International Journal of Computer Information Systems and Industrial Management Applications.ISSN 2150-7988 Volume 10 (2018) pp. 174–182c© MIR Labs, www.mirlabs.net/ijcisim/index.html

Adaptive Feature Selection and Classification Using Modified Whale Optimization Algorithm

Heba F. Eid1 and Ajith Abraham2

1Faculty of Science,Al-Azhar University,Cairo, Egypt

eid.heba@gmail.com,heba.fathy@azhar.edu.eg

2Machine Intelligence Research Labs, MIR Labs,USA

abraham.ajith@gmail.com

Abstract: Meta-heuristic algorithms gain researchers interestdue to their simplicity and adaptability. Whale optimizationalgorithm (WOA) is a recent meta-heuristic algorithm, whichshowes competition performance to other swarm algorithms.However, success and challenges concerning the WOA algo-rithm are based on its control parameter tuning and searchspace diversity. In this paper, two modified WOA algorithmsare proposed to set a proper exploration and exploitation ex-change and increase the search space diversity. Furthermore,a novel feature selection algorithm is proposed with integratedinformation gain to enhance its initialization phase. Experimen-tal results based on twenty mathematical benchmark test func-tions demonstrate the effectiveness and stability of the modi-fied WOA when compared with the basic WOA and some well-known algorithms. In addition, experimental results on nineUCI datasets shows the ability of the novel feature selection al-gorithm for selecting the most informative features for classifi-cation tasks, due to its fast convergence and fewer chances toget stuck at local minima.

Keywords: Meta-heuristic algorithm , Whale Optimization , Fea-ture selection , Information Gain , Classification.

I. Introduction

Feature selection plays a pivotal role in data mining andpattern recognition. For high-dimensional datasets, hugenumber of features may contain lot of redundancy. Thissignificantly degrade the learning speed of the classificationmodels as well as their accuracy [19]. Therefore, a gooddimensionality reduction method is a critical procedure inpattern recognition, which contributes towards boosting theperformance of a classification model.

Global optimization concerns about finding the optimal val-ues of the solutions variables in order to meet a certain cri-

teria, has captured the research interest over the years [8][7]. However, classical optimization algorithms require enor-mous computational efforts, which tend to fail as the problemsearch space increases. This motivates for employing meta-heuristics algorithms which show higher computational effi-ciency in avoiding local minima [15] [6] [21]. Meta-heuristicalgorithms solve many kind of optimization problems byimitating biological or physical phenomenas. They can bedivided into three main categories: evolutionary , trajectory,and swarm methods [1] [2].

Swarm-based algorithms imitate the social behavior of naturalcreatures such as ants [3], bees [16], fishes [12], particleswarms [4] and bats [20]. The intelligence derived withswarm based algorithms is self-organizing, distributed anddecentralized control. Due to their inherent advantages, suchalgorithms can be applied to various applications includingFeature selection problems.

Whale optimization algorithm (WOA) is a relatively newmeta-heuristic optimization technique proposed by Mirjaliliand Lewis [13], which mimics the hunting behavior of thehumpback whales. However, WOA is easily trapped intolocal optimum and sometimes provide poor convergence, asthe dimension of the search space expansion. Consequently, anumber of variants are proposed to improve the performanceof the basic WOA.

Ling et al. developed an improved version of WOA based ona Levy flight trajectory, and called the Levy flight trajectory-based whale optimization algorithm (LWOA). The Levy flighttrajectory help to increase the diversity of the population andenhancing its capability of avoiding the local optimal optima[10].

Hu et al. introduce different inertia weights into whale opti-mization algorithm (IWOA). Results illustrates a very com-petitive performance of IWOAs for prediction compared with

MIR Labs, USA

175Adaptive Feature Selection and Classification Using Modified Whale Optimization Algorithm

PSO and basic WOA [9].

Mafarja and Mirjalili proposed two hybridized feature selec-tion models based on WOA. For which, simulated annealing(SA) algorithm is embedded to WOA algorithm in the firstmodel, while it is used to enhance the best solution foundso far by the WOA algorithm in the second model. Theexperimental results confirm the efficiency of the proposedSA-WOA models in improving the classification accuracy[11].

This paper aims to introduce two modified algorithms basedWOA. The first is Cosine adapted WOA algorithm (CaWOA)which employs the cosine function to tune the control pa-rameter of the WOA for varying exploration and exploitationcombinations over the course of iterations. While the sec-ond is based on Cosine adapted mutation / crossover WOA(CaXWOA), which enhances the local search capability ofthe CaWOA algorithm by increasing the search space diver-sity. Moreover, a novel Information gain CaXWOA algorithm(ICaXWOA) is proposed for solving feature selection prob-lems. The proposed CaWOA and CaXWOA are tested withtwenty benchmark functions, while ICaXWOA is tested onnine UCI datasets. Experimental results reveals the efficiencyof the proposed algorithms in most cases. The rest of thispaper is structured as follows: Section II briefly overviews thewhale optimization algorithm while Section III presents thedetails of the proposed CaWOA and CaXWOA algorithms.Section IV, discusses the proposed ICaXWOA based featureselection method. Experimentation design, results and com-parative analysis occupy the remainder of the paper in SectionV. Finally, Section VIII summarizes the main findings of thisstudy.

II. Whale optimization Algorithm

Whale optimization algorithm (WOA) is a recently proposedbio-inspired optimization algorithm [13]. It simulates theHumpback whales social hunting behavior in finding and at-tacking preys. WOA simulates the upward-spirals and double-loops bubble-net hunting strategy; for which, whales divedown and start creating bubbles in a spiral shape around theprey and then swim up toward the surface; as shown in figure1.

To find the global optimum for a given optimization problemusing WOA; the search process starts with assuming a set ofrandom solutions (candidate solutions). Then, a populationof search agents will update their positions towards the bestsearch agent until the termination criteria is met.

The WOA mathematical model is given by equation 1;where,a probability of 0.5 is assumed to choose between up-dating either the shrinking encircling or the spiral mechanismduring optimization:

Figure. 1: Humpback Whales bubble-net hunting strategy

−→X (t +1) =

−→X (t)−−→A .

−→D , if p < 0.5.

−→D .ebl .cos(2πl)+

−→X (t), if p ≥ 0.5.

(1)

For which, p random number ∈ [0,1] , t the current iteration,X the best solution obtained so far, X the position vector, bis a constant defining the spiral shape and l random number∈ [−1,1];

−→D is given by:

−→D = |−→C .

−→X (t)−−→X (t)| (2)

While,−→A and

−→C are coefficient vectors, calculated by:

−→A = 2−→a .−→r −−→a (3)

−→C = 2.−→r (4)

where −→a decreased linearly from 2 to 0 over the course ofiterations and −→r is a random vector ∈ [0,1].

The distance of the i th whale to the prey is indicated by:

−→D = |

−→X (t)−−→X (t)| (5)

In order to have a global optimizer, vector−→A ;1 <

−→A <−1;

is used for exploration. Whereby; the search agent posi-tion is update according to a randomly selected search agent−−→Xrand(t):

−→D = |C.

−−→Xrand(t)−

−→X (t)| (6)

−→X (t +1) =

−−→Xrand(t)−

−→A .−→D (7)

176 Eid and Abraham

III. Modified Whale optimization Algorithm

In WOA algorithm the desirable way to converge towards theglobal minimum can be divided into two conflicting phases:exploration versus exploitation. In the exploration phasewhales scatter throughout the entire search space instead ofclustering around the local minima. While, in the exploita-tion phase whales try to converge to the global minimum bysearching locally around the obtained solutions .

The WOA algorithm transits between both exploration andexploitation phase by linearly decreasing the distance controlparameter a from 2 to 0 using equation 8. Wherein, halfiterations are devoted to exploration; when |A| ≥ 1; bestsolution is the pivot to update the search agents positions .While, the other half are dedicated to exploitation; |A| < 1;the best solution obtained so far plays the role of the pivotpoint.

a = 2(1− ttmax

) (8)

Where t and tmax indicate the current iteration and the maxi-mum number of iterations respectively.

Generally, higher exploration is similar to much randomness;while higher exploitation is related to too little randomnessand will probably give low quality optimization results. Theproposed Cosine adapted WOA algorithm (CaWOA) aimsto set a right balance between exploration and exploitationphase; to guarantee an accurate approximation of the globaloptimum.

CaWOA employs a cosine function instead of the linear func-tion for the decay of the control parameter a over the courseof iterations; as given in equation 9.

a = 1+0.5Cosin(Πt

tmax) (9)

Moreover, to enhance the exploitation capability (localsearch) of the CaWOA algorithm, Cosine adapted mutation /crossover WOA (CaXWOA) is proposed. In the CaXWOAalgorithm, mutation operator attempts to change the solutionaround the best solution obtained so far X ; or around arandomly selected solution Xrand . Furthermore, Crossoveroperator is employed to obtain an intermediate solutionbetween the resultant solution from the mutation operationXmut and the solution Xt .

IV. Adaptive Modified WOA for Feature Selec-tion Problem

For solving feature selection problem, a novel Informationgain CaXWOA algorithm (ICaXWOA) is proposed. ICaX-WOA algorithm aims to deal with the binary optimizationproblems. Therefore, the whale position is represented bya binary vector; either 1 indicating that the correspondingfeature is selected or 0 for non selected features. The lengthof the vector is based on the number of features of the originaldataset. ICaXWOA adapted information gain (IG) for popu-lation initialization; for which, features with correspondingentropy is represented by 1; otherwise the value is set to 0.The IG initialization methods of ICaXWOA are used to guar-antee a large initialization in order to improve the local searchcapability; as the agents positions are commonly closest tothe optimal solution.

Feature selection has two main objectives; maximizingthe classification accuracy and minimizing the number offeatures. ICaXWOA is used to adaptively search for the bestfeature combination, which considers these two objectives.The fitness function adopted to evaluate each individualwhale positions is given by:

Fitness = αER +(1−α)|S∗||S|

(10)

where ER is the classification error rate, S∗ is the numberof selected features and S is the total number of features.α and (1−α) present the relative importance of the classi-fication accuracy and the selected features number; where,α ∈ (0.5,1].

The pseudocode of ICaXWOA is given in Algorithm 1:

V. Experiments and Discussion

VI. Results and Analysis of CaWOA and CaX-WOA

The efficiency of the CaWO and CaXWO algorithm proposedin this study was tested using 20 optimization functions.The benchmark functions are divided into three categories:unimodal, multimodal and fixed-dimension multimodal; asgiven in table 1-3. Figure 2 shows the cost function forF2,F10,F14 and F19 test problem considered in this study.

For each benchmark function, the CaWOA and CaXWOAalgorithms was run 30 independent times and statisticalresults; average cost function (av) and standard deviation(std) are recorded. CaWOA and CaXWOA were compared

177Adaptive Feature Selection and Classification Using Modified Whale Optimization Algorithm

against each other and with Particle Swarm Optimization(PSO) [4], Differential Evolution (DE)[18] and GravitationalSearch Algorithm (GSA) [17]; as reported in Table 5. Mostcomparative algorithms results are taken from [14].

Algorithm 1 Pseudocode of ICaXWO AlgorithmInput:Number of whales nNumber of optimization iterations Max Iter

Output:Optimal whale binary position X∗

1: Calculate the entropy of each feature f ∈ dataset.2: Initialize the n whales population positions ∈ entropy( f )> 1.3: Initialize a, A and C.4: t=15: while t ≤Max Iter do6: Calculate the fitness of every search agent.7: X∗ = the best search agent.8: for each search agent do9: Update a by equation 9

10: Update A, C and l11: Generate randomly p ∈ [0,1]12: if p < 0.5 then13: if |A|< 1 then14: perform Xmut= mutation(X∗)15: update Xt+1 =Crossover(Xmut ,Xt)16: else if |A| ≥ 1 then17: choose a random search agent Xrand18: perform Xmut= mutation(Xrand)19: update Xt+1 =Crossover(Xmut ,Xt)20: end if21: else if p > 0.5 then22: Update position Xt+1 by equation 1(b)23: end if24: Calculate the fitness of every search agent25: Update X∗ if a better solution exist26: end for27: t=t+128: end while29: return X∗

Unimodal functions have only one global optimum; thus, theyallow to evaluate the exploitation capability of the algorithms.According to Table 5, CaXWOA delivers better results thanWOA, CaWOA,PSO, GSA and DE. In particular, CaXWOAis the most efficient optimizer for functions F1,F2 and F7 andthe second best for functions F3−F6. Also, the test remarks alarge difference in performance of CaWOA versus CaXWOAwhich is directly related to applying the mutation/crossoveroperators. Hence, the CaXWOA algorithm can provide verygood exploitation.

Multimodal functions present a good optimization challengeas they possess many local minima; whose number increasesexponentially as the expansion of the problem dimensions. Asa result, multimodal functions allow to asses the explorationcapability. Fixed-dimension multimodal functions provide a

different search space compared to multimodal functions.

Table 5, results indicate that CaXWOA shows the best per-formance in case of functions F8,F10,F16−F18 and F20. Pro-duces a similar results to WOA and CaWOA for function F9,and similar to DE for function F11. While given the secondbest performance for function F12,F14 and F19. This is dueto adapting cosine function for a better exchange between ex-ploration and exploitation, which leads CaXWOA algorithmtowards the global optimum.

The convergence curves of the WOA, CaWOA , and CaX-WOA over the different runs are provided in Figure 3 and 4.As illustrated, the CaXWOA algorithm shows a rapid con-vergence behavior from the initial steps of iterations whenoptimizing the test functions. This behavior shows that theCaXWOA algorithm benefits from a good balance of explo-ration and exploitation; and the crossover diversity; whichconsequently assists the CaXWOA algorithm to avoid beingtrapped into local optimal solutions.

VII. Results and Analysis of ICaXWOA

To estimate the performance of the proposed ICaXWO algo-rithm; experiments are performed on Nine datasets from theUCI machine learning repository [5], as given in Table4. The9 datasets were chosen to have various numbers of features,classes and instances.

For each dataset, the instances are divided randomly intothree sets: training, validation and test sets. In order to ensurethe statistical significance and the stability of the obtainedresults; the partitioning of the data instances are repeatedfor 30 independent runs. For each run, the average accuracy(Av Acc), best accuracy (Best Acc) and the standard deviation(Std); are recorded on the unseen test sets.

Table 6, illustrates the overall performance of the proposedICaXWOA feature selection algorithm, to asses the effect ofhybridizing IG with CaXWOA algorithm. Likewise, ICaX-WOA is compared with state of the art feature selection meth-ods such as particle swarm optimization (PSO), genetic algo-rithm (GA) and ant colony optimization (ACO). From Table6, it is evident that the ICaXWOA outperforms GA, PSOand ACO feature selection algorithm in term of the aver-age accuracy on all datasets, except for the Diabetic dataset.Meanwhile, in all datasets, ICaXWOA shows a better perfor-mance in term of standard deviation values, which indicatesthe stability of ICaXWOA feature selection algorithm againstGA, PSO and ACO feature selection algorithm. To examinethe feature selection capability of the ICaXWOA, it is testedon different well known classifiers SVM, NB, J48 and KNN;as shown in table 7. ICaXWOA shows a significant superi-ority for reducing the number of feature, hence increasingthe classification accuracy. The superior performance of theICaXWOA is justifiable since it adopts IG to guarantee largeinitialization to enhance the local searching capability.

178 Eid and Abraham

(a) F2 (b) F10 (c) F14 (d) F19

Figure. 2: Graphical presentations of the benchmark functions

Table 1: Unimodal optimization functions.RangeDimFunction Fmin

F1(x) = ∑ni=1 x2

i 0[-100,100]30F2(x) = ∑

ni=1 |xi|+∏

ni=1 |xi| 0[-10,10]30

F3(x) = ∑ni=1(∑

ij−1 x j) 0[-100,100]30

F4(x) = maxi{|xi|,1≤ i≤ n} 0[-100,100]30F5(x) = ∑

n−1i=1 [100(xi+1− x2

i )2 +(xi−1)2] 0[-30,30]30

F6(x) = ∑ni=1([xi +0.5])2 0[-100,100]30

F7(x) = ∑ni=1 ix4

i + random[0,1) 0[-1.28,1.28]30

Table 2: Multimodal optimization functionsFunction RangeDim Fmin

F8(x) = ∑ni=1−xisin(

√|xi|) -418.98295[-500,500]30

F9(x) = ∑ni=1[x

2i −10cos(2πxi)+10] 0[-5.12,5.12]30

F10(x) =−20exp(−0.2√

1n ∑

ni=1 x2

i − exp( 1n ∑

ni=1 cos(2πxi))+20+ e 0[-32,32]30

F11(x) = 14000 ∑

ni=1 x2

i −∏ni=1 cos( xi√

i)+1 0[-600,600]30

F12(x) = π

n 10sin(πy1)+∑n−1i=1 (yi−1)2[1+10sin2(πyi+1)]+(yn−1)2 +∑

ni=1 u(xi,10,100,4) 0[-50,50]30

yi = 1+ xi+14 u(xi,a,k,m) =

k(xi−a)m xi > a0−a < xi < ak(−xi−a)m xi <−a

F13(x) = 0.1{sin2(3πx1)+∑ni=1(xi−1)2[1+ sin2(3πxi +1)]+(xn−1)2[1+ sin2(2π)xn]}+∑

ni=1 u(xi,5,100,4) 0[-50,50]30

Table 3: Fixed-dimension multimodal optimization functions.Function RangeDim Fmin

F14(x) = ∑1 1i=1[ai−

x1(b2i +biX2)

b2i +biX3+x4

]2 0.00030[-5,5]4

F15(x) = (x2− 5.14π2 x2

1 +5π

x1−6)2 +10(1− 18π)cosx1 +10 0.398[-5,5]2

F16(x) = [1+(x1 + x2 +1)2(19−14x1 +3x21−14x2 +6x1x2 +3x2

2)]× [30+(2x1−3x2)2× (18−32x1 = 12x2

1 +48x2−36x1x2 +27x22)] 3[-2,2]2

F17(x) = ∑4i=1 ciexp(−∑

3j=1 ai j(x j− pi j)

2) -3.86[1,3]3F18(x) = ∑

4i=1 ciexp(−∑

6j=1 ai j(x j− pi j)

2) -3.32[0,1]6F19(x) = ∑

7i=1[(X−ai)(X−ai)

T + ci]−1 -10.4028[0,10]4

F20(x) = ∑1 0i=1[(X−ai)(X−ai)

T + ci]−1 10.5363[0,10]4

Table 4: Datasets DescriptionDataset #Classes#Instances#Features

Australian 269014German Credit 2100024

Sonar 220860Zoo 710117

NSL-KDD 4596041Diabetic 2115119

Heart Disease 227013Segment 7231019

Liver Disorders 23456

179Adaptive Feature Selection and Classification Using Modified Whale Optimization Algorithm

Figure. 3: Best fitness convergence curves of WOA, CaWOA and CaXWOA

Table 5: Comparison results obtained for WOA, CaWOA and ICaXWOA for different optimization functions.Function WOA CaWOA CaXWOA PSO GSA DE

stdav stdav stdav stdav stdav stdavF1 4.91e-301.41e-30 1.5669e-932.963e-94 00 0.0002020.000136 9.67e-172.53e-16 5.9e-148.2e-14F2 2.39e-211.06e-21 7.9734e-602.3851e-60 00 0.0454210.042144 0.1940740.055655 9.9e-101.5e-09F3 2.9310e-065.3901e-07 1.530e-34.8321e-8 1.918e-089.5739e-10 22.1192470.12562 318.9559896.5347 7.4e-116.8e-11F4 0.397470.072581 0.143240.020328 0.0260338.0795e-4 0.3170391.086481 1.7414527.35487 00F5 0.76362627.86558 10.39927.481 0.6476226.93 60.1155996.71832 62.2253467.54309 00F6 0.5324293.116266 0.369010.64294 0.000765540.0013559 8.28e-050.000102 1.74e-162.5e-16 00F7 0.0011490.001425 0.00241310.017488 0.00108880.00042081 0.0449570.122854 0.043390.089441 0.001270.00463F8 695.7968-5080.76 232.7-62569 173.4-12565 1152.814-4841.29 493.0375-2821.07 574.7-11080.1F9 00 00 00 11.6293846.70423 7.47006825.96841 38.869.2

F10 9.8975727.4043 8.8818e-16 2.234e-15 08.8818e-16 0.509010.276015 0.236280.062087 4.2e-089.7e-08F11 0.001580.000289 0.0331010.0000604 00 0.0077240.009215 5.04034327.70154 00F12 0.2148640.339676 0.017240.031696 0.000108263.8796e-05 0.0263010.006917 0.951141.799617 8e-157.9e-15F13 0.2660881.889015 0.296820.71698 01.3498e-32 0.0089070.006675 7.1262418.899084 4.8e-145.1e-14F14 0.0003240.000572 0.000242070.00066615 0.00034207 0.00013148 0.0002220.000577 0.0016470.003673 4.5e-14 0.00033F15 2.7e-050.397914 0.39789 7.7385e-06 0.39789 1.3038e-06 00.39789 00.39789 0.39789 9.9e-09F16 3 4.22e-15 3 0.00082618 1.13e-153 3 1.33e-15 3 4.17e-15 3 2e-15F17 0.002706-3.85616 -3.8628 0.021346 0-3.8628 -3.8628 2.58e-15 -3.8628 2.29e-15 N/AN/AF18 0.098696-3.2202 0.198-3.321 0.017434-3.322 0.060516-3.26634 0.023081-3.31778 N/AN/AF19 3.829202-8.18178 3.0643-8.8001 -10.403 1.3485 3.087094-8.45653 2.014088-9.68447 3.9e-07-10.403F20 2.414737-9.34238 -10.536 3.1414 1.8067e-15-10.536 1.782786-9.95291 -10.536 2.6e-15 -10.536 1.9e-07

180 Eid and Abraham

Table 6: Performance Results of ICaXWOA, GA, PSO and ACO Feature Selection algorithm on different DatasetsDataset ACOPSOGAWOAICaXWOA

Australian Av Acc 0.88464 0.83900.82460.82890.8256Std 0.0047 0.02400.07310.02280.0202

Best Acc 0.8898 0.85300.87440.85530.8656German Credit Av Acc 0.7436 0.70810.68890.71330.7140

Std 0.0110 0.01680.02070.02000.0367Best Acc 0.7540 0.72400.73330.74510.7490

Sonar Av Acc 0.9519 0.81300.78570.75400.8543Std 0.01065 0.02550.03460.06910.0341

Best Acc 0.9519 0.87510.85710.87200.9188Zoo Av Acc 0.9818 0.94060.95120.85500.9569

Std 0.0080 0.03240.06460.06900.0278Best Acc 0.9960 0.97300.97140.96010.9647

NSL-KDD Av Acc 0.9577 0.92600.92410.90510.9318Std 0.0015 0.03510.02510.03490.0214

Best 0.92520.94080.9567Acc 0.9581 0.9411Diabetic Av 0.60310.6872Acc 0.7504 0.64510.6931

Std 0.00161 0.03940.03470.01690.0393Best 0.62310.6944Acc 0.7748 0.66810.6897

Heart Disease Av Acc 0.8356 0.82600.77000.78010.7633Std 0.0155 0.02400.03600.02100.0209

Best Acc 0.9518 0.88710.90590.91020.7801Segment Av Acc 0.9652 0.91520.94310.91500.9515

Std 0.0038 0.01670.01470.01770.0043Best Acc 0.9679 0.94620.95210.95150.9605

Liver Disorders Av Acc 0.7120 0.61200.70300.67800.7004Std 0.0168 0.04600.12630.05240.1185

Best Acc 0.7589 0.65510.75730.73730.7354

Table 7: Comparison Results of ICaXWOA feature selection Algorithm on different DatasetsDataset F-measure#FeaturesMethod

KNNJ48NBSVMAustralian 0.77100.556514All 0.8565 0.8434

0.83620.76370.69858WOA 0.86080.87100.86810.85793ICaXWOA 0.8846

German Credit 72.40024All 75.500 0.714072.20012WOA 0.7450 0.73800.72400.7330

0.80700.76609ICaXWOA 0.8340 0.7436Sonar 0.71150.66820.634660All 0.8365

0.71150.69230.668238WOA 0.84660.70190.663527ICaXWOA 0.9855 0.9519

Zoo 0.910817All 0.96039 0.94050.92070.930712WOA 0.9505 0.90990.92090.970310ICaXWOA 0.9901 0.98180.9819

NSL-KDD 0.63550.769841All 0.9582 0.93370.60120.860228WOA 0.9798 0.95170.66290.954514ICaXWOA 0.9827 0.9577

Diabetic 0.56380.569019All 0.6359 0.615915WOA 0.6342 0.63250.62990.56567ICaXWOA 0.8279 0.68720.67250.5943

Heart Disease 0.559213All 0.8518 0.78880.77789WOA 0.8333 0.81110.82960.82597ICaXWOA 0.9878 0.83560.91480.8518

Segment 0.80380.645019All 0.9645 0.95360.79690.808213WOA 0.9636 0.95800.82690.98088ICaXWOA 0.9892 0.9652

Liver Disorders 0.55360.59426All 0.6869 0.56230.49860.60104WOA 0.6289 0.6226

3ICaXWOA 0.9797 0.71200.78410.5797

181Adaptive Feature Selection and Classification Using Modified Whale Optimization Algorithm

VIII. Conclusion

This paper proposed two variants of meta heuristic algorithmsnamed CaWOA and CaXWOA based on WOA algorithm.In the proposed CaWOA, cosine decay function is used tobalance the exploration and exploitation of the search spaceover the course of iterations. While, CaXWOA algorithm in-tegrate mutation and crossover operators to insure the searchspace diversity. Twenty benchmark test functions were labor-ing to verify the performance of the proposed CaWOA andCaXWOA algorithm. Experimental results reveal that the pro-posed improved algorithms with nonlinearly distance controlstrategies and search space diversity can provide highly com-petitive results, due to fast convergence and fewer chances toget stuck at local minima.

This paper also consider the feature selection problem inwhich the ICaXWOA algorithm is proposed. For which, in-formation gain (IG) is used to guarantee a large initializationfor the ICaXWOA algorithm. Results on nine UCI datasetsconcluded that the proposed ICaXWOA is able to out performthe current well-known feature selection algorithms in theliterature.

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Figure. 4: Best fitness convergence curves of WOA, CaWOAand CaXWOA

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Author Biographies

Heba F. Eid is an Assistant Professor at Mathematics andComputer Department, Faculty of Science, Al-Azhar Uni-versity, Egypt. She received her M.S. degree in Distributeddatabase systems and Ph.D. degree in Network IntrusionDetection, both from Faculty of Science, Al-Azhar Univer-sity, Egypt. Her research interests include multi-disciplinaryenvironment involving machine learning, computational in-telligence, pattern recognition, computer vision, metaheuris-tics and cyber security. Dr.Heba has served as the programcommittee member of various international conferences andreviewer for various international journals.

Ajith Abraham is the Director of Machine Intelligence Re-search Labs (MIR Labs), a Not-for-Profit Scientific Network

for Innovation and Research Excellence connecting Industryand Academia. The Network with Head quarters in Seattle,USA has currently more than 1,000 scientific members fromover 100 countries. He also works as a Research Professorin VSB-Technical University of Ostrava, Czech Republic.As an Investigator / Co-Investigator, he has won researchgrants worth over 100+ Million US from Australia, USA, EU,Italy, Czech Republic, 100+ France, Malaysia and China. Dr.Abraham works in a multi-disciplinary environment involv-ing machine intelligence, cyber-physical systems, Internet ofthings, network security, sensor networks, Web intelligence,Web services, data mining and applied to various real worldproblems. In these areas he has authored / coauthored morethan 1,300+ research publications out of which there are 100+books covering various aspects of Computer Science. Oneof his books was translated to Japanese and few other arti-cles were translated to Russian and Chinese. About 1000+publications are indexed by Scopus and over 700 are indexedby Thomson ISI Web of Science. Some of the articles areavailable in the ScienceDirect Top 25 hottest articles. He has700+ co-authors originating from 40+ countries. Dr. Abra-ham has more than 30,000+ academic citations (h-index of 81as per google scholar). He has given more than 100 plenarylectures and conference tutorials (in 20+ countries). For hisresearch, he has won seven best paper awards at prestigiousInternational conferences held in Belgium, Canada, Bahrain,Czech Republic, China and India.

Since 2008, Dr. Abraham is the Chair of IEEE SystemsMan and Cybernetics Society Technical Committee on SoftComputing (which has over 200+ members) and served as aDistinguished Lecturer of IEEE Computer Society represent-ing Europe (2011-2013).

Currently Dr. Abraham is the editor-in-chief of Engi-neering Applications of Artificial Intelligence (EAAI) andserves/served the editorial board of over 15 International Jour-nals indexed by Thomson ISI. He is actively involved in theorganization of several academic conferences, and some ofthem are now annual events. Dr. Abraham received Ph.D.degree in Computer Science from Monash University, Mel-bourne, Australia (2001) and a Master of Science Degreefrom Nanyang Technological University, Singapore (1998).More information at: http://www.softcomputing.net/