CLUSTERING TECHNIQUES TO ANALYSES IN DENSITY BASED SOCIAL NETWORKS

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1 Iteratioal Joural of Computer Egieerig ad Applicatios, Volume VII, Issue II, Part I, August 14 CLUSTERING TECHNIQUES TO ANALYSES IN DENSITY BASED SOCIAL NETWORKS P. Logamai 1, Mrs. S. C. Puitha 2 1 Research Scholar, PSGR Krishammal College for Wome, Coimbatore 2 HOD, Dept.of Computer Sciece, PSGR Krishammal College for Wome, Coimbatore ABSTRACT: The Web has become a uprecedeted world-wide repository of kowledge. It cotais valuable iformatio for maagers, aalysts, ad all types of kowledge workers, yet, the Web is dyamic ad oisy. Hece, kowledge discovery from the Web, while beig challegig, is a essetial tool for the kowledge ecoomy. Social etworks have attracted much attetio recetly. Social etwork aalysis fids its applicatio i may curret busiess areas. Differet studies have bee coducted to automatically extract social etworks amog various kids of etities from the Web. Commuity detectio is oe of the most importat ad iterestig research areas i social etwork aalysis. Clusterig documets eables the user to have a good overall view of the iformatio cotaied i the documets that he has. However, existig algorithms suffer from various aspects; hard clusterig algorithms are usually iefficiet. We propose Clusterig algorithm based o Desity i social etworks (DBCASN). It requires oly a similarity measure for clusterig ad uses radomizatio to help make the clusterig efficiet. Compariso with existig hard clusterig algorithms like K-meas ad its variats shows that the proposed method is both effective ad efficiet. Keywords: Web Miig, Clusterig, Social Networks, DBSCAN, CURE [1] INTRODUCTION Clusterig belogs to the set of mathematical problems which aim at classificatio ad assigmet of data or objects to related sets or classes. The act of classificatio could well be applied through supervised or usupervised learig methods [1]. I the Supervised model, Patters are leart usig some familiar, previously classified data. Multi-layered Perceptio - MLP, Support Vector Machie - SVM, ad Decisio Trees are illustrious examples of such learig algorithms. This type of learig may be called the learig by example methodology. O the other had, ad i the usupervised method, maily amed clusterig, etities are classified i homogeeous classes so that eighborig patters are assembled i similar collectios. I this approach object- 172

2 Clusterig Techiques To Aalyses I Desity Based Social Networks class associatio is ot previously kow ad clusters are formed based o some object similarity criteria. As usupervised learig models, such as clusterig, ca semi-cosciously detect well separated classes amogst available data based o their itrisic features, they have bee extesively used i differet scietific fields. Their use ca sigificatly vary from Medicie ad its applicatio to disease detectio, to Itrusio Detectio Systems (IDS) for etwork activity divisio ito two typical types of itrusive ad o-itrusive. New applicatios of clusterig have bee foud i data (web) miig ad adaptive systems where user characteristics modelig, sessio detectio ad etc ca be achieved through modified clusterig algorithms. Patter recogitio ca also be a importat field of clusterig applicatio. Most clusterig techiques assume a well defied distictio betwee the clusters so that each patter ca oly belog to oe cluster at a time. This suppositio ca eglect the atural ability of objects existig i multiple clusters. For this reaso ad with the aid of fuzzy logic, fuzzy clusterig ca be employed to overcome this weakess. The membership of a patter i a give cluster ca vary betwee 0 ad 1. I this model oe sigle patter ca have differet degrees of membership i various clusters. A patter belogs to the cluster where it has the highest membership value. I this paper we aim to propose a Desity based clusterig techique which is capable of detectig the most appropriate umber of clusters based o a desity factor. This algorithm is completely isesitive to the iitial umber of employed clusters; however the iitial value should always be lower tha the optimal cluster umber. Although a very low umber of iitial clusters will icrease the computatio time ad CPU usage but it will prevet the algorithm from choosig the icorrect umber of clusters. The method discovers the umber of clusters by itelligetly splittig capable clusters ad creatig ew cluster ceters through outlier detectio. [2] RELATED WORK Clusterig is importat i may differet fields such as data miig [3], image compressio [11] ad iformatio retrieval [13]. [8] provides a extesive survey of various clusterig techiques. I this sectio, we highlight the work most related to our research. We ca divide clusterig algorithms ito hard ad soft clusterig algorithms. Accordig to [10], there are four differet kids of clusterig algorithms: hierarchical, partitio, model fittig ad desity based. These algorithms form clusters by puttig each item ito a sigle cluster. Soft clusterig allows each item to associate with multiple clusters, by itroducig a membership fuctio W ij betwee each cluster-item pair to measure the degree of associatio. Expectatiomaximizatio [6] serves as the basis of may soft-clusterig algorithms. A good survey of such algorithms ca be foud i [1]. May clusterig techiques have bee used for documet clusterig. Most of the early work [7, 15] applied traditioal clusterig algorithms like K-meas to the sets of documets to be clustered. Willett [21] provided a survey o applyig hierarchical clusterig algorithms ito clusterig documets. 173

3 Iteratioal Joural of Computer Egieerig ad Applicatios, Volume VII, Issue II, Part I, August 14 Cuttig et al. [4] proposed speedig up the partitio-based clusterig by usig techiques that provide good iitial clusters. Two techiques, Buckshot ad Fractioatio are metioed. Buckshot selects a small sample of documets to pre-cluster usig a stadard clusterig algorithm ad assigs the rest of the documets to the clusters formed. Fractioatio splits the N documets ito m buckets where each bucket cotais N/m documets. Fractioatio takes a iput parameter, which idicates the reductio factor for each bucket. The stadard clusterig algorithm is applied so that if there are documets i each bucket, they are clustered ito / clusters. Now each of these clusters is treated as if they were idividual documets ad the whole process is repeated util K clusters are left. Most of the algorithms above use a word-based approach to fid the similarity betwee two documets. I [22] a phrase-based approach called STC (suffix-tree clusterig) was proposed. STC uses a suffix-tree to form commo phrases of documets eablig it to form clusters depedig ot oly o idividual words but also o the orderig of the words. Various other clusterig techiques have bee applied to documet clusterig. This icludes usig associatio rules ad hyper graph partitioig [12], self-orgaizig maps [16], eural etworks [19, 14], ad EM-based techiques [9]. [2.1] INITIAL CLUSTER GENERATION At this step the iput is aalyzed, iitial clusters are produced ad outliers are removed. The first thig for SISC to do is to decide what costitute as similar documets. Essetially, we eed to fid a threshold value such that two documets are cosidered similar if ad oly if f ( x, y). Sice SISC is desiged to adapt to differet similarity measures f, it is ot reasoable for the user to supply a value for. As a result, SISC determies the appropriate value of based o the iput documets. The value of ca either be too high, such that o documets will be clustered at the ed; or too low, such that all documets will be clustered ito oe cluster. Thus, the algorithm chooses such that half 1 of the documets are assiged at least to oe cluster cetroid. This is doe by the followig method: 1. Pick a set of k documets, assigig each oe as the iitial cluster cetroid of a cluster. 2. Pick as the largest value such that for half of the documets q i the data set, there exists a p such that f ( p, q), p C, q D where C is the set of cluster cetroids ad D is the documet set. This ca be doe by calculatig all the similarity values f ( p, q), p C, q D ad sortig them. This esures that at least half of the documets are close to at least oe of the clusters, so that eough iterestig clusters ca be foud. A issue here is how the iitial cluster cetroids are picked. The simple way is to pick a radom set of documets. However, sice the iitial cluster cetroids ca have a sigificat effect o the algorithm, it pays to be more careful. We wat to avoid pickig too may cluster cetroids that are close to oe aother (so they should actually 174

4 Clusterig Techiques To Aalyses I Desity Based Social Networks belog to the same cluster). Oe way to overcome it is to start with pickig a radom documet as the first cetroids, ad the pick the documet that is least similar to it as the secod cetroids. Subsequet cetroids are chose such that they are farthest away from those cetroids that are already picked. [3] DETECTION OF COMMUNITIES IN WEIGHTED NETWORKS A fudametal problem i the aalysis of etwork data is the detectio of etwork commuities, groups of desely itercoected odes, which may be overlappig or disjoit. Network commuities play importat orgaizatioal ad fuctioal roles i complex etworks. Cosequetly, the idetificatio of commuities i complex etworks has become oe of the most active areas of research i etwork theory. Complex etworks are the structural skeleto of complex systems, which are ubiquitous i ature, society ad techology. A etwork is represeted by a graph, G ( V, E), where the set of odes E represets the etities of the system ad the set of liks E represets the relatioship betwee these etities. Give a set of data objects O { o1, o2,..., o} with associated positive weights α i ad a set of edges ( i, j) E with associated positive weights (e.g., similarities w ij ), where i j 1,2,...,. We address the partitioal clusterig problem of fidig a sigle partitio C { C1, C2,..., Ck} of data objects O { o1, o2,..., o} ito a fixed umber of k clusters. That is, each data object is assiged to exactly oe of those clusters ad every cluster has at least oe object. This ca be formulated as a optimizatio problem by defiig biary decisio variables: 1, if oi Cq x iq, 0, otherwise 1, if a object oq is selected as a cluster y q, 0, otherwise where i, q 1,2,...,. The partitioal clusterig problem ca the be formulated as a Boolea programmig problem: maximize 1 f ( x, y) β1 αi xiq yq β2 wij xiq x 1 q1 i1 q1 i1 ji1 β w y y (1) 3 subject to q1 i1 pq p1 q p1 p q x 1, i 1,2,...,, (2) iq x 1, q 1,2,...,, (3) iq jq y q 175

5 Iteratioal Joural of Computer Egieerig ad Applicatios, Volume VII, Issue II, Part I, August 14 q1 y q iq y q k, (4) x, i, q 1,2,...,, (5) x {0,1}, i, q 1,2,...,, (6) iq y {0,1}, q 1,2,...,, (7) q where β 1, β2, β3 are the weightig parameters, specifyig the relative cotributios of the terms to the hybrid objective fuctio f, which β β, β [0,1 ] where β β β 1. [3.1] EFFECTIVENESS OF CLUSTERING 1, We did may experimets with the documet sets of differet sizes that are take from the above-metioed test bed. All the algorithms were ru to produce the same umber of clusters with same iput parameter settigs. SISC formed clusters for each of the differet categories i the documet sets, while the other algorithms (K-Meas, Fractioatio ad Buckshot) did ot. I additio, the other algorithms formed clusters with documets of may categories that are ot related to each other. To test the effectiveess of our approach, we deliberately dowloaded some documets that are related to more tha oe of the categories listed above (For example, documets about baseball movies which iclude both baseball ad movies). K-Meas, Fractioatio ad Buckshot formed oly clusters about baseball ad Movies ad did ot form a cluster for documets related to both categories. However, SISC formed a cluster for baseball-movies ad put the documets related to baseball-movies i that cluster. This shows the effectiveess of our method compared to other algorithms. Figure 1 shows sample output from oe of the experimets with a documet set of 500 documets picked from 12 of the categories metioed above. The categories iclude Food, agets, XML, Jorda (the middle east coutry), Geetic algorithms, baseball, movies, Astroomy, Michael Jorda, Cosciousess, Virus ad baseball-movies. All the algorithms were ru with a iput umber of 12 clusters. Other algorithms formed 12 clusters but they did ot form a cluster for baseball movies. SISC formed a cluster for that as show i the above table. Sice SISC starts with twice the actual umber of clusters ad combies the clusters, we also tested other algorithms with twice the umber of clusters as iput. However, they failed to produce the correct clusters eve with twice the actual umber of clusters. [3.2] DBCASN ALGORITHM Step 1. Set the cluster assigmet for all poits as uclassified. Step 2. Specify the memberships threshold parameters 1 ad 2, set t=1. Step 3. Fid a uclassified core poit p with parameters 1 ad

6 Clusterig Techiques To Aalyses I Desity Based Social Networks Step 4. Mark p to be classified. Start a ew cluster C t ad assig p to this cluster. Step 5. Fid all the uclassified poits i the eighborhood set N p; 1 ad add to seed set created S. Step 6. Get a poit q i S, mark q to be classified, assig q to the cluster C t, ad remove q from S. Step 7. Check if q is a core poit with parameters 1 ad 2, add all the uclassified poits i the eighborhood set N p; 1 to the set S. Step 8. Repeat Steps 6 ad 7 util the set is empty. Step 9. t t 1ad repeat Steps 4-7 util there is o uclassified core poit. Step 10. Mark all uclassified poits as oise. Ed [4] EXPERIMENTS AND RESULTS Proposed algorithm shows stregths i may areas but it lacks the ability to determie the appropriate umber of clusters for patter classificatio ad requires the user to defie the correct umber of clusters. May applicatios of clusterig like patter recogitio or itrusive data classificatio require the clusterig algorithm to decide o the proper umber of clusters, as the correct umber of classes is ot a priori kow. This criterio serves as a great factor for the algorithms with a predefied umber of clusters; however i heuristics which have a adaptive approach to cluster umber assessmet, this factor caot be used. This is because the objective fuctio will decrease with the icrease of the umber of clusters ad hece causes further cluster splittig which results i a icorrect umber of clusters (the umber of clusters will most likely ed up beig idetical to the umber of available patters). For this reaso usig the objective fuctios as the basis for successful split assessmet is ureasoable. We defie ad apply CDC for split success compariso. FACT is comprised of 3 mai steps which are further explaied i the followig paragraphs: Step 1 Iitializatio The existig versio is applied to the set of available patters by settig the iitial cluster umber ad m to 2. The outputs of this step are the prelimiary values for U ad CDC. Step 2 Outlier Detectio a) Cluster Member Assigmet: Every patter i the clusterig algorithm has a membership degree i all available clusters. The process of patter to cluster assigmet is doe through allocatig the patter to the cluster i which it has the highest membership degree. Matrix M, [m ij ] c* is defied as follows: 177

7 Iteratioal Joural of Computer Egieerig ad Applicatios, Volume VII, Issue II, Part I, August 14 M ij U ij, 0, if else c MaxU ij U ij i1 (6) b) Local Outlier Detectio: I this sub step the cadidates i each cluster to be the fial outliers over all of the patters are selected. This process selects the patter with the lowest o-zero membership value i vector M i where i shows the curret cluster (7). Cadidate Mi( M i j1 ij ) where M ij 0 (7) c) Fial Outlier Selectio ad Splittig: The patter with the lowest value i the Cadidate vector (OP) is selected as the ultimate outlier. The coordiates of OP are used as the basis for the ceter of a ew cluster. Let OP = {op 1, op 2 op r } be the outlier poit, the ew cluster ceter will be calculated usig (Eq.8): Ceter (c+1) = OP + λ (8) Where λ = (λ 1, λ 2 λ r ) ~ 0. Havig calculated the value of the ew cluster ceter, the previous compositio of patter classificatios ca be altered ad rearraged based o c+ 1 cluster. Matrix U is updated usig (Eq. 4) where the upper boud of k is c+1.the modified versio of fuzzy C-meas is ow tued usig the calculated U ad c+1 umber of clusters ad is used to create the ew cluster compositio. After havig split the cluster formatio ito a ew arragemet, the CDC will be updated (Eq. 9). The value obtaied from the divisio of the ew CDC to the former CDC is multiplied by a coefficiet, α, which is betwee 0 ad 1. To show that splittig has improved the clusterig, θ t+1 should be larger tha θ t ad thus the splittig procedure is cofirmed ad stabilized. The value for α is usually set to 0.2. The θ is amed the Feedback Cotrol Parameter (FCP) which cotrols the system behavior usig a feedback from the prior iteratio. c 1 t1 M ij i1 j1 CDC (9) CDC ) t1 t 1 ( ) (1 CDC t t (10) If the splittig has bee usuccessful 2.c is repeated with the ext patter i the Cadidate vector. 178

8 Clusterig Techiques To Aalyses I Desity Based Social Networks Step 3 Test If oe of the patters available i the Cadidate vector ca serve as a successful splittig poit for improvig the curret cluster arragemet, the algorithm will termiate with the curret compositio o had else it will icrease the umber of clusters by oe uit ad resume algorithm executio. DBSCAN could idetify all the clusters properly. But DBSCAN depeds o some of the user parameters which have to be data specific. The rage of such parameters do ot vary too much may of them beig from 0 1. Cure could idetify several clusters with high purity which K- meas ad DBSCASN failed to idetify. Our experimets suggest that DBCASN faired well for low-dimesioal data. Also, if the desity of clusters did ot vary too much, DBCASN fairly idetified all the clusters. But if the size of the data icreases ad if shapes ad desity of clusters vary too much, DBCASN resulted i combiig or splittig those clusters. [5] CONCLUSION I this paper, we itroduced DBCASN (Ehaced DBSCAN) algorithm based o similarity measures, ad applied it to detect social etwork clusterig. The algorithm itroduces various techiques such as radomizatio to help make clusterig efficiet. Our experimets show that DBCASN algorithm is able to discover clusters that caot be detected by a high degree of efficiecy. To avoid redudacy i the result, our model selects oly the most iterestig clusters for the fial clusterig. We develop the algorithm DBCASN to efficietly determie the combied clusterig solutio. The clusterig quality ad the efficiecy of DBCASN are demostrated i the experimetal sectio. 179

9 Iteratioal Joural of Computer Egieerig ad Applicatios, Volume VII, Issue II, Part I, August 14 REFERENCES [1] Everitt, B.S., Ladau, S., Leese, M., Cluster Aalysis, Lodo: New York, Halsted Press, [2] J.L. Bezdek, Patter Recogitio With Fuzzy Objective Fuctio Algorithms, Pleum Press, Nyew York, NY [3] M.S. Che, J. Ha, ad P.S. Yu, Data Miig: A Overview from a Database Perspective, IEEE Trasactios o Kowledge ad Data Egieerig, 8(6): , [4] Douglass R. Cuttig, David R. Karger, Ja O. Pederse, Joh W. Tukey, Scatter/Gather: A Cluster-based Approach to Browsig Large Documet Collectios, I Proceedigs of the Fifteeth Aual Iteratioal ACM SIGIR Coferece, pp , Jue [5] Dea, P. M. Ed., Molecular Similarity i Drug Desig, Blackie Academic & Professioal, 1995, pp [6] A.P. Dempster, N.M. Laird, ad D. B. Rubi, Maximum likelihood from icomplete data via the EM algorithm, Joural of the Royal Statistical Society, Series B, 39(1), 1-38, [7] D. R. Hill, A vector clusterig techique, i: Samuelso (Ed.), Mechaized Iformatio Storage, Retrieval ad Dissemiatio, North-Hollad, Amsterdam, [8] A.K. Jai, M.N. Murty ad P.J. Fly, Data Clusterig: A Review, ACM Computig Surveys. 31(3): , Sept [9] Kamal Nigam, Adrew Kachites Mccallum, Sebastia Thru ad Tom Mitchell, Text Classificatio from Labeled ad Ulabeled Documets usig EM. Machie Learig 39(2-3): , [10] W.J. Krzaowski ad F.H. Marriott, Multivariate Aalysis: Classificatio, Covariace Structures ad Repeated Measuremets. Arold, Lodo, [11] Y. Lide, A. Buzo ad R.M. Gray, A Algorithm for Vector Quatizatio Desig, IEEE Trasactios o Commuicatios, 28(1), [12] Jerome Moore, Eui-Hog (Sam) Ha, Daiel Boley, Maria Gii, Robert Gross, Kyle Hastigs, George Karypis, Vipi Kumar, ad Bamshad Mobasher, Web Page Categorizatio ad Feature Selectio Usig Associatio Rule ad Pricipal Compoet Clusterig, I Proceedigs of seveth Workshop o Iformatio Techologies ad Systems (WITS'97), December [13] M.N. Murty ad A. K. Jai, Kowledge-based clusterig scheme for collectio maagemet ad retrieval of library books, Patter recogitio 28, , [14] F. Murtagh, A survey of recet advaces i hierarchical clusterig algorithms, The Computer Joural, 26(4): , [15] Alberto Muoz, Compoud key word geeratio from documet databases usig a Hierarchical clusterig ART Model, Itelliget Data Aalysis, 1(1), Ja [16] J. J. Rocchio, Documet retrieval systems optimizatio ad evaluatio, Ph.D. Thesis, Harvard Uiversity,

10 Clusterig Techiques To Aalyses I Desity Based Social Networks [17] Dmitri Roussiov, Kristie Tolle, Marshall Ramsey ad Hsichu Che, Iteractive Iteret search through Automatic clusterig: a empirical study, I Proceedigs of the Iteratioal ACM SIGIR Coferece, pages , [18] Robert E. Tarja, Data Structures ad Network Algorithms, Society for Idustrial ad Applied Mathematics, [19] last visited September 27 th, [20] Wog, S.K.M., Cai, Y.J., ad Yao, Y.Y, Computatio of Term Associatio by eural Network. I Proceedigs of the Sixteeth Aual Iteratioal ACM SIGIR Coferece o Research ad Developmet i Iformatio Retrieval, pp , [21] P.Willett, V. Witerma ad D. Bawde, "Implemetatio of Nearest Neighbour Searchig i a Olie Chemical Structure Search System, Joural of Chemical Iformatio ad Computer Scieces, 26, 36-41,1986. [22] P.Willett, Recet treds i hierarchical documet clusterig: a critical review, Iformatio processig ad maagemet, 24: , [23] O.Zamir, O.Etzioi, Web documet clusterig: a feasibility demostratio, i Proceedigs of 19 th iteratioal ACM SIGIR coferece o research ad developmet i iformatio retrieval (SIGIR 98), 1998, pp