A Comprehensive Review of Overlapping Community Detection Algorithms for Social Networks

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International Journal of Engineering Researh and Appliations (IJERA) ISSN: 2248-9622 National Conferene on Advanes in Engineering and Tehnology (AET- 29th Marh 2014) RESEARCH ARTICLE OPEN ACCESS A

1 International Journal of Engineering Researh and Appliations (IJERA) ISSN: National Conferene on Advanes in Engineering and Tehnology (AET- 29th Marh 2014) RESEARCH ARTICLE OPEN ACCESS A Comprehensive Revie of Overlapping Community Detetion Algorithms for Soial Netorks Ashish Kumar Singh 1, Sapna Gambhir 2 1 (YMCA University of Siene and Tehnology ashebdeveloper@gmail.om) 2 (YMCA University of Siene and Tehnology sapnagambhir@gmail.om) Abstrat Community struture is an interesting feature found in many soial netorks hih signifies that there is intense interation beteen some individuals. These ommunities have a tendeny to overlap ith eah other as there are nodes that an belong to multiple ommunities simultaneously. Detetion of suh overlapping ommunities is a hallenging task; it still remains a topi of interest for the researhers as it ansers many questions about the behavior of the netork and its operation as a funtion of its struture. This paper revies overlapping ommunity detetion tehniques proposed so far and points out their strengths and eaknesses. The paper also presents insightful harateristis and limitations of the existing state of art algorithms to solve the problem of overlapping ommunity detetion. Keyords Overlapping Community detetion, Online Soial Netorks, Complex Netorks, Community Struture. I. INTRODUCTION Online soial netorks have beome a primary means of ommuniation noadays; they attrat a ide variety of audiene. Nearly every person has a profile on Faebook, Google plus, Orkut, Titter et hih are olletively termed as Soial Netorking Sites (SNS). People usually ommuniate to others via these SNS and this ommuniation has attrated a lot of researh fous in reent years under the domain named Soial Netork Analysis. A soial netork is a graphial representation of the ommuniation among people, here people are represented as nodes and the edges beteen a pair of nodes represent some kind of ommuniation beteen them. A very interesting feature in soial netorks is the formation of Communities. A ommunity is a group of individuals in a soial netork ho ommuniate more frequently ith eah other than ith others outside the group. When a the soial netork is represented as a graph G (V, E), here V representing the individuals and E representing the onnetions among them, then a ommunity C G suh that the number of edges going outside from the verties in C is far less than the number of edges ith both verties inside C. The detetion of suh ommunities is not trivial and is quite hallenging as it is ompletely different from to similar and ell studied problems in omputer siene namely Clustering and Graph Partitioning. The first most hallenge in the domain of ommunity detetion is that there is no generally aepted definition of a ommunity; still there are a large number of ommunity detetion algorithms available hih produe effetive results. Most of the ommunity detetion algorithms do not take in to aount the overlapping beteen ommunities, hih is a serious ase in SNSs. Communities in soial netorks, tends to overlap ith eah other hih means that a vertex hih is a member of one ommunity an also be a member of another ommunity as shon in Fig 1. The idea of overlapping ommunities makes the problem of ommunity detetion tougher as the result of the algorithms ould no be a Cover, a set of ommunities of hih a vertex is a member. Most of the ommunity detetion algorithms start resulting in bad assignments of ommunities to verties in the overlapping ase as they generally merge to ommunities ith dense overlaps into a single ommunity. Fig 1: Illustration of overlapping ommunities, nodes shon in red olor 5 P a g e

The major ontributions of this paper ill be: To serve as a base for those starting researh in this diretion. To provide them ith the existing state of art algorithms for the researh problem.

2 International Journal of Engineering Researh and Appliations (IJERA) ISSN: National Conferene on Advanes in Engineering and Tehnology (AET- 29th Marh 2014) This paper presents a systemati and organized study of overlapping ommunity detetion tehniques. The strengths and eaknesses of eah tehnique is also a matter of fous in this paper. The major ontributions of this paper ill be: To serve as a base for those starting researh in this diretion. To provide them ith the existing state of art algorithms for the researh problem. To make them aare of the hallenges in the diretion and the solutions proposed so far. The paper is organized in to setions namely Problem Formulation hih learly states the problem of overlapping ommunity detetion, Tehniques hih explains the tehniques used so far to solve the problem and their orresponding strengths and eaknesses, and at last Conlusion hih sums up the ork onduted and the future diretions for ork. II. PROBLEM FORMULATION Given a graph G (V, E ), here V is the set of Verties and E is the set of edges assign to eah vertex v V a over C here C represents the set of ommunities of hih v is a member. V =n, E =m For dense graphs m= O (n 2 ) and for sparse graphs m=o (n). III. TECHNIQUES The algorithms for overlapping ommunity detetion an be broadly lassified into folloing ategories: a) Link Partitioning Algorithms b) Clique Based Algorithms ) Agent Based and Dynami Algorithms d) Fuzzy Algorithms e) Loal Expansion and Optimization Algorithms We ill explore eah of them one by one, and ill point out their relative strengths and eaknesses. a) Link Partitioning Algorithms The basi idea of link partitioning algorithms is to partition links to disover the ommunities. To steps of every link partitioning algorithms are: Step 1: Construt the Dendrogram. Step 2: Partition the Dendrogram at some threshold. A node ill be identified as overlapping if the links to the node are present in more than one luster. Links are partitioned by hierarhial lustering in [1] on the basis of edge similarity. If e are given a pair of links eik and e jk, the edge similarity beteen these to links is alulated by Jaard index as: S( jk, ik) i j i j e e N N N N N i is the set of nodes hih are in the neighborhood of node i inluding node i. After alulating edge similarities linkage lustering is done to find hierarhial ommunities. Generally single linkage hierarhial lustering is done beause of its simpliity and effiieny hih enables us to apply it on large netorks. Other lustering methods inlude average and omplete hierarhial lustering. Initially every node belongs to its on ommunity, and then links ith highest similarities are merged into a single ommunity, this proess is repeated until all the links belong to a single ommunity. This hole merging proess is stored in a Dendrogram hih reords the hierarhial ommunity organization. Fig 2: Illustration of a Dendrogram; y axis represents similarity (linkage distane) and x axis denotes node indies. This Dendrogram is then ut at a threshold value of partition density to reveal ommunities as shon in Fig 2. Partition density attains a global maximum at some level in the Dendrogram; it is average at the top of Dendrogram and attains the loest value at the leaves of the Dendrogram. The idea of link partitioning is quite natural and intuitive but it an t guarantee better results than node partitioning algorithms as it is also based on the ambiguous definition of ommunity [2]. The omplexity is O (nk 2 max), here k max is the maximum degree of any node in the netork. b) Clique Based Algorithms A lique is a maximal subgraph in hih all nodes are adjaent to eah other. The input to Clique based algorithms is a netork graph G and an integer k. Clique based algorithms have folloing steps in general: Step 1: Find all liques of size k in the given netork. Step 2: Construt a lique graph. Any to k-liques are adjaent if they share k-1 nodes. Step 3: Eah onneted omponents in the lique graph form a ommunity. CPM (Clique Perolation Method) is based on the assumption that a netork is omposed of liques hih overlap ith eah other. CPM finds overlapping 6 P a g e

3 International Journal of Engineering Researh and Appliations (IJERA) ISSN: National Conferene on Advanes in Engineering and Tehnology (AET- 29th Marh 2014) ommunities by searhing for adjaent liques. As a vertex an be a member of more than one lique, so overlap is possible beteen ommunities. The parameter k is of utmost importane in finding ommunities via CPM, Empirially small values of k have shon effetive results [3] [4]. An effiient implementation of the CPM method is CFinder. CPM is suitable for dense graphs here liques are present. In ase there are fe liques only CPM fails to produe meaningful overs. Example 1: shoing the orking of lique perolation as shon in Fig 3. Fig 3: A netork ith 6 k-liques here k=3 Clearly the netork has 6 liques of size 3, first of all these are identified by the CPM as {1, 2, 3}, {1,3,4}, {4,5,6}, {5,6,7}, {5,6,8}, {6,7,8}. After finding the liques, a lique graph is formed in hih to liques are adjaent if they share k-1 nodes as shon in Fig 4. Fig 4: shoing the lique graph for the netork in Fig 3 To ommunities ill be shon as result and they are: {1,2,3,4} and {4,5,6,7,8} The major disadvantage of CPM is that it fails to terminate for large netorks. Some argue that CPM is more like a pattern mathing algorithm as it searhes for a partiular pattern in the given netork on the basis of input parameter k. To other Clique based algorithms are CPM [5] and SCPM[6]. CPM is for eighted netorks, it introdues the onept of intensity threshold. Only the liques ith subgraph intensity greater than the threshold are inluded in the ommunity. CPM produes ommunities ith smoother ontours as ompared to CPM. SCPM is faster than CPM as it doesn t proess the netork for all values of k, instead it proesses only for a given value of k. SCPM suits for eighted netorks having hierarhial ommunity struture. ) Agent Based and Dynami Algorithms Three famous algorithms that ome under this ategory are SLPA [7], COPRA [8], and Label Propagation algorithm [9]. SLPA is Speaker-Listener label propagation algorithm, in hih a node is alled speaker if it is spreading information and is alled a listener if it is onsuming information. Labels are spread aording to pair ise interation rules. In SLPA a node an have many labels depending upon the underlying information it has learned from the netork. The time omplexity of SLPA is O(tm) here t is the number of iterations and m is number of edges. The best part of SLPA is that it doesn t require any prior knoledge about the number of ommunities in the netork. In other to algorithms the node forgets the information it has learned in previous iterations but in SLPA eah node has a stored memory in hih it stores all the information it has learned about the netork in form of labels. Whenever a node observes more labels in surrounding, it is more likely that it ill spread those labels to other nodes. The Label Propagation algorithm desribed in [9] is extended to overlapping ase by alloing a node to have multiple labels. Initially all nodes have their on unique label, labels are updated upon iterations depending upon the labels oupied by the maximum neighbors. Nodes ith same labels form a ommunity. LPA as modified by Gregory [8], he introdued Community Overlap Propagation Algorithm (COPRA). In COPRA eah label onsists of a belonging oeffiient and a ommunity identifier. The sum of belonging oeffiients of ommunities over all neighbors is normalized. A node updates its belonging oeffiient in a synhronous fashion by averaging the belonging oeffiients of all its neighbors at eah step. The parameter v ontrols the number of ommunities of hih a node an be a member. The time omplexity of COPRA is O (vmlog(vm/n)). Aording to benhmarks in [10] COPRA provides the best results for overlapping ommunities. An important optimization in LPA an be to avoid unneessary updates, hih ill redue the exeution time. d) Fuzzy Algorithms The overlap beteen ommunities an be of to types, one is the risp overlap in hih eah node either belongs to a ommunity or doesn t, the belonging fator is 1 for all the ommunities a node is a member. The other type of overlap is the fuzzy overlap in hih eah node an be a member of ommunities ith belonging fator in the range 0 to 1.The membership strength of a node to a ommunity is denoted by b n and if e sum the belonging oeffiients 7 P a g e

4 International Journal of Engineering Researh and Appliations (IJERA) ISSN: National Conferene on Advanes in Engineering and Tehnology (AET- 29th Marh 2014) of a vertex for all the ommunities of hih it is a member the result ill be 1. C b n =1 here C The major drabak of fuzzy based overlapping ommunity detetion methods is the need to alulate the dimensionality k of the membership vetor; this value is generally passed as a parameter to the algorithms, hile some algorithms alulate it from the data. Only a fe fuzzy methods have shon good results. In [10], authors proposed an algorithm ith the ombination of spetral lustering, fuzzy means and optimization of a quality funtion. They propose a method to detet up to k ommunities by using the fuzzy means lustering algorithm after onverting the input netork to a k- dimensional Eulidean spae. The auray and omputational effiieny of the algorithm is heavily dependent upon the parameter k. Nepsuz [11] model the problem of overlapping ommunity detetion as an optimization problem onstrained nonlinearly hih an be solved by simulated annealing methods. The objetive funtion required to be minimized in this method is: f n i 1 j 1 ij( xij x ij) n Where ij denotes a predefined eight and denotes prior similarity beteen nodes i and j. Similarity xij is defined as: x ij i j a a Where ai is the fuzzy membership of node i in ommunity, subjeted to onstraints of total membership and non empty ommunity. To determine the value of k, it is inreased repeatedly until the value of ommunity struture doesn t improve as measured by modified fuzzy modularity funtion, Q defined as: 1 kk i j Q [ Aij ]ai aj 2m 2m i, j A hybrid approah [18] based on Bayesian Non-negative Matrix Fatorization to ahieve soft partitioning of the netork in omputationally effetive manner is proposed. The advantage of this approah is that it doesn t suffer from the problem of resolution limit. This approah is a mix of dimensionality redution and feature extration in mahine learning. The problem ith NMF approah is that it is omputationally ineffiient beause of large matrix multipliations. e) Loal Expansion and Optimization Algorithms These algorithms rely on a loal benefit funtion hih enodes the quality of densely onneted subgraphs. The goal of these algorithms is to expand partial or natural ommunities so as to maximize the 2 x ij loal benefit funtion. The quality of disovered ommunities heavily depends upon the quality of seed ommunities. A lique serves as a better seed than a single node. EAGLE [12] reates a Dendrogram by using agglomerative frameork. First of all maximal liques are identified, and initialized as seed ommunities, then similarity values are omputed and ommunities ith maximum similarity are merged. The optimal ut of the Dendrogram is alulated using extended modularity funtion defined in [13]. EAGLE is omputationally expensive even ithout taking into aount the time required for finding maximal liques. GCE [14] also uses liques as seed ommunities and expands them using a loal fitness funtion. Communities are merged if they are found similar to previously deteted ommunities. The similarity is omputed using the distane funtion defined as: min( 1, 2 ) If the distane is smaller than the value speified by parameter then ommunities 1 and 2 are merged. The time omplexity of GCE is O (mh) here m is number of edges and h is the number of liques. In [15], author proposed another to step tehnique in hih nodes are first of all ranked aording to some riterion, and then highly ranked nodes are removed until small disjoint luster ores are formed. In the seond step i.e Iterative San (IS) these ores at as seed ommunities hih are expanded by adding or removing nodes until a loal density funtion annot be improved further. The density funtion used is given as: f () in in out in is total internal eight and out is the total external eight of ommunity. The orst ase omplexity of this tehnique is O(n 2 ). IS sometimes results in disonneted omponents as the algorithm allos removal of nodes during expansion, so CIS [16] as introdued in hih onnetedness is heked after eah iteration. OSLOM [17] orks by omparing the statistial signifiane of a luster ith the global null model (i.e. the random graph onfiguration model) during the expansion phase. To gro the ommunity r value is omputed for eah neighbor, hih is the umulative probability of having more internal edges in the ommunity than the number of edges from neighbors in the null model. If the umulative distribution of smallest r value is lesser than a tolerane value, the node is onsidered signifiant and is added to the ommunity otherise seond smallest r value is onsidered. The average time omplexity is O (n 2), it is dependent upon the underlying ommunity struture of the input netork. The main problem ith OSLOM is 8 P a g e

5 International Journal of Engineering Researh and Appliations (IJERA) ISSN: National Conferene on Advanes in Engineering and Tehnology (AET- 29th Marh 2014) that it results in signifiant number of singleton ommunities or outliers. To detet both stati and temporal ommunities ilcd [18] intrinsi longitudinal ommunity detetion as proposed hih updates ommunities by adding nodes depending upon hether the number of their first, seond robust neighbors is greater than an expeted value or not. The algorithm depends upon to parameters one for adding nodes to the ommunity and another for merging to ommunities. Reently there have been many improvements in the loal optimization and expansion algorithms. IV. CONCLUSION Overlapping ommunity detetion approahes have attrated a lot of attention of researhers in reent years and there is a onsiderable inrease in the number of algorithms published for solving the issue as it has appliations in various domains like mirobiology, soial siene and physis. Analyzing ommunity struture in soial netork has emerged as a topi of groing interest as it shos the interplay beteen the strutures of the netork and its funtioning. This paper tries to revie all popular algorithms for overlapping ommunity detetion ith their strengths and eaknesses. We have tried our best to revie all popular algorithms, but the study is by no means omplete as there are neer algorithms disovered at a fast rate beause of the groing interest of researhers in this domain. REFERENCES [1] Ahn, Y.-Y., Bagro, J. P., and S. Lehmann, Link ommunities reveal multisale omplexity in netorks, Nature -466, 2010, [2] S.Fortunato, Community detetion in graphs, Physis Report, 486(3), 2010, [3] Palla, G., Derenyi,Farkas, I., and Visek, T., Unovering the overlapping ommunity struture of omplex netorks in nature and soiety, Nature-435, 2005, [4] Lanihinetti, A., Fortunato, S., and Kertesz, J., Deteting the overlapping and hierarhial ommunity struture of omplex netorks, Ne Journal Physis, Cornell University, U.S.A., 11, 2009, [5] Farkas, I., Abel,D., Palla, G., and Visek, T. Weighted netork modules, Ne Journal Physis, Cornell University, U.S.A., 9(6), 2007, [6] Kumpula, J. M., Kivela Sequential algorithm for fast lique perolation. Physis Revie, Cornell University, U.S.A., 78( 2), 1-8. [7] Xie, J., Szymanski, B. K., and Liu, X., SLPA: Unovering overlapping ommunities in soial netorks via a speaker-listener interation dynami proess, Proeeding of ICDM Workshop, IEEE, 2011, [8] S.Gregory, Finding overlapping ommunities in netorks by label propagation, Ne Journal Physis, Cornell University, U.S.A., 12, 2010, [9] Raghavan, U. N., Albert, R., and Kumara, S., Near linear time algorithm to detet ommunity strutures in large-sale netorks. Physis Revie, Cornell University, U.S.A., 76, 2007, [10] Zhang S., Wang R.S., Zhang X.S, Identifiation of overlapping ommunity struture in omplex netorks using fuzzy -means lustering, Elsevier, 374(1),2007, [11] Nepusz Y., Petroz A., Negyessy L., and Bazso F,Fuzzy, Communities and the onept of bridgeness in omplex netorks, Physis Revie, Cornell University, 77, 2008, [12] Shen, H., Cheng, X., Cai, K., and Hu, M.-B. Detet overlapping and hierarhial ommunity struture, Physia A, 388, 2009, 1-7. [13] Shen, H., Cheng, X., and Guo, J., Quantifying and identifying the overlapping ommunity struture in netorks, J. Stat. Meh., 07, 2009, [14] Lee, C., Reid, F., MDaid, A., and Hurley, N., Deteting highly overlapping ommunity struture by greedy lique expansion, Proeeding of SNAKDD Workshop, 2010, [15] Baumes, J., Goldberg, M., Krishnamoorthy, M., Magdon-Ismail, M., and Preston, N., Finding ommunities by lustering a graph into overlapping subgraphs, Proeeding of IADIS, 5(1), 2005, [16] S.Kelley, The existene and disovery of overlapping ommunities in large-sale netorks, Ph.D. thesis, Rensselaer Polytehni Institute, Troy, NY, [17] Cazabet R., Amblard F., and Hanahi C, Detetion of overlapping ommunities in dynamial soial netorks, Proeedings of SOCIALCOM, 2010, [18] Psorakis I., Roberts S. and Ebden Mark, Overlapping ommunity detetion using Bayesian non-negative matrix fatorization, Physis Revie E, 83, 2011, P a g e

A Review on Overlapping Community Detection Algorithms

Review Paper A Review on Overlapping Community Detection Algorithms Authors 1 G.T.Prabavathi*, 2 Dr. V. Thiagarasu Address For correspondence: 1 Asst Professor in Computer Science, Gobi Arts & Science