Computers and Mathematics with Applications. An evaluation study of clustering algorithms in the scope of user communities assessment

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1 Computers nd Mthemtis with Applitions 58 (29) Contents lists ville t SieneDiret Computers nd Mthemtis with Applitions journl homepge: An evlution study of lustering lgorithms in the sope of user ommunities ssessment Pntelis N. Krmolegkos, Chrlmpos Z. Ptrikkis, Nikolos D. Doulmis, Pngiotis T. Vlhes, Ionnis G. Nikolkopoulos Ntionl Tehnil University of Athens, Teleommunitions Lortory, 9, Heroon Polytehniou str., Zogrfou, Athens, , Greee r t i l e i n f o s t r t Artile history: Reeived 1 Otoer 27 Reeived in revised form 28 April 29 Aepted 29 My 29 Keywords: Spetrl lustering Modeling Soil networking User profile Performne evlution In this pper, we provide the results of ongoing work in Mgnet Beyond projet, regrding soil networking servies. We introdue n integrted soil networking frmework through the definition or the pproprite notions nd metris. This llows one to run n evlution study of three widely used lustering methods (k-mens, hierrhil nd spetrl lustering) in the sope of soil groups ssessment nd in regrd to the rdinlity of the profile used to ssess users preferenes. Suh n evlution study is performed in the ontext of our servie requirements (i.e. on the sis of equl-sized group formtion nd of mximiztion of interests ommonlities etween users within eh soil group). The experimentl results indite tht spetrl lustering, due to the optimiztion it offers in terms of normlized ut minimiztion, is pplile within the ontext of Mgnet Beyond soiliztion servies. Regrding profile s rdinlity impt on the system performne, this is shown to e highly dependent on the underlying distriution tht hrterizes the frequeny of user preferenes pperne. Our work lso inorportes the introdution of heuristi lgorithm tht ssigns new users tht join the servie into pproprite soil groups, one the servie hs een initilized nd the groups hve een ssessed using spetrl lustering. The results lerly show tht our pproh is le to dhere to the servie requirements s new users join the system, without the need of n itertive spetrl lustering pplition tht is omputtionlly demnding. 29 Elsevier Ltd. All rights reserved. 1. Introdution The reent prolifertion of pplitions tht support soiliztion through the internet suh s newsgroups, virtul ht rooms, instnt messging progrms nd, ltely, welogs, hs given rise to new form of networking onept, lled soil networking. Soiliztion hs eome driving fore of networking pplitions design nd development; mny servies re now deployed in the sope of ringing together (in networking terms) people with ommon interests. Expliit expression of interest through ustomized user profiles [1] nd/or impliit inferene of user preferenes through monitoring of their we tivities [2] re used to support the soil networking frmework. Within suh ontext, one of the most hllenging tsks is the ssessment of the exhiited soil groups, nd the design of pproprite frmeworks tht exploit the ommonlities etween users interests to rete virtul ommunities tht promote effiient soiliztion. However, despite the undne of virtul meeting points nd the relevnt servies, in the virtul ommunities, with little sense of the presene of other people, individuls hve diffiult time forming oopertive reltionships [3]. Finding the right person to ontt is still Corresponding uthor. Tel.: ; fx: E-mil ddresses: pkrmol@teleom.ntu.gr (P.N. Krmolegkos), ptr@teleom.ntu.gr (C.Z. Ptrikkis), ndoulm@s.ntu.gr (N.D. Doulmis), pnvlh@teleom.ntu.gr (P.T. Vlhes), gnikolkopoulos@teleom.ntu.gr (I.G. Nikolkopoulos) /$ see front mtter 29 Elsevier Ltd. All rights reserved. doi:1.11/j.mw

2 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) tril nd error proedure whih is minly sed on intuition nd personl experienes []. Suh effiieny shortge of severl methods tht re used to promote soil networking is omplemented y relevnt lk of evlution studies regrding the performne ssessment of lgorithms tht provide the frmework for networked soiliztion. In this sope, this pper presents nd evlutes n integrted theoretil frmework for soil networking servie, s this hs emerged out of the definition of pilot servies of the IST MAGNET Beyond projet [5]. MAGNET projet nd its suessor MAGNET Beyond fous on the development of user-entri usiness model onepts for seure Personl Networks (PNs) in multi-network, multi-devie, nd multi-user environments, nd the design/development of novel personl network pplitions nd servies. In the sope of this work, we propose nd evlute the frmework of user profile sed soiliztion servie whose purpose is the utomted formtion of groups of interests etween MAGNET users. In rief, the servie is initilized y n initil pool of users tht is registered to soil mthing server whih ollets ll the ville profiles. At system initiliztion, the users re prtitioned into groups in wy tht the following two preonditions re held: () ll users within eh group get s mny ontt points s possile, whih trnsltes to the requirement for the retion of equl sized groups, nd () the degree of interests ommonlity within eh group is mximized (i.e. the users of eh distint group must hve s mny interests in ommon s possile). Then, t eh new user s rrivl, proposed lgorithm ples him t group in wy suh tht requirements () nd () re dhered to, during the dynmi proess of user joins. The servie introdued herein, nmed Iereker, hs een seleted for implementtion during pilot pplitions deployment, nd will e prt of lrger MAGNET Beyond tested. Iereker s pplition senrio inorportes mny spets relted to seure Personl Networking; this work fouses on the design nd evlution of mehnisms tht pertin to soil networking spets nd, nmely, it ddresses the issues of (i) the lustering lgorithm tht will e used for prtitioning users into soil groups (ii) modeling onepts of the user profile struture (iii) heuristi lgorithm tht will determine the dynmi system ehvior (plement of new users into ppropritely seleted groups so tht the system requirements re dhered to) nd (iv) study of the impt of profile size in reltion to the overll system performne. In terms of user profiling, we fous on modeling spets (profile rdinlity, proility distriution of userrepresenttive keywords), nd not on lexil issues (e.g. resolving the presene of more thn one synonyms, et.); suh issues hve een topis for other res of reserh (e.g. stemming lgorithms [,7]) whih re lso under onsidertion for future versions of our proposed servie. We model the user profile s n unordered set, omprising n distint keywords tht represent user preferenes. In the sope of studying the impt of profile rdinlity ( u, the set of keywords profile omprises) we vry u nd exmine the onsequenes on the system ehvior oth in stti (initil user prtitioning) nd dynmi (new users joining the servie) ehvior. For the lustering qulity ssessment, we rely on theoretil foundtions of spetrl lustering, whih is our lgorithmi frmework for the system s initil user prtitioning nd on the evlution of ertin metris ( nd stndrd devition of users prtitioning distriution) tht indite the performne of the exmined lustering method in regrd to our servie requirements. We introdue the onepts of semnti proximity (p s ), semnti distne (d s ) nd semnti entroid (µ s ) tht will e used s inputs to the lustering lgorithms whih will e evluted in the sope of stti groups ssessment. It is to e noted tht the term semnti proximity hs lso een used in other work [8], inditing the degree of ommon peer users interests in terms of files. We use the sme term herein, so s to indite the degree of oneptul loseness etween two users, on the ses of their interests, s these re expressed in their profiles. We redefine it in the sope of soil networking s p ij s = ij / u (i.e. the rtio of two profiles u i, u j ommon keywords ( ij ) to the rdinlity of the profile set ( u )). It is evident tht semnti proximity tkes vlues etween (no ommon keyword) nd 1 (identil profiles). We give the definition of its ounterprt metri, semnti distne (d ij s ) whih is given y d ij s = 1 p ij s. As we show in Setion 3.2, the ltter quntity stisfies ll the prerequisites of metri nd vries etween (identil profiles) nd 1 (mximum distne etween two profiles, when they don t shre ny ommon keywords). These two metris re used to trnsform the profile sets into the relevnt metri (distne) nd similrity spes, in whih two speifi reltionl lustering lgorithms operte: hierrhil nd spetrl lustering. We lso introdue the onept of semnti entroid (µ s ) whih will help us, on one hnd, to dpt k-mens lustering in the idiosynrsies of our semnti frmework nd, on the other hnd, to propose heuristi lgorithm for the dynmi updte of lusters during the rrivl of new users to the servie. Hving expressed the profiles reltions into well defined reltionl (distne/similrity) spes, the next step of our study is to ssess the performne (in terms of dherene to our servie requirements) of three very populr lustering lgorithms (i.e. k-mens, hierrhil lustering nd spetrl lustering). We use the metri of (P s ) whih expresses the semnti proximity (p s ) verged over the memers of eh luster nd over ll existing lusters of the network. In suh ontext, we sustntite, through experimentl results, the ppliility of spetrl lustering in terms of onformne with our requirements, nd we provide rief explntion of these results using theoretil foundtions of the speifi lgorithm. The lst ontriution of this work is the introdution of heuristi lgorithm tht performs very quik nd effiient ssignment of new users tht join the servie, without hving to go through re-initiliztion of the system, whih would e ineffiient, sine (i) it would require eigen-deomposition of lrge mtries (s will e riefly explined in Setion.3, spetrl lustering relies on suh n eigen-deomposition) (ii) it would proly rete lrge sle group reorgniztion sine the outome of spetrl lustering is not deterministi (hving users onstntly relloted into different groups would e uneptle). Our proposed lgorithm mnges to mintin dynmi updte proess tht dheres to our servie

3 15 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) requirements, nd its performne depends lrgely on the distriution of user s preferenes, on the initil user pool on whih the system ws initilized, nd on the rdinlity of the profile used to desrie users interests. This pper is strutured s follows: Setion 2 riefly desries the pplition senrio of Iereker nd ites severl relevnt works in regrd to user profile modeling nd soil groups identifition on the sis of lustering methods; Setion 3 provides the overll theoretil frmework tht will e used for the evlution of our soil servie, while Setion desries the lustering lgorithms tht will e evluted in our work. Setion 5 introdues our heuristi lgorithms, in regrd to the dynmi ehvior of the system; Setion desries the experimentl setup nd the relevnt results; Setion 7 onludes the pper y presenting nd overview of our work nd diretions towrds upoming extensions in the sope of MAGNET Beyond soil networking servies. 2. Relted work Applition senrio One of Iereker s min gols is the retion of soil groups etween MAGNET users. The pplition senrio (regrding the soilizing spet of the servie) inorportes soil-mthing server, where the users register t the eginning of the session, y sumitting to the server their personl informtion through their profiles; sed on these profiles (more detils on profile modeling re given in Setion 3.1) the server prtitions the users into groups, so s to () keep the size of the groups equl: ssuming n initil numer of N users whih we wnt to prtition into R groups, the purpose is to rete groups whose size is s lose to the vlue N/R s possile nd () rete groups with users shring s mny ommon interests s possile. Bsed on this initil users deomposition into soil groups, the system my susequently ommodte in n effetive wy new user rrivls (the term effetive implying oth dherene to our servie requirements nd low lgorithmi omplexity). The requirement for retion of eqully-sized groups is sed on severl riteri tht pertin to the speifi instntition of the soiliztion servie. In Iereker, we intend to inorporte soiliztion frmework tht will suit the idiosynrsies of the overll pplition. The servie will e deployed in n d-ho mnner, i.e. on speifi osions, suh s usiness meetings, onferenes, workshops, exhiitions; suh events re usully ttended y people tht need to intert with eh other, on the sis of ommon interests. Therefore, we keep in mind tht we re ddressing short-term user intertions, on limited physil spe. These spets rete some devitions from the soil networking onept found in yerspe, either in the se of p2p prdigm or/nd soil networking pplitions per. se (e.g. Feook). In suh view, it eomes evident tht effiient soiliztion inorportes oth the mximiztion of user interests nd the voidne of gret imlnes in group sizes distriution. In 5 hour event, we wnt to void distriution omprising severl groups of 5 1 people (or event the retion of single person groups, i.e. isolted users), nd few others mde up of severl hundreds of persons. Furthermore, sine Iereker is intended to e deployed in onferene-like kind of events, there is going to e need for preliminry resoures (i.e. filities) provisioning, for the ommodtion of the soil groups yielded y the pplition. Sine there will not e ny priori user interests ssessment nd in the view of provisioning for vile usiness senrio, it is more effiient nd fesile to provision equl resoures for eh group. Requirement is more or less self-evident, sine it is esily understood tht the users within group must shre s mny ommon interests s possile. In our ontext, nd s will e showsed in Setion, the notion of user interests mximiztion is deoupled from the groups size, y verging (normlizing) the interests ommonlity. Severl works hve een proposed in the ontext of user ommunities ssessment, oth in fixed nd moile networks. Seitz et l., [9] present mehnism tht omines moile lustering nd dt lustering so s to rete groups of moile users. Informtion out the users is sed in profiles, nd the group formtion relies on exhiited profile similrities, n pproh tht will lso e undertken in the work presented in this pper. However, there is n expliit need for n priori definition of group hrteristis nd rules tht moile node must omply with, so s to eome memer of group. In our pproh, the usge of spetrl lustering llows for n utomti reognition of group ptterns, without ny need for previous definition of group hrteristis. Furthermore, we void the need for neighor disovery nd spnning tree formtion nd mintenne, whih re essentil prts of the forementioned lgorithm. Phtk et l., (22) [2] ddress simultneously oth the issues of user nd URL lustering. Their pproh relies on the disovery of ptterns in the we ess hits of users so s to rete reommendtion mehnism in moile we lients. Vrious distne metris used in lustering re evluted, using frmework tht relies minly on metri of entropy tht depends only on the originl dt, i.e. the entries of the inidene mtrix tht the lustering is sed on. The speifi work presents severl ommonlities with our proposed frmework: definition of metris neessry to the lustering proess, evlution of the lustering proess, inorportion of reltion lustering. However we extend the uthors pproh y running lrger sle omprtive study out how populr lustering lgorithms in ommunities ssessment ehve, under vrious onditions. The topis of ommunity struture nd ommunity evolution hve een in the fous of severl other works. In [1], the uthors investigte the time dependene of overlpping ommunities on lrge sle, nd thus unover si reltionships hrterizing ommunity evolution. They use s se studies, networks tht pture the ollortion etween sientists nd the lls etween moile phone users. The work presented in [11] ddresses the issues of deteting nd hrterizing this ommunity strutures exhiited in vriety of soil nd iologil networks. The work dels with the onept of modulrity, whih is defined s the numer of edges (s up to multiplitive onstnt) flling within groups minus the expeted numer in n equivlent network with edges pled t rndom. Other pprohes tht trget the effiient disovery of ommunities within severl types of networks re presented in [12,13].

4 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) A very interesting study on the effet of user profile size in respet to the qulity of user ommunities orgniztion is performed y Lnieri et l. (23) [1]. A numer of virtul users is hrterized sed on set of pre-defined keywords, nd re susequently prtitioned in severl lusters through n hierrhil gglomertive lustering tehnique (HAC). The outome of eh lustering proess (in respet to profile size) is then ompred with referene lustering produed y humn evlution. Finlly, in nother work tht is similr with the ojetives of this pper, Sotiropoulos et l. (2) [15] ompre different lustering pprohes for reting groups etween users of ommon interests, with the purpose of reting reommendtion servie. The profile vetors re ssemled through the users intertion with video-store pplition. The tested uses profile pool of 15 users, nd ompres the performne of vrious lustering methods, ut without exmining the impt of profile size on the lustering qulity, whih is entrl spet of this work. 3. User profile-bsed semnti frmework As ws stted in the introdution, the proposed semnti frmework for the ssessment of user groups relies on three losely interonneted spets. The first issue tht needed to e ddressed ws the onstrution of profile model tht ws mthemtilly onsistent with the overll frmework. Mny uthors [1,1] hve ddressed this issue y representing the user profile s multi-dimensionl vetor, whose vriles orrespond to keywords tht represent user s preferenes. For resons tht will eome more pprent in the following susetions, we void suh definition nd we model the user profile s n unordered setof user-representtive keywords (ted simply s keywords in the rest of this pper). The next importnt step ws to perform n evlution study of the most ommon lustering lgorithms nd in this sope we hd to provide definitions regrding severl metris nd notions used y these lgorithms. For exmple, k-mens lustering requires the definition of entroids, whih re used t eh itertion of the method so s to evlute the ojetive funtion (sum of points entroids distnes within eh luster); spetrl lustering nd hierrhil lustering require the ssessment of similrities nd distnes respetively etween sets to e lustered. We provide definitions for ll these notions nd rete frmework on whih these three si lustering methods re pplied. Finlly, the lst piee of puzzle regrding our proposed frmework reltes to the definition of heuristi set of rules tht would define the dynmi system s ehvior in terms of new user s rrivls tht tke ple fter system s initiliztion. Sine new user s rrivls nnot e predited, the purpose is to introdue method tht provides ompromise etween effetiveness nd low lgorithmi omplexity, so to llow the system to hve low response time in regrd to new servie joins Profile modeling In order to enle personliztion of servies, it is impertive tht list of the ttriutes hrterizing the user is mde ville to the servie provider. Suh list is usully provided through stndrdized user profiles, whih ording to the definition of ETSI [17] is the totl set of user-relted informtion, preferenes, rules nd settings, whih ffets the wy in whih user experienes terminls, devies nd servies. Regrding profile extrtion omposition, there hve een mny relevnt implementtions proposed nd deployed. One ommon pproh is the impliit profile onstrution, through the monitoring of user tivities [1], e.g. visited wesites [2, 18], preferenes in onsumer goods [15] et. In suh se, the servie provides utomted mehnisms tht follow user s hits nd onstrut the relevnt profile through semnti interprettion of his intertion with the pplition. Another methodology relies on the expliit onstrution of the profile, using textul desriptions tht represent his preferenes [19]. In the ltter se, the min tsk regrding the retion of more strt representtion of user preferenes is delegted to methods tht extrt the tul semnti ontent of the text. Suh methods (e.g. vetor spe model [2,21]) query the doument nd retrieve the importnt, i.e. representtive words (keywords). In our study, we do not ddress issues relted to profile informtion extrtion. Insted, we ssume tht we hve list of words tht represent the user s preferenes, ignoring the wy this list hs een quired nd the initil profile struture (i.e. whether it is plin text or tree struture omposed of keywords). Our min onern fouses on two spets of profile representtion: () its rdinlity, (i.e. the numer of keywords tht will e finlly used to hrterize user) nd () the proility distriution of the keywords. Regrding the study of the profile rdinlity, we evlute its impt on the qulity of the soil grouping, ssuming tht eh profile u is represented s n unordered set omposed of n distint keywords w i, i = 1, 2,..., n. For the distriution of the keywords frequeny of ppernes, we dopt the ssumptions tht the frequeny of the keywords follows (i) Zipf s lw, whih intuitively trnsltes to the ft tht there re few keywords ppering very often, while the mjority of the ville keywords is rrely used nd (ii) Uniform distriution. The first ssumption lies on the sis of Zipf s lw extensive usge for user preferenes modeling in vrious relevnt studies [22 2]; therefore it is sfe to ssume tht profiles whih re generted from monitoring user tivities [25 27] lso exhiit Zipfin distriution. The Zipf distriution is given y P(k, ) = 1/[k ζ (α)] nd it expresses the proility of pperne of the kth symol (sorted 1 in order of desending frequeny of pperne) of the voulry from whih 1 The term sorted in this se pplies to the relevnt frequeny of keyword ppernes nd is not relted with their position in the user profile, whih is onsidered s n unordered set of words.

5 152 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) the profiles re ssemled; ζ (α) is the Riemnn s zet funtion nd α the skewness prmeter of the distriution. In the experiments we hve ssumed tht without loss of generlity tht the profiles re onstruted from pool of 5 keywords nd we hve lso used α = 1.5, sed on other relevnt studies tht model distriutions of user preferenes [27]. In order, however, to test the system into n extreme disperse of users preferenes distriution nd to indite tht the system ehvior is lrgely dependent on suh distriution, we perform our experiments ssuming lso tht the pperne of profile keywords re equiprole, whih is sustntited y the doption of Uniform distriution for keywords frequeny Soil networking metris Hving defined oneptul model for the user profile, the next issue we tkle reltes to the definition of n pproprite metri tht will llow us to define reltions etween different profiles. In terms of modeling the dissimilrity etween user profiles, we hoose not to dopt the Eulidin distne whih hd een extensively used for mesuring the dissimilrity etween textul douments, sine we do not model the profile s vetor. Hene, it is impertive to devise relevnt metri tht is pplile within our generi frmework in the gol of providing the pproprite sustrtum for lustering methods to identify our soil groups. In the sope, therefore, of oming up with n pproprite distne metri, we introdue the onept of semnti distne etween two user profiles u i nd u j, whih is defined s d s (u i, u j ) = 1 ij u = 1 pij s where α ij indites the numer of ommon elements etween profiles u i nd u j, u expresses the rdinlity of the profiles (we ssume tht t eh instne of our frmework ll profiles re of the sme rdinlity). This is onformnt with the mthemtil definition of metri spe sine the ltter is defined [28] s tuple (M, s) where M is set (in our se M is the profile whih is set of keywords) nd s is metri on M, i.e. funtion d s : M M R suh tht (i) d s (u i, u j ) : it is evident from the definition tht d ij s [, 1], with d ij s shre no ommon keyword (ii) d s (u i, u j ) = d s (u j, u i ): esily derived from the definition of semnti proximity (iii) d s (u i, u j ) d s (u i, u k ) + d s (u k, u j ): repling d s (u i, u j ) from Eq. (1) we get d s (u i, u j ) d s (u i, u k ) + d s (u k, u j ) 1 [ ij u 1 ik u u ( ik + kj ) ( ik + kj ) ij u. ] + [ = if u i = u j nd d ij s 1 kj u ] ij (1) = 1 if the two profiles The lst inequlity is lwys true: the left hnd side is sum of positive ( ik + kj ) nd negtive ( ij ) term, therefore it tkes its mximum vlue when ( ik + kj ) is mximized nd ij is minimized. The former se ours when profiles u i, u j nd u k hve ll of their keywords in ommon, in whih se however ik = kj = ij = u nd ( ik + kj ) ij = u whih is the mximum vlue of the left hnd side of the lst inequlity. (iv) d s (u i, u j ) = if nd only if u i = u j, whih goes y the profile definition we provided t the eginning of this setion s n unordered set of keywords; it should e noted tht hd we defined the profile s vetor in multidimensionl spe, the speifi metri property would not e vlid, sine vetor defines defult order in the sequene of vlues. In the sme ontext of estlishing metri tht indites semnti distne etween two profile sets, we introdue its ounterprt metri, i.e. semnti proximity etween two user profiles u i nd u j whih is defined s p ij = ij / u i.e. the rtio of the ommon profile keywords to the profile rdinlity. The definition of suh proximity mesure is neessry for the pplition of spetrl lustering tht uses, s input, similrity mtrix S = [p ij ], where p ij indites the similrity etween profiles u i nd u j. Therefore, in the sope of providing omprison etween luster methods tht is s fir s possile, we opt for the definition of similrity mesure tht is diretly derived from the previously defined semnti distne. Intuitively, this stems from the definition of semnti distne itself; sine the ltter vries etween nd 1 (1 eing the mximum possile distne etween two profiles) nd is given y (1), it is evident tht the term ij / u quntifies the normlized similrity etween profiles u i nd u j. Finlly the lst notion we re going to need definition for, reltes to the entroid of group, whih is n essentil spet for k-mens nd severl versions of hierrhil lustering. The ommon definition of luster entroid whih is used during the lustering proess of multidimensionl dt is ttriuted to point whose oordintes equl to the verge of the respetive group memers oordintes. Sine our profiles re omposed of keywords, the verging opertion nnot e pplied in our se; we therefore provide our frmework with n lterntive definition for luster entroid, or group 2 (2) 2 The terms luster nd group re used interhngely in this pper.

6 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) representtive s it will e lled in the rest of this pper, sed on the notion of semnti distne s ws introdued in the previous prgrphs: for eh group k = 1, 2,..., R, we define s group representtive µ k the group memer yielded y the following eqution: µ k = rg min i j k d ij s i.e, the group representtive is the point whose sum of semnti distnes from the rest of the group memers is minimum. As will e evident from the susequent hpters, suh definition llows us to (i) run n evlution study for k-mens lustering the ontext of our semnti frmework nd (ii) to exeute fst heuristi lgorithm tht ples new users into lredy ssessed groups without; the ltter lgorithm is introdued in following susetion.. Soil groups ssessment Vrious methods hve een used in the sope of identifying user ommunities in networking environments; one of the most ommon tehniques [29,3] is the pplition of lustering methods tht re ville in the mthemtil literture (i.e. k-mens, hierrhil lustering [31] et) whih is the pproh tht we lso follow in this work. We hve seleted, for our evlution study, three of the most ommonly used lustering lgorithms (i.e. k-mens, spetrl lustering nd hierrhil lustering). These lustering lgorithms hve een seleted for omprison on the sis of their widespred doption in soil networking frmeworks. Severl inditive exmples of their ppliility n e found in [32,12,33,3]. The following susetions provide rief introdution to these three lustering tehniques. For more detils, the reder is referred to the relevnt ittions..1. k-mens lustering K-mens [31] is simple unsupervised lustering lgorithm tht uses, s input, the numer of lusters nd entroid (entrl point) for eh of these lusters. The lgorithm proeeds y itertively ssigning eh dt point to entroid (nd therefore luster), then re-lulting new entroids, nd so on, until it onverges. The finl gol is the minimiztion of n ojetive funtion whih expresses the sum of squred distnes etween the dt points nd the entroids. The eqution to e minimized is given in (). J = R j=1 N x (j) i i=1 µ j where, R is the numer of lusters, N the numer of dt points, x (j) i the ith dt point ssigned to entroid µ j nd represents hosen distne mesure (in our se, semnti distne)..2. Hierrhil lustering Hierrhil lustering [31] is simple tehnique tht is divided into two mjor lgorithmi sudivisions: divisive nd gglomertive methods. The first lss of lgorithms proeeds y suessively deomposing the ensemle of dt points (whih re initilly onsidered s n integrted group) into smller nd smller lusters, until eh dt point omposes stnd-lone luster. The gglomertive methods, whih will e used in this work, elorte the lustering proess the other wy round, strting y integrting the dt points into suessively lrger lusters, until ll of them re merged into one luster. Agglomertive lustering tehniques re further distinguished ording to the metri tht is used to identify the distnes etween dt points nd/or lusters, so s to mke the relevnt deisions t eh step of the lgorithm regrding the neessry lusters /dt points merge. So, for exmple, when, in order to ssess two luster s distne, the minimum distne etween their memers is inorported, the respetive method is lled single linkge hierrhil lustering; when the verge distne etween the dt points of the two lusters is tken into ount, we get the verge linkge hierrhil lustering, nd so on. In the sope of this work, the distne metri inorported in our versions of hierrhil lustering is, one gin, the semnti distne. (3) ().3. Spetrl lustering Spetrl lustering [35] is more reently introdued unsupervised lerning tehnique tht uses the symmetri similrity mtrix of dt points nd the numer of lusters s input to the lgorithm. From the vetor representtion of eh dt point, similrity mtrix S = [s ij ] is onstruted, where s ij indites the similrity etween profiles u i nd u j, s this ws introdued in Setion 3.2. An intuitive wy of onsidering spetrl lustering is the grph theoreti view; in suh view, dt points to e lustered re represented s verties of grph nd their onnetions s weighted edges, where the weights orrespond to the degree of similrities etween the respetive verties. Spetrl lustering optimizes the vlue of the R-wy normlized ut; in rief,

7 15 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) K-Mens Hierrhil Spetrl 15 K-Mens Hierrhil Spetrl K-Mens Hierrhil Spetrl Fig. 1. Stndrd devition versus profile rdinlity of 1-luster distriutions resulting from pplition of the three lustering lgorithms for Zipfin users preferenes distriution nd 5 (), 1 () nd 5 () users. for eh luster, the normlized ut equls the rtio etween the sum of the edge weights tht espe the luster to the sum of the totl weights of the luster s verties (the weight of vertex is the sum of the weights of the edges inident to the speifi vertex). The R-wy normlized ut is given y the following eqution s R ij i A r,j A r C R = (5) r=1 s ij i A r,j V where A r represents the rth luster, V the totl of grph s verties nd s ij the similrity metri etween vertex i nd j. As will e shown in the experimentl results, the minimiztion of (5) y spetrl lustering, mkes the speifi lgorithm pplile in the ontext of the MAGNET Beyond soilwre, sine it llows for the retion of soil groups of similr size, whih is one of Iereker s min sopes. Sine the emergene of spetrl lustering, mny lgorithmi vritions hve een proposed [3 39]; the one dopted herein, s proposl for the ssessment of user ommunities, is the one presented in y Shortreed et l., 25 [38]; resons for the seletion of the speifi version of spetrl lustering minly relte to oth its proven effiieny nd its ese of deployment. In rief, the steps tht will e used to lssify our user profiles into groups re summrized elow: From S, we ompute mtrix P = Z 1 S where Z = dig(z i ), z i = N j=1 s ij, N eing the totl numer of users. Susequently, we ompute the first R eigenvetors v 1, v 2,..., v R of P, where R is the numer of lusters. Finlly, the rows of tle V = [v 1, v 2,..., v R ] re lustered s points in R-dimensionl spe, using fuzzy -mens lustering. ()

8 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) K-Mens Hierrhil 7 Spetrl 2 K-Mens Hierrhil Spetrl K-Mens Hierrhil Spetrl Fig. 2. Stndrd devition versus profile rdinlity of 1-luster distriutions resulting from pplition of the three lustering lgorithms for Uniform users preferenes distriution nd 5 (), 1 () nd 5 () users. 5. New user rrivls/user deprtures After initilizing the system through the pplition of lustering method, the next step is to provision for the ommodtion of new lients tht dynmilly join the system. One solution is to repetitively run the seleted lustering method eh time new user rrives. Sine our method of seletion (s will e justified in the relevnt setion) is spetrl lustering, suh n pproh requires the eigendeomposition of mtries of order N (the numer of servie lients) nd it hs the dvntge tht the system would lwys yield the optiml lustering. The term optiml, in this se, refers to the minimiztion of (5), whih s is proven in the experimentl results ommodtes lso for Iereker s servie requirements. However, in the ontext of our servie, there is signifint reson tht renders suh poliy ineffiient. It is known tht mtrix eigendeomposition is proess of high omputtionl omplexity, nmely of O(n 3 ). In our se, the fst plement of new user joining the system is of signifintly higher importne thn the preservtion of the optiml normlized ut vlue within our group formtion. This is muh more evident in rowded event (for whih Iereker is destined to e deployed) with lot of new servie users rriving nd reting highly demnding omputtionl proess of deomposing lrge mtries into their eigenvlues nd eigenvetors. Furthermore, nother reson for voiding reursive eigendeomposition pproh reltes to the ft tht the outome of the spetrl lustering lgorithm is not deterministi; in this ontext, iterting spetrl lustering eh time new user rrives would proly result in users groups rellotions, whih would mke our pproh ineffiient. Therefore, insted of dopting the forementioned solution, we propose heuristi pproh of redued omputtionl omplexity tht (s proven in the experimentl results) is le to effiiently trk the system s progression y providing fst nd effetive user ssignments into groups with the ost of slight devition from the optiml normlized ut vlue (whih, s ws stted, is of seondry importne in our se). Moreover, it ples eh new user in the most pproprite group without the need of group re-orgniztion, while it keeps oth the degree of interests ommonlity high within eh group nd the size of the groups lose to N/R.

9 15 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) K-Mens.3 Hierrhil Spetrl K-Mens Hierrhil Spetrl K-Mens Hierrhil Spetrl Fig. 3. Averge Semnti System Proximity versus profile rdinlity of 1-luster distriutions resulting from pplition of the three lustering lgorithms for Zipfin users preferenes distriution nd 5 (), 1() nd 5 () users User groups ssignment Assuming the system hs een initilized y deomposing the users into groups through pplition of spetrl lustering, the first step of the dynmi plement lgorithm relies on the identifition of the group representtives, whih re extrted fter the ssessment of the initil groups; we use the definition of group representtives tht ws provided in Setion 3.2. This proess retes set of representtive profiles µ i, i = 1, 2,..., R, for eh group A r, r = 1, 2,..., R. When new user joins the Iereker servie, two lists of groups re seleted: () the list of groups G 1, whose representtives hve the minimum semnti distne (see Eq. (1)) from the new user s profile u, i.e. G 1 = rg min i=1,2,...,r d µι u; in the se more thn one groups shre ommon minimum semnti distne, they re ll pled in group G 1. () the list of groups G 2 whose rdinlity is loser to the verge group rdinlity, i.e. G 2 = rg min i=1,2,...,r A Ai. The group to whih the new user will e ssigned is seleted rndomly from G 1 G 2 or from G 1 G 2, if the former set is empty; eh memer of the intersetion (or the union) hs equl proility of eing seleted. The rndomness is introdued sine we do not hve ny priori reson for ising our seletion over on group or the other. Tle 1 summrizes our proposed lgorithm Cluster reomposition/rrivls & deprtures In order to ddress the issue of the hnges inflited in the luster ompositions y users rrivls nd deprtures into/from the servie, we provision for luster merging/splitting lgorithm whose purpose is to sfegurd the semnti ohesion of the groups.

10 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) K-Mens Hierrhil Spetrl Averge Cl K-Mens Hierrhil Spetrl K-Mens Hierrhil Spetrl Averge Cl Fig.. versus profile rdinlity of 1-luster distriutions resulting from pplition of the three lustering lgorithms for Uniform users preferenes distriution nd 5 (), 1 () nd 5 () users users 1 users 5 users users.2 1 users 5 users Fig. 5. for Zipfin () nd Uniform () users distriutions versus profile rdinlity, fter the system s initiliztion through the pplition of spetrl lustering. Upon n rrivl nd/or deprture, the devition of the filesets within eh luster is lulted. If this devition is greter thn threshold, mening tht the ontent of the luster s peers strts to eome inoherent, i-prtitioning (splitting)

11 158 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) Fig.. of our proposed heuristi for system tht is initilized y prtitioning 5 () 1 () nd 5 () users into 1 lusters, ssuming Zipfin distriution of users interests. Tle 1 Our user-group ssignment heuristi. System Initiliztion - Initiliztion of the system nd ssessment of R soil groups using spetrl lustering - Identifition of group representtives µ i, i = 1, 2,..., R using Eq. (3) Dynmi User Plements When new user (with profile u) rrives: 1. rete set of groups G 1, : G 1 = rg min i=1,2,...,r d µιu, using Eq. (1) 2. rete set of groups G 2, : G 2 = rg min i=1,2,...,r A Ai where Ai is the group s i rdinlity 3.. if G 1 G 2 selet (rndomly) the group j to ssign the user from G 1 G else, selet j (rndomly) from G 1 G 2. relulte µ j proess is initited. During the split, the stti optiml (spetrl) lustering lgorithm is used. The proess yields two new lusters. To void ontinuous luster splitting, merge proess is lso tivted. More espeilly, the dynmi ptterns of users leving/joining Iereker mke prole tht progressively severl lusters strt to eome semntilly lose. In suh ontext, periodi omprison of the profiles of groups representtives is performed. If these profiles re found to hve (semnti) distne whih is elow speifi threshold, the two lusters merge. These two proesses (group merging/splitting) t omplementrily so tht () the initil semnti onsisteny of the groups is mintined nd () we void over-prtitioning users into multiple groups Algorithmi omplexity The lgorithm is of muh lower omputtionl omplexity thn the mtrix eigendeomposition proess inorported in spetrl lustering. More speifilly, our lgorithm hs omplexity of O(R), R eing the numer of soil groups of the

12 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) Fig. 7. of our proposed heuristi for system tht is initilized y prtitioning 5 () 1 () nd 5 () users into 1 lusters, ssuming Uniform distriution of users interests. system while the eigendeomposition is of O(n 3 ) order, n eing the numer of Iereker s users. Furthermore, it is proven to effiiently trk the system progression nd user joins, without the need to find eigenvetor of suessively lrger order mtries.. Experimentl results.1. Experimentl setup We onsider n infrstruture-sed d ho network, where lustering server quires eh user s profile, nd provides deomposition of the popultion into pproprite soil groups, so s to () rete s onsistent groups s possile (the users within groups should present the highest possile profile similrities) () rete equl-sized groups. As ws lso stted in Setion 1, the seond requirement stems from the ft tht in Iereker servie we trget n unstrutured pproh in terms of ommunities formtion (i.e. there will e no predefined topis of interest round whih the users should e lustered). Therefore we hve no priori reson for ising one group over the other, sine the min purpose of the pplition is the soiliztion of users, rther thn the identifition of speifi topis of interest, round whih the lusters (groups) should e formed. The user s deomposition into soil groups onsists of two phses: (i) n initil ssessment of soil groups with the servie users tht re present t the system s initiliztion (ii) n on-line lgorithm tht ples new users t the lusters s quikly nd effiiently s possile without disturing the existing groups (merging/splitting groups whenever neessry). We hve used syntheti profiles, with vrying rdinlity, whih vries in the experiments from 1 to 5 keywords; we hve ssumed voulry of 5 totlly ville words, whose frequeny distriution follows either Zipf s lw with skewness prmeter α = 1.5 or Uniform distriution (we run the experiments under oth ssumptions). The onepts of distne, similrity nd entroid tht re inorported in the relevnt lustering lgorithms hve een repled y the respetive definitions introdued in Setion 3.2.

13 151 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) Averge Cl Averge Cl Fig. 8. tht is yielded fter itertive spetrl lustering pplition t eh new user s rrivl, for system tht is initilized y prtitioning 5 () 1 () nd 5 () users into 1 lusters, ssuming Zipfin distriution of users interests. We should note here tht there will not e ny ditionry-sed restrition on the users, i.e. there will not e speifi pool of keywords from whih the servie lients should ompose their profile. The 5 words restrition is just n ssumption mde for the ske of experimenttion. Furthermore, s ws lso stted in the previous setion, the present study does not ddress issues suh s word dismigution, presene of one or more synonyms/hyponyms et. within the profiles. Suh spets hve een the topis of other extended studies [,7] whose results we intend to inorporte in the finl instntition of our frmework. However, severl studies [,1] indite tht spn of 5 words, with eh one of them stnding for distint onept (e.g. fter pproprite stemming tehniques hve een pplied), onstitute n dequte syntheti dtset. Assessing the performne of soil networking servie is lerly not trivil tsk. Humn intertions with the system nd the soiliztion spet of suh n pplition render its evlution inherently sujetive. In the sope, however, of providing metri tht is s ojetive s possile, we introdue the (P S ) metri, given y the following eqution: P S = 1 R R k=1 1 A k i,j A k i j u = 1 R R k=1 1 A k i,j A k p ij s (7) where R is the numer of lusters, ij the numer of ommon elements etween profiles i nd j, u the profile rdinlity nd A k the rdinlity of the kth group. P S provides n (ojetive) indition out the verge numer of ommon elements shred y eh servie user, verged over ll lusters. In order to use this mesure lso in the sope of evluting the impt of profile rdinlity vritions, we hoose to use normlized metri (the numer of ommon elements is divided y the profile rdinlity); otherwise n inrese of u would lso yield respetive inrese of P S. Suh metri is inditive of the overll system s performne nd is not sujet to user-dependent pereptions out the servie; we will use it to evlute

14 Averge Cl P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) Fig. 9. tht is yielded fter itertive spetrl lustering pplition t eh new user s rrivl, for system tht is initilized y prtitioning 5 () 1 () nd 5 () users into 1 lusters, ssuming Uniform distriution of users interests. (i) the performne of the lustering lgorithms we ompre (ii) the impt of profile rdinlity vritions nd (iii) our heuristi method of dynmi user plement into soil groups. The first setion of experiments is devoted to n evlution of the stti system ehvior (i.e. how the system responds in the initil users prtitioning under vrious profile rdinlities used nd under the ssumptions of oth Zipfin nd Uniform preferenes distriution). The seond setion ssesses the performne of the servie in dynmi ontext of new users joins/deprtures. The system is evluted under different initil user pools, nd the results lerly indite tht the rdinlity of the initilizing set is determining ftor for the system progression. The metris tht re used to evlute the servie performne re () the stndrd devition of the resulting distriution ( lower stndrd devition indites more equlsized groups) nd () the..2. Stti system view We ompre the performne of three widely used lustering lgorithms k-mens, hierrhil nd spetrl lustering in terms of their onformne with our servie requirements. The dopted k-mens implementtion is the one desried in Setion.1. The initil group representtives re R (the numer of lusters) rndomly seleted profiles round whih the other user profiles re grouped: eh profile is ssigned to the group representtive from whih it hs the minimum (semnti) distne; when this initil group ssessment is ompleted, the tul group representtives re estlished nd the distnes of eh profile from the respetive groups re relulted; the itertion proeeds until the lgorithm onverges. Regrding hierrhil lustering, we hve hosen to ompre the performne of the omplete linkge version, sine it gve the est results (in terms of onformne with our servie requirements) ompred to other implementtions of this lgorithm (i.e. verge linkge, single linkge, entroid nd medin methods). Finlly, the spetrl lustering method tht ws tested is the one presented in Setion.3. The similrity mtrix S tht ws used s input to the spetrl method enompssed entries p ij whih re given y (2).

15 1512 P.N. Krmolegkos et l. / Computers nd Mthemtis with Applitions 58 (29) % Devition etween Averge Semnti System Proximity vlues % Devition etween Averge Semnti System Proximity vlues % Devition etween Averge Semnti System Proximity vlues Fig. 1. Perentile devition etween of our proposed heuristi nd the tht would e yielded y repetitive prtitioning of using spetrl lustering on eh new user rrivl; the figures ssume Zipfin distriution of users preferenes nd initil pools of 5 (), 1 () nd 5 () users. A metri tht expresses the suitility of eh lgorithm in the ontext of our frmework is stndrd devition: the lower the stndrd devition t eh distriution, the loser the rdinlity of eh group to the verge luster rdinlity (whih is prerequisite for our frmework). Fig. 1 provides the resulting stndrd devition of the distriutions resulting from the pplition of k-mens, hierrhil nd spetrl lustering, respetively, versus profile rdinlity; the keywords frequeny distriution is ssumed Zipfin in this se. Three experiments were onduted, eh one prtitioning different numer of users (5, 1 nd 5) so s to evlute the impt of the initil pool of users in the stndrd devition with whih the system is initilized. Fig. 2 repets the sme experiment, ssuming Uniform user preferenes distriution this time. The results ppering on oth figures indite spetrl lustering s outperformne on the two other lustering methods, sine the respetive prtitioning is hrterized y signifintly lower stndrd devition for ll used profile rdinlities, irrespetive of the ssumed preferenes distriution nd initil users group size. Spetrl lustering, due to the optimiztion it offers in terms of normlized ut (see (5)), mkes the lgorithm pplile in the ontext of MAGNET Beyond soil servies. Figs. 1 nd 2 lso provide first feedk regrding the role of the profile rdinlity in respet to the system lustering qulity, whih seems to e losely relted to the underlying ssumption in respet to user interests distriution. All three digrms ppering in Fig. 1 indite tht the stndrd devition remins more or less unffeted y the inrese of the profile rdinlity. In ontrst to these inditions, Fig. 2 provides more ler inditions regrding the orreltion etween these two vlues, sine k-mens nd hierrhil lustering provide lower stndrd devition vlues s the profile inreses in terms of enompssed keywords. In ft, for numer of keywords equl to nd more, k-mens gives distriutions very lose (in terms of stndrd devition vlues) to the ones resulting in the pplition of spetrl lustering. However, spetrl lustering still gives the est performne, nd sueeds in reting more equl sized groups thn the other lgorithms, even in this se, nd for ll vlues of u. The next ouple of figures (Figs. 3 nd ) fous on the ssessment of, in respet to the profile rdinlity. Fig. 3 presents the results for Zipfin user preferenes distriution while Fig. repets the sme experiment under the ssumption tht these preferenes re uniformly distriuted (in terms of frequeny of ppernes).