Analysis of Documents Clustering Using Sampled Agglomerative Technique

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1 Aalysis of Documets Clusterig Usig Sampled Agglomerative Techique Omar H. Karam, Ahmed M. Hamad, ad Sheri M. Moussa Abstract I this paper a clusterig algorithm for documets is proposed that adapts a samplig-based pruig strategy to simplify hierarchical clusterig. The algorithm ca be applied to ay text documets data set whose etries ca be embedded i a high dimesioal Euclidea space i which every documet is a vector of real umbers. This paper presets the results of a experimetal study of the proposed documet clusterig techique. The performace of the method is illustrated i terms of quality of clusters. Idex Terms Agglomerative clusterig, Documet clusterig, ad k-meas clusterig. D I. INTRODUCTION ocumet Clusterig has bee extesively ivestigated as a methodology for improvig documet search ad retrieval. The geeral assumptio is that mutually similar documets will ted to be relevat to the same queries, ad hece, that automatic determiatio of groups of such documets ca improve recall ad precisio by effectively broadeig a search request []. May techiques are used for documet clusterig [],[5],[6],[7]. The two mai approaches used for documet clusterig are the agglomerative hierarchical ad the k-meas clusterig techiques. k-meas is a partitioal clusterig techique based o the idea that a ceter poit (cetroid), represetig the average poit of the data poits grouped i oe cluster, ca represet a cluster. Give the umber of required clusters (k) ad the iitial k ceter poits (cetroids), documets ca be clustered by assigig each documet to the cluster havig the earest cetroid. This is doe by measurig similarity through the distace fuctio betwee the documet ad each of the k cetroids. A ew cetroid is the recomputed for each ewly created cluster, ad the whole process is repeated util o chage i the k cetroids or the Omar H. Karam, Departmet of Iformatio Systems, Faculty of Computer ad Iformatio Scieces; Ai Shams Uiversity, Cairo, 566, EgyptPhoe: () Fax: () ohkaram@hotmail.com). Ahmed M. Hamad, Professor of Computer Systems, Departmet of Iformatio Systems, Faculty of Computer ad Iformatio Scieces, Ai Shams Uiversity, Cairo, 566, Egypt Phoe: () Fax: () ( amhamad@yahoo.com). Sheri M. Moussa, Departmet of Iformatio Systems, Faculty of Computer ad Iformatio Scieces Ai Shams Uiversity, Cairo, 566, detected chage is less tha a determied threshold. O the other had, the agglomerative clusterig algorithm is a hierarchical techique that produces a ested sequece of partitios, with a sigle, all-iclusive cluster at the top ad sigleto clusters of idividual poits at the bottom [],[9]. It starts with each documet as a idividual cluster, ad at each iteratio, merges the most similar or closest pair of clusters util oe cluster is obtaied. Therefore, clusterig should stop before obtaiig the sigle cluster depedig o a specified coditio, such as the umber of clusters required, or the quality of the clusters to obtai. Agglomerative hierarchical clusterig is ofte portrayed as better tha K-meas, although slower. It is also superior to k-meas clusterig, especially for buildig documet hierarchies. [],[],[],[8]. The traditioal agglomerative hierarchical clusterig procedure is summarized as follows []:. Compute the similarity betwee all pairs of clusters, i.e., calculate a similarity matrix whose ij th etry gives the similarity betwee the i th ad j th clusters.. Merge the most similar (closest) two clusters.. Update the similarity matrix to reflect the pairwise similarity betwee the ew cluster ad the origial clusters. 4. Repeat steps ad util oly a sigle cluster remais. There are differet hierarchical clusterig algorithms [],[],[8]. The oly real differece betwee these differet hierarchical schemes is how they choose which clusters to merge, i.e., how they choose to defie cluster similarity.(i.e. Itra-Cluster Similarity Techique (IST), Cetroid Similarity Techique (CST), ad Uweighted Pair Group Method with Arithmetic mea (UPGMA)). Amog the several obstacles to be faced i text miig, the amout of preprocessig that has to be applied to a documet for text miig purposes, ad the documets mathematical represetatio [4]. I this paper, a agglomerative techique is applied to documet clusterig that adapts a samplig-based pruig strategy to simplify hierarchical clusterig. The algorithm ca be applied to ay text documets data set whose etries ca be embedded i a high dimesioal Euclidea space (i.e. i which every documet is a vector of real umbers). The proposed algorithm is followed by a experimetal study ad the obtaied results while varyig its differet parameters ad observig their effect o the resultig cluster qualities. Egypt Phoe: () Fax: () ( shero@usa.com).

2 This paper is orgaized as follows. Sectio discusses the preparatio of text documets i order to be clustered. Sectio explais the method used i our system for documet clusterig, ad sectio 4 presets the results of experimets evaluatig the performace of the system. Fially, sectio 5 cocludes the paper. II. DOCUMENTS PREPARATION I order to apply ay clusterig algorithm o text documets, some steps should be followed [],[],[4]. These are: a) Preprocessig Iitially, Very commo words, (i.e. prepositios ad o-cotet bearig words, ofte kow as stop words), are removed completely from documets. I additio, stemmig is applied where differet forms of a word are reduced to a sigle stem form. I our work, Porter s suffix strippig algorithm is used []. Now documets are ready to be mathematically represeted. b) Mathematical Represetatio I our system, the vector space model is used, where each documet is represeted by the (TF) vector, d, i the multidimesioal space of documet words. The Term- Frequecy vector is: d = (tf, tf, L, tf ) () tf where tf i is the frequecy of the ith term i the documet. Give a set, S, of documets ad their correspodig vector represetatios, the cetroid vector, c, is defied to be: c = d () S d S which is obtaied by averagig the weights of the various terms preset i the documets of S, where d is the documet vector obtaied from the set S. Thus, the vector space model of a text data set is cosidered to be a word-by-documet matrix whose rows are words ad colums are documet vectors. c) Dimesio Space Costructio Sice the documet vectors are of high dimesioality, pruig ca be used to reduce the dimesioality. A threshold P is give, ad words havig a frequecy less tha this threshold are removed completely from the documet vectors. At this stage, documet vectors legths are ot uified. Therefore, a superset vector is created that cotais all words i all the documets after pruig. This superset vector is the compared to each documet vector, ad each documet vector is mapped from its ow space to the superset vector space. If a word foud i the superset vector is missig i the documet vector, it is added to the documet vector with term frequecy zero. Thus a dimesio space is costructed, where each word i a documet vector is cosidered to be a dimesio. d) Similarity Measure: Documet vectors are ow ready for clusterig, where similar documet vectors are grouped together i the same cluster. The similarity measure betwee ay two vectors is computed usig the Mikowski distace fuctio, d q q q /q ( i, j) = ( x x + x x + L+ x x ) i j i () where i represets the ith documet vector ad j represets the jth documet vector, x ip is the word umber p i the ith documet vector; x jp is the word umber p i the jth documet vector, q is the power of the distace fuctio. This similarity measure ca be oe of the followig approaches: a) Sigle likage, b) Complete likage, ad c) Cetroids similarity [8]. I this work, the third approach is used, where similarity betwee two clusters is measured betwee the cetroids of each. The cetroid of a cluster is its average elemet. III. THE PROPOSED CLUSTERING ALGORITHM The proposed clusterig algorithm reads the whole collectio of documets to create the correspodig documet vectors, which are prued by the give threshold, P. The dimesio space is the costructed as explaied, ad a radom sample, R, is chose from the data set. Agglomerative clusterig is the applied to this chose sample usig the Cetroid Similarity Techique (CST), where at each successive iteratio, pairs of clusters havig their similarity measuremet value below a icremetig step value, are merged together ito oe cluster. At the ext iteratio, the icremetig step is icreased ad the procedure is repeated util the give agglomerative distace threshold, A, is exceeded. This agglomerative distace threshold at which the agglomeratio stops, that is, the distace betwee clusters, is take as the quality measure for the agglomerative clusters. Whe agglomeratio stops, the umber of the created clusters is cosidered to be the umber of the clusters that will cotai all the documet vectors of the whole data set, ad the computed cetroids of the created clusters are the iitial cetroids for the documet vectors of the whole data set. Idividual documets that have ot bee merged yet with other clusters are cosidered to be idividual clusters, havig the idividual documet vector as the cetroid vector of the cosidered cluster. Hece, the first ru of k-meas algorithm is applied, where each documet vector of the whole data set is assiged to the cluster havig the earest or the most similar cetroid vector. The quality of a obtaied cluster for these documets assigmet is take as the itra-cluster similarity measure, that is, the sum of the distaces betwee each documet vector ad j ip jp

3 the cetroid vector of the cluster to which this documet is attached. This value is the ormalized by dividig it by the umber of documets assiged to the cosidered cluster. The total quality value is computed by summig up the quality values of all the created clusters, which is ormalized by further dividig this total value by the umber of the created clusters. That is, cluster quality equals: = k k j= i= ( d ij c j ) (4) where d ij is the ith documet vector i the data set ad belogs to the jth cluster, c j is the cetroid vector of the jth cluster, k is the umber of the required clusters ad is the umber of documets i the whole data set. The complexity of the proposed clusterig algorithm is O(m + k), where m is the umber of chose documets i the radom sample, k is the umber of created clusters, ad is the umber of documets i the whole data set. set. The rows represet the umber of cotaied words (obtaied from the superset vector) ad the colums represet the umber of cosidered documet vectors. It is clear that as the pruig threshold value (P) icreases, the matrices size decreases. At higher pruig thresholds, the matrices size are almost similar for both sample sizes R = % ad %. Fig. Matrices Sizes for Costructed Dimesio Spaces TABLE I K VALUE AT DIFFERENT AGGLOMERATIVE THRESHOLDS WITH SAMPLE SIZE = % Pruig A = 5 A = A = 5 A = IV. EXPERIMENTS AND RESULTS The proposed clusterig algorithm is studied by examiig it o the NSF (Natioal Sciece Foudatio) data set obtaied by dowloadig 75 abstracts of the grats awarded by the NSF. These abstracts icluded subjects Such as astroomy, populatio studies, udergraduate educatio, materials, mathematics, biology, health, oceaography, computer sciece ad chemistry. Differet pruig thresholds are applied o the data set with P =,, 4, 5, 6, 7 where most of the documet vectors cotaied o words at P = 7. After creatig the correspodig superset vector ad costructig the dimesio space, samples of R = %, % were chose to ru the agglomerative clusterig approach o these sample documet vectors. At this stage, the Euclidea distace fuctio (q = ) is used to compute distaces betwee the vectors. Differet agglomerative distace thresholds are also applied, A = 5,, 5, ad where the umber of the created clusters at A = was oly two. The effect of varyig these parameters o the umber of the created agglomerative clusters ad the quality of the fial resultat clusters are moitored. Figure () represets a graph showig the sizes of the created matrices of the dimesio spaces costructed for the chose sample at R = % ad % ad for the whole data Matrices Sizes Pruig R = % R = % k-meas TABLE K VALUE AT DIFFERENT AGGLOMERATIVE THRESHOLDS WITH SAMPLE SIZE =% Pruig A = 5 A = A = TABLE K VALUE AT DIFFERENT PRUNING THRESHOLDS WITH SAMPLE SIZE = % TABLE 4 Agglomerative P = P = P = 4 P = 5 P = 6 P = K VALUE AT DIFFERENT PRUNING THRESHOLDS WITH SAMPLE SIZE = %

4 4 Agglomerative Tables () ad () shows k value at differet agglomerative thresholds A, for R = % ad % respectively. The more the pruig threshold P icreases, i other words, the more the documet vectors are reduced, the less the umber of created agglomerative clusters obtaied (k value). O the other had, tables () ad (4) shows k value at differet pruig thresholds P for R = % ad % respectively. It was foud that the more the agglomerative distace threshold A icreases, the less the umber of created agglomerative clusters obtaied (k value) P = P = 4 P = 5 P = 6 P = Pruig Agglo. =5 Agglo. = Agglo. =5 Agglo. = By studyig the pruig threshold effect o the cluster quality of the resultat clusters from our proposed algorithm as show i figures () ad () for R = % ad % respectively ad for differet values of A, it was foud that as the pruig threshold P icreases, the resultat cluster quality icreases except for the highest pruig threshold P = 7 where the resultat cluster quality decreased agai. This is due to the removal of may words from the documet vectors that distiguish documets from oe aother Agglomerative Prue =4 Prue =6 Prue =5 Prue =7 Fig. 4 Agglomerative Effect o At Differet Pruig s with Sample Size = % Fig. Pruig Effect o At Differet Agglomerative s with Sample Size = % Pruig Agglo. =5 Agglo. = Agglo. =5 Fig. Pruig Effect o At Differet Agglomerative s with Sample Size = % 5 5 Agglomerative Prue =4 Prue =6 Prue =5 Prue =7 Fig. 5 Agglomerative Effect o At Differet Pruig s with Sample Size = % As for the effect of the agglomerative distace threshold, A, o the resultat cluster quality for R = % ad % respectively ad for differet P values as show i figures (4) ad (5), it was foud that the more the agglomerative distace threshold A icreases, the higher is the cluster quality of the resultat clusters.

5 5 After studyig the effect of both pruig ad agglomerative distace thresholds o the resultat cluster quality, it ca be summarized that at the same value of the agglomerative threshold, A, the variatio i the resultat cluster quality at the differet pruig thresholds, P is high. But at the same value of the pruig threshold, P, the variatio i the resultat cluster quality at the differet agglomerative thresholds, A, is low. This is valid for both the sample sizes, R = %, %. V. CONCLUSION I this paper, we applied a agglomerative techique to documet clusterig that adapts a samplig-based pruig strategy to simplify hierarchical clusterig depedig o the required quality for the obtaied clusters. The proposed algorithm combies the agglomerative hierarchical approach with the first ru of k-meas approach to provide k disjoit clusters. A experimetal study was coducted to evaluate the differet parameters affectig the resultat cluster quality of the obtaied clusters specifically the pruig threshold, the agglomerative threshold for the sample sizes of % ad %. It was show that the variatio i the resultat cluster quality at the differet pruig thresholds is high, versus the variatio i the resultat cluster quality at the differet agglomerative thresholds, thus pruig threshold effect is domiat. REFERENCES [] [] J. Ha, M. Kamber. Data Miig Cocepts ad Techiques. Morga Kaufma Publishers. Pages 5 88 ad 48 45,. [] [] I. S. Dhillo ad D. S. Modha. Cocept Decompositios for Large Sparse Text Data usig Clusterig. Techical Report RJ 47, IBM Almada Research ceter,. [] [] M. Steibach, G. Karypis, as V. Kumar. A Compariso of Documet Clusterig Techiques. I KDD workshop o Text Miig,. [4] [4] J.L. Neto, A.D. Satos, C.A.A. Kaester, ad A.A. Freitas. Documet Clusterig ad Text Summarizatio. I Proceedigs, 4 th Iteratioal Coferece o Practical Applicatios of Kowledge Discovery ad Data Miig (PADD-), Lodo: The Practical Applicatio Compay,. [5] [5] N. Turee ad F. Rousselot. Evaluatio of Four Clusterig Methods used i Text Miig, 999. [6] [6] M. Meila, ad D. Hackerma, A Experimetal Compariso of Several Clusterig ad Iitializatio Methods, (Techical Report 98-6). Microsoft Research Redmod, WA, 998. [7] [7] C. Wei, Y. Lee ad C. Hsu. Empirical Compariso of Fast Clusterig Algorithms for Large Data Sets. Proceedigs of the rd Hawaii Iteratioal Coferece o System Scieces, 998. [8] [8] M. J. A. Berry, G. Lioff. Data Miig Techiques for Marketig, Sales, ad Customer Support. Joh Wiley & Sos. Pages 87 5, 997. [9] [9] D. Fisher. Iterative optimizatio ad simplificatio of hierarchical clusterigs. J. Art. Itell. Res., 4:47--79, 996. [] [] D. Cuttig, D. Karger, J. Pederse, ad J. Tukey. Scatter/gather: a cluster-based approach to browsig large documet collectios. I 5th A It ACM SIGIR Coferece o Research ad Developmet i Iformatio Retrieval (SIGIR'9), pages 8--9, 99. [] [] M.F. Porter, A Algorithm for Suffix Strippig, Program 4 (), Pages -7, July 98.

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