A system based on a modified version of the FCM algorithm for profiling Web users from access log

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1 A syste based on a odfed verson of the FCM algorth for proflng Web users fro access log Paolo Corsn, Laura De Dosso, Beatrce Lazzern, Francesco Marcellon Dpartento d Ingegnera dell Inforazone va Dotsalv, -563 Psa ITALY e-al: {p.corsn, l.dedosso, b.lazzern, f.arcellon}@et.unp.t Abstract In ths paper, we present a syste based on an approprately targeted verson of the well-nown fuzzy C-eans (FCM) algorth to deterne a sall nuber of profles of typcal Web ste users fro the Web access log. These profles can be extreely useful, for nstance, to custoze the Web ste, or to send personalzed advertseents. After flterng the access log, for nstance, by elnatng occasonal users, the FCM algorth clusters the users of the Web ste nto groups characterzed by a set of coon nterests and represented by a prototype, whch defnes the profle of the group typcal eber. To show the effectveness of our syste, we descrbe how the profles deterned by the FCM algorth are a concse representaton of the assocaton rules dscovered applyng the well-nown A-pror algorth to the raw access log data. Keywords: Web nng, user profle, fuzzy c- eans, assocaton rules. Introducton The rapd developent of the World Wde Web as a edu for coerce and nforaton dssenaton has generated a growng nterest n tools able to cluster the users nto dfferent groups and generatng coon user profles fro the Web access log. The dentfcaton of these profles can be extreely useful, for nstance, to E-coerce copanes to send targeted advertseents, to gude the user navgaton and to defne ther aret strategy. The dentfcaton of Web user profles has been nvestgated n the recent lterature by usng dfferent technques [6][8]. In ths wor, we present a systeatc approach to deterne a sall nuber of profles of typcal Web ste users fro the Web access log. We assue that Web pages of the ste have been prearranged nto a nuber of dfferent classes, dependng on the specfc topc whch s prncpally dealt wth n the pages. Ths assupton s not a ltaton as ost Web coercal portals use such organzaton. Each user s, therefore, represented by the nuber of accesses to each class (or topc, n the followng). The set of users s frstly fltered to reove possble nose, such as occasonal users. Then, the fuzzy C- eans (FCM) algorth [] wth an approprate dstance functon s appled to the fltered data to fnd out a sall nuber of clusters. The optal nuber of these clusters s deterned by usng the Xe-Ben ndex [7]. The prototype of each cluster suarzes the navgaton preferences of the users strongly belongng to the cluster, thus dentfyng the profle of ts typcal ebers. The ebershp of each user to a cluster can be nterpreted as the affnty degree of the user wth the profle. We appled our syste to Web access log data collected by a coercal web portal durng an observaton perod of 3 days and contanng,49,46 users wth accesses to 38 dfferent topcs. After the flterng of the raw data reoved over 7% of the users, profles were deterned as optal suarzng representaton of the users nterests. To valdate the results of our syste, we appled the well-nown A-pror algorth proposed by Agrawal and Srant [] to deterne a set of assocaton rules between topcs. The support and

2 confdence of each rule were evaluated based on the nuber of users. We show that the profles deterned by the FCM algorth are a concse representaton of the assocaton rules wth the hghest supports and confdences. The Proflng Syste Let M be the nuber of topcs. Each user u can be represented as a pont u = u,..., u ] n the space M [,, M R, where u, s the nuber of accesses of user u to the topc durng the observaton te. Users are arrayed nto an NxM atrx, where rows and coluns represent, respectvely, users and topcs. Snce Web portals are typcally vsted by a large aount of users, the nuber of rows s of the order of llons. Further, as a user s generally nterested n a few topcs, the atrx s very sparse. These two characterstcs contrbute to ae the proflng process hard. In the experents shown n ths paper, the nuber N of users s,49,46, the nuber M of topcs s 38, the total nuber of accesses s 3,96,483. Further, the dstrbuton of the nuber of accesses aong the varous topcs shows a large varablty rangng fro,9 to,558,. Our syste conssts of two odules n cascade. The frst odule, denoted FILTER, explots soe consderatons on the Web user behavor to reduce nose and possbly decrease the nuber of users and the nuber of topcs. The second odule, denoted PROFILER, adopts the well-nown fuzzy C-eans algorth, odfed by usng an approprate dstance rather than the classcal Eucldean dstance, to cluster the fltered user atrx and dscover a set of profles of typcal users. In the followng, we exane each odule n detal. 3 The FILTER odule The FILTER odule reduces nosy nforaton fro the access log by applyng the followng four steps n sequence: 3. Reovng occasonal users Users who have vsted a very few pages of the portal cannot be consdered as sound saples of the body of users. Indeed, f the nuber s proportonally relevant wth respect to the total nuber of users, these occasonal users could sgnfcantly affect the proflng process, thus leadng the syste to dentfy profles whch do not correspond to typcal users. In our syste, a user s udged to be occasonal whether he/she has accessed a nuber of pages lower than a fxed threshold α. In the experents, we set α to 4. Usng ths threshold, we reoved approxately the 5% of the users, wth a 7% reducton of the total nuber of accesses. 3. For each user, reovng occasonal accesses to topcs n whch the user s not really nterested Durng the navgaton on the portal pages, users can access nadvertently topcs whch they are not really nterested n. Obvously, we expect that the nuber of accesses to these topcs s a odest percentage of the total nuber of accesses. To reove the occasonalty fro the typcal behavor of the user, we set to zero the nuber of accesses to a topc when t s less than a fxed percentage α of the total nuber of accesses by the user. The nuber of occasonal accesses whch are set to zero s not lost, but s collected nto a vrtual topc, denoted Other. Ths topc wll be used n step 4 of the FILTER. In the experents, settng α to 5%, only % of the accesses are consdered occasonal. 3.3 Reovng topcs of poor nterest Soe topcs could be accessed by a very sall nuber of users durng the observaton perod. Ths occurs, for nstance, for those topcs such as Holdays whch are nterestng for the users only n soe perods of the year. If the percentage of users whch have vsted pages of the topc s low, the topc wll characterze no profle. We recall that the profles wll be deterned so as to represent the behavor of typcal users. Thus, we reove the topcs whch have not been accessed by a nuber of users larger than a fxed threshold α 3. In the experents, we set α 3 to.5%. No topc was dscarded wth ths threshold. 3.4 Reovng focused users and undecded users Profles of typcal users are often used to decde aret strateges or place targeted advertseents. To ths a, profles characterzed by only one topc, that s, profles whch represent focused users, or profles characterzed by too any topcs, that s, profles whch represent undecded users, ay not be nterestng and, worst, ght hde ore coercally nterestng profles. To avod these undesrable results, we reove users wth accesses to only one topc and users wth the nuber of accesses to the vrtual topc Other larger than a fxed percentage α 5 of the total nuber of accesses of the

3 user. In the experents, α 5 was set to 7%. The reoval of focused and undecded users further reduces the nuber of users of approxately the 3% and % of the ntal nuber of users, respectvely. These reductons lead us to conclude that a large aount of the portal users focus ther accesses on only one topc. On the other hand, a few users are characterzed by an undecded behavor. Analyzng the results produced by the FILTER odule appled to the test Web access log, we can conclude that the flterng process strongly reduces the nuber of users (fro,49,46 to 335,53) and the total nuber of accesses (fro 3,96,483 to 5,83,874). Obvously, ths reducton speeds up the executon of the clusterng algorth used to deterne the profles. Fgures and show the dstrbuton of the users aong the 38 topcs before and after the flterng process. It can be noted that the relatve rato between bars of the hstogra n Fg. s approxately antaned n Fg.. Ths confrs that the paraeters used n the flterng process allow reducng the nuber of users wthout alterng ther dstrbuton aong the topcs Fgure : Dstrbuton of the users before the flterng process Fgure : Dstrbuton of the users after the flterng process 4 The PROFILER odule Let U = [ ] be the vector of the N users survved after the flterng process. Each user can be represented as a vector u = [,..., ] n the,, space R of the topcs whch have not been elnated n step 3 of the FILTER odule. The coordnates of each vector correspond to the nuber of accesses to each topc. We observe that, n the proflng perspectve, the behavor of a user s ore accurately descrbed by the relatve orentaton of the vector rather than ts agntude. Indeed, two users who access the sae topcs wth the sae proporton of the total nuber of accesses, though a dfferent nuber of tes, can be consdered as saples of a sae behavoral profle. Ths observaton leads us to state that the ore two users are slar, the less the apltude of the angle α fored by the correspondng vectors and, consequently, the hgher the value of the cosne of α. Snce the coordnates u, of each vector û vary on postve values, the cosne can assue only values n [,]. Thus, we can defne the dsslarty d u, u ) between two users û and û as: ( d u, u ) = cos( α) ( where d ( u, u ) s called the cosne dstance, and cos( α ) = u u, wth the Eucldean nor, s the cosne of the angle fored by û and û. To speed up the coputaton of the cosne, we prelnarly noralze the users. To cluster the users, we apply the verson of the FCM algorth proposed n [3]. Here, n place of the Eucldean dstance, the dsslarty easure between two users s coputed as the cosne dstance. Thus, the crteron functon to be nzed becoes: J N C ( P V ) = ( A (, d(, v ). = = where P= [ A,..., A C ] s a fuzzy partton of the set U of users, A ) s the ebershp value of user ( u û to cluster A, V= [ v,..., v C ] are the C prototypes of the clusters n P, and s the fuzzfcaton constant. The optal partton P s coputed by

4 usng an teratve ethod based on successve P, J,V. nzaton of the functons J ( ) and ( ) To nze J ( P, ), we apply the Lagrange ultpler ethod wth the constrant ( ) = and obtan the followng forula: A ( u ) C A = = () C ( ) d, v = ( ) d, v To nze J (,V ) u, we apply agan the Lagrange, f = f = ultpler ethod wth the constrant v and get the followng forula (see [3] for a deonstraton): v, f = N = M N t= = ( A ( ( A (,, t () To deterne the optal nuber of clusters whch partton the users, we executed the FCM wth ncreasng values of the nuber C (fro 6 to 3) of clusters and assessng the goodness of each resultng partton usng the Xe-Ben ndex [7]. We plotted the Xe-Ben ndex versus C and chose, as optal nuber of clusters, the value of C correspondng to the frst dstnctve local nu [5]. We found out C= as optal nuber of clusters. To speed up the executon of FCM and decrease the eory occupaton, we adopted the pleentaton suggested n [4]. In the experents, the executon te of FCM on a GHz Pentu IV wth GB RAM and FreeBSD 4.5 as operatng syste was of the order of a few nutes, whch s acceptable for ths type of applcaton. Due to the sparseness of the user atrx, we executed the FCM algorth wth the fuzzfcaton coeffcent set to.5. Usng an accuracy error equal to., we observed that the FCM converges after 5 5 teratons. Fg. 3 shows one of the profles dentfed by the FCM algorth. Here, only the topcs wth a consderable nuber of accesses are reported. The users who are represented by ths profle are characterzed by a strong nterest n Football, a good nterest n Sport, a odest nterest n Cars and Motorcycles, Cnea and Musc, and a scarce nterest n the other topcs. The profle sees to dentfy users who navgate the Web portal n search of news to fll ther spare te. We recall that a profle s a vrtual user and s represented as a unt vector n the space R of the topcs. 5 Valdaton To valdate the results acheved by our syste, we appled the A-Pror algorth to the raw access log data to dscover assocaton rules between topcs []. We a to verfy f the relatons between topcs hghlghted by the assocaton rules wth hgh support and confdence are contaned n the profles deterned by our syste. In fact, these relatons suarze the behavor of typcal users. An assocaton rule s defned as an plcaton n the for Tl Tr, where T l and T r are sets of topcs. The plcaton expresses the fact that users, who have accessed the set of topcs T l, have also accessed the set T r. The relevance and relablty of an assocaton rule s deterned by ts support and ts confdence. The support s defned as the rato (expressed n percentage) between the users who have accessed all the topcs n the set Tl Tr and the total nuber of users; the confdence concdes wth the rato (expressed n percentage) between the users who have accessed all the topcs n the set Tl T r and the users who have accessed all the topcs n the set T l Car-Mcycle Cnea Musc Fgure 3: One of the profles Sport Football We executed the A-Pror algorth n such a way as to dscover assocaton rules wth support and confdence larger than.% and 5%, respectvely. To valdate the results obtaned by our syste, we analyzed n detal the assocaton rules as follows. For each profle deterned by the syste, we pced the topc (prevalent topc) wth the hghest value. For nstance, n the profle n Fg. 3, we

5 pced topc Football. Then, we selected all assocaton rules (relevant assocaton rules) wth the prevalent topc n the set T l. We observed that all the sgnfcant topcs of the profle were n the set T r of the relevant assocaton rules wth the hghest supports and confdences. As an exaple, Table shows the set of the relevant assocaton rules selected for topc Football wth the hghest supports and confdences. We can observe that the sets T r of the rules contan all the sgnfcant topcs of the profle n Fg. 3. Ths confrs that the relatons hghlghted n the profle are really the relatons exstng between the topcs n the data set. Table : Relevant assocaton rules for Football. Assocaton Rules Support Confdence Football => Sport 4.% 44.6% Football => Cnea.4% 5.% Football => Musc.39% 4.76% Football => Car-Motorcycle.35% 4.37% 6 Conclusons In ths paper, we have shown a syste to deterne a sall nuber of profles of typcal Web ste users fro the Web access log. The an features of ths syste are an effcent flterng odule, whch reduces drastcally the aount of raw access log data, and the FCM clusterng algorth wth an approprate defnton of dstance. To explan how the flterng process does not elnate relevant nforaton and the FCM wors n an effectve way, we have appled the A-Pror algorth to the raw access log data to dscover assocaton rules between topcs. We have shown how the profles deterned by the syste are a concse representaton of the assocaton rules wth hgh support and confdence. References [] R. Agrawal, R. Srant (994). Fast Algorths for Mnng Assocaton Rules. In Proceedngs of the th VLDB Conference, pp , Santago, Chle. [] J.C. Bezde (98). Pattern Recognton wth Fuzzy Obectve Functon Algorths. Plenu, New Yor. [3] F. Klawonn, A. Keller (999), Fuzzy Clusterng Based on Modfed Dstance Measures. In: D.J. Hand, J.N. Ko, M.R. Berthold (eds.): Advances n Intellgent Data Analyss, Sprnger, Berln, pp [4] J.F. Kolen, T. Hutcheson (). Reducng the te coplexty of the fuzzy C-eans algorth. IEEE Transactons on Fuzzy Systes vol., no., pp [5] M. Setnes, H. Roubos (). GA-fuzzy odelng and classfcaton: Coplexty and perforance. IEEE Transactons on Fuzzy Systes, vol. 8, no. 5, pp [6] K.A. Sth, A. Ng (3). Web page clusterng usng a self-organzng ap of user navgaton patterns. Decson Support Systes, vol. 35, pp [7] X.L. Xe, G. Ben (99). A valdty easure for fuzzy clusterng. IEEE Transactons on Pattern Analyss and Machne Intellgence, vol. 3, no. 8, pp [8] Y. Xe, V.V. Proha (). Web User Clusterng fro Aceess-Log Usng Belef Functon. In Proceedngs of K-Cap, pp. -8, October - 3, Vctora, Canada.