Cancer Classification Based on Support Vector Machine Optimized by Particle Swarm Optimization and Artificial Bee Colony

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1 molecules Artcle Cancer Classfcaton Based on Support Vector Machne Optmzed by Partcle Swarm Optmzaton and Artfcal Bee Colony Lngyun Gao 1 ID, Mngquan Ye 1, * and Changrong Wu 2 1 School of Medcal Informaton, Wannan Medcal College, Wuhu , Chna; annngxa55@163.com 2 School of Mamatcs and Computer Scence, Anhu Normal Unversty, Wuhu , Chna; wcr193@126.com * Correspondence: ymq@wnmc.edu.cn; Tel.: Receved: 27 October 2017; Accepted: 23 November 2017; Publshed: 29 November 2017 Abstract: Intellgent optmzaton algorthms have advantages n dealng wth complex nonlnear problems accompaned by good flexblty and adaptablty. In ths paper, FCBF (Fast Correlaton-Based Feature selecton) method s used to flter rrelevant and redundant features n order to mprove qualty of cancer classfcaton. Then, we perform classfcaton based on SVM (Support Vector Machne) optmzed by PSO (Partcle Swarm Optmzaton) combned wth ABC (Artfcal Bee Colony) approaches, whch s represented as PA-SVM. The proposed PA-SVM method s appled to nne cancer datasets, ncludng fve datasets of outcome predcton and a proten dataset of ovaran cancer. By comparson wth or classfcaton methods, results demonstrate effectveness and robustness of proposed PA-SVM method n handlng varous types of data for cancer classfcaton. Keywords: ntellgent optmzaton; cancer classfcaton; PSO; ABC; SVM 1. Introducton Owng to no obvous early symptoms of cancer, most of patents are dagnosed at an advanced stage [1], whch usually results n hgh costs wth a poorer prognoss. In addton to uncontrolled growth, cancer cells nvade surroundng normal tssue and even move through body s crculatory system or lymphatc system to or parts of body [2]. The probablty of recurrence or metastass after surgery s hgher than 90% after fve years, as cancer treatment s not thorough. To date, problem of completely clearng remanng cancer cells s not solved, and recurrence rate and mortalty rate of cancer are stll qute hgh. If we can make full use of avalable human expresson profles and realze repeatable dagnoses, re s no doubt that t wll brng great convenence to cancer patents. The analyss of mcroarray gene expresson data [3] and proten expresson data can be used to grasp nformaton of physologcal actvtes at molecular level, whch s wdely used n feld of bomedcne. However, a large number of rrelevant and redundant values exst n expresson profles. Moreover, hgh dmensonalty and small sample brng great dffcultes to data processng. Thus, researchers have proposed varous methods [4 8] to deal wth se problems. Up to now, many machne learnng algorthms have been appled to classfcaton study of bonformatcs, such as random forest [9], k-nearest neghbor, neural network [10], and SVM (Support Vector Machne). Besdes se, re are also some ensemble classfers [11 14]. Among m, DNA recombnaton spots were dentfed by a web server RSpot-EL based on ensemble learnng [13]. A two-layer ensemble classfer named 2L-pRNA makes t possble to effcently dentfy pw-nteractng RNAs and r functon [14]. In addton, classfer was operated wth SVM algorthm. Anor method based on SVM model s Enhancer-2L, whch s a two-layer predctor Molecules 2017, 22, 2086; do: /molecules

2 Molecules 2017, 22, of 10 for dentfyng enhancers and r strength [15]. SVM has dstnctve advantages n handlng data wth hgh dmensonalty and a small sample sze. In addton, nonlnear data can be mapped nto hgh dmensonal space rely on kernel functon, and turned nto lnear separable problem [16]. The kernel functon of RBF (Radal Bass Functon) [17] s wdely used due to ts superorty n parameter and classfcaton performance. Notably, choce of penalty factor C and kernel parameter σ of SVM affects classfcaton results. Many researchers have used a varety of search methods to fnd optmal parameters [18 21]. At same tme, parameters of SVM have been optmzed by many ntellgent algorthms n Reference [21]. Intellgent optmzaton algorthms are developed by smulatng or revealng some natural phenomena, and are wdely used n many research felds because of r versatlty [22 25]. The PSO (Partcle Swarm Optmzaton) algorthm has been successfully appled to cancer classfcaton because of ts smplcty and generalty [26]. However, PSO s easly falls nto local optmal soluton. In addton, ABC (Artfcal Bee Colony) algorthm possesses good global convergence and extensve applcablty [27]. However, ABC s unsatsfactory at explotaton [28]. The use of a sngle optmzaton algorthm presents shortcomngs of low precson and weak generalzaton ablty n solvng complex problems. To furr explore applcaton of ntellgent optmzaton n bonformatcs, PSO and ABC are combned n ths paper, whch means ablty of explotaton and exploraton are combned for bnary and multclass cancer classfcaton. In ths paper, FCBF (Fast Correlaton-Based Feature selecton) method [29] s employed to remove redundant and rrelevant features, PSO optmzaton results are taken as ntal values of ABC, and n cancer classfcaton model s constructed after parameters are tuned; ths hybrd method s represented as PA-SVM. Nne cancer datasets are utlzed for experments, and n compared wth or classfcaton methods: LIBSVM (A Lbrary for Support Vector Machne), GA-SVM (Genetc Algorthm combned wth SVM), PSO-SVM (Partcle Swarm Optmzaton combned wth SVM), and ABC-SVM (Artfcal Bee Colony combned wth SVM). The results demonstrate that proposed PA-SVM method presented n ths paper has good robustness and acheves more accurate classfcaton results. Ths work ams to provde cancer classfcaton results for reference and to make a contrbuton to clncal dagnoss and treatment of dfferent types of cancer. 2. Results 2.1. Feature Selecton Wthn nne cancer datasets, number of features ranges from 2000 to tens of thousands; breast cancer dataset beng largest wth 24,481 attrbutes. Snce a large number of rrelevant and redundant attrbutes are nvolved n se expresson data, cancer classfcaton task s made more complcated. If complete data s used to perform cancer classfcaton, accuracy wll be not so accurate, and hgh computatonal tme and cost wll be ncurred. Therefore, relable FCBF method [29] s adopted to select a subset of dscrmnatory features before classfcaton. By dscardng attrbutes wth lttle or no effect, FCBF provdes good performance wth full consderaton of feature correlaton and redundancy. In ths paper, we standardzed data frst, and n performed feature selecton by FCBF n Weka. The number of reduced attrbutes s shown n Table 1. As shown from ths table, number of attrbutes subtracted s far less than orgnal number. Among m, number of attrbutes of breast cancer decreased from 24,481 to 92, whle number of attrbutes of lung cancer decreased from 2880 to 6. Furrmore, proteomc spectra of ovaran cancer nclude 30 reduced attrbutes, whle orgnal number was 15,154. Consequently, number of orgnal features s reduced by a large amount, and computatonal cost s reduced as well.

3 Molecules 2017, 22, of 10 Table 1. Reduced attrbutes by FCBF. Datasets Orgnal Attrbutes Reduced Attrbutes Breast cancer 24, Lung cancer NervSys Prostate cancer 12, Colon caner Leukema 12, Ovaran cancer 15, DLBCL DLBCL DLBCL represents dffuse large B-cell lymphoma Cancer Classfcaton The classfcaton experment n ths paper was carred out under a Matlab envronment. Nne subsets after feature reducton were used as nput data of proposed PA-SVM classfer for classfcaton. In order to verfy effectveness of proposed method, we compared t wth LIBSVM method of default parameters n Weka, as well as wth GA-SVM, PSO-SVM, and ABC-SVM n Matlab. Among se technques, SVM used n ths experment s derved from LIBSVM package developed by Prof. Chh-Jen Ln. GA-SVM used genetc algorthm (GA) to optmze SVM parameters and appled optmzed SVM to classfy cancer datasets. GA has characterstcs of parallel computng, whch s sutable for large-scale complex problem optmzaton. PSO-SVM utlzed PSO to optmze parameters of SVM. PSO s easy to mplement wth few parameters to adjust, whle t also has advantages of fast convergence speed and strong versatlty. ABC-SVM employed ABC to fnd optmal parameters of SVM, whch takes full advantage of good global convergence and flexblty of ABC. Therefore, PA-SVM algorthm proposed n ths paper can combne explotaton of PSO and exploraton of ABC, and overcome dsadvantages of PSO easly fallng nto local optmum as well as weak explotaton of ABC. In addton, due to small number of selected features, 10-fold cross valdaton was used. For purpose of avodng nstable operaton results, each experment was run 10 tmes, and optmal classfcaton accuracy was selected for comparson. The fnal classfcaton results are shown n Table 2. Table 2. Classfcaton accuracy of dfferent methods. Datasets No. of Attrbutes LIBSVM (%) GA-SVM 1 (%) PSO-SVM 2 (%) ABC-SVM 3 (%) PA-SVM 4 (%) Breastcancer Lung cancer NervSys Prostate cancer Colon caner Leukema Ovaran cancer DLBCL DLBCL GA-SVM method s genetc algorthm combned wth SVM; 2 PSO-SVM denotes partcle swarm optmzaton combned wth SVM; 3 ABC-SVM means artfcal bee colony method s used to optmze SVM; 4 PA-SVM combnes partcle swarm optmzaton wth artfcal bee colony to optmze SVM. The bold n table represents optmal value. As seen from Table 2, accuracy of last column, whch represents classfcaton result of proposed PA-SVM method, always obtans optmal values. Among se cancer datasets, for fve groups of patents wth outcome predcton, such as breast cancer and nervsys, proposed PA-SVM method acheved same accuracy as ABC-SVM, and both were hgher than or methods. As for lung cancer, best result was obtaned by PA-SVM and PSO-SVM. Ths showed that PA-SVM approach descrbed n ths paper has superor outcome predcton. To elaborate, leukema

4 Molecules 2017, 22, of 10 Molecules 2017, 22, of 10 elaborate, dataset contans leukema three dsease dataset types, contans andthree all ofdsease se methods types, and canall acheve of se 100% methods classfcaton can acheve accuracy. 100% classfcaton Concernng accuracy. protenconcernng data of ovaran proten cancer, data constructed of ovaran cancer, classfcaton constructed model obtaned classfcaton 100% model accuracy. obtaned Ths study 100% saccuracy. sgnfcant Ths for women study s who sgnfcant have a for hghwomen rsk of who ovaran have cancer a hgh due rsk to aof famly ovaran or cancer personal due hstory a of famly cancer. or Wth personal regard hstory DLBCL1 of cancer. and DLBCL2, Wth regard proposed to DLBCL1 PA-SVM and DLBCL2, acheved proposed hghest performance PA-SVM acheved compared to hghest orperformance classfcatoncompared approaches. to or classfcaton approaches. In order to show effect of varous methods ntutvely, we converted data n Table 2 to a lne chart. Snce classfcaton accuracy for prostate, leukema, and ovaran datasets was 100%, y were not shown n fgure. The detals of of remanng sx sxdatasets can canbe be seen seen n n Fgure Fgure 1. Cancer classfcaton accuracy (%) of dfferent methods. It can be seen that PA-SVM has optmal accuracy for all cancer datasets studed. Also, n It can be seen that PA-SVM has optmal accuracy for all cancer datasets studed. Also, n experments t can be observed that ABC-SVM and PA-SVM mantan better robustness, whle experments t can be observed that ABC-SVM and PA-SVM mantan better robustness, whle GA-SVM GA-SVM and PSO-SVM easly fall nto local optmal soluton. Accordngly, proposed and PSO-SVM easly fall nto local optmal soluton. Accordngly, proposed PA-SVM approach PA-SVM approach always obtans best classfcaton performance and has good robustness. Ths always obtans best classfcaton performance and has good robustness. Ths ndcates that PA-SVM ndcates that PA-SVM s able to handle multple types of data wth better performance n cancer s able to handle multple types of data wth better performance n cancer prognoss, dentfcaton, prognoss, dentfcaton, and classfcaton compared to or methods employed. and classfcaton compared to or methods employed Dscusson The complextyand and varabltyof of cancer cancer greatly greatly ncreases ncreases dffculty dffculty of clncal of clncal treatment. treatment. In addton, In addton, patents patents stll stll have have a large a large probablty probabltyof of recurrence recurrenceafter after treatment, whch whchs sstll stll a serous threat to to people s health. Thus, Thus, early early dagnossand and prognossof of cancers sof ofgreat sgnfcance. However, re are many problems durng handlng of of gene expresson data, such as as hgh dmenson, small smallsample samplesze, sze, and andlarge largenose. In Inorder order to to obtan obtan truly truly valuable valuable genes, genes, a varety a varety of methods of methods are are proposed proposed for for feature feature selecton selecton and and classfcaton classfcaton predcton. predcton. Intellgent optmzaton algorthms have advantages of of fast fast convergence, smple operaton, adaptablty, and robustness, and and y y are are appled appled n n many many felds. felds. In In ths ths paper, paper, FCBF FCBF method method was was used used to flter to flter rrelevant rrelevant and and redundant redundant attrbutes, attrbutes, and and obtaned obtaned subsets subsets were were nput nput nto nto constructed constructed classfcaton classfcaton model model based based on PSO on and PSO ABC. and In ABC. ths paper, In ths paper, optmal soluton optmal obtaned soluton obtaned by PSO s by taken PSO s astaken ntalzaton as ntalzaton of ABC of algorthm, ABC algorthm, and thus and thus advantages advantages of PSO of PSO and and ABC ABC were were combned combned to consttute to consttute PA-SVM PA-SVM classfer. classfer. It It has has been been observed that that proposed methodcan alwaysget best results through classfcatonof of dfferent cancer datasets wth a low number of of selected selected genes. genes. In In addton, addton, ths ths paper paper also also used used ovaran ovaran cancer cancer proten proten expresson expresson data data for cancer for cancer classfcaton classfcaton because because of mportance of mportance of proten molecules. of proten The molecules. results demonstrated The results demonstrated that proposed that PA-SVM proposed methodpa-svm has greater method advantages has greater for cancer advantages prognoss, for dentfcaton, cancer prognoss, and dentfcaton, classfcaton, as and well classfcaton, handlng as well of multple as handlng types of of datasets. multple types of datasets. The causes of cancer are full of complexty and varety; refore, sngle type of data probably not provdes an adequate explanaton or makes a perfect predcton. We wll thus combne multple

5 Molecules 2017, 22, of 10 The causes of cancer are full of complexty and varety; refore, sngle type of data probably not provdes an adequate explanaton or makes a perfect predcton. We wll thus combne multple types of data n future n order to acheve a comprehensve analyss. In addton, oretcal mechansm of ntellgent optmzaton stll lacks a complete mamatcal foundaton. Furr study and n-depth research are needed. At same tme, clncal valdaton s also necessary n order to make research more conducve to human lfe. 4. Materals and Methods 4.1. Cancer Datasets The datasets used n experment were all derved from Kent Rdge Bo-medcal Dataset Repostory, mentoned n Reference [30]. These datasets nclude breast cancer, colon cancer, DLBCL, lung cancer, leukema, nervsys (central nervous system embryonal tumor), ovaran cancer, and prostate cancer. A detaled descrpton of se datasets s shown n Table 3. Table 3. Detals of cancer datasets. Datasets Samples No. of Attrbutes Classes Labels Breast cancer 97 24,481 2 outcome predcton Lung cancer outcome predcton NervSys outcome predcton Prostate cancer 21 12,600 2 outcome predcton Colon caner cancer or not Leukema 72 12,582 3 mult-category Ovaran cancer ,154 2 proten data DLBCL two category DLBCL outcome predcton In addton to colon, DLBCL1, leukema, and ovaran datasets, remanng datasets concerned outcome predcton of cancer patents, ndcatng a predcted relapse or non-relapse. It s worth notng that ovaran cancer measures proten expresson data. The goal of ths experment was to dentfy proteomc patterns n serum that dstngush ovaran cancer from non-cancer. Among m, DLBCL dataset ncluded two categores: DLBCL1 and DLBCL2. The frst s DLBCL versus Follcular Lymphoma (FL) morphology. The second s outcome predcton data of 58 cases of DLBCL samples, some of m from cured patents and ors from patents wth fatal or refractory dsease. Besdes DLBCL, colon cancer dataset contaned 62 samples collected from colon cancer patents, characterzed by a common malgnant tumor n gastrontestnal tract. Also, leukema dataset of 72 samples ncluded three categores: ALL, MLL, and AML. They stand for acute lymphoblastc leukema, mxed lneage leukema, and acute myelod leukema, respectvely Partcle Swarm Optmzaton (PSO) Algorthm The PSO algorthm orgnated from study of brd predaton behavor, frst proposed by Kennedy and Eberhart n The algorthm s easy to mplement and rules are smple. The poston of each partcle represents a potental soluton, each partcle has a ftness value determned by ftness functon, and each partcle has three characterstcs: poston, velocty, and ftness value. The flowchart of PSO algorthm s shown n Fgure 2.

6 Molecules 2017, 22, of 10 Molecules 2017, 22, of 10 Fgure 2. The flowchart of PSO algorthm. Suppose Suppose that that n n feasble feasble soluton soluton D-dmensonal D-dmensonal space, space, populaton populaton of n of partcles n partcles s X s = [X1, X2,, Xn]. The poston and velocty of -th partcle are X = [x1, x2,, xd] and V X = [X = [v1, v2,, 1, X 2,..., X n ]. The poston and velocty of -th partcle are X = [x 1, x 2,..., x D ] and V vd], respectvely, where velocty determnes drecton and dstance of partcle movement. = [v 1, v 2,..., v D ], respectvely, where velocty determnes drecton and dstance of The partcle partcles movement. move n The partcles feasble move soluton n space, feasble and soluton ndvdual space, poston and s ndvdual updated by poston trackng s personal best poston P updated by trackng personal and best global poston best P poston Pg. The personal best poston s best and global best poston P g. The personal best locaton wth best ftness value experenced by ndvdual: P poston s best locaton wth best ftness value experenced by = ndvdual: [p1, p2,, P pd]. The global best = [p 1, p 2,..., p D ]. poston s optmal poston wth best ftness for all partcles n populaton: Pg The global best poston s optmal poston wth best ftness for all partcles n = populaton: [pg1, pg2,, pgd]. P The partcle updates velocty and poston through global and personal best postons. The g = [p g1, p g2,..., p gd ]. The partcle updates velocty and poston through global and personal formula best postons. s represented The formula as: s represented as: k 1 k k k k k v d v d cr 11( p d xd) cr 2 2( p gd xd ) v k+1 (1) d = ωvd k d + 1, c 1r 1 (pd k 2,, D xk d ) + c 2r 2 (p k gd xk d ) (1) d = 1, 2,..., D k 1 k k 1 xd xd vd (2) d x1, k+1 d 2, =, Dx d k ; + vk+1 d 1, 2,, n (2) d = 1, 2,..., D; = 1, 2,..., n where k s current teraton number, ω s nerta weght, c1 and c2 denote cogntve and socal where learnng k s current factors, teraton and r1 and number, r2 are unformly ω s nerta dstrbuted weght, numbers c 1 and n c 2 denote nterval (0, cogntve 1). In order and to avod socal a learnng blnd search, factors, and poston r 1 and and r 2 velocty are unformly of each dstrbuted partcle has numbers a certan n lmt nterval nterval [Xmn, (0, 1). Xmax] In order and to [Vmn, avod Vmax]. a blnd search, poston and velocty of each partcle has a certan lmt nterval [X mn, X max ] and [V mn, V max ] Artfcal Bee Colony (ABC) Algorthm 4.3. Artfcal Bee Colony (ABC) Algorthm Karaboga successfully appled bee colony algorthm to extreme value optmzaton Karaboga successfully appled bee colony algorthm to extreme value optmzaton problem n At same tme, he systematcally put forth ABC algorthm, whch smulates problem n At same tme, he systematcally put forth ABC algorthm, whch smulates bees garng nectar n nature. In ths algorthm, bees are dvded nto three types: employed bees, bees garng nectar n nature. In ths algorthm, bees are dvded nto three types: employed bees, onlooker bees, and scout bees, and y fnd optmal soluton through collecton and sharng onlooker bees, and scout bees, and y fnd optmal soluton through collecton and sharng of of nectar. The procedure of ABC algorthm s presented n Fgure 3. nectar. The procedure of ABC algorthm s presented n Fgure 3. In ABC algorthm, poston of each food source represents a feasble soluton of problem to be optmzed. The enrchment of each source corresponds to ftness of each soluton. Frst, feasble soluton x s ntalzed n D-dmensonal space, and = 1, 2,, N, each food source attracts one employed bee, so poston of source s poston of employed bee.

7 better one s chosen. If source has not been changed by multple searches, and number of tmes exceeds lmt, employed bees dentty wll become scout bees, and anor soluton s generated randomly. The formula for producng a new food source s as follows: x x rand(0, 1)( x x ) (5) mn max mn Molecules 2017, 22, of 10 Ths method not only mproves qualty of soluton, but also ncreases dversty, whch s benefcal to fndng global optmal soluton. Fgure 3. The flowchart of ABC algorthm. Fgure 3. The flowchart of ABC algorthm. In ABC algorthm, poston of each food source represents a feasble soluton of problem to be optmzed. The enrchment of each source corresponds to ftness of each soluton. Frst, feasble soluton x s ntalzed n D-dmensonal space, and = 1, 2,..., N, each food source attracts one employed bee, so poston of source s poston of employed bee. Onlooker bees determne locaton accordng to selecton probablty of ftness value that employed bees remembered: P = f t (3) N f t n n=1 where ft s ftness of -th food source, and P s selecton probablty. Then, onlooker bees do neghborhood search accordng to formula: x k+1 = x k + r (xk xk j ) (4) where = j, j = 1, 2,..., N, and x k s current food source poston, and r s a random number n range of ( 1, 1). Subsequently, ftness values before and after search are compared, and better one s chosen. If source has not been changed by multple searches, and number of tmes exceeds lmt, employed bees dentty wll become scout bees, and anor soluton s generated randomly. The formula for producng a new food source s as follows: x = x mn + rand(0, 1)(x max x mn ) (5)

8 SymmetrcalUncertAttrbuteSetEval attrbute evaluator n Weka to select gene subsets, and se subsets were nput nto constructed cancer classfcaton model for classfcaton evaluaton. The whole process of experment s shown n Fgure 4. SVM fnds classfcaton nterval of two knds of samples as large as possble by lookng for an optmal classfcaton hyperplane that satsfes requrements. When dealng wth non-lnear Molecules samples, 2017, 22, kernel 2086 functon s used to map data nto a hgh-dmensonal space, so that data can 8 of 10 be lnearly separable. The search for optmal hyperplane can be converted to mnmzaton of followng equaton by ntroducng penalty factor C and slack varable ξ. Ths method not only mproves qualty of soluton, but also ncreases dversty, whch s N 1 2 benefcal to fndng global optmal f soluton. C 2 1 T (6) 4.4. The Proposed PA-SVM Algorthm y ( ( x ) b) 1 s. t. 0 Takng nto account large number of rrelevant and redundant values n gene expresson data, we utlzed where ω s FCBF hyperplane feature selecton normal method vector, and [26] b combned s threshold. wth SymmetrcalUncertAttrbuteSetEval The feature map ψ(x) s a kernel attrbute functon evaluator that satsfes n Weka tomercer select gene condton. subsets, Snce and ths se paper subsets adopts were wdely nput used nto RBF constructed kernel cancer functon, classfcaton ts value model s manly for classfcaton affected by evaluaton. kernel functon The whole parameter process σ. of It can experment be seen that s shown penalty factor C and kernel functon parameter σ have a great nfluence on classfcaton n Fgure 4. performance of SVM. Fgure 4. The whole frame of proposed PA-SVM algorthm. Fgure 4. The whole frame of proposed PA-SVM algorthm. Ths artcle uses easy-to-use LIBSVM package developed by professor Chh-Jn Ln of SVM Tawan fnds Unversty, classfcaton whch can nterval solve ofcomplex two knds problem of samples of mult-class largepattern as possble recognton. by lookng The for an optmal proposed classfcaton method PA-SVM hyperplane employs that PSO satsfes and ABC to optmze requrements. penalty When factor dealng C and parameter wth non-lnear σ of RBF kernel functon n SVM. samples, kernel functon s used to map data nto a hgh-dmensonal space, so that data can be The personal and global best values are determned by makng full use of optmal value n lnearly separable. The search for optmal hyperplane can be converted to mnmzaton of optmzaton process and ntroducton of mutaton, whch gves PSO good explotaton followng abltes. equaton The solutons by ntroducng of parameters penalty bestc and factor bestg C found and slack by PSO varable are used ξ. as ntal values of food sources n ABC algorthm, thus uncertanty of random values can be avoded to some f = 2 1 ω 2 + C N ξ { =1 y s.t. (ω T (6) ϕ(x ) + b) 1 ξ ξ 0 where ω s hyperplane normal vector, and b s threshold. The feature map ψ(x) s a kernel functon that satsfes Mercer condton. Snce ths paper adopts wdely used RBF kernel functon, ts value s manly affected by kernel functon parameter σ. It can be seen that penalty factor C and kernel functon parameter σ have a great nfluence on classfcaton performance of SVM. Ths artcle uses easy-to-use LIBSVM package developed by professor Chh-Jn Ln of Tawan Unversty, whch can solve complex problem of mult-class pattern recognton. The proposed method PA-SVM employs PSO and ABC to optmze penalty factor C and parameter σ of RBF kernel functon n SVM.

9 Molecules 2017, 22, of 10 The personal and global best values are determned by makng full use of optmal value n optmzaton process and ntroducton of mutaton, whch gves PSO good explotaton abltes. The solutons of parameters bestc and bestg found by PSO are used as ntal values of food sources n ABC algorthm, thus uncertanty of random values can be avoded to some extent. Bestc means best value of parameter C found by PSO, whle bestg s best value of RBF kernel functon parameter. Then, as PA-SVM takes full use of exploraton of scout bees n ABC, t s more conducve to dscover global optmum by overcomng shortcomng of PSO, whch s easly trapped n local optmal. Ths method combnes advantages of PSO and ABC algorthms by strkng a balance between exploraton and explotaton. The hgher classfcaton accuracy s man purpose of optmzng SVM, and ftness functon n ths paper s drectly represented as value of classfcaton accuracy, whch s expressed as follows: F = V accuracy (7) In ths study, dmenson parameter D s 2, populaton sze s set to 30, number of teratons s 100, lmt s 50, and a 10-fold cross valdaton method s used to assess classfcaton accuracy. Acknowledgments: Ths artcle was supported by Natonal Natural Scence Foundaton of Chna ( ), Humantes and Socal Scences Plannng Project of Mnstry of Educaton (16YJAZH071), Anhu Provncal Natural Scence Foundaton of Chna ( MF142), as Natural Scence Research Key Project of Anhu Colleges (KJ2014A266, KJ2016A275). We sncerely acknowledge excellent scholars who provded publc resources n ths research. Author Contrbutons: M.Y. conceved and desgned experments. L.G. desgned and performed experments, analyzed data, and wrote paper. C.W. asssted n desgn and performance of expermental work. All authors read and approved fnal manuscrpt. Conflcts of Interest: The authors declare no conflct of nterest. References 1. Clémentduchêne, C.; Carnn, C.; Gullemn, F.; Martnet, Y. How accurate are physcans n predcton of patent survval n advanced lung cancer. Oncologst 2010, 1, [CrossRef] [PubMed] 2. Chambers, A.F.; Groom, A.C.; Macdonald, I.C. Dssemnaton and growth of cancer cells n metastatc stes. Nat. Rev. Cancer 2002, 2, [CrossRef] [PubMed] 3. Nguyen, T.; Khosrav, A.; Creghton, D.; Nahavand, S. A novel aggregate gene selecton method for mcroarray data classfcaton. Pattern Recogn. Lett. 2015, 60, [CrossRef] 4. Dettlng, M.; Bühlmann, P. Boostng for tumor classfcaton wth gene expresson data. Bonformatcs 2003, 19, [CrossRef] [PubMed] 5. L, B.; Zheng, C.H.; Huang, D.S.; Zhang, L.; Han, K. Gene expresson data classfcaton usng locally lnear dscrmnant embeddng. Comput. Bol. Med. 2010, 40, [CrossRef] [PubMed] 6. Vantha, C.D.A.; Devaraj, D.; Venkatesulu, M. Gene expresson data classfcaton usng Support Vector Machne and mutual nformaton-based gene selecton. Proceda Comput. Sc. 2015, 47, [CrossRef] 7. Kar, S.; Sharma, K.D.; Matra, M. Gene selecton from mcroarray gene expresson data for classfcaton of cancer subgroups employng PSO and adaptve K-nearest neghborhood technque. Expert. Syst. Appl. 2015, 42, [CrossRef] 8. Lu, H.; Yang, L.; Yan, K.; Xue, Y.; Gao, Z. A cost-senstve rotaton forest algorthm for gene expresson data classfcaton. Neurocomputng 2017, 228, [CrossRef] 9. Statnkov, A.; Wang, L.; Alfers, C.F. A comprehensve comparson of random forests and support vector machnes for mcroarray-based cancer classfcaton. BMC Bonform. 2008, 9, [CrossRef] [PubMed] 10. Fara, A.W.; Da, S.A.; De, S.R.T.; Costa, M.A.; Braqa, A.P. A rankng approach for probe selecton and classfcaton of mcroarray data wth artfcal neural networks. J. Comput. Bol. 2015, 22, [CrossRef] [PubMed] 11. Xu, R.F.; Zhou, J.Y.; Lu, B.; Yao, L.; He, Y.L.; Zou, Q.; Wang, X.L. endna-prot: Identfcaton of DNA-bndng protens by applyng ensemble learnng. Bomed. Res. Int. 2014, 2014, [CrossRef] [PubMed]

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