A Notable Swarm Approach to Evolve Neural Network for Classification in Data Mining
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1 A Notable Swarm Approach to Evolve Neural Network for Classfcaton n Data Mnng Satchdananda Dehur 1, Bjan Bhar Mshra 2 and Sung-Bae Cho 1 1 Soft Computng Laboratory, Department of Computer Scence, Yonse Unversty, 262 Seongsanno, Seodaemun-gu, Seoul , Korea. Emal:satch.lapa@gmal.com, sbcho@cs.yonse.ac.kr 2 Department of Computer Scence and Engneerng, College of Engneerng Bhubaneswar, Bhubaneswar , INDIA. Emal: msrabjan@gmal.com Abstract. Ths paper presents a novel and notable swarm approach to evolve an optmal set of weghts and archtecture of a neural network for classfcaton n data mnng. In a dstrbuted envronment the proposed approach generates randomly multple archtectures competng wth each other whle fne-tunng ther archtectural loopholes to generate an optmum model wth maxmum classfcaton accuracy. Amng at better generalzaton ablty, we analyze the use of partcle swarm optmzaton (PSO) to evolve an optmal archtecture wth hgh classfcaton accuracy. Experments performed on benchmark datasets show that the performance of the proposed approach has good classfcaton accuracy and generalzaton ablty. Further, a comparatve performance of the proposed model wth other competng models s gven to show ts effectveness n terms of classfcaton accuracy. Keywords: Partcle Swarm Optmzaton, Evolutonary Computaton, Genetc Algorthm, and Classfcaton. 1 Introducton Data mnng [1] s an nterdscplnary feld, whose core s at the ntersecton of machne learnng, statstcs, and databases. Data mnng ncludes several tasks such as classfcaton, assocaton rule mnng, clusterng, regresson, summarzaton etc. Each of these tasks can be regarded as a knd of problem to be solved by a data mnng algorthm. Therefore, the frst step n desgnng a data mnng algorthm s to defne whch task the algorthm wll address. In ths paper, we consder the problem of classfcaton n data mnng to valdate our novel evolved neural network by partcle swarm optmzaton. In general, a classfer parttons the feature space X nto C, = 1,2,..., M classes such that: ) M C φ, = 1,2,.., M, ) and ) (except for UC = X Cj Ck = φ, j k, j = 1(1) M, k = 1(1 ) M =1 fuzzy classfcaton doman) by constructng the hyper-planes or hyper-cubes. A T hyper-plane can be wrtten as: d ( x) = W. X, where W = w, w,..., w ] and [ 1 2 N
2 X = [ x1, x2,..., xn 1,1] are called the weght vector and augmented feature vector respectvely. Now the problem s to classfy an unknown sample based on the hyperplane. Varous-benchmark studes ndcate that, the success of artfcal neural networks (ANN s) for classfcaton depends on the archtecture and tranng of the network (.e. searchng an optmal sets of weghts). A large number of technques exst wth whch ANN s can be traned. Most applcatons use the back propagaton (BP) algorthm or other tranng algorthms n the feed forward ANN s. But all these tranng algorthms assume a fxed ANN s archtecture. There have been many attempts n desgnng ANN s archtectures automatcally, such as varous constructve and prunng algorthms [2]. Desgn of a near optmal ANN s archtecture can be formulated as a search problem n the network archtecture and weght space where each pont represents a type of archtecture. Gven some performance crtera, e.g., hgh classfcaton accuracy, lowest archtectural complexty, etc., the performance level of all archtectures forms a surface n the space. Although genetc algorthm (GA) [3] s a better canddate for searchng optmal neural network archtecture but t can face the problem lke permutaton, nosy ftness evaluaton, etc. [2]. Ths paper presents a novel method of evoluton of artfcal neural network usng PSO [4] that not only evolves the set of weghts but also evolves network archtecture of low complexty. Compared wth the GA, the PSO algorthm possesses some attractve propertes, such as memory and constructve cooperaton between ndvduals, whch can avod the permutaton problem. 2 Background and Related Work 2.1 Bascs of PSO Partcle swarm optmzaton (PSO), ntroduced by Kennedy and Eberhart [4] s a stochastc optmzaton technque mmckng the behavor of a flock of brds. The algorthm presented below uses the global best and local best mechansm of PSO. Let f : R n R be the ftness functon and there are n partcles, each wth n n assocated postons x and veloctes. Let R v R, =1(1 ) n poston of each partcle and let g ~ be the global best. Algorthm_PSO() { Intalze x and v, = 1(1 ) n ; ~ x x ; g ~ arg mn { f ( x ), = 1(1 n ; x ) Repeat For each partcle =1(1)n Create random vectors r 1 and r 2 ; x~ be the current best
3 x x + v ; v ( ( ~ )) ( ( ~ wv + c1 r1 x x + c2 r2 g x )) ; If f ( x ) < f ( ~ x ); ~ x x ; If f ( x ; ) < f ( g ~ ); g~ x End Untl (stoppng crteron met); } 2.2 Related Work X. Yao [2] seem to have been the frst researcher for evolutonary neural network. He used a GA algorthm to evolve the archtecture and weghts of the network. Compared to GA, PSO algorthm possesses some attractve propertes such as memory and constructve cooperaton between ndvduals, so t has more chance to fly nto the better soluton areas more quckly and dscover reasonable qualty soluton much faster. In PSO only few parameters are to be tuned. Unlke GA, the representatons of the weghts are easy and as there s no recombnaton and mutaton operator, so there s a very neglgble chance of facng the permutaton problem. Further, as there s no selecton operator n PSO, each ndvdual n an orgnal populaton has a correspondng partner n a new populaton. From the vew of the dversty of populaton, ths property s better than GA, so t can avod the premature convergence and stagnaton n GA to some extent. Zhang et al. [5] has evolved PSO based ANN s and used n modelng product qualty estmator for a fractonator of the hydrocrackng unt n the ol refnng ndustry. In ther methodology, evolvng ANN s archtecture and weghts are alternated and they used partal tranng for each ndvdual archtecture. The computaton tme of ther proposed work s qute hgh due to the partal tranng. Carvalho et al. [6] nspred by Zhang et al. works and then ntroduces the method PSO-PSO:WD based on the weght decay heurstc n the weght adjustment process n an attempt to obtan more generalzaton control. Analyzng both algorthms we found that no one has gven much emphass on how many hdden layers requred for the optmal archtecture and nor even show about ts optmalty by expermental study. Further, nether gven emphass on how the partcle s represented nor gven much mportance on numercal smulaton to show the potentalty of ther method. Further, as they are usng PT algorthm for tranng so ther method ntroduces overhead n computatonal tme. Hence to cope wth these problems we have motvated to develop a method, whch can solve the sad ssues n addton to nhertng the basc characterstcs. 3 PSO for Evolvng Swarm Network There are two major approaches to evolvng the network archtectures. One s the evoluton of "pure" archtecture wth the randomly ntalzed connecton weghts, and
4 then the connecton weghts wll be traned after a near optmal archtecture has been found. Another s the smultaneous evoluton of both archtectures and weghts [2]. Unfortunately, the former brngs out the nosy ftness evaluaton that can mslead the evoluton. Although the latter can effectvely allevate the nosy ftness evaluaton problem, the nodes often become nvolved n a movng target problem because the soluton space to be searched s too large. In general, t s the most sgnfcant reason why smultaneous optmzaton of the parameters of the entre networks can fal. In order to solve preferably the above-mentoned problems, an approach s proposed where the number of hdden layers and number of neurons n the respectve layer and set of weghts are adaptvely adjusted smultaneously. In the proposed approach, both the archtecture and the set of weghts are encoded n partcles and evolved smultaneously.e. each partcle represents a canddate soluton of the archtecture and weght space. In abstract vew, Fgure 1 shows the smultaneous evoluton of archtecture and weghts. 1) Evaluate each partcles based on the predefned crteron. 2) Fnd out the personal best (p best ) of each partcle and global best (g best ) from the swarm. 3) Update partcles velocty. 4) If the performance s satsfactory then stop, otherwse go to step 1. Fgure 1. Abstract Vew of Evolvng Swarm Network In ts current mplementatons, swarm approach to evolvng neural network s used to evolve feed forward neural networks wth a characterstc functon. We defned two characterstcs functons-one s for 2-class problem and another s for 3-class problems. In the case of 2-class problem the characterstc functons s defned as: f ( o) = 1f o θ, otherwse f ( o) = 1, where 1 θ 1 s a threshold value and o s the output produced by the output neuron. The postve value represent class 1 and the negatve value represent class 2. Smlarly, for three class problems the user has to choose two threshold valuesθ 1 and θ 2 based on that the characterstc functon s defned as: 1 f o < θ 1 f (0 ) = 0 f θ 1 o < θ. 2 1 f o θ 2 In the proposed method we restrct ourselves to put one neuron n the output layer nstead of puttng neurons based on the number of classes. However, ths s not an nherent constrant. In fact, the proposed approach has mnmal constrant on the type of artfcal neural networks, whch may be evolved. The feed forward ANNs do not have to be strctly layered or fully connected between adjacent layers. Ther may also contans hdden nodes wth dfferent transfer functons. Let us see how the proposed approach s representng the partcles as well as evaluatng the ftness of each partcle.
5 3.1 Partcle Representaton For representng the partcles we have to set the protocols such as maxmum number of hdden layers denoted as L max, and maxmum number of nodes for a partcular hdden layer, denoted as N max a pror. Based on these values the partcle can be represented as a vector notaton, P = P P,..., P., 1 2 The frst attrbute P 1 of the partcle represent the number of hdden layers n the archtecture. The value of P 1 les between 0 to L max,.e. 0 P 1 L. The feature max from P 2 to P Lmax +1 tells about the number of neurons n the respectve hdden layer. The next features stores the weghts between nput layer and 1 st hdden layer and so on except the last feature of the partcle P b. The last feature.e. P b stores the weght values of bas unt. b 3.2 Ftness evaluaton The ftness of each partcle of the proposed approach s solely determned by the classfcaton accuracy based on the confuson matrx. Let the problem be a C class problem. Then the confuson matrx for the C class problem s defned as follows. Actual Predcted C 1 C 2. C C C 1 a 11 a 12. a 1c C 2 a 21 a 22. a 2c..... C C a C1 a c2. a cc The entres n the confuson matrx have the followng meanng n the context of our study: a 11 s the number of correct predctons that an nstance s C 1, a 21 s the number of ncorrect predctons that an nstance s C 2 and so on. The classfcaton accuracy s measured by the followng formula wth a consderaton of mbalance-ness of classes. fˆ CA 1 a11 a 22 a cc = c c c c a a a j = 1 1 j j = 1 2 j j = 1 cj 4 Expermental Study The performance of the proposed model s evaluated usng the four-benchmark databases taken from the UCI machne repostory [8]. Table 1 presents a summary of the man features of each database that has been used n ths study. Table 1. Descrpton of the features of the databases employed Datasets Patterns Attrbutes Classes Patterns n Class1 Patterns n Class2 Patterns n Class3
6 IRIS WINE PIMA BUPA Parameters Setup For smulaton of the proposed models and to compare wth other competng models lke PSO-PSO:WD and PSO-PT, the dfferent parameters consdered for usng the proposed method are presented n Table 2. For all smulatons we have used g best socometry of PSO algorthm. Although ths parameter area s qute restrcted, and no systematc parameter optmzaton process has so far been attempted, however we set the parameters accordng to the suggested and wdely used parameters n lteratures [7] wth a mnor tunng such as c 1 = wand c = w. 2 Table 2. Parameters requred smulatng the proposed method Parameters of the Proposed Method PSO Parameters and Values Neural Network Parameter and Values w L max 4 c N max 10 c θ Populaton Sze 30 θ Maxmum Iteratons Cross Valdaton, Results and Dscusson We have adopted the 2-fold cross-valdaton strategy wth the ntenson of gettng good classfcaton accuracy. The dataset s randomly parttoned nto two sets of equal sze that are n turn used for buldng and testng the proposed model. Whle one part s used for buldng the proposed model the other part s used for testng the model, n a way that each one s used for opposte purpose. The percentage of correct classfcaton for each dataset usng the proposed model s presented n Table 3. Table 3. Classfcaton accuracy of proposed model Dataset Ht Percentage n Tranng Sets Ht Percentage n Test Sets Set1 Set2 Average Set1 Set2 Average IRIS WINE PIMA BUPA Wth the same protocol the average comparatve performance of the proposed
7 method wth ts rval s presented n Table 4. Table 4. Average comparatve performance Dataset/ Average Ht Percentage n Tranng Set Average Ht Percentage n Test Set Methods Proposed PSO- PSO-PT Proposed PSO- PSO-PT Model PSO:WD Model PSO:WD IRIS WINE PIMA BUPA From the results presented n Table 4 we can note that for all the datasets except BUPA the proposed method obtaned better average classfcaton accuracy n both tranng set and test set compared to the method PSO-PSO: WD and PSO-PT. In the case of BUPA even though the tranng performance of the proposed method s close or nearly better than other two methods but durng testng the performance s qute better than other two methods. The number of hdden layers and the number of neurons requred n each hdden layer for the dfferent dataset to generate the proposed archtecture s presented n Fgure 2. (a) (b) (c) Fgure 2. Archtectural Complexty of (a) Proposed Method (b) PSO-PSO:WD and (c)pso-pt In vew of the archtectural complexty, on the whole the proposed approach s complex than other two models, whereas f we compare the classfcaton accuracy the proposed approach s more promsng than the other two approaches. Therefore, f one vew from a mult-objectve perspectve no soluton s better than others and t s
8 also very dffcult to optmze both these objectves smultaneously. These two objectves are very often conflctng to each other. 5 Conclusons and Future Research In ths paper, we have proposed a novel swarm approach to evolve neural network amng to optmze smultaneously both archtecture and set of weghts. The proposed model s evaluated usng the benchmark datasets consderng the task of classfcaton n data mnng. Further, we compared our model wth two other competng models such as PSO-PSO:WD and PSO-PT. Expermental studes demonstrated that the proposed model s qute superor to other two models n term of classfcaton accuracy whereas n terms of archtectural complexty our model ntroduces lttle overhead but can be tolerable by the data mnng desgner and ultmately decson maker. Future work should consst of experments wth other large datasets as well as the fne-tunng of the parameters used n the proposed method. It would be nterestng to optmze the archtectural complexty and classfcaton accuracy consderng as a mult-objectve problem by PSO and generate the Pareto front. Acknowledgments. The authors would lke to thank the fnancal support of BK21 research program on Next Generaton Moble Software at Yonse Unversty, SOUTH KOREA. References 1. Ghosh, A., Dehur, S., Ghosh, S. (eds.): Mult-objectve Evolutonary Algorthms for Knowledge Dscovery from Databases. Sprnger-Verlag, Hedelberg, Germany (2008). 2. Yao, X., Lu, Y.: A New Evolutonary System for Evolvng Artfcal Neural Networks. IEEE Transactons on Neural Networks, vol. 8, no. 3, pp (1997). 3. Goldberg, D. E.: Genetc Algorthms n Search, Optmsaton and Machne Learnng. Addson-Wesley Pub. Co. (1989). 4. Kennedy, J., and Eberhart, R. C.: Partcle Swarm Optmsaton. In Proc. IEEE Internatonal Conference on Neural Networks, IEEE Servce Center, Pscataway, NJ, pp (1995). 5. Zhang, C., Shao, H.: An ANN s Evolved by a New Evolutonary System and ts Applcaton. In Proc. of 39th IEEE Conference on Decson and Control, Sydney, pp (2000). 6. Carvalho, M., Ludermr, T. B.: Partcle Swarm Optmsaton of Neural Network Archtectures and Weghts. In Proc. of 7th Internatonal Conference on Hybrd Intellgent Systems, IEEE Computer Socety Press, pp (2007). 7. Clerc, M., Kennedy, J.: The Partcle Swarm-Exploson, Stablty, and Convergence n a Mult-dmensonal Complex Space. IEEE Transactons on Evolutonary Computaton, vol. 6, no. 1, pp (2002). 8. Blake, C. L., Merz, C. J.: UCI Repostory of Machne Learnng Databases.
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