an intelligent parkinson’s disease diagnostic system based...

Research ArticleAn Intelligent Parkinsonrsquos Disease DiagnosticSystem Based on a Chaotic Bacterial Foraging OptimizationEnhanced Fuzzy KNN Approach

Zhennao Cai 1 Jianhua Gu1 CaiyunWen2 Dong Zhao3 Chunyu Huang4

Hui Huang 5 Changfei Tong5 Jun Li5 and Huiling Chen 5

1School of Computer Science and Engineering Northwestern Polytechnical University Xirsquoan 710072 China2Department of Radiology The First Affiliated Hospital of Wenzhou Medical University Wenzhou Zhejiang 325035 China3College of Computer Science and Technology Changchun Normal University Changchun 130032 China4College of Computer Science and Technology Changchun University of Science Technology Changchun 130032 China5College of Mathematics Physics and Electronic Information Engineering Wenzhou University Wenzhou Zhejiang 325035 China

Correspondence should be addressed to Huiling Chen chenhuilingjlugmailcom

Received 29 November 2017 Revised 2 April 2018 Accepted 21 May 2018 Published 21 June 2018

Academic Editor Dingchang Zheng

Copyright copy 2018 Zhennao Cai et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Parkinsons disease (PD) is a common neurodegenerative disease which has attracted more and more attention Many artificialintelligence methods have been used for the diagnosis of PD In this study an enhanced fuzzy k-nearest neighbor (FKNN) methodfor the early detection of PD based upon vocal measurements was developed The proposed method an evolutionary instance-based learning approach termed CBFO-FKNN was developed by coupling the chaotic bacterial foraging optimization with Gaussmutation (CBFO) approach with FKNN The integration of the CBFO technique efficiently resolved the parameter tuning issuesof the FKNN The effectiveness of the proposed CBFO-FKNN was rigorously compared to those of the PD datasets in terms ofclassification accuracy sensitivity specificity and AUC (area under the receiver operating characteristic curve) The simulationresults indicated the proposed approach outperformed the other five FKNN models based on BFO particle swarm optimizationGenetic algorithms fruit fly optimization and firefly algorithm as well as three advanced machine learning methods includingsupport vector machine (SVM) SVMwith local learning-based feature selection and kernel extreme learning machine in a 10-foldcross-validation scheme The method presented in this paper has a very good prospect which will bring great convenience to theclinicians to make a better decision in the clinical diagnosis

1 Introduction

Parkinsons disease (PD) a degenerative disorder of thecentral nervous system is the second most common neu-rodegenerative disease [1] The number of people sufferingfrom PD has increased rapidly worldwide [2] especially indeveloping countries in Asia [3] Although its underlyingcause is unknown the symptoms associated with PD can besignificantly alleviated if detected in the early stages of illness[4ndash6] PD is characterized by tremors rigidity slowed move-ment motor symptom asymmetry and impaired posture [78] Research has shown phonation and speech disorders arealso common among PD patients [9] In fact phonation and

speech disorders can appear in PD patients as many as fiveyears before being clinically diagnosed with the illness [10]The voice disorders associated with PD include dysphoniaimpairment in vocal fold vibration and dysarthria disabilityin correctly articulating speech phonemes [11 12] Little et al[13] first attempted to identify PD patients with dysphonicindicators using a combination of support vector machines(SVM) efficient learning machines and the feature selectionapproach The study results indicated that the proposedmethod efficiently identified PD patients with only fourdysphonic features

Inspired by the results obtained by Little et al [13]many other researchers conducted studies on the use of

HindawiComputational and Mathematical Methods in MedicineVolume 2018 Article ID 2396952 24 pageshttpsdoiorg10115520182396952

2 Computational and Mathematical Methods in Medicine

machine learning techniques to diagnose PD patients onthe same dataset (hereafter Oxford dataset) In [14] Dasmade a comparison of classification score for diagnosis of PDbetween artificial neural networks (ANN) DMneural andRegression and Decision Trees The ANN classifier yieldedthe best results of 929 In [15] AStrom et al designed aparallel feed-forward neural network system and yielded animprovement of 84 on PD classification In [16] Sakar et alproposed amethod that combined SVMand feature selectionusing mutual information to detect PD and obtained aclassification accuracy of 9275 In [17] a PD detectionmethod developed by Li et al using an SVM and a fuzzy-based nonlinear transformation method yielded a maximumclassification accuracy of 9347 In another study Shahbabaet al [18] compared the classification accuracies of a nonlin-ear model based on a combination of the Dirichlet processesmultinomial logit models decision trees and support vectormachines which yielded the highest classification score of877 In [19] Psorakis et al put forward novel convergencemethods and model improvements for multiclass mRVMsThe improved model achieved an accuracy of 8947 In[20] Guo et al proposed a PD detection method with amaximum classification accuracy of 931 by combinationof genetic programming and the expectation maximizationalgorithm (GP-EM) In [21] Luukka used a similarity clas-sifier and a feature selection method using fuzzy entropymeasures to detect PD and a mean classification accuracy of8503 is achieved In [22] Ozcift et al presented rotationforest ensemble classifiers with feature selection using thecorrelation method to identify PD patients the proposedmodel yielded a highest classification accuracy of 8713 In[23] Spadoto et al used a combination of evolutionary-basedtechniques and the Optimum-Path Forest (OPF) classifierto detect PD with a maximum classification accuracy of8401 In [24] Polat integrated fuzzy C-means clustering-based feature weighting (FCMFW) into a KNN classifierwhich yielded a PD classification accuracy of 9793 In[25] Chen et al combined a fuzzy k-nearest neighborclassifier (FKNN) with the principle component analysis(PCA-FKNN) method to detect PD the proposed diagnosticsystem yielded amaximum classification accuracy of 9607In [26] Zuo et al developed an PSO-enhanced FKNN basedPD diagnostic system with a mean classification accuracy of9747 In [27ndash29] Babu et al proposed a lsquoprojection basedlearning meta-cognitive radial basis function network (PBL-McRBFN)rsquo approach for the prediction of PDwhich obtainedan testing accuracy of 9687 on the gene expression datasets 9935 on standard vocal data sets 8436 on gait PDdata sets and 8232 on magnetic resonance images In [30]the hybrid intelligent system for PD detection was proposedwhich included several feature preprocessing methods andclassification techniques using three supervised classifierssuch as least-square SVM probabilistic neural networks andgeneral regression neural network the experimental resultsgives a maximum classification accuracy of 100 for thePD detection Furthermore in [31] Gok et al developed arotation forest ensemble KNN classifier with a classificationaccuracy of 9846 In [32] Shen et al proposed an enhancedSVM based on fruit fly optimization algorithm and have

achieved 9690 classification accuracy for diagnosis ofPD In [33] Peker designed a minimum redundancy max-imum relevance (mRMR) feature selection algorithm withthe complex-valued artificial neural network to diagnosisof PD and obtained a classification accuracy of 9812In [34] Chen et al proposed an efficient hybrid kernelextreme learning machine with feature selection approachThe experimental results showed that the proposed methodcan achieve the highest classification accuracy of 9647and mean accuracy of 9597 over 10 runs of 10-fold CVIn [35] Cai et al have proposed an optimal support vectormachine (SVM) based on bacterial foraging optimization(BFO) combined with the relief feature selection to predictPD the experimental results have demonstrated that theproposed framework exhibited excellent classification perfor-mance with a superior classification accuracy of 9742

Different from the work of Little et al Sakar et al [36]designed voice experiments with sustained vowels wordsand sentences from PD patients and controls The paperreported that sustained vowels had more PD-discriminativepower than the isolated words and short sentences Thestudy result achieved 775 accuracy by using SVM clas-sifier From then on several works have been proposed todetect PD using this PD dataset (hereafter Istanbul dataset)Zhang et al [37] proposed a PD classification algorithmthat integrated a multi-edit-nearest-neighbor algorithm withan ensemble learning algorithm The algorithm achievedhigher classification accuracy and stability compared withthe other algorithms Abrol et al [38] proposed a kernelsparse greedy dictionary algorithm for classification taskscomparing with kernel K-singular value decomposition algo-rithm and kernel multilevel dictionary learning algorithmThe method achieved an average classification accuracy of982 and the best accuracy of 994 on the Istanbul PDdataset with multiple types of sound recordings In [39] theauthors investigated six classification algorithms includingAdaboost support vector machines neural network withmultilayer perceptron (MLP) structure ensemble classifierK-nearest neighbor naive Bayes and presented featureselection algorithms including LASSO minimal redundancymaximal relevance relief and local learning-based featureselection on the Istanbul PD dataset The paper indicatedthat applying feature selection methods greatly increased theaccuracy of classification The SVM and KNN classifiers withlocal learning-based feature selection obtained the optimumprediction ability and execution times

As shown above ANN and SVM have been extensivelyapplied to the detection of PD However understanding theunderlying decision-making processes of ANN and SVM isdifficult due to their black-box characteristics Compared toANN and SVM FKNN ismuch simpler and yieldmore easilyinterpretable results FKNN [40 41] classifiers improvedversions of traditional k-nearest neighbor (KNN) classifiershave been studied extensively since first proposed for the useof diagnostic purposes In recent years many variant versionsof KNNs based on fuzzy sets theory and several extensionshave been developed such as fuzzy rough sets intuitionisticfuzzy sets type 2 fuzzy sets and possibilistic theory basedKNN [42] FKNN allows for the representation of imprecise

Computational and Mathematical Methods in Medicine 3

knowledge via the introduction of fuzzy measures providinga powerfulmethod of similarity description among instancesIn FKNN methods fuzzy set theories are introduced intoKNNs which assign membership degrees to different classesinstead of the distances to their k-nearest neighbors Thuseach of the instances is assigned a class membership valuerather than binary values When it comes to the voting stagethe highest class membership function value is selectedThenbased on these properties FKNN has been applied to numer-ous practical problems such as medical diagnosis problems[25 43] protein identification and prediction problems [4445] bankruptcy prediction problems [46] slope collapseprediction problems [47] and grouting activity predictionproblems [48]

The classification performance of an FKNN greatly relieson its tuning parameters neighborhood size (k) and fuzzystrength (m) Therefore the two parameters should be pre-cisely determined before applying FKNN to practical prob-lems Several studies concerning parameter tuning in FKNNhave been conducted In [46] Chen et al presented the parti-cle swarmoptimization (PSO) basedmethod to automaticallysearch for the two tuning parameters of an FKNN Accordingto the results of the study the proposed method could beeffectively and efficiently applied to bankruptcy predictionproblems More recently Cheng et al [48] developed adifferential evolution optimization approach to determinethe most appropriate tuning parameters of an FKNN andsuccessfully applied to grouting activity prediction problemsin the construction industry Later Cheng et al [47] pro-posed using firefly algorithm to tune the hyperparametersof the FKNN model The FKNN model was then appliedto slop collapse prediction problems The experiment resultsindicated that the developed method outperformed othercommon algorithms The bacterial foraging optimization(BFO) method [49] a relatively new swarm-intelligencealgorithm mimics the cooperative foraging behavior ofseveral bacteria on a multidimensional continuous searchspace and therefore effectively balances exploration andexploitation events Since its introduction BFO has beensubtly introduced to real-world optimization problems [50ndash55] such as optimal controller design problems [49] stockmarket index prediction problems [56] automatic circledetection problems involving digital images [57] harmonicestimation problems [58] active power filter design problems[59] and especially the parameter optimization of machinelearning methods [60ndash63] In [60] BFO was introducedto wavelet neural network training and applied success-fully to load forecasting In [61] an improved BFO algo-rithm was proposed to fine-tune the parameters of fuzzysupport vector machines to identify the fatigue status ofthe electromyography signal The experimental results haveshown that the proposed method is an effective tool fordiagnosis of fatigue status In [62] BFO was proposed tolearn the structure of Bayesian networks The experimentalresults verify that the proposed BFO algorithm is a viablealternative to learn the structures of Bayesian networksand is also highly competitive compared to state-of-the-art algorithms In [63] BFO was employed to optimize the

training parameters appeared in adaptive neuro-fuzzy infer-ence system for speed control of matrix converter- (MC-)fed brushless direct current (BLDC) motor The simulationresults have reported that the BFO approach ismuch superiorto the other nature-inspired algorithms In [64] a chaoticlocal search based BFO (CLS-BFO) was proposed whichintroduced the DE operator and the chaotic search operatorinto the chemotaxis step of the original BFO

Inspired from the above works in this paper the BFOmethod was integrated with FKNN for the maximum clas-sification performance In order to further improve thediversity of the bacteria swarm chaos theory combinationwith theGaussianmutationwas introduced in BFOThen theresulting CBFO-FKNN model was applied to the detectionof PD In our previous work we have applied BFO in theclassification of speech signals for PD diagnosis [35] In thiswork we have further improved the BFO by embedding thechaotic theory and Gauss mutation and combined with theeffective FKNNclassifier In order to validate the effectivenessof the proposed CBFO-FKNN approach FKNN based onfive other meta-heuristic algorithms including original BFOparticle swarm optimization (PSO) genetic algorithms (GA)fruit fly optimization (FOA) and firefly algorithm (FA) wasimplemented for strict comparison In addition advancedmachine learning methods including the support vectormachine (SVM) kernel based extreme learning machine(KELM)methods and SVMwith local learning-based featureselection (LOGO) [65] (LOGO-SVM) were compared withthe proposed CBFO-FKNN model in terms of classifica-tion accuracy (ACC) area under the receiver operatingcharacteristic curve (AUC) sensitivity and specificity Theexperimental results show that the proposed CBFO-FKNNapproach has exhibited high ACC AUC sensitivity andspecificity on both datasets This work is a fully extendedversion of our previously published conference paper [66]and that further improved method has been provided

The main contributions of this study are as follows

(a) First we introduce chaos theory and Gaussian muta-tion enhanced BFO to adaptively determine the twokey parameters of FKNN which aided the FKNNclassifier in more efficiently achieving the maximumclassification performance more stable and robustwhen compared to five other bio-inspired algorithms-based FKNN models and other advanced machinelearning methods such as SVM and KELM

(b) The resulting model CBFO-FKNN is introduced todiscriminate the persons with PD from the healthyones on the two PD datasets of UCImachine learningrepository It is promising to serve as a computer-aided decision-making tool for early detection of PD

The remainder of this paper is structured as follows InSection 2 background information regarding FKNN BFOchaos theory and Gaussian mutation is presented Theimplementation of the proposedmethodology is explained inSection 3 In Section 4 the experimental design is describedin detail The experimental results and a discussion arepresented in Section 5 Finally Section 6 concludes the paper


2 Background Information

21 Fuzzy k-Nearest Neighbor (FKNN) In this section a briefdescription of FKNN is provided A detailed description ofFKNN can be referred to in [41] In FKNN the fuzzy mem-bership values of samples are assigned to different categoriesas follows

119906119894 (119909) = sum119870119895=1 119906119894119895 (1 10038171003817100381710038171003817119909 minus 119909119895100381710038171003817100381710038172(119898minus1))sum119870119895=1 (1 10038171003817100381710038171003817119909 minus 119909119895100381710038171003817100381710038172(119898minus1)) (1)

where i=12 C j=12 K C represents the number ofclasses and K means the number of nearest neighbors Thefuzzy strength parameter (m) is used to determine how heav-ily the distance is weighted when calculating each neighborrsquoscontribution to themembership value119898 isin (1infin) 119909minus119909119895 isusually selected as the value of m In addition the Euclideandistance the distance between x and its jth nearest neighbor119909119895 is usually selected as the distance metric Furthermore119906119894119895 denotes the degree of membership of the pattern 119909119895 fromthe training set to class i among the k-nearest neighbors of119909 In this study the constrained fuzzy membership approachwas adopted in that the k-nearest neighbors of each trainingpattern (ie 119909119896) were determined and the membership of xkin each class was assigned as

119906119894119895 (119909119896) = 051 + (119899119895119870) lowast 049 if 119895 = 119894(119899119895119870) lowast 049 if 119895 = 119894 (2)

The value of 119899119895 denotes the number of neighbors belong-ing to 119895th class The membership values calculated using (2)should satisfy the following equations

119862sum119868=1

120583119894119895 = 1119895 = 1 2 sdot sdot sdot 119899 119862 is the number of classes

0 lt 119899sum119895=1

119906119894119895 lt 119899 119906119894119895 isin [0 1] (3)

After calculating all of the membership values of a querysample it is assigned to the class with which it has the highestdegree of membership ie

119862 (119909) = 119862argmax119894=1

(119906119894 (119909)) (4)

22 Bacterial Foraging Optimization (BFO) The bacterialforaging algorithm (BFO) is a novel nature-inspired opti-mization algorithm proposed by Passino in 2002 [49] TheBFO simulates the mechanism of approaching or movingaway while sensing the concentration of peripheral sub-stances in bacterial foraging process This method containsfour basic behaviors chemotaxis swarming reproductionand elimination-dispersal

221 Chemotaxis The chemotaxis behavior simulates twodifferent positional shifts of E coli bacterium that depend onthe rotation of the flagellum namely tumbling and movingThe tumbling refers to looking for new directions and themoving refers to keeping the direction going The specificoperation is as follows first a unit step is moved in a certainrandom direction If the fitness value of the new positionis more suitable than the previous one it will continueto move in that direction if the fitness value of the newposition is not better than before the tumble operation isperformed and moves in another random direction Whenthemaximumnumber of attempts is reached the chemotaxisstep is stoppedThe chemotaxis step to operate is indicated bythe following

120579119894 (119895 + 1 119896 119897) = 120579119894 (119895 119896 119897) + 119862 (119894) lowast 119889119888119905119894119889119888119905119894 = Δ (119894)radicΔ119879 (119894) Δ (119894)

(5)

where 120579119894(119895 119896 119897) is the position of the ith bacterium Thej k and l respectively indicate the number of bacterialindividuals to complete the chemotaxis reproduction andelimination-dispersal C(i) is the chemotaxis step length forthe ith bacteria to move Δ is the random vector between [-11]222 Swarming In the process of foraging the bacterialcommunity can adjust the gravitation and repulsion betweenthe cell and the cell so that the bacteria in the caseof aggregation characteristics and maintain their relativelyindependent position The gravitation causes the bacteriato clump together and the repulsion forces the bacteria todisperse in a relatively independent position to obtain food

223 Reproduction In the reproduction operation of BFOalgorithm the algorithm accumulates the fitness values ofall the positions that the bacterial individual passes throughin the chemotaxis operation and arranges the bacteria indescending order Then the first half of the bacteria dividesthemselves into two bacteria by binary fission and the otherhalf die As a result the new reproduced bacterial individualhas the same foraging ability as the original individual andthe population size of bacterial is always constant

224 Elimination-Dispersal After the algorithm has beenreproduced for several generations the bacteria will undergoelimination-dispersal at a given probability Ped and theselected bacteria will be randomly redistributed to newpositions Specifically if a bacterial individual in the bacte-rial community satisfies the probability Ped of elimination-dispersal the individual loses the original position of foragingand randomly selects a new position in the solution spacethereby promoting the search of the global optimal solution

23 ChaoticMapping Chaos as a widespread nonlinear phe-nomenon in nature has the characteristics of randomnessergodicity sensitivity to initial conditions and so on [67] Dueto the characteristics of ergodicity and randomness chaotic


motions can traverse all the states in a certain range accordingto their own laws without repetition Therefore if we usechaos variables to search optimally we will undoubtedlyhave more advantages than random search Chaos ergodicityfeatures can be used to optimize the search and avoid fallinginto the local minima therefore chaos optimization searchmethod has become a novel optimization technique Chaoticsequences generated by different mappings can be used suchas logistic map sine map singer map sinusoidal map andtent map In this paper several chaotic maps were tried andthe best one was chosen to combine with the BFO algorithmAccording to the preliminary experiment logistic map hasachieved the best results Thus the chaotic sequences aregenerated by using logistic map as follows

119909119894+1 = 119906119909119894 (1 minus 119909119894) (6)

u is the control parameter and let u = 4 When u = 4 thelogistic mapping comes into a thorough chaotic state Let119909119894 isin (0 1) and 119909119894 = 025 05 075

The initial bacterial population 120579 is mapped to the chaoticsequence that has been generated according to (6) resultingin a corresponding chaotic bacterial population pch

119901119888ℎ = 119909119894 lowast 120579 (7)

24 Gaussian Mutation The Gaussian mutation operationhas been derived from the Gaussian normal distribution andhas demonstrated its effectiveness with application to evolu-tionary search [68] This theory was referred to as classicalevolutionary programming (CEP)The Gaussian mutationshave been used to exploit the searching capabilities of ABC[69] PSO [70] and DE [71] Also Gaussian mutation ismore likely to create a new offspring near the original parentbecause of its narrow tail Due to this the search equationwill take smaller steps allowing for every corner of thesearch space to be explored in a much better way Henceit is expected to provide relatively faster convergence TheGaussian density function is given by

119891119892119886119906119904119904119894119886119899(01205902) (120572) = 1radic21205871205902 119890minus120572221205902 (8)

where 1205902 is the variance for each member of the population

3 Proposed CBFO-FKNN Model

In this section we described the new evolutionary FKNNmodel based on the CBFO strategy The two key parametersof FKNN were automatically tuned based on the CBFOstrategy As shown in Figure 1 the proposedmethodology hastwo main parts including the inner parameter optimizationprocedure and outer performance evaluation procedureThe main objective of the inner parameter optimizationprocedure was to optimize the parameter neighborhoodsize (k) and fuzzy strength parameter (m) by using theCBFO technique via a 5-fold cross-validation (CV) Thenthe obtained best values of (k m) were input into the FKNNprediction model in order to perform the PD diagnostic

Table 1 Description of the Oxford PD data set

Label FeatureS1 MDVPFo(Hz)S2 MDVPFhi(Hz)S3 MDVPFlo(Hz)S4 MDVPJitter()S5 MDVPJitter(Abs)S6 MDVPRAPS7 MDVPPPQS8 JitterDDPS9 MDVPShimmerS10 MDVPShimmer(dB)S11 ShimmerAPQ3S12 ShimmerAPQ5S13 MDVPAPQS14 ShimmerDDAS15 NHRS16 HNRS17 RPDES18 D2S19 DFAS20 Spread1S21 Spread2S22 PPE

classification task in the outer loop via the 10-fold CV Theclassification error rate was used as the fitness function

119891119894119905119899119890119904119904 = (sum119870119894=1 119905119890119904119905119864119903119903119900119903119894)119896 (9)

where testErrori means the average test error of the FKNNclassifier

The main steps conducted by the CBFO strategy aredescribed in detail as shown in Algorithm 1

4 Experimental Design

41 Oxford Parkinsonrsquos Disease Data The Oxford Parkinsonrsquosdisease data set was donated by Little et al [13] abbreviationas Oxford dataset The data set was used to discriminatepatients with PD from healthy controls via the detectionof differences in vowel sounds Various biomedical voicemeasurements were collected from 31 subjects 23 of themare patients with PD and 8 of them are healthy controlsThe subjects ranged from 46 to 85 years of age Each subjectprovided an average of six sustained vowel ldquoahh rdquo phona-tions ranging from 1 to 36 seconds in length [13] yielding195 total samples Each recording was subjected to differentmeasurements yielding 22 real-value features Table 1 liststhese 22 vocal features and their statistical parameters

42 Istanbul Parkinsonrsquos Disease Data The second data set inthis study was deposited by Sakar et al [36] from IstanbulTurkey abbreviation as Istanbul dataset It contained mul-tiple types of sound recordings including sustained vowels


Figure 1 Flowchart of the proposed CBFO-FKNN diagnostic system


BeginStep 1 Parameter Initialization Initialize the number of dimensions in the search space p the

swarm size of the population S the number of chemotactic steps Nc the swimming length Ns thenumber of reproduction steps Nre the number of elimination-dispersal events Ned theelimination-dispersal probability Ped the size of the step C(i) taken in the random directionspecified by the tumble

Step 2 Population Initialization Calculate chaotic sequence according to Eq (6) Thecorresponding chaotic bacterial population is calculated according to the original bacterialpopulation mapped into the chaotic sequence according to Eq (7) From the original and itscorresponding chaotic bacterial populations S superior individuals are selected as the initialsolutions of bacterial populations

Step 3 for ell=1Ned lowastElimination and dispersal looplowastfor K=1Nre lowastReproduction looplowast

for j=1Nc lowast chemotaxis looplowastIntertime=Intertime+1 lowast represent the number of iterationslowastfor i=1s

lowastfobj represents calculating the fitness of the ith bacterium at the jthchemotactic Kth reproductive and lth elimination-dispersal stepslowastJ(ijKell)=fobj(P(ijKell))lowast Jlast stores this value since a cost better than a run may be identifiedlowastJlast=J(ijKell)lowast gbest(1) stores the current optimal bacterial individuallowast

gbest(1)=P(ijKell)Tumble according to Eq(5)lowastSwim (for bacteria that seem to be headed in the right direction)lowastm=0 lowast Initialize counter for swim lengthlowastwhile mltNsm=m+1if J(ij+1Kell)ltJlast

lowast Jlast stores this value since a cost better than a run may be identifiedlowastJlast=J(ij+1Kell)Tumble according Eq(5)if JlastltGbest

lowast Gbest stores the current optimal fitness function valuelowastGbest = Jlastgbest(1)=P(ij+1Kell)

Endelse

m=NsEnd

Gaussian mutation operationMoth pos m gaus=gbest(1)lowast(1+randn(1))Moth fitness m gaus=fobj(Moth pos m gaus)Moth fitness s=fobj(gbest(1))Moth fitness comb=[Moth fitness m gausMoth fitness s][simmm]=min(Moth fitness comb)if mm==1

gbest(1)=Moth pos m gausendfitnessGbest = fobj(gbest(1))if fitnessGbestltGbest

Gbest = fitnessGbestend

EndEnd lowastGo to next bacteriumlowast

End lowastGo to the next chemotacticlowastlowastReproductionlowastJhealth=sum(J(Kell)2) lowast Set the health of each of the S bacterialowast[Jhealth sortind]=sort(Jhealth) lowastSorts the nutrient concentration in order of ascendinglowastlowast Rearrange the bacterial populationlowastP(1K+1ell)=P(sortindNc+1Kell)lowastSplit the bacteria (reproduction)lowast

for i=1Sr

Algorithm 1 Continued


lowastThe least fit do not reproduce the most fit ones split into two identical copieslowastP(i+Sr1K+1ell)=P(i1K+1ell)

EndEnd lowastGo to next reproductionlowastlowastElimination-Dispersallowastfor m=1sif Pedgtrand lowastrandomly generates a new individual anywhere in the solution spacelowast

Reinitialize bacteria mEnd

EndEnd lowastGo to next Elimination-Dispersallowast

End

Algorithm 1 The steps of CBFO

numbers words and short sentences from 68 subjectsSpecifically the training data collected from 40 personsincluding 20 patients with PD ranging from 43 to 77 and20 healthy persons ranging from 45 to 83 while testing datawas collected from 28 different patients with PD ranging 39and 79 In this study we selected only 3 types of sustainedvowel recordings a o and u with similar data type to theOxford PD dataset We merged them together and produceda database which contains total 288 sustained vowels samplesand the analyses were made on these samples As shownin Table 2 a group of 26 linear and time-frequency basedfeatures are extracted for each voice sample

43 Experimental Setup The experiment was performed ona platform of Windows 7 operating system with an Intel (R)Xeon (R) CPU E5-2660 v3 26 GHz and 16GB of RAMTheCBFO-FKNN BFO-FKNN PSO-FKNN GA-FKNN FOA-FKNN FA-FKNN SVM and KELM classification modelswere implemented with MATLAB 2014b The LIBSVM pack-age [72] was used for the SVM classification The algo-rithm available at httpwww3ntuedusghomeegbhuangwas used for the KELM classification The CBFO-FKNNmethod was implemented from scratch The data was scaledinto a range of [0 1] before each classification was conducted

The parameters C and 120574 in 119870(119909 119909119894) = exp(minus120574119909 minus 1199091198942)used during the SVM and KELM classifications were deter-mined via the grid search method the search ranges weredefined as 119862 isin 2minus5 2minus3 215 and 120574 isin 2minus15 2minus13 25A population swarm size of 8 chemotactic step number of25 swimming length of 4 reproduction step number of 3elimination-dispersal event number of 2 and elimination-dispersal probability of 025 were selected for the CBFO-FKNN The chemotaxis step value was established throughtrial and error as shown in the experimental results sectionThe initial parameters of the other four meta-heuristic algo-rithms involved in training FKNN are chosen by trial anderror as reported in Table 3

44 Data Classification A stratified k-fold CV [73] was usedto validate the performance of the proposed approach andother comparative models In most studies k is given thevalue of 10 During each step 90 of the samples are used

Table 2 Description of the Istanbul PD data set

Label FeatureS1 Jitter(local)S2 Jitter(local absolute)S3 Jitter(rap)S4 Jitter(ppq5)S5 Jitter(ddp)S6 Number of pulsesS7 Number of periodsS8 Mean periodS9 Standard dev of periodS10 Shimmer(local)S11 Shimmer(local dB)S12 Shimmer(apq3)S13 Shimmer(apq5)S14 Shimmer(apq11)S15 Shimmer(dda)S16 Fraction of locally unvoiced framesS17 Number of voice breaksS18 Degree of voice breaksS19 Median pitchS20 Mean pitchS21 Standard deviationS22 Minimum pitchS23 Maximum pitchS24 AutocorrelationS25 Noise-to-HarmonicS26 Harmonic-to-Noise

to form a training set and the remaining samples are used asthe test set Then the average of the results of all 10 trials iscomputed The advantage of this method is that all of the testsets remain independent ensuring reliable results

A nested stratified 10-fold CV which has been widelyused in previous research was used for the purposes ofthis study [74] The classification performance evaluationwas conducted in the outer loop Since a 10-fold CV wasused in the outer loop the classifiers were evaluated in one


Table 3 Parameter setting of other optimizers involved in trainingFKNN

Parameters GA PSO FA FOAPopulation size 8 8 8 8Max iteration 250 250 250 250Search space [2minus8 28] [2minus8 28] [2minus8 28] [2minus8 28]Crossover rate 08 - - -Mutation rate 005 - - -Acceleration constants - 2 - -Inertia weight - 1 - -Differential weight - -Alpha - - 05 -Beta - - 02 -Gamma - - 1 -ax - - - 20bx - - - 10ay - - - 20by - - - 10

independent fold of data and the other nine folds of datawere left for training The parameter optimization processwas performed in the inner loop Since a 5-fold CV was usedin the inner loop the CBFO-FKNN searched for the optimalvalues of k and m and the SVM and KELM searched for theoptimal values of C and 120574 in the remaining nine folds of dataThe nine folds of data were further split into one fold of datafor the performance evaluation and four folds of data wereleft for training

45 Evaluation Criteria ACC AUC sensitivity and speci-ficity were taken to evaluate the performance of differentmodels These measurements are defined as

119860119862119862 = 119879119875 + 119879119873(119879119875 + 119865119875 + 119865119873 + 119879119873) times 100 (10)

119878119890119899119904119894119905119894V119894119905119910 = 119879119875(119879119875 + 119865119873) times 100 (11)

119878119901119890119888119894119891119894119888119894119905119910 = 119879119873(119865119875 + 119879119873) times 100 (12)

where TP is the number of true positives FN means thenumber of false negatives TN represents the true negativesand FP is the false positives AUC [75] is the area under theROC curve

5 Experimental Results and Discussion

51 Benchmark Function Validation In order to test the per-formance of the proposed algorithm CBFO 23 benchmarkfunctions which include unimodal multimodal and fixed-dimension multimodal were used to do experiments Thesefunctions are listed in Tables 4ndash6 where Dim represents thedimension Range is the search space and 119891min is the bestvalue

In order to verify the validity of the proposed algo-rithm the original BFO Firefly Algorithm(FA)[76] FlowerPollination Algorithm (FPA)[77] Bat Algorithm (BA)[78]Dragonfly Algorithm (DA)[79] Particle Swarm Optimiza-tion (PSO)[80] and the improved BFO called PSOBFO werecompared on these issues The parameters of the abovealgorithm are set according to their original papers and thespecific parameter values are set as shown in Table 7 Inorder to ensure that the results obtained are not biased 30independent experiments are performed In all experimentsthe number of population size is set to 50 and the maximumnumber of iterations is set to 500

Tables 8ndash10 show average results (Avg) standard devia-tion (Stdv) and overall ranks for different algorithms dealingwith F1-23 issues It should be noted that the rankingis based on the average result (Avg) of 30 independentexperiments for each problem In order to visually comparethe convergence performance of our proposed algorithmand other algorithms Figures 2ndash4 use the logarithmic scalediagram to reflect the convergence behaviors In Figures2ndash4 we only select typical function convergence curvesfrom unimodal functions multimodal functions and fixed-dimension multimodal functions respectively The resultsof the unimodal F1-F7 are shown in Table 8 As shownthe optimization effect of CBFO in F1 F2 F3 and F4 isthe same as the improved PSOBFO but the performance isimproved compared with the original BFO Moreover Fromthe ranking results it can be concluded that compared withother algorithms CBFO is the best solution to solve theproblems of F1-F7

With respect to the convergence trends described inFigure 2 it can be observed that the proposed CBFO iscapable of testifying a very fast convergence and it can besuperior to all other methods in dealing with F1 F2 F3 F4F5 and F7 For F1 F2 F3 and F4 the CBFO has converged sofast during few searching steps compared to other algorithmsIn particular when dealing with cases F1 F2 F3 and F4 thetrend converges rapidly after 250 iterations

The calculated results for multimodal F8-F13 are tabu-lated in Table 9 It is observed that CBFO has attained theexact optimal solutions for 30-dimension problems F8 andF12 in all 30 runs From the results for F9 F10 F11 andF13 problems it can be agreed that the CBFO yields verycompetitive solutions compared to the PSOBFO Howeverbased on rankings theCBFO is the best overall technique andthe overall ranks show that the BFO FA BA PSO FPA andDA algorithms are in the next places respectively

According to the corresponding convergence trendrecorded in Figure 3 the relative superiority of the proposedCBFO in settling F8 F11 and F12 test problems can berecognized In tackling F11 the CBFO can dominate all itscompetitors in tackling F11 only during few iterations Onthe other hand methods such as FPA BA DA and PSOstill cannot improve the quality of solutions in solving F11throughout more steps

The results for F14 to F23 are tabulated in Table 10The results in Table 10 reveal that the CBFO is the bestalgorithm and can outperform all other methods in dealingwith F15 problems In F16 F17 and F19 it can be seen that


Table 4 Unimodal benchmark functions

Function Dim Range 119891min

1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0

Table 5 Multimodal benchmark functions


1198918 (119909) = 119899sum119894=1

minus119909119894 sin(radic10038161003816100381610038161199091198941003816100381610038161003816) 30 [-500500] -4189829lowast51198919 (119909) = 119899sum

119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0

11989110 (119909) = minus20 exp(minus02radic 1119899119899sum119894=1

1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)

119896 (119909119894 minus 119886) 119909119894 gt 1198860 minus119886 lt 119909119894 lt 119886119896 (119909119894 minus 119886) 119909119894 lt minus119886

11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1

(119909i minus 1])2 [1 + sin2 (3120587119909i + 1)] + (119909n minus 1)2 [1 + sin2 (2120587119909n)] 30 [-5050] 0

+ nsumi=1

119906(119909i 5 100 4)

the optimization effect of all the algorithms is not muchdifferent In dealing with F20 case the CBFOrsquos performanceis improved compared to original BFO and the improvedPSOBFO Especially in solving F18 the proposed algorithmis much better than the improved PSOBFO From Figure 4we can see that the convergence speed of the CBFO is betterthan other algorithms in dealing with F15 F18 F19 and F20For F15 it surpasses all methods

In order to investigate significant differences of obtainedresults for the CBFO over other competitors the Wilcoxonrank-sum test [81] at 5 significance level was also employedin this paper The p values of comparisons are reported inTables 11ndash13 In each table each p value which is not lower

than 005 is shown in bold face It shows that the differencesare not significant

The p values are also provided in Table 11 for F1-F7Referring to the p values of the Wilcoxon test in Table 11it is verified that the proposed algorithm is statisticallymeaningful The reason is that all p values are less than 005except PSOBFO in F1 F2 F3 and F4 According to the pvalues in Table 12 all values are less than 005 except PSOBFOin F11 problem Hence it can be approved that the results ofthe CBFO are statistically improved compared to the othermethods As can be seen from the p value in Table 13 theCBFO algorithm is significantly better than the PSOBFOFPA BA and PSO for F14-F23


Table 6 Fixed-dimension multimodal benchmark functions


11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316

11989117 (119909) = (1199092 minus 5141205872 11990921 + 51205871199091 minus 6)2 + 10 (1 minus 18120587) cos1199091 + 10 2 [-55] 0398

11989118 (119909) = [1 + (1199091 + 1199092 + 1)2 (19 minus 141199091 + 311990921 minus 141199092 + 611990911199092 + 311990922)] 2 [-22] 3times [30 + (21199091 minus 31199092)2 119905119894119898119890119904 (18 minus 321199091 + 1211990921 + 481199092 minus 3611990911199092 + 2711990922)]11989119 (119909) = minus 4sum

119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1

[(119883 minus 119886119894) (119883 minus 119886119894)T + 119888119894]minus1 4 [010] -101532

11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1


Table 7 Parameters setting for the involved algorithms

Method Population size Maximum generation Other parametersBFO 50 500 Δ isin [-1 1]BA 50 500 Q Frequencyisin[0 2] A Loudness 05 r Pulse rate 05DA 50 500 119908 isin [09 02] s = 01 a = 01 c = 07 f = 1 e = 1FA 50 500 1205730=1 120572 isin [0 1] 120574=1FPA 50 500 switch probability p=08 120582=15PSO 50 500 inertial weight=1 c1=2 c2=2PSOBFO 50 500 inertial weight=1 c1=12 c2=05 Δ isin [-1 1]

The results demonstrate that the utilized chaotic mappingstrategy and Gaussian mutation in the CBFO technique haveimproved the efficacy of the classical BFO in a significantmanner On the one hand applying the chaotic mappingstrategy to the bacterial population initialization process canspeed up the initial exploration of the algorithmOn the otherhand adding Gaussian mutation to the current best bacterialindividual in the iterative process helps to jump out of thelocal optimum In conclusion the proposed CBFO can makea better balance between explorative and exploitative trendsusing the embedded strategies

52 Results on the Parkinsonrsquos Disease Many studies havedemonstrated that the performance of BFO can be affectedheavily by the chemotaxis step size C(i) Therefore we havealso investigated the effects of C(i) on the performance of theCBFO-FKNN Table 14 displays the detailed results of CBFO-FKNNmodel with different values ofC(i) on the two datasetsIn the table the mean results and their standard deviations(in parentheses) are listed As shown the CBFO-FKNN

model performed best with an average accuracy of 9697an AUC of 09781 a sensitivity of 9687 and a specificityof 9875 when C(i) = 01 on the Oxford dataset and anaverage accuracy of 8368 an AUC of 06513 a sensitivityof 9692 and a specificity of 3333 when C(i) = 02 on theIstanbul dataset Furthermore the CBFO-FKNN approachalso yielded the most reliable results with the minimumstandard deviation when C(i) = 01 and C(i) = 02 on theOxford dataset and Istanbul dataset respectively Thereforevalues of 01 and 02 were selected as the parameter value ofC(i) for CBFO-FKNNon the two datasets respectively in thesubsequent experimental analysis

The ACC AUC sensitivity specificity and optimal (km)pair values of each fold obtained via the CBFO-FKNNmodelwith C(i) = 01 and C(i) = 02 on the Oxford dataset andIstanbul dataset are shown in Tables 15 and 16 respectivelyAs shown each fold possessed a different parameter pair(k m) since the parameters for each set of fold data wereautomatically determined via the CBFO method With theoptimal parameter pair the FKNN yielded different optimal


Table 8 Results of unimodal benchmark functions (F1-F7)

F CBFO PSOBFO BFO FA FPA BA DA PSO

F1Avg 0 0 873E-03 984E-03 145E+03 170E+01 215E+03 145E+02Stdv 0 0 385E-03 320E-03 407E+02 209E+00 113E+03 156E+01Rank 1 1 3 4 7 5 8 6


F3Avg 0 0 496E-12 259E+03 199E+03 115E+02 146E+04 596E+02Stdv 0 0 897E-12 838E+02 484E+02 368E+01 891E+03 157E+02Rank 1 1 3 7 6 4 8 5

F4Avg 0 0 324E-02 843E-02 258E+01 378E+00 295E+01 494E+00Stdv 0 0 599E-03 160E-02 396E+00 302E+00 822E+00 434E-01Rank 1 1 3 4 7 5 8 6

F5Avg 290E+01 0 655E+04 233E+02 257E+05 448E+03 496E+05 177E+05Stdv 262E-02 0 NA 430E+02 188E+05 124E+03 646E+05 495E+04Rank 2 1 5 3 7 4 8 6

F6Avg 134E-01 371E-01 211E+03 114E-02 153E+03 170E+01 206E+03 139E+02Stdv 176E-02 599E-02 115E+04 471E-03 423E+02 251E+00 152E+03 167E+01Rank 2 3 8 1 6 4 7 5

F7Avg 362E-04 488E-03 377E-03 108E-02 460E-01 189E+01 692E-01 105E+02Stdv 321E-04 344E-03 333E-03 279E-03 142E-01 200E+01 379E-01 244E+01Rank 1 3 2 4 5 7 6 8

Sum of ranks 9 11 27 27 45 35 50 44Average rank 12857 15714 38571 38571 64286 5 71429 62857Overall rank 1 2 3 3 7 5 8 6

Table 9 Results of multimodal benchmark functions (F8-F13)


F8Avg -347E+04 -255E+03 -247E+03 -655E+03 -758E+03 -745E+03 -544E+03 -705E+03Stdv 179E+04 580E+02 525E+02 670E+02 212E+02 656E+02 555E+02 598E+02Rank 1 7 8 5 2 3 6 4

F9Avg -289E+02 -290E+02 -288E+02 337E+01 144E+02 273E+02 171E+02 378E+02Stdv 298E-01 0 861E-01 113E+01 168E+01 308E+01 415E+01 246E+01Rank 2 1 3 4 5 7 6 8

F10Avg -966E+12 -107E+13 -908E+12 547E-02 131E+01 556E+00 102E+01 871E+00Stdv 321E+11 397E-03 734E+11 131E-02 159E+00 377E+00 215E+00 394E-01Rank 2 1 3 4 8 5 7 6

F11Avg 0 0 499E-03 653E-03 149E+01 635E-01 165E+01 104E+00Stdv 0 0 318E-03 263E-03 338E+00 631E-02 841E+00 633E-03Rank 1 1 3 4 7 5 8 6

F12Avg 134E-11 127E-08 304E-10 249E-04 116E+02 133E+01 790E+04 549E+00Stdv 346E-11 202E-08 597E-10 106E-04 475E+02 493E+00 426E+05 904E-01Rank 1 3 2 4 7 6 8 5

F13Avg 420E-02 992E-02 992E-02 318E-03 618E+04 277E+00 446E+05 290E+01Stdv 464E-02 252E-08 417E-10 253E-03 934E+04 437E-01 719E+05 658E+00Rank 2 3 3 1 7 5 8 6



Table 10 Results of fixed-dimension multimodal benchmark functions (F14-F23)


F14Avg 983E+00 311E+00 296E+00 182E+00 104E+00 453E+00 130E+00 441E+00Stdv 451E+00 171E+00 222E+00 842E-01 156E-01 391E+00 696E-01 320E+00Rank 8 5 4 3 1 7 2 6

F15Avg 433E-04 949E-04 624E-04 285E-03 744E-04 829E-03 373E-03 141E-03Stdv 165E-04 300E-04 225E-04 471E-03 141E-04 135E-02 595E-03 404E-04Rank 1 4 2 6 3 8 7 5

F16Avg -103E+00 -103E+00 -103E+00 -103E+00 -103E+00 -103E+00 -103E+00 -103E+00Stdv 523E-06 160E-04 796E-06 336E-09 255E-08 894E-04 347E-06 249E-03Rank 1 1 1 1 1 1 1 1


F18Avg 300E+00 301E+00 300E+00 300E+00 300E+00 310E+00 300E+00 324E+00Stdv 200E-04 653E-03 313E-04 259E-08 160E-06 865E-02 609E-07 361E-01Rank 1 6 1 1 1 6 1 8



F21Avg -603E+00 -101E+01 -980E+00 -792E+00 -101E+01 -464E+00 -661E+00 -367E+00Stdv 974E-01 427E-02 128E+00 347E+00 130E-01 243E+00 262E+00 131E+00Rank 6 1 3 4 1 7 5 8

F22Avg -645E+00 -101E+01 -102E+01 -989E+00 -102E+01 -503E+00 -735E+00 -433E+00Stdv 122E+00 960E-01 961E-01 194E+00 487E-01 293E+00 298E+00 167E+00Rank 6 3 1 4 1 7 5 8

F23Avg -691E+00 -973E+00 -998E+00 -105E+01 -102E+01 -536E+00 -635E+00 -442E+00Stdv 130E+00 182E+00 163E+00 107E-06 494E-01 290E+00 336E+00 133E+00Rank 5 4 3 1 2 7 6 8


Table 11 The calculated p-values from the functions (F1-F7) for the CBFO versus other optimizers

Problem PSOBFO BFO FA FPA BA DA PSOF1 1 173E-06 173E-06 173E-06 173E-06 173E-06 173E-06F2 1 173E-06 173E-06 173E-06 173E-06 173E-06 173E-06F3 1 173E-06 173E-06 173E-06 173E-06 173E-06 173E-06F4 1 173E-06 173E-06 173E-06 173E-06 173E-06 173E-06F5 173E-06 173E-06 604E-03 173E-06 173E-06 173E-06 173E-06F6 173E-06 173E-06 173E-06 173E-06 173E-06 173E-06 173E-06F7 192E-06 352E-06 173E-06 173E-06 173E-06 173E-06 173E-06

classification performance values in each fold This wasattributed to the adaptive tuning of the two parameters by theCBFO based on the specific distribution of each data set

In order to investigate the convergence behavior of theproposed CBFO-FKNN method the classification error rateversus the number of iterations was recorded For simplicity

herein we take the Oxford dataset for example Figures5(a)ndash5(d) display the learning curves of the CBFO-FKNNfor folds 1 3 5 and 7 in the 10-fold CV respectively Asshown all four fitness curves of CBFO converged into aglobal optimum in fewer than 20 iterations The fitnesscurves gradually improved from iterations 1 through 20 but


Figure 2 Convergence curves of unimodal functions



Problem PSOBFO BFO FA FPA BA DA PSOF8 173E-06 173E-06 173E-06 192E-06 173E-06 173E-06 192E-06F9 173E-06 689E-05 173E-06 173E-06 173E-06 173E-06 173E-06F10 173E-06 490E-04 173E-06 173E-06 173E-06 173E-06 173E-06F11 1 173E-06 173E-06 173E-06 173E-06 173E-06 173E-06F12 352E-06 579E-05 173E-06 173E-06 173E-06 173E-06 173E-06F13 173E-06 192E-06 361E-03 173E-06 173E-06 173E-06 173E-06

Figure 3 Convergence curves of multimodal functions

exhibited no significant improvements after iteration 20The fitness curves ceased after 50 iterations (the maximumnumber of iterations) The error rates of the fitness curvesdecreased rapidly at the beginning of the evolutionary processand continued to decrease slowly after a certain number ofiterations During the latter part of the evolutionary processthe fitness curves remained stable until the stopping criteria

the maximum number of iterations were satisfied Thus theproposed CBFO-FKNN model efficiently converged towardthe global optima

To validate the effectiveness of the proposed methodthe CBFO-FKNN model was compared to five other meta-heuristic algorithms-based FKNN models as well as threeother advanced machine learning approaches including


Figure 4 Convergence curves based on fixed-dimension multimodal functions


Problem PSOBFO BFO FA FPA BA DA PSOF14 634E-06 698E-06 522E-06 318E-06 222E-04 173E-06 106E-04F15 388E-06 831E-04 173E-06 124E-05 192E-06 429E-06 192E-06F16 235E-06 750E-01 173E-06 173E-06 173E-06 197E-05 173E-06F17 192E-06 360E-01 173E-06 173E-06 173E-06 260E-06 173E-06F18 235E-06 845E-01 173E-06 173E-06 173E-06 173E-06 173E-06F19 192E-06 822E-02 173E-06 173E-06 173E-06 819E-05 173E-06F20 341E-05 894E-04 644E-01 260E-06 173E-06 382E-01 173E-06F21 173E-06 213E-06 499E-03 173E-06 822E-03 704E-01 634E-06F22 388E-06 260E-06 164E-05 173E-06 185E-02 185E-01 892E-05F23 124E-05 260E-05 173E-06 173E-06 196E-02 405E-01 102E-05


Table 14 Detailed results of CBFO-FKNN with different values of C(i) on the two datasets

C(i) Oxford dataset Istanbul datasetACC AUC Sen Spec ACC AUC Sen Spec

005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)

Figure 5 Learning curves of CBFO for fold 2 (a) fold 4 (b) fold 6 (c) and fold 8 (d) during the training stage


Table 15 Detailed classification results of CBFO-FKNN on the Oxford dataset

Fold CBFO-FKNNNo ACC AUC Sen Spec 119896 1198981 09474 09667 09333 10000 1 1772 10000 10000 10000 10000 1 2943 09500 09688 09375 10000 1 3924 09500 09375 10000 08750 1 6895 09500 09667 09333 10000 1 9336 09000 09412 08824 10000 1 7267 10000 10000 10000 10000 1 9218 10000 10000 10000 10000 1 7619 10000 10000 10000 10000 1 89510 10000 10000 10000 10000 1 725Mean 09697 09781 09687 09875 1 651

Table 16 Detailed classification results of CBFO-FKNN on theIstanbul dataset


Figure 6 Comparison results obtained on theOxford dataset by thenine methods

SVM KELM and SVM with local learning-based featureselection (LOGO-SVM) As shown in Figure 6 the CBFO-FKNN method performed better than other competitorsin terms of ACC AUC and sensitivity on the Oxford

Figure 7 Comparison results obtained on the Istanbul dataset bythe nine methods

dataset We can see that the CBFO-FKNN method yieldsthe highest average ACC value of 9697 followed byPSO-FKNN LOGO-SVM KELM SVM FOA-FKNN FA-FKNN and BFO-FKNN GA-FKNN has got the worstresult among the all methods On the AUC metric OBF-FKNN obtained similar results with FA-FKNN followed byFOA-FKNN GA-FKNN PSO-FKNN BFO-FKNN KELMand LOGO-SVM and SVM has got the worst result Onthe sensitivity metric CBFO-FKNN has achieved obvi-ous advantages LOGO-FKNN ranked second followed byKELM SVM PSO-FKNN FOA-FKNN FA-FKNN and GA-FKNN BFO-FKNN has got the worst performance Onthe specificity metric FA-FKNN achieved the maximumresults GA-FKNN and FOA-FKNN have achieved similarresults which ranked second followed by BFO-FKNN PSO-FKNN CBFO-FKNN and SVM KELM and LOGO-SVMhave obtained similar results both of which got the worstperformance Regarding the Istanbul dataset CBFO-FKNNproduced the highest result with the ACC of 8368 whilethe LOGO-SVM and PSO-FKNN method yields the secondbest average ACC value as shown in Figure 7 followed by


(a) (b)

(c) (d)

Figure 8 Training accuracy surfaces of SVM and KELM via the grid search method on the Oxford dataset (a) Fold 2 for SVM (b) Fold 4for SVM on the data (c) Fold 6 for KELM on the data (d) Fold 8 for SVM on the data

KELM SVM FOA-FKNN FA-FKNN BFO-FKNN andGA-FKNN FromFigures 6 and 7 we can also find that theCBFO-FKNN can yield a smaller or comparative standard deviationthan the other counterparts in terms of the four performancemetrics on the both datasets Additionally we can find thatthe SVM with local learning-based feature selection canimprove the performance of the two datasets It indicates thatthere are some irrelevant features or redundant features inthese two datasets It should be noted that the LOGOmethodwas used for feature selection all the features were rankedby the LOGO then all the feature subsets were evaluatedincrementally and finally the feature subset achieved the bestaccuracy was chosen as the one in the experiment

According to the results the superior performance of theproposed CBFO-FKNN indicates that the proposed methodwas the most robust tool for detection of PD among thenine methods The main reason may lie in that the OBLmechanism greatly improves the diversity of the populationand increases the probability of BFO escaping from the localoptimum Thus it gets more chances to find the optimalneighborhood size and fuzzy strength values by the CBFOwhich aided the FKNN classifier inmore efficiently achievingthe maximum classification performance Figure 8 displaysthe surface of training classification accuracies achieved bythe SVM and KELMmethods for several folds of the trainingdata via the grid search strategy on the Oxford dataset


Table 17 The confusion matrix obtained by CBFO-FKNN via 10-fold CV for each group

Male Predicted PD Predicted healthActual PD 97 3Actual health 2 16Female Predicted PD Predicted healthActual PD 44 3Actual health 2 28Old Predicted PD Predicted healthActual PD 87 4Actual health 0 18Young Predicted PD Predicted healthActual PD 56 0Actual health 0 30

Through the experimental process we can find the originalBFO is more prone to overfitting this paper introduceschaotic initialization enriches the diversity of the initialpopulation and improves the convergence speed of thepopulation as well in addition this paper also introducedGaussian mutation strategy for enhancing the ability of thealgorithm to jump out of local optimum so as to alleviatethe overfitting problem of FKNN in the process of classifi-cation

We have also investigated whether the diagnosis wasaffected by age and gender Herein we have taken the Oxforddataset for example The dataset was divided by the age(old or young) and gender (male or female) respectivelyRegarding the age we have chosen the mean age of 658 yearsas the dividing point The samples in the old group are morethan 658 and the samples in the young group are less than658 Therefore we can obtain four groups of data includingmale group female group old group and young group Theclassification results of the four groups in terms of confusionmatrix are displayed in Table 17 As shown we can find thateither in the male group or in the female group 3 PD sampleswere wrongly classified as healthy ones and 2 healthy sampleswere misjudged as PD ones It indicates that the gender haslittle impact on the diagnostic results In the old group wecan find that 4 PD samples were wrongly identified as healthyones However none of the samples were misjudged in theyoung group It suggests that the speech samples in the oldgroup are much easier to be wrongly predicted than those inthe young group

To further investigate the impact of gender and age on thediagnosis results We have further divided the samples intomale group and female group on the premise of young andold age and old group and young group on the premise ofmale and female respectively So we can obtain 8 groups asshown in Table 18 and the detailed classification results aredisplayed in terms of confusionmatrix As shownwe can findthat the probability of the sample being misclassified is closerin the old group and young group on the premise of male andfemale It can be also observed that there was no sample beingwrongly predicted in male and female groups on the premise

of young persons while there was one sample being wronglypredicted in male and female groups on the premise of oldpersons respectively We can arrive at the conclusion thatthe presbyphonic may play a confounding role in the femaleand male dysphonic set and the results of diagnosis were lessaffected by gender

The classification accuracies of other methods applied tothe diagnosis of PD are presented for comparison in Table 19As shown the proposed CBFO-FKNN method achievedrelatively high classification accuracy and therefore it couldbe used as an effective diagnostic tool

6 Conclusions and Future Work

In this study we have proposed a novel evolutionary instance-based approach based on a chaotic BFO and applied it todifferentiating the PD from the healthy people In the pro-posedmethodology the chaos theory enhanced BFO strategywas used to automatically determine the two key parametersthereby utilizing the FKNN to its fullest potentialThe resultssuggested that the proposed CBFO-FKNN approach outper-formed five other FKNN models based on nature-inspiredmethods and three commonly used advancedmachine learn-ing methods including SVM LOGO-SVM and KELM interms of various performance metrics In addition the simu-lation results indicated that the proposedCBFO-FKNNcouldbe used as an efficient computer-aided diagnostic tool forclinical decision-makingThrough the experimental analysiswe can arrive at the conclusion that the presbyphonic mayplay a confounding role in the female and male dysphonicset and the results of diagnosis were less affected by genderAdditionally the speech samples in the old group are mucheasier to be wrongly predicted than those in the younggroup

In future studies the proposed method will be imple-mented in a distributed environment in order to furtherboost its PD diagnostic efficacy Additionally implementingthe feature selection using CBFO strategy to further boostthe performance of the proposed method is another futurework Finally due to the small vocal datasets of PD we willgeneralize the proposed method to much larger datasets inthe future

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of article

Acknowledgments

This research is supported by the National Natural ScienceFoundation of China (61702376 and 61402337) This researchis also funded by Zhejiang Provincial Natural Science Foun-dation of China (LY17F020012 LY14F020035 LQ13F020011and LQ13G010007) and Science and Technology Plan Projectof Wenzhou of China (ZG2017019 H20110003 Y20160070and Y20160469)


Table 18 The confusion matrix obtained by CBFO-FKNN for each group with precondition

Old

Male Predicted PD Predicted healthActual PD 62 1

Actual health 0 6Female Predicted PD Predicted health

Actual PD 27 1Actual health 0 12

Young




Male

Old Predicted PD Predicted healthActual PD 61 2

Actual health 0 6Young Predicted PD Predicted health


Female




Table 19 Comparison of the classification accuracies of various methods

Study Method Accuracy ()Little et al (2009) Pre-selection filter + Exhaustive search + SVM 914(bootstrap with 50 replicates)Shahbaba et al (2009) Dirichlet process mixtures 877(5-fold CV)Das (2010) ANN 92 (hold-out)Sakar et al (2010) Mutual information based feature selection + SVM 9275(bootstrap with 50 replicates)Psorakis et al (2010) Improved mRVMs 8947(10-fold CV)Guo et al (2010) GP-EM 931(10-fold CV)Ozcift et al (2011) CFS-RF 871(10-fold CV)Li et al (2011) Fuzzy-based non-linear transformation + SVM 9347(hold-out)Luukka (2011) Fuzzy entropy measures + Similarity classifier 8503(hold-out)

Spadoto et al (2011)Particle swarm optimization + OPF 7353(hold-out)

Harmony search + OPF 8401(hold-out)Gravitational search algorithm + OPF 8401(hold-out)

AStrom et al (2011) Parallel NN 9120(hold-out)Chen et al(2013) PCA-FKNN 9607(10-fold CV)

Babu et al (2013) projection based learning for meta-cognitive radialbasis function network (PBL-McRBFN) 9935 (hold-out)

Hariharan et al (2014) integration of feature weighting method featureselection method and classifiers 100(10-fold CV)

Cai et al (2017) support vector machine (SVM) based on bacterialforaging optimization (BFO) 9742(10-fold CV)

This Study CBFO-FKNN 9789(10-fold CV)


References

[1] L M de Lau and M M Breteler ldquoEpidemiology of Parkinsonrsquosdiseaserdquo The Lancet Neurology vol 5 no 6 pp 525ndash535 2006

[2] S K van den Eeden C M Tanner A L Bernstein et alldquoIncidence of Parkinsonrsquos disease variation by age gender andraceethnicityrdquo American Journal of Epidemiology vol 157 no11 pp 1015ndash1022 2003

[3] E R Dorsey R Constantinescu J P Thompson et al ldquoPro-jected number of people with Parkinson disease in the mostpopulous nations 2005 through 2030rdquo Neurology vol 68 no5 pp 384ndash386 2007

[4] N Singh V Pillay and Y E Choonara ldquoAdvances in thetreatment of Parkinsonrsquos diseaserdquo Progress in Neurobiology vol81 no 1 pp 29ndash44 2007

[5] B T Harel M S Cannizzaro H Cohen N Reilly and PJ Snyder ldquoAcoustic characteristics of Parkinsonian speech Apotential biomarker of early disease progression and treatmentrdquoJournal of Neurolinguistics vol 17 no 6 pp 439ndash453 2004

[6] J Rusz R Cmejla H Ruzickova and E Ruzicka ldquoQuantitativeacoustic measurements for characterization of speech and voicedisorders in early untreated Parkinsonrsquos diseaserdquo The Journal ofthe Acoustical Society of America vol 129 no 1 pp 350ndash3672011

[7] J Jankovic ldquoParkinsons disease clinical features and diagnosisrdquoJournal of Neurology Neurosurgery amp Psychiatry vol 79 pp368ndash376 2008

[8] J Massano and K P Bhatia ldquoClinical approach to Parkinsonrsquosdisease features diagnosis and principles of managementrdquoCold Spring Harbor Perspectives inMedicine vol 2 no 6 ArticleID a008870 2012

[9] A K Ho R Iansek C Marigliani J L Bradshaw and SGates ldquoSpeech impairment in a large sample of patients withParkinsonrsquos diseaserdquo Behavioural Neurology vol 11 no 3 pp131ndash137 1998

[10] B Harel M Cannizzaro and P J Snyder ldquoVariability infundamental frequency during speech in prodromal and incip-ient Parkinsonrsquos disease A longitudinal case studyrdquo Brain andCognition vol 56 no 1 pp 24ndash29 2004

[11] R J Baken and R F Orlikoff Clinical Measurement of SpeechandVoice Singular PublishingGroup SanDiego CAUSA 2ndedition 2000

[12] L Brabenec J Mekyska Z Galaz and I Rektorova ldquoSpeechdisorders in Parkinsonrsquos disease early diagnostics and effects ofmedication and brain stimulationrdquo Journal of Neural Transmis-sion vol 124 no 3 pp 303ndash334 2017

[13] M A Little P E McSharry E J Hunter J Spielman and L ORamig ldquoSuitability of dysphonia measurements for telemoni-toring of Parkinsonrsquos diseaserdquo IEEE Transactions on BiomedicalEngineering vol 56 no 4 pp 1015ndash1022 2009

[14] R Das ldquoA comparison of multiple classification methods fordiagnosis of Parkinson diseaserdquo Expert Systems with Applica-tions vol 37 no 2 pp 1568ndash1572 2010

[15] F Astrom and R Koker ldquoA parallel neural network approachto prediction of Parkinsonrsquos Diseaserdquo Expert Systems withApplications vol 38 no 10 pp 12470ndash12474 2011

[16] CO Sakar andOKursun ldquoTelediagnosis of parkinsonrsquos diseaseusing measurements of dysphoniardquo Journal of Medical Systemsvol 34 no 4 pp 591ndash599 2010

[17] D-C Li C-W Liu and S C Hu ldquoA fuzzy-based datatransformation for feature extraction to increase classification

performance with small medical data setsrdquoArtificial Intelligencein Medicine vol 52 no 1 pp 45ndash52 2011

[18] B Shahbaba and R Neal ldquoNonlinear models using Dirichletprocessmixturesrdquo Journal ofMachine Learning Research vol 10pp 1829ndash1850 2009

[19] I Psorakis T Damoulas and M A Girolami ldquoMulticlassrelevance vector machines sparsity and accuracyrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 21 no 10pp 1588ndash1598 2010

[20] P F Guo P Bhattacharya and N Kharma ldquoAdvances inDetecting ParkinsonsDiseaserdquoMedical Biometrics pp 306ndash3142010

[21] P Luukka ldquoFeature selection using fuzzy entropymeasures withsimilarity classifierrdquo Expert Systems with Applications vol 38no 4 pp 4600ndash4607 2011

[22] A Ozcift and A Gulten ldquoClassifier ensemble construction withrotation forest to improve medical diagnosis performance ofmachine learning algorithmsrdquoComputerMethods andProgramsin Biomedicine vol 104 no 3 pp 443ndash451 2011

[23] A A Spadoto R C Guido F L Carnevali A F Pagnin A XFalcao and J P Papa ldquoImproving Parkinsonrsquos disease identifica-tion through evolutionary-based feature selectionrdquo Conferenceproceedings IEEE Engineering in Medicine and Biology Societyvol 2011 pp 7857ndash7860 2011

[24] K Polat ldquoClassification of Parkinsonrsquos disease using featureweighting method on the basis of fuzzy C-means clusteringrdquoInternational Journal of Systems Science vol 43 no 4 pp 597ndash609 2012

[25] H-L Chen C-C Huang X-G Yu et al ldquoAn efficient diagnosissystem for detection of Parkinsonrsquos disease using fuzzy k-nearestneighbor approachrdquo Expert Systems with Applications vol 40no 1 pp 263ndash271 2013

[26] W-L Zuo Z-Y Wang T Liu and H-L Chen ldquoEffectivedetection of Parkinsonrsquos disease using an adaptive fuzzy 119896-nearest neighbor approachrdquo Biomedical Signal Processing andControl vol 8 no 4 pp 364ndash373 2013

[27] G Sateesh Babu and S Suresh ldquoParkinsonrsquos disease predictionusing gene expression- A projection based learning meta-cognitive neural classifier approachrdquo Expert Systems with Appli-cations vol 40 no 5 pp 1519ndash1529 2013

[28] G S Babu S Suresh and B S Mahanand ldquoA novel PBL-McRBFN-RFE approach for identification of critical brainregions responsible for Parkinsonrsquos diseaserdquo Expert Systems withApplications vol 41 no 2 pp 478ndash488 2014

[29] G Sateesh Babu S Suresh K Uma Sangumathi and H J KimldquoA Projection Based Learning Meta-cognitive RBF NetworkClassifier for Effective Diagnosis of Parkinsonrsquos Diseaserdquo inAdvances in Neural Networks ndash ISNN 2012 vol 7368 of LectureNotes in Computer Science pp 611ndash620 Springer Berlin Ger-many 2012

[30] MHariharan K Polat and R Sindhu ldquoA new hybrid intelligentsystem for accurate detection of Parkinsonrsquos diseaserdquo ComputerMethods and Programs in Biomedicine vol 113 no 3 pp 904ndash913 2014

[31] M Gok ldquoAn ensemble of k-nearest neighbours algorithmfor detection of Parkinsonrsquos diseaserdquo International Journal ofSystems Science vol 46 no 6 pp 1108ndash1112 2015

[32] L Shen H Chen Z Yu et al ldquoEvolving support vectormachines using fruit fly optimization for medical data classi-ficationrdquo Knowledge-Based Systems vol 96 pp 61ndash75 2016


[33] M Peker B Sen and D Delen ldquoComputer-aided diagnosisof Parkinsonrsquos disease using complex-valued neural networksand mRMR feature selection algorithmrdquo Journal of HealthcareEngineering vol 6 no 3 pp 281ndash302 2015

[34] H-L Chen G Wang C Ma Z-N Cai W-B Liu and S-JWang ldquoAn efficient hybrid kernel extreme learning machineapproach for early diagnosis of Parkinsonrsquos diseaserdquo Neurocom-puting vol 184 no 4745 pp 131ndash144 2016

[35] Z Cai J Gu and H-L Chen ldquoA New Hybrid IntelligentFramework for Predicting Parkinsonrsquos Diseaserdquo IEEE Accessvol 5 pp 17188ndash17200 2017

[36] B E Sakar M E Isenkul C O Sakar et al ldquoCollection andanalysis of a Parkinson speech dataset with multiple typesof sound recordingsrdquo IEEE Journal of Biomedical and HealthInformatics vol 17 no 4 pp 828ndash834 2013

[37] H Zhang L Yang Y Liu et al ldquoClassification of Parkinsonrsquosdisease utilizing multi-edit nearest-neighbor and ensemblelearning algorithms with speech samplesrdquo Biomedical Engineer-ing Online vol 15 no 1 2016

[38] V Abrol P Sharma and A K Sao ldquoGreedy dictionary learningfor kernel sparse representation based classifierrdquo Pattern Recog-nition Letters vol 78 pp 64ndash69 2016

[39] I Canturk and F Karabiber ldquoA Machine Learning System fortheDiagnosis of ParkinsonrsquosDisease fromSpeech Signals and ItsApplication to Multiple Speech Signal Typesrdquo Arabian Journalfor Science and Engineering vol 41 no 12 pp 5049ndash5059 2016

[40] A Jozwik ldquoA learning scheme for a fuzzy k-NN rulerdquo PatternRecognition Letters vol 1 no 5-6 pp 287ndash289 1983

[41] J M Keller M R Gray and J A Givens ldquoA fuzzy K-nearestneighbor algorithmrdquo IEEE Transactions on Systems Man andCybernetics vol SMC-15 no 4 pp 580ndash585 1985

[42] J Derrac S Garcıa and F Herrera ldquoFuzzy nearest neighboralgorithms Taxonomy experimental analysis and prospectsrdquoInformation Sciences vol 260 pp 98ndash119 2014

[43] D-Y Liu H-L Chen B Yang X-E Lv L-N Li and J LiuldquoDesign of an enhanced Fuzzy k-nearest neighbor classifierbased computer aided diagnostic system for thyroid diseaserdquoJournal of Medical Systems vol 36 no 5 pp 3243ndash3254 2012

[44] J Sim S-Y Kim and J Lee ldquoPrediction of protein solvent acces-sibility using fuzzy k-nearest neighbor methodrdquo Bioinformaticsvol 21 no 12 pp 2844ndash2849 2005

[45] Y Huang and Y Li ldquoPrediction of protein subcellular locationsusing fuzzy k-NNmethodrdquo Bioinformatics vol 20 no 1 pp 21ndash28 2004

[46] H-L Chen B Yang G Wang et al ldquoA novel bankruptcy pre-diction model based on an adaptive fuzzy k-nearest neighbormethodrdquoKnowledge-Based Systems vol 24 no 8 pp 1348ndash13592011

[47] M-Y Cheng and N-D Hoang ldquoA Swarm-Optimized FuzzyInstance-based Learning approach for predicting slope col-lapses inmountain roadsrdquoKnowledge-Based Systems vol 76 pp256ndash263 2015

[48] M-Y Cheng and N-D Hoang ldquoGroutability estimation ofgrouting processes with microfine cements using an evolution-ary instance-based learning approachrdquo Journal of Computing inCivil Engineering vol 28 no 4 Article ID 04014014 2014

[49] KM Passino ldquoBiomimicry of bacterial foraging for distributedoptimization and controlrdquo IEEE Control Systems Magazine vol22 no 3 pp 52ndash67 2002

[50] L Liu L Shan Y Dai C Liu and Z Qi ldquoA Modified QuantumBacterial Foraging Algorithm for Parameters Identification of

Fractional-Order Systemrdquo IEEE Access vol 6 pp 6610ndash66192018

[51] B Hernandez-Ocana O Chavez-Bosquez J Hernandez-Torruco J Canul-Reich and P Pozos-Parra ldquoBacterial ForagingOptimization Algorithm for Menu Planningrdquo IEEE Access vol6 pp 8619ndash8629 2018

[52] A M Othman and H A Gabbar ldquoEnhanced microgriddynamic performance using a modulated power filter based onenhanced bacterial foraging optimizationrdquo Energies vol 10 no6 2017

[53] S S Chouhan A Kaul U P Singh and S Jain ldquoBacterialForaging Optimization Based Radial Basis Function NeuralNetwork (BRBFNN) for Identification and Classification ofPlant Leaf Diseases An Automatic Approach Towards PlantPathologyrdquo IEEE Access vol 6 pp 8852ndash8863 2018

[54] B Turanoglu and G Akkaya ldquoA new hybrid heuristic algorithmbased on bacterial foraging optimization for the dynamicfacility layout problemrdquo Expert Systems with Applications vol98 pp 93ndash104 2018

[55] X Lv H Chen Q Zhang X Li H Huang and G WangldquoAn improved bacterial-foraging optimization-based machinelearning framework for predicting the severity of somatizationdisorderrdquo Algorithms vol 11 no 2 article 17 2018

[56] RMajhi G Panda BMajhi andG Sahoo ldquoEfficient predictionof stock market indices using adaptive bacterial foraging opti-mization (ABFO) and BFO based techniquesrdquo Expert Systemswith Applications vol 36 no 6 pp 10097ndash10104 2009

[57] S Dasgupta S Das A Biswas and A Abraham ldquoAutomaticcircle detection on digital images with an adaptive bacterialforaging algorithmrdquo SoftComputing vol 14 no 11 pp 1151ndash11642010

[58] S Mishra ldquoA hybrid least square-fuzzy bacterial foragingstrategy for harmonic estimationrdquo IEEE Transactions on Evo-lutionary Computation vol 9 no 1 pp 61ndash73 2005

[59] S Mishra and C N Bhende ldquoBacterial foraging technique-based optimized active power filter for load compensationrdquoIEEE Transactions on Power Delivery vol 22 no 1 pp 457ndash4652007

[60] M Ulagammai P Venkatesh P S Kannan and N PrasadPadhy ldquoApplication of bacterial foraging technique trainedartificial and wavelet neural networks in load forecastingrdquoNeurocomputing vol 70 no 16-18 pp 2659ndash2667 2007

[61] Q Wu J F Mao C F Wei et al ldquoHybrid BF-PSO and fuzzysupport vector machine for diagnosis of fatigue status usingEMG signal featuresrdquo Neurocomputing vol 173 pp 483ndash5002016

[62] C Yang J Ji J Liu J Liu and B Yin ldquoStructural learning ofBayesian networks by bacterial foraging optimizationrdquo Interna-tional Journal of Approximate Reasoning vol 69 pp 147ndash1672016

[63] T S Sivarani S Joseph Jawhar C Agees Kumar and K PremKumar ldquoNovel bacterial foraging-based ANFIS for speed con-trol of matrix converter-fed industrial BLDC motors operatedunder low speed and high torquerdquo Neural Computing andApplications pp 1ndash24 2016

[64] F Zhao Y Liu Z Shao X Jiang C Zhang and J Wang ldquoAchaotic local search based bacterial foraging algorithm and itsapplication to a permutation flow-shop scheduling problemrdquoInternational Journal of Computer Integrated Manufacturingvol 29 no 9 pp 962ndash981 2016

[65] Y Sun S Todorovic and S Goodison ldquoLocal-learning-basedfeature selection for high-dimensional data analysisrdquo IEEE


Transactions on Pattern Analysis and Machine Intelligence vol32 no 9 pp 1610ndash1626 2010

[66] H Chen J Lu Q Li C Lou D Pan and Z Yu ldquoA New Evolu-tionary Fuzzy Instance-Based Learning Approach Applicationfor Detection of Parkinsonrsquos Diseaserdquo in Advances in Swarmand Computational Intelligence Y Tan Y Shi F Buarque et alEds vol 9141 of Lecture Notes in Computer Science pp 42ndash50Springer International Publishing 2015

[67] T Kapitaniak ldquoContinuous control and synchronization inchaotic systemsrdquo Chaos Solitons amp Fractals vol 6 no C pp237ndash244 1995

[68] T Back and H-P Schwefel ldquoAn overview of evolutionary algo-rithms for parameter optimizationrdquo Evolutionary Computationvol 1 no 1 pp 1ndash23 1993

[69] X Cheng and M Jiang ldquoAn improved artificial bee colonyalgorithm based on Gaussian mutation and chaos disturbancerdquoLecture Notes in Computer Science vol 7331 no 1 pp 326ndash3332012

[70] N Higashi and H Iba ldquoParticle swarm optimization withGaussian mutationrdquo in Proceedings of the 2003 IEEE SwarmIntelligence Symposium SIS 2003 pp 72ndash79 April 2003

[71] C Jena M Basu and C K Panigrahi ldquoDifferential evolutionwith Gaussian mutation for combined heat and power eco-nomic dispatchrdquo Soft Computing vol 20 no 2 pp 681ndash6882016

[72] C Chang and C Lin ldquoLIBSVM a Library for support vectormachinesrdquo ACM Transactions on Intelligent Systems and Tech-nology vol 2 no 3 article 27 2011

[73] S L Salzberg ldquoOn comparing classifiers pitfalls to avoidand a recommended approachrdquo Data Mining and KnowledgeDiscovery vol 1 no 3 pp 317ndash328 1997

[74] A Statnikov I Tsamardinos Y Dosbayev and C F Alif-eris ldquoGEMS a system for automated cancer diagnosis andbiomarker discovery from microarray gene expression datardquoInternational Journal of Medical Informatics vol 74 no 7-8 pp491ndash503 2005

[75] T Fawcett ldquoROC graphs Notes and practical considerations forresearchersrdquo Machine Learning vol 31 pp 1ndash38 2004

[76] A H Gandomi X-S Yang S Talatahari and A H AlavildquoFirefly algorithm with chaosrdquo Communications in NonlinearScience and Numerical Simulation vol 18 no 1 pp 89ndash98 2013

[77] X S Yang ldquoFlower pollination algorithm for global optimiza-tionrdquo in Unconventional Computation and Natural Computa-tion vol 7445 of Lecture Notes in Computer Science pp 240ndash249 Springer Berlin Germany 2012

[78] X-S Yang ldquoA new metaheuristic bat-inspired AlgorithmrdquoStudies in Computational Intelligence vol 284 pp 65ndash74 2010

[79] S Mirjalili ldquoDragonfly algorithm a new meta-heuristic opti-mization technique for solving single-objective discrete andmulti-objective problemsrdquo Neural Computing and Applicationsvol 27 pp 1053ndash1073 2016

[80] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks pp 1942ndash1948 Perth Australia December 1995

[81] J Derrac S Garcıa D Molina and F Herrera ldquoA practicaltutorial on the use of nonparametric statistical tests as amethodology for comparing evolutionary and swarm intelli-gence algorithmsrdquo Swarm and Evolutionary Computation vol1 no 1 pp 3ndash18 2011

Stem Cells International

Hindawiwwwhindawicom Volume 2018


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EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

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ObesityJournal of



Computational and Mathematical Methods in Medicine


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Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom


machine learning techniques to diagnose PD patients onthe same dataset (hereafter Oxford dataset) In [14] Dasmade a comparison of classification score for diagnosis of PDbetween artificial neural networks (ANN) DMneural andRegression and Decision Trees The ANN classifier yieldedthe best results of 929 In [15] AStrom et al designed aparallel feed-forward neural network system and yielded animprovement of 84 on PD classification In [16] Sakar et alproposed amethod that combined SVMand feature selectionusing mutual information to detect PD and obtained aclassification accuracy of 9275 In [17] a PD detectionmethod developed by Li et al using an SVM and a fuzzy-based nonlinear transformation method yielded a maximumclassification accuracy of 9347 In another study Shahbabaet al [18] compared the classification accuracies of a nonlin-ear model based on a combination of the Dirichlet processesmultinomial logit models decision trees and support vectormachines which yielded the highest classification score of877 In [19] Psorakis et al put forward novel convergencemethods and model improvements for multiclass mRVMsThe improved model achieved an accuracy of 8947 In[20] Guo et al proposed a PD detection method with amaximum classification accuracy of 931 by combinationof genetic programming and the expectation maximizationalgorithm (GP-EM) In [21] Luukka used a similarity clas-sifier and a feature selection method using fuzzy entropymeasures to detect PD and a mean classification accuracy of8503 is achieved In [22] Ozcift et al presented rotationforest ensemble classifiers with feature selection using thecorrelation method to identify PD patients the proposedmodel yielded a highest classification accuracy of 8713 In[23] Spadoto et al used a combination of evolutionary-basedtechniques and the Optimum-Path Forest (OPF) classifierto detect PD with a maximum classification accuracy of8401 In [24] Polat integrated fuzzy C-means clustering-based feature weighting (FCMFW) into a KNN classifierwhich yielded a PD classification accuracy of 9793 In[25] Chen et al combined a fuzzy k-nearest neighborclassifier (FKNN) with the principle component analysis(PCA-FKNN) method to detect PD the proposed diagnosticsystem yielded amaximum classification accuracy of 9607In [26] Zuo et al developed an PSO-enhanced FKNN basedPD diagnostic system with a mean classification accuracy of9747 In [27ndash29] Babu et al proposed a lsquoprojection basedlearning meta-cognitive radial basis function network (PBL-McRBFN)rsquo approach for the prediction of PDwhich obtainedan testing accuracy of 9687 on the gene expression datasets 9935 on standard vocal data sets 8436 on gait PDdata sets and 8232 on magnetic resonance images In [30]the hybrid intelligent system for PD detection was proposedwhich included several feature preprocessing methods andclassification techniques using three supervised classifierssuch as least-square SVM probabilistic neural networks andgeneral regression neural network the experimental resultsgives a maximum classification accuracy of 100 for thePD detection Furthermore in [31] Gok et al developed arotation forest ensemble KNN classifier with a classificationaccuracy of 9846 In [32] Shen et al proposed an enhancedSVM based on fruit fly optimization algorithm and have

achieved 9690 classification accuracy for diagnosis ofPD In [33] Peker designed a minimum redundancy max-imum relevance (mRMR) feature selection algorithm withthe complex-valued artificial neural network to diagnosisof PD and obtained a classification accuracy of 9812In [34] Chen et al proposed an efficient hybrid kernelextreme learning machine with feature selection approachThe experimental results showed that the proposed methodcan achieve the highest classification accuracy of 9647and mean accuracy of 9597 over 10 runs of 10-fold CVIn [35] Cai et al have proposed an optimal support vectormachine (SVM) based on bacterial foraging optimization(BFO) combined with the relief feature selection to predictPD the experimental results have demonstrated that theproposed framework exhibited excellent classification perfor-mance with a superior classification accuracy of 9742

Different from the work of Little et al Sakar et al [36]designed voice experiments with sustained vowels wordsand sentences from PD patients and controls The paperreported that sustained vowels had more PD-discriminativepower than the isolated words and short sentences Thestudy result achieved 775 accuracy by using SVM clas-sifier From then on several works have been proposed todetect PD using this PD dataset (hereafter Istanbul dataset)Zhang et al [37] proposed a PD classification algorithmthat integrated a multi-edit-nearest-neighbor algorithm withan ensemble learning algorithm The algorithm achievedhigher classification accuracy and stability compared withthe other algorithms Abrol et al [38] proposed a kernelsparse greedy dictionary algorithm for classification taskscomparing with kernel K-singular value decomposition algo-rithm and kernel multilevel dictionary learning algorithmThe method achieved an average classification accuracy of982 and the best accuracy of 994 on the Istanbul PDdataset with multiple types of sound recordings In [39] theauthors investigated six classification algorithms includingAdaboost support vector machines neural network withmultilayer perceptron (MLP) structure ensemble classifierK-nearest neighbor naive Bayes and presented featureselection algorithms including LASSO minimal redundancymaximal relevance relief and local learning-based featureselection on the Istanbul PD dataset The paper indicatedthat applying feature selection methods greatly increased theaccuracy of classification The SVM and KNN classifiers withlocal learning-based feature selection obtained the optimumprediction ability and execution times

As shown above ANN and SVM have been extensivelyapplied to the detection of PD However understanding theunderlying decision-making processes of ANN and SVM isdifficult due to their black-box characteristics Compared toANN and SVM FKNN ismuch simpler and yieldmore easilyinterpretable results FKNN [40 41] classifiers improvedversions of traditional k-nearest neighbor (KNN) classifiershave been studied extensively since first proposed for the useof diagnostic purposes In recent years many variant versionsof KNNs based on fuzzy sets theory and several extensionshave been developed such as fuzzy rough sets intuitionisticfuzzy sets type 2 fuzzy sets and possibilistic theory basedKNN [42] FKNN allows for the representation of imprecise

















119862sum119868=1


0 lt 119899sum119895=1

119906119894119895 lt 119899 119906119894119895 isin [0 1] (3)


119862 (119909) = 119862argmax119894=1

(119906119894 (119909)) (4)



120579119894 (119895 + 1 119896 119897) = 120579119894 (119895 119896 119897) + 119862 (119894) lowast 119889119888119905119894119889119888119905119894 = Δ (119894)radicΔ119879 (119894) Δ (119894)

(5)







119909119894+1 = 119906119909119894 (1 minus 119909119894) (6)



119901119888ℎ = 119909119894 lowast 120579 (7)


119891119892119886119906119904119904119894119886119899(01205902) (120572) = 1radic21205871205902 119890minus120572221205902 (8)







119891119894119905119899119890119904119904 = (sum119870119894=1 119905119890119904119905119864119903119903119900119903119894)119896 (9)


















Endelse

m=NsEnd






for i=1Sr







End















119860119862119862 = 119879119875 + 119879119873(119879119875 + 119865119875 + 119865119873 + 119879119873) times 100 (10)

119878119890119899119904119894119905119894V119894119905119910 = 119879119875(119879119875 + 119865119873) times 100 (11)

119878119901119890119888119894119891119894119888119894119905119910 = 119879119873(119865119875 + 119879119873) times 100 (12)













1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0



1198918 (119909) = 119899sum119894=1


119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0


1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)


11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1


+ nsumi=1

119906(119909i 5 100 4)








11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



































119862sum119868=1


0 lt 119899sum119895=1

119906119894119895 lt 119899 119906119894119895 isin [0 1] (3)


119862 (119909) = 119862argmax119894=1

(119906119894 (119909)) (4)



120579119894 (119895 + 1 119896 119897) = 120579119894 (119895 119896 119897) + 119862 (119894) lowast 119889119888119905119894119889119888119905119894 = Δ (119894)radicΔ119879 (119894) Δ (119894)

(5)







119909119894+1 = 119906119909119894 (1 minus 119909119894) (6)



119901119888ℎ = 119909119894 lowast 120579 (7)


119891119892119886119906119904119904119894119886119899(01205902) (120572) = 1radic21205871205902 119890minus120572221205902 (8)







119891119894119905119899119890119904119904 = (sum119870119894=1 119905119890119904119905119864119903119903119900119903119894)119896 (9)


















Endelse

m=NsEnd






for i=1Sr







End















119860119862119862 = 119879119875 + 119879119873(119879119875 + 119865119875 + 119865119873 + 119879119873) times 100 (10)

119878119890119899119904119894119905119894V119894119905119910 = 119879119875(119879119875 + 119865119873) times 100 (11)

119878119901119890119888119894119891119894119888119894119905119910 = 119879119873(119865119875 + 119879119873) times 100 (12)













1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0



1198918 (119909) = 119899sum119894=1


119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0


1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)


11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1


+ nsumi=1

119906(119909i 5 100 4)








11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





















119909119894+1 = 119906119909119894 (1 minus 119909119894) (6)



119901119888ℎ = 119909119894 lowast 120579 (7)


119891119892119886119906119904119904119894119886119899(01205902) (120572) = 1radic21205871205902 119890minus120572221205902 (8)







119891119894119905119899119890119904119904 = (sum119870119894=1 119905119890119904119905119864119903119903119900119903119894)119896 (9)


















Endelse

m=NsEnd






for i=1Sr







End















119860119862119862 = 119879119875 + 119879119873(119879119875 + 119865119875 + 119865119873 + 119879119873) times 100 (10)

119878119890119899119904119894119905119894V119894119905119910 = 119879119875(119879119875 + 119865119873) times 100 (11)

119878119901119890119888119894119891119894119888119894119905119910 = 119879119873(119865119875 + 119879119873) times 100 (12)













1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0



1198918 (119909) = 119899sum119894=1


119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0


1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)


11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1


+ nsumi=1

119906(119909i 5 100 4)








11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of































Endelse

m=NsEnd






for i=1Sr







End















119860119862119862 = 119879119875 + 119879119873(119879119875 + 119865119875 + 119865119873 + 119879119873) times 100 (10)

119878119890119899119904119894119905119894V119894119905119910 = 119879119875(119879119875 + 119865119873) times 100 (11)

119878119901119890119888119894119891119894119888119894119905119910 = 119879119873(119865119875 + 119879119873) times 100 (12)













1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0



1198918 (119909) = 119899sum119894=1


119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0


1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)


11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1


+ nsumi=1

119906(119909i 5 100 4)








11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
























End















119860119862119862 = 119879119875 + 119879119873(119879119875 + 119865119875 + 119865119873 + 119879119873) times 100 (10)

119878119890119899119904119894119905119894V119894119905119910 = 119879119875(119879119875 + 119865119873) times 100 (11)

119878119901119890119888119894119891119894119888119894119905119910 = 119879119873(119865119875 + 119879119873) times 100 (12)













1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0



1198918 (119909) = 119899sum119894=1


119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0


1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)


11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1


+ nsumi=1

119906(119909i 5 100 4)








11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
























119860119862119862 = 119879119875 + 119879119873(119879119875 + 119865119875 + 119865119873 + 119879119873) times 100 (10)

119878119890119899119904119894119905119894V119894119905119910 = 119879119875(119879119875 + 119865119873) times 100 (11)

119878119901119890119888119894119891119894119888119894119905119910 = 119879119873(119865119875 + 119879119873) times 100 (12)













1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0



1198918 (119909) = 119899sum119894=1


119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0


1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)


11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1


+ nsumi=1

119906(119909i 5 100 4)








11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















1198911 (119909) = 119899sum119894=1

1199091198942 30 [-100 100] 0

1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 30 [-10 10] 0

1198913 (119909) = 119899sum119894=1

( 119894sum119895minus1

119909119895)2 30 [-100 100] 0

1198914 (119909) = max119894

10038161003816100381610038161199091198941003816100381610038161003816 1 le 119894 le 119899 30 [-100 100] 0

1198915 (119909) = 119899minus1sum119894=1

[100(119909119894+1 minus 1199091198942)2 + (119909119894 minus 1)2] 30 [-30 30] 0

1198916 (119909) = 119899sum119894=1

([119909119894 + 05])2 30 [-100 100] 0

1198917 (119909) = 119899sum119894=1

1198941199091198944 + 119903119886119899119889119900119898[0 1) 30 [-128 128] 0



1198918 (119909) = 119899sum119894=1


119894=1

[1199091198942 minus 10 cos (2120587119909119894) + 10] 30 [-512512] 0


1199091198942) minus exp(1119899119899sum119894=1

cos (2120587119909119894)) + 20 + 119890 30 [-3232] 0

11989111 (119909) = 14000119899sum119894=1

1199091198942 minus 119899prod119894=1

cos( 119909119894radic119894) + 1 30 [-600600] 0

11989112 (119909) = 120587119899 10 sin (1205871199101) + 119899minus1sum119894=1

(119910119894 minus 1)2 [1 + 10 sin2 (120587119910119894+1)] + (119910119899 minus 1)2 30 [-5050] 0

+ 119899sum119894=1

119906 (119909119894 10 100 4)

119910119894 = 1 + 119909119894 + 14 119906 (119909119894 119886 119896 119898)


11989113 (119909) = 01 sin2 (31205871199091) + nsumi=1


+ nsumi=1

119906(119909i 5 100 4)








11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















11989114 (119909) = ( 1500 + 25sum119895=1

1119895 + sum2119894=1 (119909119894 minus 119886119894119895)6)

minus1

2 [-6565] 1

11989115 (119909) = 11sum119894=1

[119886119894 minus 1199091 (1198872119894 + 1198871198941199092)1198872119894 + 1198871198941199093 + 1199094 ]2

4 [-5 5] 000030

11989116 (119909) = 411990921 minus 2111990941 + 1311990961 + 11990911199092 minus 411990922 + 411990942 2 [-55] -10316



119894=1

119888119894 exp(minus 3sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 3 [13] -386

11989120 (119909) = minus 4sum119894=1

119888119894 exp(minus 6sum119895=1

119886119894119895 (119909119895 minus 119901119894119895)2) 6 [01] -332

11989121 (119909) = minus 5sum119894=1


11989122 (119909) = minus 7sum119894=1


11989123 (119909) = minus 10sum119894=1































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of










































































005 09542 09417 09666 09167 08230 06180 09694 02667(00370) (00774) (00356) (01620) (00636) (01150) (00413) (02108)

01 09697 09781 09687 09875 08054 05946 09559 02333(00351) (00253) (00432) (00395) (00414) (00746) (00297) (01405)

015 09489 09479 09358 09600 08155 06074 09648 02500(00629) (00609) (01158) (00843) (00669) (01204) (00450) (02257)

02 09589 09466 09600 09333 08368 06512 09691 03333(00469) (00860) (00555) (01610) (00283) (00698) (00360) (01571)

025 09587 09459 09669 09250 08257 06385 09603 03167(00536) (00901) (00459) (01687) (00770) (01560) (00328) (02987)

03 09639 09689 09670 09708 08090 06165 09478 02833(00352) (00308) (00454) (00623) (00439) (01112) (00534) (02491)

(a) (b)

(c) (d)












(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





























(a) (b)

(c) (d)

















Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
































Acknowledgments




Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





















Old




Young




Male




Female














References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















References



























































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of












































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















an intelligent parkinson’s disease diagnostic system based...

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