized and the optimal exemplar list for the EEG signals isgenerated

34 Time Complexity and Description e similarity rela-tionship can be measured by Euclidean distance betweendata defined as d(xi xj) in this study e proposed algo-rithm FEEC consists of two stages namely compressionstage and optimization stage After compression the scale ofsimilarity matrix reduces from N2 to Nc so the optimizationstage has the time complexity of O(c2) erefore thecomplexity of FEEC is considerably promising

Based on the theoretical analysis above the proposedFEEC for incomplete data can be summarized asAlgorithm 1

4 Experimental Study

To comprehensively evaluate the proposed algorithm FEECwe have conducted several experiments based on bothsynthetic and real datasets We also compare our new modelwith basic exemplar-based clusteringmodel namely AP andEEM to show these experimental results we choose fourperformance indices in this section In our experiments allthe algorithms were implemented using 2010a Matlab on aPCwith 64 bit MicrosoftWindows 10 an Intel(R) Core(TM)i7-4712MQ and 8GB memory

41 Data Preparation We choose Aggregation [32] as shownin Figure 5 and the BonnEEG signal datasets in this sectioneBonn dataset [9 10] is from the University of Bonn Germany(httpepileptologie-bonndecmsuploadworkgrouplehnertzeegdatahtml)e EEG dataset contains five groups (A to E andeach group contains 100 single channel EEG segments of 236sduration e sampling rate of all the datasets was 1736HzFigure6 shows five healthy and epileptic EEG signals and Ta-ble 2 lists detailed descriptions of these signals Table 3 shows abrief description of these datasets To construct the incompletedata scenario we randomly choose 80 data as complete dataand the remaining 20 as the incomplete dataWe utilize KPCAto extract features from EEG signals in this section

42 Performance Indices Here we give the definitions of thethree adopted performance indices ENERGY NMI andaccuracy Along with the description in [12 16 30 33 34]we call the result outputted by these involved models ascluster and the true labels as class

421 ENERGY Since all the mentioned clustering algo-rithms are optimized respectively by the energy functionsof the same type we can compare them in terms of theirenergy values defined as follows

ENERGY 1113944k

1113944i

d xk xki1113872 1113873 (20)

where xk denotes the kth exemplar xki is the ith data point inkth cluster and d(xk xki) is the Euclidean distance between xk

and xki which can be seen as a measurement of energy

Enhanced optimizationmethod

Figure 3 Case (i) xα is an exemplar

Enhanced optimizationmethod

Figure 4 Case (ii) xα is not an exemplar

6 Computational and Mathematical Methods in Medicine

R2 Snew xα xα( 1113857 minus Snew xα xEnew(α)1113872 1113873 + max 1113944eisinE

R2e R2α1113864 1113865

(19)

In sum the new target function equation (12) is opti-mized and the optimal exemplar list for the EEG signals isgenerated

34 Time Complexity and Description e similarity rela-tionship can be measured by Euclidean distance betweendata defined as d(xi xj) in this study e proposed algo-rithm FEEC consists of two stages namely compressionstage and optimization stage After compression the scale ofsimilarity matrix reduces from N2 to Nc so the optimizationstage has the time complexity of O(c2) erefore thecomplexity of FEEC is considerably promising

Based on the theoretical analysis above the proposedFEEC for incomplete data can be summarized asAlgorithm 1

4 Experimental Study

To comprehensively evaluate the proposed algorithm FEECwe have conducted several experiments based on bothsynthetic and real datasets We also compare our new modelwith basic exemplar-based clusteringmodel namely AP andEEM to show these experimental results we choose fourperformance indices in this section In our experiments allthe algorithms were implemented using 2010a Matlab on aPCwith 64 bit MicrosoftWindows 10 an Intel(R) Core(TM)i7-4712MQ and 8GB memory

41 Data Preparation We choose Aggregation [32] as shownin Figure 5 and the BonnEEG signal datasets in this sectioneBonn dataset [9 10] is from the University of Bonn Germany(httpepileptologie-bonndecmsuploadworkgrouplehnertzeegdatahtml)e EEG dataset contains five groups (A to E andeach group contains 100 single channel EEG segments of 236sduration e sampling rate of all the datasets was 1736HzFigure6 shows five healthy and epileptic EEG signals and Ta-ble 2 lists detailed descriptions of these signals Table 3 shows abrief description of these datasets To construct the incompletedata scenario we randomly choose 80 data as complete dataand the remaining 20 as the incomplete dataWe utilize KPCAto extract features from EEG signals in this section

42 Performance Indices Here we give the definitions of thethree adopted performance indices ENERGY NMI andaccuracy Along with the description in [12 16 30 33 34]we call the result outputted by these involved models ascluster and the true labels as class

421 ENERGY Since all the mentioned clustering algo-rithms are optimized respectively by the energy functionsof the same type we can compare them in terms of theirenergy values defined as follows

ENERGY 1113944k

1113944i

d xk xki1113872 1113873 (20)

where xk denotes the kth exemplar xki is the ith data point inkth cluster and d(xk xki) is the Euclidean distance between xk

and xki which can be seen as a measurement of energy

Enhanced optimizationmethod

Figure 3 Case (i) xα is an exemplar

Enhanced optimizationmethod

Figure 4 Case (ii) xα is not an exemplar

6 Computational and Mathematical Methods in Medicine

422 NMI NMI has been widely used to evaluate theclustering quality as well and its value can be calculated bythe following equation

NMI 1113936

|C|i1 1113936

|C|j1 Nijln NNijNiNj1113872 1113873

1113936

|C|i1 Niln NiN( 11138571113872 1113873 1113936

|C|j1 Njln NjN1113872 11138731113872 1113873

1113969 (21)

where Nij is how clusters fit the classes Ni is the number ofdata points in ith cluster Nj is the number of data in jthclass and N is the total number of data points

423 Accuracy Accuracy is a more direct measure toreflect the effectiveness of clustering algorithms which isdefined as

accuracy 1113936

Ni1 δ cimap 1113954ci( 1113857( 1113857

N (22)

where ci is the real label of data points and 1113954ci is the obtainedclustering label δ(i j) 1 if i j δ(i j) 0 otherwiseFunction map(middot) maps each obtained cluster to real classand the optimized mapping function can be found inHungarian algorithm

e values of NMI and Acc range from 0 to 1 and themore it is close to 1 the more effective the clustering al-gorithm is What is worth to mention is that we put in thefollowing relevant tables to show better precision As to theperformance index ENERGY the smaller the value is thebetter the clustering algorithm is

43 Experimental Results and Discussion e parametersinvolved FAP AP and EEM are in line with [13 17 29] epreference s(i i) is set to be the median value of similaritiesbetween data We run each algorithm over 10 runs undersame parameters the average results are shown in Table 4Moreover the detailed comparison in terms of the above 3terms NMI accuracy and ENERGY are shown inFigures 7ndash12 and Table 4 respectively

By analyzing Figures 7ndash11 and Table 4 in detail we canconclude the following

Input Given incomplete data X [XcXl] isin RNtimesDXc

Output Valid exemplar set E(1) Compression Apply basic exemplar-based clustering algorithm to the complete data Xc(2) Get the potential exemplar set Enew by equation (11) and construct the new similarity matrix Snew isin RNtimesc(3) Generate the expansion order o on the potential exemplar list Enew(4) Let t 1(5) for e isin o do(6) if e isin E then(7) compute R1α R1 by equations (15) and (16)(8) if R1α gt 0 then(9) for forallxi isin Xe set E(xi) S(i) (10) end(11) else(12) compute R2e R2α R2 by equations (17)ndash(19)(13) if R2α gtR2e then(14) for forallxi isin Xe

eα set E(xi) α(15) else(16) for forallxi isin Xe set E(xi) S(i)

(17) else(18) if R2gt 0 then(19) Accept the new exemplar α(20) end(21) end(22) t t+ 1(23) end(24) Until converge

ALGORITHM 1 Fast enhanced exemplar-based clustering algorithm

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

Figure 5 Description of Aggregation data

Computational and Mathematical Methods in Medicine 7

(1) e proposed algorithm FEEC can cluster data with80 complete data and 20 incomplete data and inmost cases the performance is very convincing Spe-cifically for both Aggregation and epileptic EEG signals

FEEC performs best in terms of NMI accuracy andENERGY

(2) As to the computational time compared with EEMFEEC takes less time us with the assistance of

minus500

0

500

minus500

0

500

minus200

0

200

minus200

0

200

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

minus10000

1000

Am

plitu

des (microV

)

Time (seconds)

Time (seconds)(d)

(c)

(b)

(a)

(e)

Time (seconds)

Time (seconds)

Time (seconds)

Figure 6 Typical EEG signals in groups AndashE

Table 2 Description of healthy and epileptic EEG data

Subjects Groups Size of data DescriptionsHealthy A 100 Signals captured from volunteers with eyes open

B 100 Signals captured from volunteers with eyes closedEpileptic C 100 Signals captured from volunteers during seizure silence intervals

D 100 Signals captured from volunteers during seizure silence intervalsE 100 Signals captured from volunteers during seizure activity

Table 3 Brief description of Aggregation and Bonn Epileptic EEG signals

Datasets Number of objects Number of attributes Number of clustersAggregation 788 2 7Bonn 500 6 5

8 Computational and Mathematical Methods in Medicine

compression stage the time complexity of FEEC hasbeen reduced and the efficiency is improved as wellAnd FEEC has an equivalent computational timewith FAP Comparing other criteria of FEEC andFAP it is worthwhile to spend more time

(3) e proposed FEEC needs no more parametersexcept for preferences while the performance of FAP

relies much on k which determines the number ofnearest exemplars Accordingly in terms of the in-volved datasets in this section FEEC would achievesatisfactory clustering results

Table 4 Average experimental results over 10 runs on Aggregation and Bonn epileptic EEG signals

Dataset Algorithms NMI Accuracy ENERGY Time

Aggregation

FEEC 09636 09530 352238 954FAP 09017 09130 360979 965AP 08455 07016 412264 2859EEM 08765 07208 383829 16804

Bonn epileptic EEG signals

FEEC 09038 09786 160287 375FAP 08794 09445 174422 365AP 03324 04387 301812 397EEM 03728 04991 205051 601

070

075

080

085

090

095

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 7 Comparison of NMI on Aggregation dataset

065

070

075

080

085

090

095

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 8 Comparison of accuracy on Aggregation dataset

3300

3400

3500

3600

3700

3800

3900

4000

4100

4200

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 9 Comparison of accuracy on Aggregation

030

040

050

060

070

080

090

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 10 Comparison of NMI on Bonn epileptic EEG signals

Computational and Mathematical Methods in Medicine 9

5 Conclusions

e diagnosis and treatment of epilepsy is always a signif-icant direction for both machine learning and brain scienceis paper newly proposes a fast exemplar-based clusteringmethod for incomplete EEG signal e FEEC method in-cludes two stages namely compression and optimizatione performance of the proposed clustering algorithm iscomprehensively verified by the experiments on twodatasets

Although most recognition methods of epilepsy arebased on EEG signals at present researchers also have tostudy on other neuroimaging modalities such as corticalelectroencephalography (ECoG) functional infrared opticalimaging (fNIR) functional magnetic resonance imaging(fMRI) positron emission tomography (PET) and mag-netoencephalography (MEG) Considering the fact that thebrain activity is a nonlinear networked and unstable

complex system we would focus on the multimodal clus-tering model for these neuroimaging modality signals infuture

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was supported in part by the 2018 Natural ScienceFoundation of Jiangsu Higher Education Institutions undergrant no 18KJB5200001 the Natural Science Foundation ofJiangsu Province under grant no BK20161268 and theHumanities and Social Sciences Foundation of the Ministryof Education under grant no 18YJCZH229

References

[1] H Gao H Miao L Liu J Kai and K Zhao ldquoAutomatedquantitative verification for service-based system design avisualization transform tool perspectiverdquo InternationalJournal of Software Engineering and Knowledge Engineeringvol 28 no 10 pp 1369ndash1397 2018

[2] H Gao W Huang and X Yang ldquoApplying probabilisticmodel checking to path planning in an intelligent trans-portation system using mobility trajectories and their sta-tistical datardquo Intelligent Automation and Soft Computingvol 25 no 3 Article ID 5478C559 2019

[3] H Gao W Huang X Yang Y Duan and Y Yin ldquoTowardservice selection for workflow reconfiguration an interface-based computing solutionrdquo Future Generation ComputerSystems vol 87 pp 298ndash311 2018

[4] H Gao W Huang Y Duan et al ldquoResearch on cost-drivenservices composition in an uncertain environmentrdquo Journal ofInternet Technology vol 20 no 3 pp 755ndash769 2019

[5] L Wang K C L Wong H Zhang H Liu and P ShildquoNoninvasive computational imaging of cardiac electro-physiology for 3-D infarctrdquo IEEE Transactions on BiomedicalEngineering vol 58 no 4 pp 1033ndash1043 2011

[6] Y Xia H Zhang L Xu et al ldquoAn automatic cardiac ar-rhythmia classification system with wearable electrocardio-gramrdquo IEEE Access vol 6 pp 16529ndash16538 2018

[7] C Cortes and V Vapnik ldquoSupport-vector networksrdquo Ma-chine Learning vol 20 no 3 pp 273ndash297 1995

[8] Y Peng and B L Lu ldquoImmune clonal algorithm based featureselection for epileptic EEG signal classificationrdquo in Proceed-ings of the 2012 11th International Conference on InformationScience Signal Processing and 9eir Applications (ISSPA)Montreal Quebec Canada July 2012

[9] Y Jiang D Wu Z Deng et al ldquoSeizure classification fromEEG signals using transfer learning semi-supervised learningand TSK fuzzy systemrdquo IEEE Transactions on Neural Systemsand Rehabilitation Engineering vol 25 no 12 pp 2270ndash22842017

[10] Z Jiang F-L Chung and SWang ldquoRecognition of multiclassepileptic EEG signals based on knowledge and label space

040

050

060

070

080

090

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 11 Comparison of accuracy on Bonn epileptic EEG signals

1500

1700

1900

2100

2300

2500

2700

2900

3100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 12 Comparison of ENERGY on Bonn epileptic EEGsignals

10 Computational and Mathematical Methods in Medicine

inductive transferrdquo IEEE Transactions on Neural Systems andRehabilitation Engineering vol 27 no 4 pp 630ndash642 2019

[11] Z Iscan Z Dokur and T Demiralp ldquoClassification ofelectroencephalogram signals with combined time and fre-quency featuresrdquo Expert Systems with Applications vol 38no 8 pp 10499ndash10505 2011

[12] Y Jiang F- Chung S Wang Z Deng J Wang and P QianldquoCollaborative fuzzy clustering from multiple weightedviewsrdquo IEEE Transactions on Cybernetics vol 45 no 4pp 688ndash701 2015

[13] B J Frey and D Dueck ldquoClustering by passing messagesbetween data pointsrdquo Science vol 315 no 5814 pp 972ndash9762017

[14] V Kolmogorov and C Rother ldquoComparison of energyminimization algorithms for highly connected graphsrdquo inProceedings of the 9th European Conference on ComputerVision (ECCV) vol 3952 Graz Austria May 2006

[15] M F Tappen and W T Freeman ldquoComparison of graph cutswith belief propagation for stereo using identical MRF pa-rametersrdquo in Proceedings of the Ninth IEEE InternationalConference on Computer Vision pp 900ndash906 Nice FranceOctober 2003

[16] A Bi and S Wang ldquoIncremental enhanced α-expansion movefor large data a probability regularization perspectiverdquo In-ternational Journal of Machine Learning and Cyberneticsvol 8 no 5 pp 1615ndash1631 2016

[17] Y Zheng and P Chen ldquoClustering based on enhancedα-expansion moverdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 10 pp 2206ndash2216 2013

[18] B R Greene S Faul W Marnane G LightbodyI Korotchikova and G Boylan ldquoA comparison of quanti-tative EEG features for neonatal seizure detectionrdquo ClinicalNeurophysiology vol 119 no 6 pp 1248ndash1261 2008

[19] C W N F C W Fadzal W Mansor L Y Khuan andA Zabidi ldquoShort-time fourier transform analysis of EEGsignal from writingrdquo in Proceedings of the 2012 IEEE 8thInternational Colloquium on Signal Processing and itsApplications Malacca Malaysia March 2012

[20] E A Vivaldi and A Bassi ldquoFrequency domain analysis ofsleep EEG for visualization and automated state detectionrdquo inProceedings of the 2006 International Conference of the IEEEEngineering in Medicine and Biology Society New York NYUSA September 2006

[21] D Hu W Li and X Chen ldquoFeature extraction of motorimagery eeg signals based on wavelet packet decompositionrdquoin Proceedings of the 2011 IEEEICME International Confer-ence on Complex Medical Engineering pp 694ndash697 HarbinChina May 2011

[22] Z Zhang H Kawabata and Z Q Liu ldquoEEG analysis usingfast wavelet transformrdquo in Proceedings of the SMC 2000Conference Proceedings 2000 IEEE International Conferenceon Systems Man and Cybernetics Nashville TN USA Oc-tober 2000

[23] K Murphy Y Weiss and M Jordan ldquoLoopy belief propa-gation for approximate inference an empirical studyrdquo inProceedings of the 15th Conference on Uncertainty in ArtificialIntelligence Bellevue WA USA August 2013

[24] K Wang J Zhang D Li X Zhang and T Guo Adaptiveaffinity propagation clusteringrdquo 2008 httpsarxivorgabs08051096

[25] J Vlasblom and S J Wodak ldquoMarkov clustering versus af-finity propagation for the partitioning of protein interactiongraphsrdquo vol 10 no 1 pp 99-100 2009

[26] X Mishra R Guan L Wang Z Pei and Y Liang ldquoAnincremental affinity propagation algorithm and its applica-tions for text clusteringrdquo in Proceedings of the 2009 Inter-national Joint Conference on Neural Networks pp 2914ndash2919Atlanta GA USA June 2009

[27] L Sun and C Guo ldquoIncremental affinity propagation clus-tering based on message passingrdquo IEEE Transactions onKnowledge and Data Engineering vol 26 no 11 pp 2731ndash2744 2014

[28] I Givoni and B Frey ldquoSemi-supervised affinity propagationwith instance-level constraintsrdquo Journal of Machine LearningResearchmdashProceedings Track vol 5 pp 161ndash168 2009

[29] L Sun C Guo C Liu and H Xiong ldquoFast affinity propa-gation clustering based on incomplete similarity matrixrdquoKnowledge and Information Systems vol 51 no 3 pp 941ndash963 2017

[30] A Bi F Chung S Wang Y Jiang and C Huang ldquoBayesianenhanced α-expansion move clustering with loose link con-straintsrdquo Neurocomputing vol 194 pp 288ndash300 2016

[31] S Guha A Meyerson N Mishra R Motwani andL OrsquoCallaghan ldquoClustering data streams theory and prac-ticerdquo IEEE Transactions on Knowledge and Data Engineeringvol 15 no 3 pp 515ndash528 2003

[32] A Gionis H Mannila and P Tsaparas ldquoClustering aggre-gationrdquo ACM Transactions on Knowledge Discovery fromData vol 1 no 1 p 4 2007

[33] Y Jiang Z Deng F-L Chung et al ldquoRecognition of epilepticEEG signals using a novel multiview TSK fuzzy systemrdquo IEEETransactions on Fuzzy Systems vol 25 no 1 pp 3ndash20 2017

[34] Y Jiang F-L Chung H Ishibuchi Z Deng and S WangldquoMultitask TSK fuzzy system modeling by mining intertaskcommon hidden structurerdquo IEEE Transactions on Cyberneticsvol 45 no 3 pp 548ndash561 2015

Computational and Mathematical Methods in Medicine 11

(1) e proposed algorithm FEEC can cluster data with80 complete data and 20 incomplete data and inmost cases the performance is very convincing Spe-cifically for both Aggregation and epileptic EEG signals

FEEC performs best in terms of NMI accuracy andENERGY

(2) As to the computational time compared with EEMFEEC takes less time us with the assistance of

minus500

0

500

minus500

0

500

minus200

0

200

minus200

0

200

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

minus10000

1000

Am

plitu

des (microV

)

Time (seconds)

Time (seconds)(d)

(c)

(b)

(a)

(e)

Time (seconds)

Time (seconds)

Time (seconds)

Figure 6 Typical EEG signals in groups AndashE

Table 2 Description of healthy and epileptic EEG data

Subjects Groups Size of data DescriptionsHealthy A 100 Signals captured from volunteers with eyes open

B 100 Signals captured from volunteers with eyes closedEpileptic C 100 Signals captured from volunteers during seizure silence intervals

D 100 Signals captured from volunteers during seizure silence intervalsE 100 Signals captured from volunteers during seizure activity

Table 3 Brief description of Aggregation and Bonn Epileptic EEG signals

Datasets Number of objects Number of attributes Number of clustersAggregation 788 2 7Bonn 500 6 5

8 Computational and Mathematical Methods in Medicine

compression stage the time complexity of FEEC hasbeen reduced and the efficiency is improved as wellAnd FEEC has an equivalent computational timewith FAP Comparing other criteria of FEEC andFAP it is worthwhile to spend more time

(3) e proposed FEEC needs no more parametersexcept for preferences while the performance of FAP

relies much on k which determines the number ofnearest exemplars Accordingly in terms of the in-volved datasets in this section FEEC would achievesatisfactory clustering results

Table 4 Average experimental results over 10 runs on Aggregation and Bonn epileptic EEG signals

Dataset Algorithms NMI Accuracy ENERGY Time

Aggregation

FEEC 09636 09530 352238 954FAP 09017 09130 360979 965AP 08455 07016 412264 2859EEM 08765 07208 383829 16804

Bonn epileptic EEG signals

FEEC 09038 09786 160287 375FAP 08794 09445 174422 365AP 03324 04387 301812 397EEM 03728 04991 205051 601

070

075

080

085

090

095

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 7 Comparison of NMI on Aggregation dataset

065

070

075

080

085

090

095

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 8 Comparison of accuracy on Aggregation dataset

3300

3400

3500

3600

3700

3800

3900

4000

4100

4200

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 9 Comparison of accuracy on Aggregation

030

040

050

060

070

080

090

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 10 Comparison of NMI on Bonn epileptic EEG signals

Computational and Mathematical Methods in Medicine 9

5 Conclusions

e diagnosis and treatment of epilepsy is always a signif-icant direction for both machine learning and brain scienceis paper newly proposes a fast exemplar-based clusteringmethod for incomplete EEG signal e FEEC method in-cludes two stages namely compression and optimizatione performance of the proposed clustering algorithm iscomprehensively verified by the experiments on twodatasets

Although most recognition methods of epilepsy arebased on EEG signals at present researchers also have tostudy on other neuroimaging modalities such as corticalelectroencephalography (ECoG) functional infrared opticalimaging (fNIR) functional magnetic resonance imaging(fMRI) positron emission tomography (PET) and mag-netoencephalography (MEG) Considering the fact that thebrain activity is a nonlinear networked and unstable

complex system we would focus on the multimodal clus-tering model for these neuroimaging modality signals infuture

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was supported in part by the 2018 Natural ScienceFoundation of Jiangsu Higher Education Institutions undergrant no 18KJB5200001 the Natural Science Foundation ofJiangsu Province under grant no BK20161268 and theHumanities and Social Sciences Foundation of the Ministryof Education under grant no 18YJCZH229

References

[1] H Gao H Miao L Liu J Kai and K Zhao ldquoAutomatedquantitative verification for service-based system design avisualization transform tool perspectiverdquo InternationalJournal of Software Engineering and Knowledge Engineeringvol 28 no 10 pp 1369ndash1397 2018

[2] H Gao W Huang and X Yang ldquoApplying probabilisticmodel checking to path planning in an intelligent trans-portation system using mobility trajectories and their sta-tistical datardquo Intelligent Automation and Soft Computingvol 25 no 3 Article ID 5478C559 2019

[3] H Gao W Huang X Yang Y Duan and Y Yin ldquoTowardservice selection for workflow reconfiguration an interface-based computing solutionrdquo Future Generation ComputerSystems vol 87 pp 298ndash311 2018

[4] H Gao W Huang Y Duan et al ldquoResearch on cost-drivenservices composition in an uncertain environmentrdquo Journal ofInternet Technology vol 20 no 3 pp 755ndash769 2019

[5] L Wang K C L Wong H Zhang H Liu and P ShildquoNoninvasive computational imaging of cardiac electro-physiology for 3-D infarctrdquo IEEE Transactions on BiomedicalEngineering vol 58 no 4 pp 1033ndash1043 2011

[6] Y Xia H Zhang L Xu et al ldquoAn automatic cardiac ar-rhythmia classification system with wearable electrocardio-gramrdquo IEEE Access vol 6 pp 16529ndash16538 2018

[7] C Cortes and V Vapnik ldquoSupport-vector networksrdquo Ma-chine Learning vol 20 no 3 pp 273ndash297 1995

[8] Y Peng and B L Lu ldquoImmune clonal algorithm based featureselection for epileptic EEG signal classificationrdquo in Proceed-ings of the 2012 11th International Conference on InformationScience Signal Processing and 9eir Applications (ISSPA)Montreal Quebec Canada July 2012

[9] Y Jiang D Wu Z Deng et al ldquoSeizure classification fromEEG signals using transfer learning semi-supervised learningand TSK fuzzy systemrdquo IEEE Transactions on Neural Systemsand Rehabilitation Engineering vol 25 no 12 pp 2270ndash22842017

[10] Z Jiang F-L Chung and SWang ldquoRecognition of multiclassepileptic EEG signals based on knowledge and label space

040

050

060

070

080

090

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 11 Comparison of accuracy on Bonn epileptic EEG signals

1500

1700

1900

2100

2300

2500

2700

2900

3100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 12 Comparison of ENERGY on Bonn epileptic EEGsignals

10 Computational and Mathematical Methods in Medicine

inductive transferrdquo IEEE Transactions on Neural Systems andRehabilitation Engineering vol 27 no 4 pp 630ndash642 2019

[11] Z Iscan Z Dokur and T Demiralp ldquoClassification ofelectroencephalogram signals with combined time and fre-quency featuresrdquo Expert Systems with Applications vol 38no 8 pp 10499ndash10505 2011

[12] Y Jiang F- Chung S Wang Z Deng J Wang and P QianldquoCollaborative fuzzy clustering from multiple weightedviewsrdquo IEEE Transactions on Cybernetics vol 45 no 4pp 688ndash701 2015

[13] B J Frey and D Dueck ldquoClustering by passing messagesbetween data pointsrdquo Science vol 315 no 5814 pp 972ndash9762017

[14] V Kolmogorov and C Rother ldquoComparison of energyminimization algorithms for highly connected graphsrdquo inProceedings of the 9th European Conference on ComputerVision (ECCV) vol 3952 Graz Austria May 2006

[15] M F Tappen and W T Freeman ldquoComparison of graph cutswith belief propagation for stereo using identical MRF pa-rametersrdquo in Proceedings of the Ninth IEEE InternationalConference on Computer Vision pp 900ndash906 Nice FranceOctober 2003

[16] A Bi and S Wang ldquoIncremental enhanced α-expansion movefor large data a probability regularization perspectiverdquo In-ternational Journal of Machine Learning and Cyberneticsvol 8 no 5 pp 1615ndash1631 2016

[17] Y Zheng and P Chen ldquoClustering based on enhancedα-expansion moverdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 10 pp 2206ndash2216 2013

[18] B R Greene S Faul W Marnane G LightbodyI Korotchikova and G Boylan ldquoA comparison of quanti-tative EEG features for neonatal seizure detectionrdquo ClinicalNeurophysiology vol 119 no 6 pp 1248ndash1261 2008

[19] C W N F C W Fadzal W Mansor L Y Khuan andA Zabidi ldquoShort-time fourier transform analysis of EEGsignal from writingrdquo in Proceedings of the 2012 IEEE 8thInternational Colloquium on Signal Processing and itsApplications Malacca Malaysia March 2012

[20] E A Vivaldi and A Bassi ldquoFrequency domain analysis ofsleep EEG for visualization and automated state detectionrdquo inProceedings of the 2006 International Conference of the IEEEEngineering in Medicine and Biology Society New York NYUSA September 2006

[21] D Hu W Li and X Chen ldquoFeature extraction of motorimagery eeg signals based on wavelet packet decompositionrdquoin Proceedings of the 2011 IEEEICME International Confer-ence on Complex Medical Engineering pp 694ndash697 HarbinChina May 2011

[22] Z Zhang H Kawabata and Z Q Liu ldquoEEG analysis usingfast wavelet transformrdquo in Proceedings of the SMC 2000Conference Proceedings 2000 IEEE International Conferenceon Systems Man and Cybernetics Nashville TN USA Oc-tober 2000

[23] K Murphy Y Weiss and M Jordan ldquoLoopy belief propa-gation for approximate inference an empirical studyrdquo inProceedings of the 15th Conference on Uncertainty in ArtificialIntelligence Bellevue WA USA August 2013

[24] K Wang J Zhang D Li X Zhang and T Guo Adaptiveaffinity propagation clusteringrdquo 2008 httpsarxivorgabs08051096

[25] J Vlasblom and S J Wodak ldquoMarkov clustering versus af-finity propagation for the partitioning of protein interactiongraphsrdquo vol 10 no 1 pp 99-100 2009

[26] X Mishra R Guan L Wang Z Pei and Y Liang ldquoAnincremental affinity propagation algorithm and its applica-tions for text clusteringrdquo in Proceedings of the 2009 Inter-national Joint Conference on Neural Networks pp 2914ndash2919Atlanta GA USA June 2009

[27] L Sun and C Guo ldquoIncremental affinity propagation clus-tering based on message passingrdquo IEEE Transactions onKnowledge and Data Engineering vol 26 no 11 pp 2731ndash2744 2014

[28] I Givoni and B Frey ldquoSemi-supervised affinity propagationwith instance-level constraintsrdquo Journal of Machine LearningResearchmdashProceedings Track vol 5 pp 161ndash168 2009

[29] L Sun C Guo C Liu and H Xiong ldquoFast affinity propa-gation clustering based on incomplete similarity matrixrdquoKnowledge and Information Systems vol 51 no 3 pp 941ndash963 2017

[30] A Bi F Chung S Wang Y Jiang and C Huang ldquoBayesianenhanced α-expansion move clustering with loose link con-straintsrdquo Neurocomputing vol 194 pp 288ndash300 2016

[31] S Guha A Meyerson N Mishra R Motwani andL OrsquoCallaghan ldquoClustering data streams theory and prac-ticerdquo IEEE Transactions on Knowledge and Data Engineeringvol 15 no 3 pp 515ndash528 2003

[32] A Gionis H Mannila and P Tsaparas ldquoClustering aggre-gationrdquo ACM Transactions on Knowledge Discovery fromData vol 1 no 1 p 4 2007

[33] Y Jiang Z Deng F-L Chung et al ldquoRecognition of epilepticEEG signals using a novel multiview TSK fuzzy systemrdquo IEEETransactions on Fuzzy Systems vol 25 no 1 pp 3ndash20 2017

[34] Y Jiang F-L Chung H Ishibuchi Z Deng and S WangldquoMultitask TSK fuzzy system modeling by mining intertaskcommon hidden structurerdquo IEEE Transactions on Cyberneticsvol 45 no 3 pp 548ndash561 2015

Computational and Mathematical Methods in Medicine 11

compression stage the time complexity of FEEC hasbeen reduced and the efficiency is improved as wellAnd FEEC has an equivalent computational timewith FAP Comparing other criteria of FEEC andFAP it is worthwhile to spend more time

(3) e proposed FEEC needs no more parametersexcept for preferences while the performance of FAP

relies much on k which determines the number ofnearest exemplars Accordingly in terms of the in-volved datasets in this section FEEC would achievesatisfactory clustering results

Table 4 Average experimental results over 10 runs on Aggregation and Bonn epileptic EEG signals

Dataset Algorithms NMI Accuracy ENERGY Time

Aggregation

FEEC 09636 09530 352238 954FAP 09017 09130 360979 965AP 08455 07016 412264 2859EEM 08765 07208 383829 16804

Bonn epileptic EEG signals

FEEC 09038 09786 160287 375FAP 08794 09445 174422 365AP 03324 04387 301812 397EEM 03728 04991 205051 601

070

075

080

085

090

095

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 7 Comparison of NMI on Aggregation dataset

065

070

075

080

085

090

095

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 8 Comparison of accuracy on Aggregation dataset

3300

3400

3500

3600

3700

3800

3900

4000

4100

4200

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 9 Comparison of accuracy on Aggregation

030

040

050

060

070

080

090

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 10 Comparison of NMI on Bonn epileptic EEG signals

Computational and Mathematical Methods in Medicine 9

5 Conclusions

e diagnosis and treatment of epilepsy is always a signif-icant direction for both machine learning and brain scienceis paper newly proposes a fast exemplar-based clusteringmethod for incomplete EEG signal e FEEC method in-cludes two stages namely compression and optimizatione performance of the proposed clustering algorithm iscomprehensively verified by the experiments on twodatasets

Although most recognition methods of epilepsy arebased on EEG signals at present researchers also have tostudy on other neuroimaging modalities such as corticalelectroencephalography (ECoG) functional infrared opticalimaging (fNIR) functional magnetic resonance imaging(fMRI) positron emission tomography (PET) and mag-netoencephalography (MEG) Considering the fact that thebrain activity is a nonlinear networked and unstable

complex system we would focus on the multimodal clus-tering model for these neuroimaging modality signals infuture

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was supported in part by the 2018 Natural ScienceFoundation of Jiangsu Higher Education Institutions undergrant no 18KJB5200001 the Natural Science Foundation ofJiangsu Province under grant no BK20161268 and theHumanities and Social Sciences Foundation of the Ministryof Education under grant no 18YJCZH229

References

[1] H Gao H Miao L Liu J Kai and K Zhao ldquoAutomatedquantitative verification for service-based system design avisualization transform tool perspectiverdquo InternationalJournal of Software Engineering and Knowledge Engineeringvol 28 no 10 pp 1369ndash1397 2018

[2] H Gao W Huang and X Yang ldquoApplying probabilisticmodel checking to path planning in an intelligent trans-portation system using mobility trajectories and their sta-tistical datardquo Intelligent Automation and Soft Computingvol 25 no 3 Article ID 5478C559 2019

[3] H Gao W Huang X Yang Y Duan and Y Yin ldquoTowardservice selection for workflow reconfiguration an interface-based computing solutionrdquo Future Generation ComputerSystems vol 87 pp 298ndash311 2018

[4] H Gao W Huang Y Duan et al ldquoResearch on cost-drivenservices composition in an uncertain environmentrdquo Journal ofInternet Technology vol 20 no 3 pp 755ndash769 2019

[5] L Wang K C L Wong H Zhang H Liu and P ShildquoNoninvasive computational imaging of cardiac electro-physiology for 3-D infarctrdquo IEEE Transactions on BiomedicalEngineering vol 58 no 4 pp 1033ndash1043 2011

[6] Y Xia H Zhang L Xu et al ldquoAn automatic cardiac ar-rhythmia classification system with wearable electrocardio-gramrdquo IEEE Access vol 6 pp 16529ndash16538 2018

[7] C Cortes and V Vapnik ldquoSupport-vector networksrdquo Ma-chine Learning vol 20 no 3 pp 273ndash297 1995

[8] Y Peng and B L Lu ldquoImmune clonal algorithm based featureselection for epileptic EEG signal classificationrdquo in Proceed-ings of the 2012 11th International Conference on InformationScience Signal Processing and 9eir Applications (ISSPA)Montreal Quebec Canada July 2012

[9] Y Jiang D Wu Z Deng et al ldquoSeizure classification fromEEG signals using transfer learning semi-supervised learningand TSK fuzzy systemrdquo IEEE Transactions on Neural Systemsand Rehabilitation Engineering vol 25 no 12 pp 2270ndash22842017

[10] Z Jiang F-L Chung and SWang ldquoRecognition of multiclassepileptic EEG signals based on knowledge and label space

040

050

060

070

080

090

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 11 Comparison of accuracy on Bonn epileptic EEG signals

1500

1700

1900

2100

2300

2500

2700

2900

3100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 12 Comparison of ENERGY on Bonn epileptic EEGsignals

10 Computational and Mathematical Methods in Medicine

inductive transferrdquo IEEE Transactions on Neural Systems andRehabilitation Engineering vol 27 no 4 pp 630ndash642 2019

[11] Z Iscan Z Dokur and T Demiralp ldquoClassification ofelectroencephalogram signals with combined time and fre-quency featuresrdquo Expert Systems with Applications vol 38no 8 pp 10499ndash10505 2011

[12] Y Jiang F- Chung S Wang Z Deng J Wang and P QianldquoCollaborative fuzzy clustering from multiple weightedviewsrdquo IEEE Transactions on Cybernetics vol 45 no 4pp 688ndash701 2015

[13] B J Frey and D Dueck ldquoClustering by passing messagesbetween data pointsrdquo Science vol 315 no 5814 pp 972ndash9762017

[14] V Kolmogorov and C Rother ldquoComparison of energyminimization algorithms for highly connected graphsrdquo inProceedings of the 9th European Conference on ComputerVision (ECCV) vol 3952 Graz Austria May 2006

[15] M F Tappen and W T Freeman ldquoComparison of graph cutswith belief propagation for stereo using identical MRF pa-rametersrdquo in Proceedings of the Ninth IEEE InternationalConference on Computer Vision pp 900ndash906 Nice FranceOctober 2003

[16] A Bi and S Wang ldquoIncremental enhanced α-expansion movefor large data a probability regularization perspectiverdquo In-ternational Journal of Machine Learning and Cyberneticsvol 8 no 5 pp 1615ndash1631 2016

[17] Y Zheng and P Chen ldquoClustering based on enhancedα-expansion moverdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 10 pp 2206ndash2216 2013

[18] B R Greene S Faul W Marnane G LightbodyI Korotchikova and G Boylan ldquoA comparison of quanti-tative EEG features for neonatal seizure detectionrdquo ClinicalNeurophysiology vol 119 no 6 pp 1248ndash1261 2008

[19] C W N F C W Fadzal W Mansor L Y Khuan andA Zabidi ldquoShort-time fourier transform analysis of EEGsignal from writingrdquo in Proceedings of the 2012 IEEE 8thInternational Colloquium on Signal Processing and itsApplications Malacca Malaysia March 2012

[20] E A Vivaldi and A Bassi ldquoFrequency domain analysis ofsleep EEG for visualization and automated state detectionrdquo inProceedings of the 2006 International Conference of the IEEEEngineering in Medicine and Biology Society New York NYUSA September 2006

[21] D Hu W Li and X Chen ldquoFeature extraction of motorimagery eeg signals based on wavelet packet decompositionrdquoin Proceedings of the 2011 IEEEICME International Confer-ence on Complex Medical Engineering pp 694ndash697 HarbinChina May 2011

[22] Z Zhang H Kawabata and Z Q Liu ldquoEEG analysis usingfast wavelet transformrdquo in Proceedings of the SMC 2000Conference Proceedings 2000 IEEE International Conferenceon Systems Man and Cybernetics Nashville TN USA Oc-tober 2000

[23] K Murphy Y Weiss and M Jordan ldquoLoopy belief propa-gation for approximate inference an empirical studyrdquo inProceedings of the 15th Conference on Uncertainty in ArtificialIntelligence Bellevue WA USA August 2013

[24] K Wang J Zhang D Li X Zhang and T Guo Adaptiveaffinity propagation clusteringrdquo 2008 httpsarxivorgabs08051096

[25] J Vlasblom and S J Wodak ldquoMarkov clustering versus af-finity propagation for the partitioning of protein interactiongraphsrdquo vol 10 no 1 pp 99-100 2009

[26] X Mishra R Guan L Wang Z Pei and Y Liang ldquoAnincremental affinity propagation algorithm and its applica-tions for text clusteringrdquo in Proceedings of the 2009 Inter-national Joint Conference on Neural Networks pp 2914ndash2919Atlanta GA USA June 2009

[27] L Sun and C Guo ldquoIncremental affinity propagation clus-tering based on message passingrdquo IEEE Transactions onKnowledge and Data Engineering vol 26 no 11 pp 2731ndash2744 2014

[28] I Givoni and B Frey ldquoSemi-supervised affinity propagationwith instance-level constraintsrdquo Journal of Machine LearningResearchmdashProceedings Track vol 5 pp 161ndash168 2009

[29] L Sun C Guo C Liu and H Xiong ldquoFast affinity propa-gation clustering based on incomplete similarity matrixrdquoKnowledge and Information Systems vol 51 no 3 pp 941ndash963 2017

[30] A Bi F Chung S Wang Y Jiang and C Huang ldquoBayesianenhanced α-expansion move clustering with loose link con-straintsrdquo Neurocomputing vol 194 pp 288ndash300 2016

[31] S Guha A Meyerson N Mishra R Motwani andL OrsquoCallaghan ldquoClustering data streams theory and prac-ticerdquo IEEE Transactions on Knowledge and Data Engineeringvol 15 no 3 pp 515ndash528 2003

[32] A Gionis H Mannila and P Tsaparas ldquoClustering aggre-gationrdquo ACM Transactions on Knowledge Discovery fromData vol 1 no 1 p 4 2007

[33] Y Jiang Z Deng F-L Chung et al ldquoRecognition of epilepticEEG signals using a novel multiview TSK fuzzy systemrdquo IEEETransactions on Fuzzy Systems vol 25 no 1 pp 3ndash20 2017

[34] Y Jiang F-L Chung H Ishibuchi Z Deng and S WangldquoMultitask TSK fuzzy system modeling by mining intertaskcommon hidden structurerdquo IEEE Transactions on Cyberneticsvol 45 no 3 pp 548ndash561 2015

Computational and Mathematical Methods in Medicine 11

5 Conclusions

e diagnosis and treatment of epilepsy is always a signif-icant direction for both machine learning and brain scienceis paper newly proposes a fast exemplar-based clusteringmethod for incomplete EEG signal e FEEC method in-cludes two stages namely compression and optimizatione performance of the proposed clustering algorithm iscomprehensively verified by the experiments on twodatasets

Although most recognition methods of epilepsy arebased on EEG signals at present researchers also have tostudy on other neuroimaging modalities such as corticalelectroencephalography (ECoG) functional infrared opticalimaging (fNIR) functional magnetic resonance imaging(fMRI) positron emission tomography (PET) and mag-netoencephalography (MEG) Considering the fact that thebrain activity is a nonlinear networked and unstable

complex system we would focus on the multimodal clus-tering model for these neuroimaging modality signals infuture

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was supported in part by the 2018 Natural ScienceFoundation of Jiangsu Higher Education Institutions undergrant no 18KJB5200001 the Natural Science Foundation ofJiangsu Province under grant no BK20161268 and theHumanities and Social Sciences Foundation of the Ministryof Education under grant no 18YJCZH229

References

[1] H Gao H Miao L Liu J Kai and K Zhao ldquoAutomatedquantitative verification for service-based system design avisualization transform tool perspectiverdquo InternationalJournal of Software Engineering and Knowledge Engineeringvol 28 no 10 pp 1369ndash1397 2018

[2] H Gao W Huang and X Yang ldquoApplying probabilisticmodel checking to path planning in an intelligent trans-portation system using mobility trajectories and their sta-tistical datardquo Intelligent Automation and Soft Computingvol 25 no 3 Article ID 5478C559 2019

[3] H Gao W Huang X Yang Y Duan and Y Yin ldquoTowardservice selection for workflow reconfiguration an interface-based computing solutionrdquo Future Generation ComputerSystems vol 87 pp 298ndash311 2018

[4] H Gao W Huang Y Duan et al ldquoResearch on cost-drivenservices composition in an uncertain environmentrdquo Journal ofInternet Technology vol 20 no 3 pp 755ndash769 2019

[5] L Wang K C L Wong H Zhang H Liu and P ShildquoNoninvasive computational imaging of cardiac electro-physiology for 3-D infarctrdquo IEEE Transactions on BiomedicalEngineering vol 58 no 4 pp 1033ndash1043 2011

[6] Y Xia H Zhang L Xu et al ldquoAn automatic cardiac ar-rhythmia classification system with wearable electrocardio-gramrdquo IEEE Access vol 6 pp 16529ndash16538 2018

[7] C Cortes and V Vapnik ldquoSupport-vector networksrdquo Ma-chine Learning vol 20 no 3 pp 273ndash297 1995

[8] Y Peng and B L Lu ldquoImmune clonal algorithm based featureselection for epileptic EEG signal classificationrdquo in Proceed-ings of the 2012 11th International Conference on InformationScience Signal Processing and 9eir Applications (ISSPA)Montreal Quebec Canada July 2012

[9] Y Jiang D Wu Z Deng et al ldquoSeizure classification fromEEG signals using transfer learning semi-supervised learningand TSK fuzzy systemrdquo IEEE Transactions on Neural Systemsand Rehabilitation Engineering vol 25 no 12 pp 2270ndash22842017

[10] Z Jiang F-L Chung and SWang ldquoRecognition of multiclassepileptic EEG signals based on knowledge and label space

040

050

060

070

080

090

100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 11 Comparison of accuracy on Bonn epileptic EEG signals

1500

1700

1900

2100

2300

2500

2700

2900

3100

1 2 3 4 5 6 7 8 9 10Times

FEECFAP

APEEM

Figure 12 Comparison of ENERGY on Bonn epileptic EEGsignals

10 Computational and Mathematical Methods in Medicine

inductive transferrdquo IEEE Transactions on Neural Systems andRehabilitation Engineering vol 27 no 4 pp 630ndash642 2019

[11] Z Iscan Z Dokur and T Demiralp ldquoClassification ofelectroencephalogram signals with combined time and fre-quency featuresrdquo Expert Systems with Applications vol 38no 8 pp 10499ndash10505 2011

[12] Y Jiang F- Chung S Wang Z Deng J Wang and P QianldquoCollaborative fuzzy clustering from multiple weightedviewsrdquo IEEE Transactions on Cybernetics vol 45 no 4pp 688ndash701 2015

[13] B J Frey and D Dueck ldquoClustering by passing messagesbetween data pointsrdquo Science vol 315 no 5814 pp 972ndash9762017

[14] V Kolmogorov and C Rother ldquoComparison of energyminimization algorithms for highly connected graphsrdquo inProceedings of the 9th European Conference on ComputerVision (ECCV) vol 3952 Graz Austria May 2006

[15] M F Tappen and W T Freeman ldquoComparison of graph cutswith belief propagation for stereo using identical MRF pa-rametersrdquo in Proceedings of the Ninth IEEE InternationalConference on Computer Vision pp 900ndash906 Nice FranceOctober 2003

[16] A Bi and S Wang ldquoIncremental enhanced α-expansion movefor large data a probability regularization perspectiverdquo In-ternational Journal of Machine Learning and Cyberneticsvol 8 no 5 pp 1615ndash1631 2016

[17] Y Zheng and P Chen ldquoClustering based on enhancedα-expansion moverdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 10 pp 2206ndash2216 2013

[18] B R Greene S Faul W Marnane G LightbodyI Korotchikova and G Boylan ldquoA comparison of quanti-tative EEG features for neonatal seizure detectionrdquo ClinicalNeurophysiology vol 119 no 6 pp 1248ndash1261 2008

[19] C W N F C W Fadzal W Mansor L Y Khuan andA Zabidi ldquoShort-time fourier transform analysis of EEGsignal from writingrdquo in Proceedings of the 2012 IEEE 8thInternational Colloquium on Signal Processing and itsApplications Malacca Malaysia March 2012

[20] E A Vivaldi and A Bassi ldquoFrequency domain analysis ofsleep EEG for visualization and automated state detectionrdquo inProceedings of the 2006 International Conference of the IEEEEngineering in Medicine and Biology Society New York NYUSA September 2006

[21] D Hu W Li and X Chen ldquoFeature extraction of motorimagery eeg signals based on wavelet packet decompositionrdquoin Proceedings of the 2011 IEEEICME International Confer-ence on Complex Medical Engineering pp 694ndash697 HarbinChina May 2011

[22] Z Zhang H Kawabata and Z Q Liu ldquoEEG analysis usingfast wavelet transformrdquo in Proceedings of the SMC 2000Conference Proceedings 2000 IEEE International Conferenceon Systems Man and Cybernetics Nashville TN USA Oc-tober 2000

[23] K Murphy Y Weiss and M Jordan ldquoLoopy belief propa-gation for approximate inference an empirical studyrdquo inProceedings of the 15th Conference on Uncertainty in ArtificialIntelligence Bellevue WA USA August 2013

[24] K Wang J Zhang D Li X Zhang and T Guo Adaptiveaffinity propagation clusteringrdquo 2008 httpsarxivorgabs08051096

[25] J Vlasblom and S J Wodak ldquoMarkov clustering versus af-finity propagation for the partitioning of protein interactiongraphsrdquo vol 10 no 1 pp 99-100 2009

[26] X Mishra R Guan L Wang Z Pei and Y Liang ldquoAnincremental affinity propagation algorithm and its applica-tions for text clusteringrdquo in Proceedings of the 2009 Inter-national Joint Conference on Neural Networks pp 2914ndash2919Atlanta GA USA June 2009

[27] L Sun and C Guo ldquoIncremental affinity propagation clus-tering based on message passingrdquo IEEE Transactions onKnowledge and Data Engineering vol 26 no 11 pp 2731ndash2744 2014

[28] I Givoni and B Frey ldquoSemi-supervised affinity propagationwith instance-level constraintsrdquo Journal of Machine LearningResearchmdashProceedings Track vol 5 pp 161ndash168 2009

[29] L Sun C Guo C Liu and H Xiong ldquoFast affinity propa-gation clustering based on incomplete similarity matrixrdquoKnowledge and Information Systems vol 51 no 3 pp 941ndash963 2017

[30] A Bi F Chung S Wang Y Jiang and C Huang ldquoBayesianenhanced α-expansion move clustering with loose link con-straintsrdquo Neurocomputing vol 194 pp 288ndash300 2016

[31] S Guha A Meyerson N Mishra R Motwani andL OrsquoCallaghan ldquoClustering data streams theory and prac-ticerdquo IEEE Transactions on Knowledge and Data Engineeringvol 15 no 3 pp 515ndash528 2003

[32] A Gionis H Mannila and P Tsaparas ldquoClustering aggre-gationrdquo ACM Transactions on Knowledge Discovery fromData vol 1 no 1 p 4 2007

[33] Y Jiang Z Deng F-L Chung et al ldquoRecognition of epilepticEEG signals using a novel multiview TSK fuzzy systemrdquo IEEETransactions on Fuzzy Systems vol 25 no 1 pp 3ndash20 2017

[34] Y Jiang F-L Chung H Ishibuchi Z Deng and S WangldquoMultitask TSK fuzzy system modeling by mining intertaskcommon hidden structurerdquo IEEE Transactions on Cyberneticsvol 45 no 3 pp 548ndash561 2015

Computational and Mathematical Methods in Medicine 11

inductive transferrdquo IEEE Transactions on Neural Systems andRehabilitation Engineering vol 27 no 4 pp 630ndash642 2019

[11] Z Iscan Z Dokur and T Demiralp ldquoClassification ofelectroencephalogram signals with combined time and fre-quency featuresrdquo Expert Systems with Applications vol 38no 8 pp 10499ndash10505 2011

[12] Y Jiang F- Chung S Wang Z Deng J Wang and P QianldquoCollaborative fuzzy clustering from multiple weightedviewsrdquo IEEE Transactions on Cybernetics vol 45 no 4pp 688ndash701 2015

[13] B J Frey and D Dueck ldquoClustering by passing messagesbetween data pointsrdquo Science vol 315 no 5814 pp 972ndash9762017

[14] V Kolmogorov and C Rother ldquoComparison of energyminimization algorithms for highly connected graphsrdquo inProceedings of the 9th European Conference on ComputerVision (ECCV) vol 3952 Graz Austria May 2006

[15] M F Tappen and W T Freeman ldquoComparison of graph cutswith belief propagation for stereo using identical MRF pa-rametersrdquo in Proceedings of the Ninth IEEE InternationalConference on Computer Vision pp 900ndash906 Nice FranceOctober 2003

[16] A Bi and S Wang ldquoIncremental enhanced α-expansion movefor large data a probability regularization perspectiverdquo In-ternational Journal of Machine Learning and Cyberneticsvol 8 no 5 pp 1615ndash1631 2016

[17] Y Zheng and P Chen ldquoClustering based on enhancedα-expansion moverdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 10 pp 2206ndash2216 2013

[18] B R Greene S Faul W Marnane G LightbodyI Korotchikova and G Boylan ldquoA comparison of quanti-tative EEG features for neonatal seizure detectionrdquo ClinicalNeurophysiology vol 119 no 6 pp 1248ndash1261 2008

[19] C W N F C W Fadzal W Mansor L Y Khuan andA Zabidi ldquoShort-time fourier transform analysis of EEGsignal from writingrdquo in Proceedings of the 2012 IEEE 8thInternational Colloquium on Signal Processing and itsApplications Malacca Malaysia March 2012

[20] E A Vivaldi and A Bassi ldquoFrequency domain analysis ofsleep EEG for visualization and automated state detectionrdquo inProceedings of the 2006 International Conference of the IEEEEngineering in Medicine and Biology Society New York NYUSA September 2006

[21] D Hu W Li and X Chen ldquoFeature extraction of motorimagery eeg signals based on wavelet packet decompositionrdquoin Proceedings of the 2011 IEEEICME International Confer-ence on Complex Medical Engineering pp 694ndash697 HarbinChina May 2011

[22] Z Zhang H Kawabata and Z Q Liu ldquoEEG analysis usingfast wavelet transformrdquo in Proceedings of the SMC 2000Conference Proceedings 2000 IEEE International Conferenceon Systems Man and Cybernetics Nashville TN USA Oc-tober 2000

[23] K Murphy Y Weiss and M Jordan ldquoLoopy belief propa-gation for approximate inference an empirical studyrdquo inProceedings of the 15th Conference on Uncertainty in ArtificialIntelligence Bellevue WA USA August 2013

[24] K Wang J Zhang D Li X Zhang and T Guo Adaptiveaffinity propagation clusteringrdquo 2008 httpsarxivorgabs08051096

[25] J Vlasblom and S J Wodak ldquoMarkov clustering versus af-finity propagation for the partitioning of protein interactiongraphsrdquo vol 10 no 1 pp 99-100 2009

[26] X Mishra R Guan L Wang Z Pei and Y Liang ldquoAnincremental affinity propagation algorithm and its applica-tions for text clusteringrdquo in Proceedings of the 2009 Inter-national Joint Conference on Neural Networks pp 2914ndash2919Atlanta GA USA June 2009

[27] L Sun and C Guo ldquoIncremental affinity propagation clus-tering based on message passingrdquo IEEE Transactions onKnowledge and Data Engineering vol 26 no 11 pp 2731ndash2744 2014

[28] I Givoni and B Frey ldquoSemi-supervised affinity propagationwith instance-level constraintsrdquo Journal of Machine LearningResearchmdashProceedings Track vol 5 pp 161ndash168 2009

[29] L Sun C Guo C Liu and H Xiong ldquoFast affinity propa-gation clustering based on incomplete similarity matrixrdquoKnowledge and Information Systems vol 51 no 3 pp 941ndash963 2017

[30] A Bi F Chung S Wang Y Jiang and C Huang ldquoBayesianenhanced α-expansion move clustering with loose link con-straintsrdquo Neurocomputing vol 194 pp 288ndash300 2016

[31] S Guha A Meyerson N Mishra R Motwani andL OrsquoCallaghan ldquoClustering data streams theory and prac-ticerdquo IEEE Transactions on Knowledge and Data Engineeringvol 15 no 3 pp 515ndash528 2003

[32] A Gionis H Mannila and P Tsaparas ldquoClustering aggre-gationrdquo ACM Transactions on Knowledge Discovery fromData vol 1 no 1 p 4 2007

[33] Y Jiang Z Deng F-L Chung et al ldquoRecognition of epilepticEEG signals using a novel multiview TSK fuzzy systemrdquo IEEETransactions on Fuzzy Systems vol 25 no 1 pp 3ndash20 2017

[34] Y Jiang F-L Chung H Ishibuchi Z Deng and S WangldquoMultitask TSK fuzzy system modeling by mining intertaskcommon hidden structurerdquo IEEE Transactions on Cyberneticsvol 45 no 3 pp 548ndash561 2015

Computational and Mathematical Methods in Medicine 11