Comparison of Robust Nearest Neighbour fuzzy Rough Classifier (RNN-FRC) with KNN and NEC Classifiers

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1 Bchtrananda Behera et al, / (IJCIT) Internatonal Journal of Computer cence and Informaton Technologes, Vol. 5 (), 014, Comparson of obust Nearest Neghbour fuzzy ough Classfer (NN-FC) wth KNN and NEC Classfers Bchtrananda Behera 1, udhakar abat 1, M.Tech.,Computer cence and Engneerng College of Engneerng and Technology, Bhubaneswar, Inda Abstract Fuzzy rough set, generalzed from Pawlak s rough sets, were ntroduced for dealng wth contnuous or fuzzy data. Ths model has been wdely dscussed and appled these years. It s shown that the model of fuzzy rough sets s senstve to nosy samples, especally senstve to mslabelled samples. As data are usually contamnated wth nose n practce, a robust model s desrable. To handle nosy datasets a lot of robust fuzzy rough set models were desgned before. obust nearest neghbour fuzzy rough set model s best among the models. A classfcaton algorthm was mentoned before based on ths model known as robust nearest neghbour fuzzy rough classfer. In lterature there was no detal descrpton of the robust nearest neghbour fuzzy rough classfer was gven and compared t wth KNN, and NN classfers. In ths paper, we gve detal descrpton of ths classfer and compare t wth other classfers lke KNN classfer, NN classfer and Fuzzy rough classfer. In ths paper we have done some numercal experments to show that obust nearest neghbour Fuzzy ough Classfers perform best among them. Keywords Fuzzy rough set, robustness, KNN, NEC classfers. I. INTODCTION Ths Classfcaton s a form of data analyss that extracts models descrbng mportant data classes. uch models called classfers, predct categorcal (dscrete, unordered) class labels, Classfcaton s a twostep process. In the frst step, a classfcaton model s bult based on tranng data. In the second step t determnes the model s accuracy based on testng data. If the model s accuracy s acceptable, then the model s used to classfy new data. Many classfcaton methods have been proposed by researchers n machne learnng, pattern recognton, and statstcs. Classfcaton has numerous applcatons, ncludng fraud detecton, target marketng, performance predcton, manufacturng, and medcal dagnoss. In lterature a lot of classfers were dscussed. Decson tree classfer s one of the well known classfer. Gven a obect X, for whch the assocated class label s unknown, the attrbute values of the obect are tested aganst the decson tree. A path s traced from the root to a leaf node, whch holds the class predcton for the obect. Bayesan classfers are statstcal classfers. They can predct class membershp probabltes such as probablty that a gven obect belongs to a partcular class. A rule based classfer uses a set of IF-THEN rules for classfcaton. A neural network s a set of connected nput/output unts n whch each connecton has a weght assocated wth t. The weghts are adusted durng the learnng phase to help the network predct the correct class label of the nput obects.a support vector machne s another classfer that transforms tranng data nto a hgher dmenson, where t fnds the hyper plane that separates the data by class usng essental tranng obects called support vectors. K-NN classfer, n whch a new pattern s classfed nto the class wth the most members present among the K nearest neghbours[1].k-nn classfers requre computng all the dstances between the tranng sets and test sample, t s tme-consumng f the avalable samples are of very great sze. Besdes, when the number of prototypes n the tranng set s not large enough, the K-NN rule s no longer optmal. Ths problem becomes more relevant when havng few prototypes compared to the ntrnsc dmensonalty of the feature space. Neghbourhood rough set model (NEC) as a unform framework to understand and mplement neghbourhood classfers[].ths algorthm ntegrates attrbute reducton technque wth classfcaton learnng. ough set theory [3], especally fuzzy rough set theory [4], whch encapsulates two knds of uncertanty of fuzzness and roughness nto a sngle model, has attracted much attenton from the domans of granular computng, machne learnng, and uncertanty reasonng over the past decade. Fuzzy rough set theory has been successfully used n gene clusterng, feature selecton, attrbute reducton, case generaton, and rule extracton. The dependence functon, whch s defned as the rato of the szes of the lower approxmaton of classfcaton over the unverse, plays a key role n these applcatons. Ths functon underles a number of learnng algorthms, ncludng feature selecton, attrbute reducton, rule extracton, and decson trees. Due to the advantages of dependence functon of fuzzy rough set fuzzy rough set models was developed. Due to dependence functon s senstve to nose to overcome ths problem a lot of robust fuzzy rough set models were developed n past. In 003,aldo and Murakam presented a β-precson aggregaton fuzzy rough set model based on β-precson aggregaton trangular operators [5]. In 004, the model of varable precson fuzzy rough sets (VPF) was ntroduced n [6], where the fuzzy membershps of a sample to the lower and upper approxmatons are computed wth fuzzy ncluson. In 007,Hu et al. ntroduced another fuzzy rough set model based on fuzzy granulaton and fuzzy ncluson [7]. In addton, n 007,Cornels et al. presented a model called vaguely quantfed rough sets (VQ) [8], whch was used n constructng a robust feature selecton algorthm n 008 [9]. In 009, Zhao et al. constructed a new model, whch s 056

2 Bchtrananda Behera et al, / (IJCIT) Internatonal Journal of Computer cence and Informaton Technologes, Vol. 5 (), 014, called fuzzy varable precson rough sets (FVP), to handle nose of msclassfcaton and perturbaton [10]. In 010,Hu et al. ntroduced a new robust model of fuzzy rough sets, whch are called soft fuzzy rough sets, where soft threshold was used to compute fuzzy lower and upper approxmatons [11].It has a lot of advantages but n realworld applcaton, the parameters used n the models have complex nteracton ways wth nose. Therefore, t s usually dffcult to obtan an optmal value. In 01,Hu et al. ntroduced robust nearest neghbour fuzzy rough set (NN-F) model and compared NN-F model wth other robust models lke -PF, VQ, VPF, FVP and F[1]. In that paper, robust nearest neghbour fuzzy rough classfer (NN-FC) was mentoned and that classfer performed best among them; But t was not gven the detals descrpton of the NN- FC and ts comparson wth KNN and NN. In ths paper, t s dscussed and gven the explanaton of NN-FC algorthm and compared t wth other classfer lke KNN, NN and F and shown that NN-FC s best a mong them. The remander of ths paper s organzed as follows. Frst, we gve prelmnary knowledge of rough sets and fuzzy rough sets n ecton II; then, we dscuss the exstng models of robust nearest neghbour fuzzy rough set models n ecton III. Then, we ntroduce robust nearest neghbour fuzzy rough classfers (NN-FC) n secton IV. Expermental analyss s gven n ecton V. Fnally, conclusons are drawn n ecton VI. II. PELIMINAIE OF OGH ET AND FZZY OGH ET A. ough et The ough set concept can be defned qute generally by s of topologcal operatons, nteror and closure, called approxmatons. I =, A s called an nformaton table, where s a fnte and nonempty set of obects and A s a set of features used to characterze the obects. B A, a B-ndscernblty relaton s defned as IND(B) = {(x, y) a B,a = a(y)} Then the partton of generated by IND(B) s denoted by /IND(B) (or /B). The equvalence class of x nduced by B-ndscernble relaton s denoted by [x] B. Gven an arbtrary X, s an equvalence relaton on nduced by a set of attrbutes. The lower approxmatons of X wth respect to are defned as X = {x [x] X} The lower approxmaton of a set X wth respect to s the set of all obects, whch can be for certan classfed as X wth respect to (are certanly X wth respect to ) The upper approxmatons of X wth respect to are defned as X = {x [x] X φ} The upper approxmaton of a set X wth respect to s the set of all obects whch can be possbly classfed as X wth respect to (are possbly X n vew of ). -boundary regon of X s defned as BN (X) = X X The boundary regon of a set X wth respect to s the set of all obects, whch can be classfed nether as X nor as not-x wth respect to. -negatve regon of X s defned as NEG (X) = X It contans those elements whch completely do not belongs to X. The defnton of rough sets s et X s crsp (exact wth respect to ), f the boundary regon of X s empty. et X s rough (nexact wth respect to ), f the boundary regon of X s nonempty The lower approxmaton s also called -postve regon of X, denoted by PO (X).Gven a decson table D =, A D D s the decson attrbute. For B A, the postve regon of decson D on B, denoted by PO B (D), s defned as PO (D) B = BX X / D Where, /D s the set of the equvalence classes generated by D. The dependency of decson D on B s defned as PO (D) γ (D) = B Dependency s the rato of the samples n the lower approxmaton over the unverse. As the lower approxmaton s the set of obects wth consstent decsons, dependency s used to measure the classfcaton performance of attrbutes. It s expected that all the decsons of obects are consstent wth respect to the gven attrbutes. In practce, nconsstency wdely exsts n data. B. Fuzzy ough et The ough set model s constructed under the assumpton that only dscrete features exst n the nformaton system. In practce, most of classfcaton tasks are descrbed wth numercal features or fuzzy nformaton. In ths case, neghbourhood relatons or fuzzy smlarty relatons are used and neghbourhood or fuzzy granules are generated. Then, we use these granules to approxmate decson classes. Gven a nonempty unverse, s a fuzzy bnary relaton on. If satsfes (1) reflexvty: (x, x)=1 () symmetry: (x, y)= (y, x) (3)sup-mn transtvty: (x, y) sup mn {(x, z), (z, y)} z Then s a fuzzy equvalence relaton. The fuzzy equvalence class [x] assocated wth x and s a fuzzy set on, where [x] (y) = (x, y) for all yϵ. Let be a nonempty unverse, be a fuzzy equvalence relaton on and X() be the fuzzy power set of. Gven B 057

3 Bchtrananda Behera et al, / (IJCIT) Internatonal Journal of Computer cence and Informaton Technologes, Vol. 5 (), 014, a fuzzy set X X(), the lower and upper approxmatons are defned as X = nf m ax(1 (x, y), X (y)) X = sup m n( (x, y), X (y)) These approxmaton operators were dscussed n the vew pont of the constructve and axomatc approaches. In 1998, Mors and Yakout replaced fuzzy equvalence relaton wth a T-equvalence relaton and bult an axom system of the model[13], where the lower and upper approxmatons of X X() are sx = nf (N ( (x, y)), X (y)) T X = sup T ( (x, y), X (y)) Where, T s a trangular norm. In 00, based on and adzkowska and Kerre ntroduced another model [14]: ϑ σ X X = n f ϑ ( (x, y), X (y)) = sup σ (N ( (x, y)), X (y)) y In classfcaton learnng, samples are assgned wth a class label and descrbed wth a group of features. Fuzzy equvalence relatons can be generated wth numercal or fuzzy features, whle the decson varable dvdes the samples nto some subsets. In ths case, the task s to approxmate these decson classes wth the fuzzy equvalence classes nduced wth the features. Gven a decson system <,, D>, for a decson class D /D, the membershp of a sample x to D s 1x D D = 0x D Then the membershp of sample x to the fuzzy lower approxmaton of D s nf D = nf D {1 (x, y), D (y)} nf y D = {1 (x, y),1} {1 (x, y), 0} nf y D nf y D = 1 {1 (x, y)} = {1 (x, y)} If we ntroduce Gaussan functon x y G(x, y) = exp σ to compute the smlarty, 1 G(x, y) can be consdered as a pseudo-dstance functon. mlarly, the membershp of sample x to the fuzzy upper approxmaton of D s D = mn{(x, y), D (y)} sup D = sup mn{(x, y),1} sup mn{(x, y),0} D y D sup mn{(x, y)} 0 D sup D = = mn{(x, y)} We can see that D s the dstance from x to ts nearest sample from dfferent classes; whle smlarty between x and the nearest sample n D. D s the III. OBT NEAET NEIGHBO FZZY OGH ET MODEL It was shown that both d or d T depends on the nearest mss of x,.e., the nearest sample from dfferent classes of x. As we know, the statstcs of mnmum and mum are very senstve to nosy samples. Just one nosy sample would change the mnmum or mum of a random varable. The senstveness of these statstcs leads to the poor performance of fuzzy rough sets n dealng wth nosy datasets. NN-F ntroduced robust statstcs to substtute the operators of mnmum and mum n the fuzzy rough set model. o that t can be performed better n nosy envronment. A.BAIC DEFINITION Gven a random varable X and ts n samples x1, x,..., x n sorted n the ascendng order, the k-trmmed mnmum of X s x k + 1 ; the k-trmmed mum of X s xn k 1 ; k- mnmum of X s n x = n k / k medan( 1 medan( x,..., k = 1 x / k ; k- mum of X s, and k-medan mnmum of X s x, x,..., x k ); k- mum of X s n k xn ), denoted by mn k trmmed (X), k trmmed(x), mn k (X), k (X), mn k medan(x), and k medan(x), respectvely. Gven DT =, A, D, s a fuzzy smlarty relaton nduced by B s subset C and (x, y) monotonously decreases wth ther dstance x y. If d s one class of x d samples labelled wth and, then the robust fuzzy rough operators are defned as d = 1 (x, y) k trmmed mn y dk trmmed d = (x, y) T k trmmed ϑ k trmmed σ k trmmed d k trmmed mn d = 1 (x, y) y d k trmmed d = 1 1 (x, y) d k trmmed 058

4 Bchtrananda Behera et al, / (IJCIT) Internatonal Journal of Computer cence and Informaton Technologes, Vol. 5 (), 014, mn d = 1 (x, y) k y dk d = (x, y) T k ϑ k σ k d k mn d = 1 (x, y) y d k d = 1 1 (x, y) d k mn y d d = 1 (x, y) k medan k medan d = (x, y) T k medan d k medan ϑ = mn 1 (x, y) k medan y d k medan σ = k medan d k medan d d 1 1 (x, y) The aforementoned models do not compute the lower and upper approxmatons wth respect to the nearest samples as they mght be outlers. These new models use k-trmmed or the or the medan of k nearest samples to compute the membershp of fuzzy approxmatons. Ths way, the varaton of approxmatons caused by outlers s expected to be reduced; thus, the new models may be robust. Gven a bnary classfcaton task, x d1 s a normal sample, and y 1 d s an outler close to x such that xy (, 1) = 0.9.Whle as a normal sample, d s the second nearest sample of x from d, and xy (, ) = 0.. As per the classcal fuzzy rough set model, d1 = 1 ( x, y1) = = 0.1.However, f we use the 1-trmmed model, d = 1 ( x, y ) = 0.8. Ths way, the nosy 1 trmmed 1 sample s gnored n the new model. At the same tme, assume x1 d1 s the second nearest sample of y 1, and x ( 1, y 1) = Accordng to the classcal model, d(y 1) = 1 ( x, y1) = =0.1 and as per the 1- d = 1 x (, y) = 0.1. trmmed model, 1 trmmed 1 1 It s seen that although the nearest sample x s gnored, 1 stll obtans a small value of membershp. In fact, the membershp should be small enough snce y 1 s a nosy sample. Ths example shows that the proposed model can not only reduce the nfluence of nosy samples on computaton of approxmatons of normal samples but can recognze the nosy samples and gve small membershps to them as well. y IV.OBT NEAET NEIGHBO FZZY OGH CLAIFIE(NN-FC) In ths secton, we desgn a robust classfer wth NN-F approxmaton. The dea of ths classfer comes from nearest neghbour rule (NN). ample x s classfed to the class of the nearest neghbour of x. Here nearest neghbour s determned by k-trmmed, k- and k-medan. Fuzzy rough classfer (FC) s desgned as follows. Gven a set of tranng samples wth m classes, x s an unseen sample. We compute m membershps of x to fuzzy lower approxmatons of m classes. Fnally, x s classfed to the class producng the mal membershp as x belongs to ths class wth the greatest consstency. Now we replace the fuzzy lower approxmaton wth the robust fuzzy lower approxmaton for a robust classfer. We call t obust Nearest Neghbour fuzzy rough classfer (NN-FC).It works n a smlar way wth F. We compute the membershps of an unseen sample to the soft fuzzy lower approxmatons of each class. A. NN-F Algorthm Gven a set of tranng samples DT =, A, D, x s a test sample. We compute the fuzzy lower approxmaton of each canddate class wth dfferent fuzzy rough set models. The decson functon s class = arg { class, class,..., class } d 1 Where s a certan fuzzy lower approxmaton operator Formally, the classfcaton algorthm s gven n Table 1. Ths algorthm assgns x the class label whch acheves the largest A. fuzzy lower approxmaton. uppose x class. We compute class. If x really belongs to class, t wll be far from the samples n the other classes. Table 1: NN-F Classfer Input tranng set X = {(x, y ),(x, y ),...,(x, y )} 1 1 n ' ' ' ' and test set X = {x 1, x,..., x m} Process label φ Output classnum= 1 For =1:m degree φ (y, y,..., y ) For class=1:classnum end class n n -mn 1 (y, y,..., y ) ' degree(class) class(x ) arg (degree) class label(x ) eturn label label ' class k n

5 Bchtrananda Behera et al, / (IJCIT) Internatonal Journal of Computer cence and Informaton Technologes, Vol. 5 (), 014, Thus, class should be large; otherwse, class s small. Therefore, the earler algorthm s ratonal to classfy x nto the class label producng the largest fuzzy lower approxmaton f no class nose exsts. However, f there are class-nosy samples, the prevous algorthm may not work when the classcal fuzzy rough set model s employed, whle the robust model s stll effectve n ths case. ome numercal experments are descrbed to prove effectveness of NN-FC n the numercal experments secton B. obustness evaluaton of Dfferent Classfers It s also known as comparson of classfcaton performance. o obustness of dfferent classfers are evaluated usng Average classfcaton accuraces. It s the measure used to evaluate the performance of classfers. Accuracy = (correctly classfed nstances) / (Total no. of nstances)100% 1. Accuracy = (TP+TN) / (TP+FP+TN+FN). enstvty = (TP/TP+FN)100% 3. pecfcty = (TN/ TN+FP) 100% Where, TP = true postve, TN = true negatve FP = false postve, FN = false negatve In 10-fold cross-valdaton, the orgnal sample s randomly parttoned nto 10- equal sze subsamples. Of the 10 subsamples, a sngle subsample s retaned as the valdaton data for testng the model, and the remanng 9 subsamples are used as tranng data. The cross-valdaton process s then repeated 10 tmes (the folds), wth each of the 10 subsamples used exactly once as the valdaton data. The 10 results from the folds can then be averaged (or otherwse combned) to produce a sngle estmaton. The advantage of ths method over repeated random subsamplng s that all observatons are used for both tranng and valdaton, and each observaton s used for valdaton exactly once. IV. NMEICAL EXPEIMENT The smulaton process s carred on a machne havng Intel() core (TM) Duo processor.40 GHz and.00 GB of AM. The MATLAB verson used s 01(a).The smulaton was carred out wth 4 data sets collected from nversty of Calforna, Irvne(CI)Machne Learnng epostory[15]. A. Data sets Four datasets from nversty of Calforna, Irvne (CI) Machne Learnng epostory are used. The nformaton related to the datasets s shown n table. Table : ummares of data sets Dataset amples Features Classes Irs Wdbc Wne Wpbc B. Dataset plt In the process of Classfcaton, the dataset s splt nto ten parts. The randomly chosen 90% of obects are used as the tranng set and the remander 10% as the testng set. C. Parameter pecfcaton We use Gaussan kernel to compute the fuzzy smlarty relatons between samples and the kernel parameter σ = 0.15, k=3. D. mulaton esult In ths secton we do some numercal experments to show robustness of the proposed classfer. Table 3: Classfcaton accuracy(%) on real world data set Data sets Irs Nose Level KNN NEC F k- k- medan k- trmme d 0% % % % % Wne 5% % % % Wdbc 5% % % % Wpbc 5% % % Average The classfcaton accuracy of dfferent classfers computed wth 10 fold cross valdaton s shown n table 3.Frst raw data sets are taken and ts classfcaton accuraces s shown wth zero nose level. nce we know that attrbute nose has less mpact on computaton of classfcaton accuracy. o, here we do not take attrbute nose. We here only consder class nose for accuracy c0mputaton.here 5%,10% and then 15% class nose data sets are taken and classfcaton accuracy are shown n the table 3. For consderng rs data set we see that all the classfers perform well; when there s no nose and KNN classfer performs best. But n nose envronment as nose ncreases only F classfer reduces rapdly others remans nearly same. o for rs data set F classfer performs worst and others perform better on nosy data set. It s shown n fg.1. In fg., F classfer performs best and KNN classfer performs worst and k-, k-medan, k-trmmed performs average when there s no nose n the wne data set. But ntroducng nose k-trmmed, k- and k-medan performs best, NEC and F average and K-NN worst. In wdbc data set k-trmmed performs best n both noseless and nosy envronment. The k-, NEC performs well after that k-medan and K-NN.F performs worst n nosy envronment. It s shown n fg

6 Bchtrananda Behera et al, / (IJCIT) Internatonal Journal of Computer cence and Informaton Technologes, Vol. 5 (), 014, Fg.1 Varaton of classfcaton accuracy for rs data set Fg.5 Average classfcaton accuracy of dfferent classfer Fg.5 shows average classfcaton performance of NN- FC.e. k-, k-trmmed and k-medan performs best.nec performance n between NN-FC and F. Average classfcaton performance of KNN classfer s worst among these classfers. Fg. Varaton of classfcaton accuracy for wne data set VI. CONCLION AND FTE WOK KNN, NEC and F classfers are wdely dscussed and have appled n many classfcaton applcatons. mlarly obust Nearest Neghbour fuzzy rough classfers (NN- FC) s recently dscussed. All classfers are good but there was no comparson was done to show among them best. In ths paper we compared NN-FC wth KNN, NEC and F classfers on both raw and nosy data sets and shown than all three classfers of NN-FC perform best. Out of the three classfers of NN-FC, K-trmmed based NN-FC shows best result both n average and for ndvdual data sets. After NN-FC, NEC classfer s better than F classfer and Fnally KNN classfers. Our future scope s to use NN-FC for feature selecton. Fg.3 Varaton of classfcaton accuracy for wdbc data set Consderng fg.4, we see that k-trmmed performs best n raw data set and also n nosy data set. The k-, k- medan and NEC performs average. But classfcaton performance of KNN and F reduces rapdly wth ncrease n nose.f performs worst. EFEENCE [1] Duda,., Hart, P.: Pattern Classfcaton and cene Analyss.Wley,New York(1973). [] Qnghua Hu, Daren Yu, Zongxa Xe. Neghborhood classfers. Expert ystems wth Applcatons. 34 (008) [3] Z. Pawlak, ough sets, Internatonal Journal of Computer and Informaton cences 11 (198) [4] D. Dubos, H. Prade, ough fuzzy sets and fuzzy rough sets, Internatonal Journal of General ystems 17 (1990) [5] J. M. F. aldo and. Murakam, ough set analyss of a general type of fuzzy data usng transtve aggregatons of fuzzy smlarty relatons, Fuzzy ets yst., vol. 139, pp , 003. [6] A. Meszkowcz-olka and L. olka, Varable Precson Fuzzy ough ets. Transactons on ough ets I. vol. LNC-3100, Berln, Germany:prnger, 004, pp [7] Q. H. Hu, Z. X. Xe, and D.. Yu, Hybrd attrbute reducton based on a novel fuzzy-rough model and nformaton granulaton, Pattern ecognt., vol. 40, no. 1, pp , 007. [8] C. Cornels, M. De Cock, and A. M. adzkowska, Vaguely quantfed rough sets, n Proc. 11th Int. Conf. ough ets, Fuzzy ets, Data Mnng,Granular Comput., 007, pp [9] C. Cornels and. Jensen, A nose-tolerant approach to fuzzyrough feature selecton, n Proc. IEEE Int. Conf. Fuzzy yst., 008, pp Fg.4 Varaton of classfcaton accuracy for wpbc data set 061

7 Bchtrananda Behera et al, / (IJCIT) Internatonal Journal of Computer cence and Informaton Technologes, Vol. 5 (), 014, [10]. Y. Zhao, E. C. C. Tsang, and D. G. Chen, The model of fuzzy varable precson rough sets, IEEE Trans. Fuzzy yst., vol. 17, no., pp ,Apr [11] Q. H. Hu,. An, and D.. Yu, oft fuzzy rough sets for robust feature evaluaton and selecton, Inf. c., vol. 180, pp , 010. [1] Qnghua Hu, Le Zhang, huang An, Davd Zhang, Daren Yu. On robust fuzzy rough set models. IEEE Transactons on Fuzzy ystems. 01, 0(4): [13] N.N. Mors, M.M. Yakout, Axomatcs for fuzzy rough sets, Fuzzy ets and ystems 100 (1998) [14] A.M. adzkowska, E.E. Kerre, A comparatve study of fuzzy rough sets, Fuzzy ets and ystems 16 (00) [15] A. Asuncon and D. J. Newman (007). CI machne learnng repostory,chool Inf. Comput. c., nv. Calforna, Irvne, [Onlne].Avalable: ml ATHO Bchtrananda Behera receved hs B.Tech n Computer cence and Engneerng from Dhaneswar ath Insttute of Engneerng and Management tudes, Cuttack, Inda n 011 and completed M.Tech.n Computer cence and Engneerng from College of Engneerng and Technology, Bhubaneswar, Inda n 013.Hs current research nterest s oft Computng, Data mnng and Algorthms. udhakar abat has obtaned hs B.Tech. n Computer cence and Engneerng from CV aman College of Engneerng, Bhubaneswar, Inda n year 011 and receved hs M.Tech.n Computer cence and Engneerng from College of Engneerng and Technology, Bhubaneswar, nda n 013.Hs feld of nterest s oftware engneerng and Data mnng. 06