A Subtractive Relational Fuzzy C-Medoids Clustering Approach To Cluster Web User Sessions from Web Server Logs

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1 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp A Subtrative Relational Fuzzy C-Medoids Clustering Approah To Cluster Web User Sessions from Web Server Logs Dilip Singh Sisodia* Department of Computer Siene & Engineering, National Institute of Tehnology Raipur, India *Corresponding Author Shrish Verma Department of Eletronis & Teleommuniations, National Institute of Tehnology Raipur, India Om Prakash Vyas Department of Computer Siene & Engineering, International Institute of Information Tehnology Naya Raipur, India Abstrat In this paper, a subtrative relational fuzzy -medoids lustering approah is disussed to identify web user session lusters from weblogs, based on their browsing behavior. In this approah, the internal arrangement of data along with the density of pairwise dissimilarity values is favored over arbitrary starting estimations of medoids as done in the onventional relational fuzzy -medoids algorithm. It is assumed that straightforward binary session dissimilarity measure proposed and utilized as a part of prior detailed work is not espeially logial, and instintive to speak to session dissimilarities instigated from web lient's habits, interest, and expetations. The idea of augmented sessions is utilized to infer page relevane based web lient s session dissimilarity matrix. The disussed approah is applied on an augmented session dissimilarity matrix obtained from an openly aessible NASA web server log data. The produed lusters are assessed by utilizing diverse fuzzy validity measures, and results are ontrasted with onventional fuzzy -medoids lustering. Experimental results demonstrated that quality of fuzzy lusters produed by utilizing proposed subtrative relational fuzzy -medoids lustering is superior as ompared with the onventional relational fuzzy -medoids approah. Keywords: dissimilarity, fuzzy lustering, fuzzy validity measures, relational -medoids lustering, subtrative lustering, similarity, user sessions, web server logs. INTRODUCTION Web-Based appliations are growing with phenomenal rate, and this growth is instigating the zeal of analyzing the web usage data to gain extra knowledge about the users navigation patterns. The knowledge onerning the web users aesses behavior may be utilized to serve the needs of the user in a better way. The Web lients aess pattern is reorded in the form of weblogs and logs are divided into user sessions for analysis. Any knowledge extration tehnique used for knowing the user's aess behavior is applied on Web lient sessions. Web lient sessions may ontain inorret, lashing and obsure data and medoid based relational lustering approahes demonstrate extremely helpful in the grouping of web session [1]. Beause of high dimensionality and santiness of URLs in weblogs, web sessions are hard to speak by omponent vetors. The relational distane measure is favored over omponent vetor to store the pairwise onnetion between web sessions []. Though, the strategies based on relational grouping are extremely deliate to the underlying deision of group determination. In this way, the underlying estimation of group medoids might be a bottlenek to the grouping performane of these approahes [3]. In this paper, a subtrative grouping approah is used to estimate the initial value of luster medoids. The disussed approah is applied on an augmented session dissimilarity matrix obtained from an openly aessible NASA web server log data [4]. The remaining part of this paper is arranged under following setions: The related work on web user lustering is disussed in setion. In Setion 3, bakground details of augmented session similarity are reapitulated. Setion 4 presents the formulation of the idea of a proposed subtrative lustering based fuzzy relational -medoids(sc-rfcmdd) approah. In setion 5, fuzzy luster validity measures are disussed in brief. In setion 6, experiments are performed on openly available web log data, and results are disussed. Finally, this study is onluded with future work in setion

2 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp RELATED WORK In this setion, some signifiant ontributions on web user sessions lustering reviewed in brief. In [5] K-means algorithm is used to luster the user sessions. A lustering of uneven length user session based on hybrid sequene alignment measure is disussed in [6]. In [7] utilizing BIRCH algorithm author proposed a generalization based grouping strategy to develop an URL order and session lusters. In [3] a programmed revelation of lient session lusters in a fuzzy and unverifiable ondition of weblogs is done using ompetitive agglomeration for the relational data algorithm and further extended in [8]. In [9] a ube model is used for web user sessions representation and K-modes algorithm for lustering. For finding basi lusters in the weblogs and determining lassifiations demonstrating the inlinations of omparable lients authors proposed a fuzzy similarity measure the same in a relational fuzzy grouping algorithm [10]. For lustering of values in a dissimilarity matrix D, a relational fuzzy -means (RFCM) lustering is disussed in [11]. In [1] a new fuzzy - medoid (FCMdd) algorithm proposed whih starts with arbitrary estimations of medoids and iteratively settled on some final values. The FCMdd and RFCM [11] algorithms are applied on weblogs utilizing straightforward binary dissimilarity measure as suggested in [3],[8]. The onept of augmented session and intuitive dissimilarity measure is introdued in [1], and performane of proposed measures are evaluated using RFCM [13] and FCMdd [14]. In this paper, a subtrative lustering based fuzzy relational - medoids (SC-RFCMdd) approah is disussed. In the disussed approah internal arrangement of data along with the density of pairwise dissimilarity values are favored over arbitrary starting estimations of medoids. It is assumed that straightforward binary session dissimilarity measure proposed and utilized as a part of prior detailed work is not espeially logial, and instintive to speak to session dissimilarities instigated from web lient's habits, interest, and expetations[3]. BACKGROUND DETAILS OF AUGMENTED SESSION SIMILARITY For a better understanding of proposed approah, the onept of the augmented session similarity [1][13] is reapitulated in following subsetions. Web server log pre-proessing The weblogs keep a reord of metadata of all douments aessed by lients unequivoally or ertainly. Metadata is reorded in some fields and vary from one log format to other. Essentially, all format reorded information about host address and name, username, date and time, the method used for the request; protool used for aess, the status of servie, data size and user agents, et.[15]. However, all reorded entries are not useful always and inrease the size of weblogs. Therefore, leaning is performed on raw logs suh as removal of entries made by embedded objets, web robots [16], failed requests, and requests made other than GET method, et. After leaning weblogs are divided into independent user sessions using session identifiation tehniques disussed in [17],[18]. User sessions representation in vetor spae model It is assumed that; there are m users sessions are identified from the web server log S i = { S 1, S,. S m }. These m users sessions aessing n number of different pages URL s P i = { P 1, P,. P n } on a given website in some time interval. Then eah user session S i are denoted by following equation S i = {S i 1, S i, S i n }, i = 1,,, m. Where, every S k i orrespond to a harmoni mean of the frequeny the page P k within the session S i, and the time spent on the page (in seonds) P k in session S i, and represented by following matries Eq.(1) & (). Frequeny of the page S i k { Duration of the page(in seonds) Page size(in bytes) 1 n S 1 S 1 S 1 1 n R[m, n] = ( S S S ) () 1 n S m S m S m Page relevane based augmented session similarity Some impliit measures [19],[0] are used to determined the relevane of any page for partiular user [1]. The following measures are omputed to find the relevane of a web page in any user session to measure the web user onern for a web page [1]. Duration of Page(DoP) Duration of page or Page stay time defined as the time spent on a page by a web user, and it is the differene between the exat time of the request of page Pi and the time of the request for the next web page in the session from the aess log file. Eq. (3) is used to measure the duration of a web page (P i ) in user session (S k ). (DoP) Pi = Where0 (DoP) Pi 1 Time Spent on(p i ) Size of (P i ) Time Spent on(p j) Max( j Sk ) Size of (P j ) (1) (3) 1143

3 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp Frequeny of Page(FoP) Frequeny is the number of times the web page P i has been visited in the session. It seems natural to assume that web pages with a higher frequeny are of more onern to users. Eq. (4) is used to measure the frequeny of a web page (P i ) in user session (S k ). (FoP) Pi = Where 0 (FoP) Pi 1 # of visits to(p i ) Max( j Sk # of visits to(p j )) The relevane of page(rop) The relevane of page in any session is measured by giving equal importane to the duration of page and frequeny of Page. We use Eq. (5) to measure the relevane of web page (P i ) in user session (S k ). (RoP) Pi = (DoP) P i (FoP) Pi (DoP) Pi +(FoP) Pi (5) Where 0 (RoP) Pi 1 Augmented web user sessions Now, by applying equations (3) to (5) the page relevane matrix (RM m n ) is omputed. This relevane matrix will define the relevane of eah page in every session. If the page has high relevane means the user has more onern in this page. This relevane matrix is given by Eq. (6). By inorporating page relevane in web user session aess behaviour matrix, simple web user sessions onverted to augmented web user sessions. (RoP) 11 (RoP) 1 (RoP) 1n (RoP) RM m n = ( 1 (RoP) (RoP) 1 ) (6) (RoP) m1 (RoP) m (RoP) mn Now, the web sessions are onverted into augmented web user sessions AS i = {AS 1, AS, AS m } for i = 1,, m. Where, every augmented web user session is represented by AS a = {(P1, (RoP) P1, (P, (RoP) P )... (Pn, (RoP) Pn )}. Where, Pi and (RoP) Pi are the visiting page, and its relevane respetively. Page relevane based augmented session similarity Here relevane of pages aessed in user sessions is inorporated in simple osine similarity measure Eq. (5). This augmented session similarity measure may represent more realisti and represents session similarities based on the web user s habits, interest, and expetations as ompared to simple binary osine measure [3]. (4) ASS (ASa,AS b ) = m i=1 AS a (RoP) i AS b (RoP) j m i=1 AS a (RoP) i m i=1 ASb (RoP) j This augmented session similarity measure is more realisti and represents session similarities based on the web user s habits, interest, and expetations as ompared to simple binary osine measure. An URL Syntati Similarity between i th and j th Page URL In [3] authors also defined an alternative URL based syntati similarity measure to ompute the syntati similarity between any pair of URLs given by Eq. (8). USS (USa p i,usb p j) = LoP(P (a,i) ) LoP(P (b,j) ) Min (1, ) (8) Max(1,Max(LoP(P (a,i) ),LoP(P (b,j) )) 1) Where LoP(P (a,i) ) is length of URL (or number of edges) of path traversed from root node to respetive node of P i in user session US a. By applying this syntati similarity of URL s, the similarity between two augmented web user sessions (AS a p i, AS b p j ) is omputed by Eq. (9). AUSS (ASa p i,asb p j) = n n i=1 j=1 AS a (RoP) i AS b (RoP) j USS p (USa i,usb p j) n i=1 AS a (RoP) i n j=1 AS b (RoP) j Intuitive augmented session similarity Intuitive augmented session similarity utilizes the properties of two measures and onsiders the maximum optimisti aggregation of these measures to give remarkable similarities between web user sessions. Intuitive augmented session similarity omputed using Eq. (1). IASS (ASa,AS b ) = Max {ASS (ASa,AS b ), AUSS (ASa p i,asb p j) } (7) (9) (10) As a requirement of relational lustering, this augmented session similarity is onverted to the dissimilarity/distane measure. This distane measure satisfies the neessary onditions of a metri []. The augmented session dissimilarity is omputed using Eq. (6). D (ASa,AS b ) = (1 ASS (ASa,AS b )) (11) Where 0 < D (ASa, AS b ) 1, for AS a, AS b =1,...m. 1144

4 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp DESCRIPTION OF SUBTRACTIVE RELATIONAL FUZZY C-MEDOIDS(SC-RFCMDD) CLUSTERING In this setion, we are presenting the formulation of the idea of a proposed subtrative lustering based fuzzy relational - medoids(sc-rfcmdd) algorithm in details. The potential density based seletion of luster medoid[3]. To loate a delegate session as luster medoids, we look for the enters of dense areas in the given pairwise relational matrix. A subtrative lustering (SC) method [4], is applied for initial assessment of a number of luster medoids, The SC is a modified version of mountain lustering [5]. The subtrative grouping strategy aepts that every data point is a potential luster enter and, without earlier learning of the default number of enters, it asertains the probability of a data point being haraterized as a luster enter as indiated by the density of the enompassing data points [6]. We ompute the value of potential density funtion value at every augmented session by applying Eq. (1). n P 1 (AS i ) = exp ( d ij (AS i,as j ) j=1, i = 1,,, m. (1) r a ) If d ij is small then AS j and AS i would be tightly assoiated and had signifiant impat on the PDF value P 1 (AS i ); or else AS j and AS i remain loosely assoiated and had less impat on P 1 (AS i ). The parameter r a is a radius and hararized the region of intrest for the seleted augmented sessionas i. Sessions outside this span have little impat on the hose session's PDF value. In the wake of registering the PDF value at eah session; we piked the session with largest PDF value as the main illustrative luster enter v 1 by applying Eq. (10). On the off hane that there are numerous sessions with same largest PDF value then we an pik intuitively any of them. P 1 (AS k1 ) = max i=1 {P 1(AS i )} ; v 1 P 1 (AS k1 ) (13) To loate the seond illustrative luster enter, we use Eq. (8) ompute the disounted PDF value over the neighborhood defined by r b. If d ij is smaller between AS i and v 1 then effetive potential of eah sessions around v 1 will be redued due to this subtration. P (AS i ) = P 1 (AS i ) P 1 (v 1 )exp ( d ij (AS i,v 1 ) r ), i = b 1,,, m. (14) Subsequently, for all sessions, PDF values are disounted over effetual region of ontrol of r b, and highest disounted PDF value are onsidered as the next envoy luster entre v by using Eq.( 1) P (AS k ) = max i=1 {P (AS i )} ; v P (S k ) (15) In the same way, any t th illustrative luster enter is hosen, and the potential density funtion value of every session on the effetual region of ontrol throughout t th iteration is alulated by applying Eq. (13) P j (AS i ) = P j 1 (AS i ) P j 1 (v j 1 )exp ( d ij (AS i,v j 1 ) ), i =,, m. (16) r A similar method will proeed until the number of maximum illustrative luster enter v j is hoosen by applying Eq. (14) P j (AS kj ) = max i= {P j(as i )}, i =,, m. v j P j (AS kj ) (17) Fuzzy C-medoids lustering Let s assume n number of user sessions S i = { S 1, S,. S n } for i = 1,, n. Where, eah session is haraterized by a vetor of m-dimensions S i = {S 1 i, S i, S m i }, i = 1,,, n. Suppose d(s i, S j ) stand for the dissimilarity among session S i and S j and V {v 1, v, v }, v i D denotes a subset of dissimilarity matrix D with ardinality. Where D represents the set of all -subsets V of D. The fuzzy -medoids lustering is used for seleting representative medoids from the data optimizing objetive fution and membership funtions so that the total disimiliarity within eah luster is minimized using Eq. (18) and Eq. (19) F FCMdd = n ( μ f j=1 i=1 ij d(s i, v j )) (18) μ ij = (d(s i,v j )) 1 (f 1) (d(s i,v j )) 1 (f 1) j=1 (19) Where, d(s i, v j ) is the dissimilarity between session S i and medoid of luster S j and f [1, ] is fuzzifiation oeffiient [13], [14]. FUZZY CLUSTER VALIDITY MEASURES To deide the appropriate number of lusters in given dissimilarity matrix, different fuzzy luster validity measures have been proposed [7],[3].Some fuzzy validity measures used only fuzzy membership values while others onsidered both membership values as well as input relational data. The later validity measures inluding Xie and Beni (XB) index, Fukuyama and Sugeno (FS) index and separation index are 1145

5 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp onsidered more robust [8] and explained in following subsetions: Xie and Beni index (XB) The Xie and Beni (XB) index [9] defined as Eq. (0), where, the numerator indiates the ompatness of the fuzzy partition while the denominator indiates the strength of the separation between lusters. j=1 m f i=1 d(si,v j )) XB = ( μ ij 1 (0) m δ min Where, δ min is the squar of minimum Eulidean distane between the luster entres given by Eq. (1). 1 δ min = min d(v i, v j ) (1) l.k=1.. l k The Fukuyama and Sugeno (FS) index[30] FS index ombines the properties of ompatness and separation measurements. The FS index is defined by Eq. (): m FS = μ f m f i=1 j=1 ij d(s i, v j ) i=1 j=1 μ ij d(v j, v ) () Where the first term represents the geometrial ompatness of the lusters, the seond term indiates the separation between the lusters and v represents the mean of the luster entroids Eq. (3). v j v = j=1 (3) Separation Index (SI) The separation index used a minimum distane separation for partition validity [31],[3] and defined by Eq. (4). j=1 SI = ( μ ij m f i=1 d(si,v j )/ m i=1 μ ij ) m δ min (4) Where, δ min is the squar of minimum Eulidean distane between the luster entres and mean of the luster entroids given by Eq. (5) δ min = min d(v i, v ) (5) l.k=1.. l k EXPERIMENTAL RESULTS AND DISCUSSIONS In this setion, the lustering apability of the proposed approah is presented by applying it on publily aessible NASA web server log data[4]. This data set (NASA_aess_log_Aug95) ontains one month s worth of all HTTP requests from the NASA Kennedy Spae Centre s web server in Florida. The log was olleted from 00:00:00 August 1, 1995, through 3:59:59 August 31, The unompressed ontent of the dataset is MB and ontains 1,569,898 reords with timestamps having a 1-seond resolution. The disussed approah is sripted in MATLAB [33].The MATLAB programs are run on an HPZ40 workstation (with an Intel(R) Xeon(R) CPU E GHz, and 4 GB RAM), running under the MS Windows-7 operating system(64-bit). The different number of web user sessions is randomly seleted from a pre-proessed NASA aess log data set for experimentation. The log entries due to embedded web objets files(image, ions, sound files, et.) are removed from soure log files for leaning. The leaned log file is further proessed for session identifiation using thirty minutes threshold time. In this paper, merely 000 sessions are used from preproessed log file just to optimized the proessing overhead of the system. It is supposed that very small session do not ontribute any signifiant information for user session lustering. Therefore, After removing of the default root / and mini sessions of size, one from the total onsidered sessions valid sessions are redued to 1341, whih aess 589 unique URLS olletively. First, we ompute the different matries suh as frequeny of page (FoP), duration of the page (DoP), the relevane of the page (RoP), and URL s syntati similarity(uss) from the given web user sessions. Seond, we alulated different similarity/dissimilarity by applying the notion of augmented sessions(ass, AUSS, and IASS).The summary of omputed results is presented in Table 1. We used a visual assessment tendeny tehnique [34], to visualize the number of underlying lusters in dissimilarity matrix. In visual assessment tendeny method, the reordered dissimilarities between pairs of user sessions are represented using digital intensity images. The blak spots on the main diagonal of generated images represent the number of lusters, and the spot size approximates the size of the luster. In this way, the approximate number of lusters exist in relational data are known before applying lustering algorithm [35].The visual assessment tendeny images of augmented sessions dissimilarity measures(ass, AUSS, and IASS) are shown in Fig

6 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp ASS AUSS IASS Figure 1: The VAT images for augmented sessions (ASS, AUSS and IASS) dissimilarity matries of Parameters Table 1: Summary of Results Values # of preliminary sessions 000 # of legitimate sessions 1341 Matrix size (FoP/DoP/RoP) # of unique page URLs 589 Size of USS Size of IASS/ (D m m ) matrix To evaluate the performane of subtrative relational fuzzy - medoids lustering algorithm, an intuitive augmented session dissimilarity matrix of size ( ) is passed as input with default parameters. We perform multiple runs of RFCMdd and SC-RFCMdd algorithms with a hanging number of lusters (from = to 14), and fuzzifier oeffiient (f = 1.5 to.5). Following default parameters are set during exeution of RFCMdd, and SC-RFCMdd maximum number of iterations (t max = 100), Neighbourhood radius (r a =0.5 and r b =1.5r a ).The value of fuzzy luster validity measures (XB, FS and SI) are omputed and results are shown in Table. Table : RFCMdd Vs. SC-RFCMdd value of fuzzy luster validity measures (XB, FS, and SI) XB-Index FS-Index S-Index Clusters RFCMdd (f =1.7) SC-RFCMdd (f =1.5) RFCMdd (f =1.9) SC-RFCMdd (f =1.9) RFCMdd (f =1.7) SC-RFCMdd (f =1.7)

7 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp Figs., 3 and 4 show the omparative values of fuzzy validity measures (XB, FS, and SI) for web user session lusters identified by RFCMdd and SC-RFCMdd with augmented session dissimilarity measures. It is evident from Figs., 3 and 4 that quality of fuzzy lusters disovered using proposed SC-RFCMdd is better than that of those obtained with RFCMdd. Figure XB Index vs. No. of Clusters Figure 3: FS Index vs. No. of Clusters 1148

8 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp Figure 4: SI Index vs. No. of Clusters CONCLUSION AND FUTURE WORK A subtrative relational fuzzy -medoids lustering/grouping approah is disussed to find the initial luster medoids and onsequently web user sessions lusters/groups. The onnetions between web lient sessions are gotten from aess importane of pages in any sessions. The relevane of a page is a measure of lient's enthusiasm for any page URL and figured by applying harmoni mean of frequeny and duration of pages in any session. The straightforward binary web lient's sessions are hanged into augmented sessions by onsolidating relevane of page in getting to sessions. The augmented session omparability matrix is figured from page relevane matrix utilizing osine loseness measure and hanged over to dissimilarity matrix. A visual assessment tendeny tehnique is utilized to imagine the oneivable lusters in lient session dissimilarity matrix before applying any grouping algorithm. The piture produed visual assessment tehnique demonstrates the quantity of oneivable groups varying from eight to twelve. The trial omes about exhibited that nature of fuzzy lusters found by utilizing proposed subtrative relational fuzzy -medoids grouping approah is superior to that of those aquired with relational fuzzy -medoids lustering. In future, this approah an be more refined and presented in the algorithmi form. The effetiveness of this approah may be tested with some more data sets ranging from weblogs to other relational data sets. REFERENCES [1] R. Krishnapuram, A. Joshi, O. Nasraoui, and L. Yi, Low-omplexity fuzzy relational lustering algorithms for Web Mining, IEEE Transations on Fuzzy Systems, vol. 9, no. 4, pp , 001. [] R. Krishnapuram, A. Joshi, and Liyu Yi, A fuzzy relative of the k-medoids algorithm with appliation to web doument and snippet lustering, in IEEE International Fuzzy Systems. Conferene Proeedings(FUZZ-IEEE 99), 1999, vol. 3, pp [3] O. Nasraoui, F. Hihem, R. Krishnapuram, and A. Joshi, Extrating web user profiles using relational ompetitive fuzzy lustering, International Journal on Artifiial Intelligene Tools, vol. 9, no. 4, pp , 000. [4] NASA_SeverLog, NASA Kennedy Spae enter s www server log data, Available at, [Online]. Available: HTTP.html. [5] T. W. Yan, M. Jaobsen, H. Garia-Molina, and U. Dayal, From user aess patterns to dynami hypertext linking, Computer Networks and ISDN Systems, vol. 8, no. 7, pp , [6] G. Poornalatha and S. R. Prakash, Web sessions lustering using hybrid sequene alignment measure (HSAM), Soial Network Analysis and Mining, vol. 3, no., pp , 013. [7] Y. Fu, K. Sandhu, and M. Y. Shih, A generalizationbased approah to lustering of web usage sessions, in Web Usage Analysis and User Profiling, 000, pp [8] T. K. Nasraoui, Olfa, Raghu Krishnapuram, Anupam Joshi, Automati web user profiling and 1149

9 International Journal of Applied Engineering Researh ISSN Volume 1, Number 7 (017) pp personalization using robust fuzzy relational lustering, in In E-Commere and Intelligent Methods, 00, pp [9] Z. Huang, J. Ng, D. Cheung, M. Ng, and W. Ching, A ube model for web aess sessions and luster analysis, Proeedings of WEBKDD, vol. 001, no , pp , 001. [10] G. Castellano and M. A. Torsello, Categorization of web users by fuzzy lustering, in Leture Notes in Computer Siene (inluding subseries Leture Notes in Artifiial Intelligene and Leture Notes in Bioinformatis), 008, vol. 5178, no., pp. 9. [11] J. C. B. R.J. Hathaway, J.W. Davenport, Relational duals of the -means lustering algorithms, Pattern Reognition, vol., no., pp. 05 1, [1] D. S. Sisodia, S. Verma, and O. P. Vyas, Augmented Intuitive Dissimilarity Metri for Clustering Of Web User Sessions, Journal of Information Siene, DOI: / , pp. 1 1, 016. [13] D. S. Sisodia, S. Verma, and O. P. Vyas, Performane Evaluation of an Augmented Session Dissimilarity Matrix of Web User Sessions Using Relational Fuzzy C-means Clustering, International Journal of Applied Engineering and Researh, vol. 11, no. 9, pp , 016. [14] D. S. Sisodia, S. Verma, and O. P. Vyas, Quantitative Evaluation of Web User Session Dissimilarity measures using medoids based Relational Fuzzy lustering, Indian Journal of Siene and Tehnology, vol. 9, no. 8, pp. 1 9, 016. [15] D. Sisodia and S. Verma, Web Usage Pattern Analysis Through Web Logs: A Review, in IEEE 9th International Joint Conferene on Computer Siene and Software Engineering(JCSSE 01), 01, pp [16] D. S. Sisodia, S. Verma, and O. P. Vyas, A Comparative Analysis of Browsing Behavior of Human Visitors and Automati Software Agents, Amerian Journal of Systems and Software, vol. 3, no., pp , 015. [17] M. Spiliopoulou, B. Mobasher, B. Berendt, and M. Nakagawa, A Framework for the Evaluation of Session Reonstrution Heuristis in Web-Usage Analysis, INFORMS Journal on Computing, vol. 15, no., pp , 003. [18] D. S. Sisodia, S. Verma, and O. P. Vyas, Agglomerative Approah for Identifiation and Elimination of Web Robots from Web Server Logs to Extrat Knowledge about Atual Visitors, Journal of Data Analysis and Information Proessing, vol. 3, no., pp. 1 10, 015. [19] P. K. Chan, A non-invasive learning approah to building web user profiles, in Proeedings of Workshop on Web Usage Analysis(KDD-99), 1999, pp [0] J. Xiao, Measuring similarity of interests for lustering Web-users, in Proeedings 1th Australasian Database Conferene. ADC 001, 001, pp [1] H. Liu and V. Keselj, Combined mining of Web server logs and web ontents for lassifying user navigation patterns and prediting users future requests, Data and Knowledge Engineering, vol. 61, no., pp , 007. [] A. Huang, Similarity measures for text doument lustering, in Proeedings of the sixth New Zealand omputer siene researh student onferene (NZCSRSC008), 008, pp [3] D. S. Sisodia, S. Verma, and O. Vyas, A Disounted Fuzzy Relational Clustering of Web Users Using Intuitive Augmented Sessions Dissimilarity Metri, IEEE Aess, vol. 4, no. 1, pp , 016. [4] S. L. Chiu, Fuzzy model identifiation based on luster estimation., Journal of Intelligent and Fuzzy Systems, vol., no. 3, pp , [5] R. R. Yager and D. P. Filev, Approximate lustering via the mountain method, IEEE Transations on Systems, Man, and Cybernetis, vol. 4, no. 8, pp , [6] D. S. Sisodia, S. Verma, and O. P. Vyas, A Conglomerate Relational Fuzzy Approah for Disovering Web User Session Clusters from Web Server Logs, International Journal of Engineering and Tehnology, vol. 8, no. 3, pp , 016. [7] W. Wang and Y. Zhang, On fuzzy luster validity indies, Fuzzy Sets and Systems, vol. 158, no. 19, pp , 007. [8] H. L. Shieh, Robust validity index for a modified subtrative lustering algorithm, Applied Soft Computing Journal, vol., pp , 014. [9] Xuanli Lisa Xie and G. Beni, A Validity Measure For Fuzzy Clustering, IEEE Transation on Pattern Analysis and Mahine Intelligene, vol. 13, no. 8, pp , [30] Y. Fukuyama and M. Sugeno, A new method of hoosing the number of lusters for the fuzzy -means method, in Proeedings of the 5th Fuzzy Systems Symposium, 1989, pp [31] A. M. Bensaid, L. Hall, J. C. Bezdek, L. P. Clarke, M. L. Silbiger, J. A. Arrington, and R. F. Murtagh, Validity Guided (re) lustering with appliations to image segmentation, IEEE Transations on Fuzzy Systems, vol. 4, no., pp , [3] N. Zahid, M. Limouri, and A. Essaid, A new lustervalidity for fuzzy lustering, Pattern Reognition, vol. 3, no. 7, pp , [33] MATLAB(01a), Software pakage. [Online]. Available: [34] T. C. Havens, S. Member, and J. C. Bezdek, An Effiient Formulation of the Improved Visual Assessment of Cluster Tendeny ( ivat ) Algorithm, IEEE Transations on Knowledge and Data Engineering, vol. 4, no. 5, pp , 01. [35] L. A. Wang, X. Geng, J. Bezdek, C. Lekie, and K. Ramamohanarao, ivat and avat: Enhaned Visual Analysis for Cluster Tendeny Assessment and Data Partitioning, in Advanes in Knowledge Disovery and Data Mining, 010, pp