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112 6 Web Usage Miningthe links (underlined, followed by the corresponding link times) are the click-able hypertext,corresponding to links in the connectivity graph. The computation of similarity among WebFig. 6.1. A usage snapshot exampleusers’ results in an m × m matrix, called users’ similarity matrix (SM). Assuming that the sixnavigation paths be the access traces of six users identified by u 1 ,u 2 ,...,u 6 . By using eq.6.1-6.4, we⎡obtain the following similarity measures⎤ ⎡⎤1 .224 1 1 .894 .8941 .177 .875 .972 .802 .894.224 1 .224 .224 .25 .25.177 1 .354 .125 .378 .316SM1 =1 .224 1 1 .894 .894⎢ 1 .224 1 1 .894 .894, SM2 =.875 .354 1 .795 .953 .894⎥ ⎢ .972 .125 .795 1 .756 .87⎥⎣ .894 .25 .894 .894 1 .75 ⎦ ⎣ .802 .378 .953 .756 1 .837⎦.894 .25 .894 .894 .75 1.894 .316 .894 .87 .837 1⎡⎤ ⎡⎤1 .224 .885 .988 .949 .9761 .01 .096 .618 .096 .08.224 1 .35 .205 .162 .27.01 1 .02 .006 .027 .02SM3 =.885 .35 1 .863 .779 .92⎢ .988 .205 .863 1 .968 .964⎥, SM4 =.096 .02 1 .063 .027 .271⎢ .618 .006 .063 1 .066 .069⎥⎢⎣.949 .164 .779 .968 1 .895.976 .27 .92 .964 .895 1⎥⎦⎢⎣.096 .027 .735 .066 1 .362.08 .02 .271 .069 .362 1⎥⎦A Clustering AlgorithmData PreprocessingData preprocessing is necessary, as the interest items need to be extracted from the access logfiles. A Web page may be considered as an interest item, or a group of them may be taken intoa ”semantic” interest item set.
6.1 Modeling Web User Interests using Clustering 113The data in the SM matrix also need to be preprocessed. In most cases, we are interestedin those users among them higher similar interests are shown with respect to a particularsimilarity measure. For this purpose, a similarity threshold, λ, is determined to split the userclusters. Users with similarity measure greater than or equal to λ are considered in a samecluster. For instance, if λ = 0.9, SM2 becomes the following SM5 after preprocessing.⎡⎤1 0 0 .972 0 00 1 0 0 0 0SM5 =0 0 1 0 .935 0⎢ .972 0 0 1 0 0⎥⎣ 0 0 .935 0 1 0⎦0 0 0 0 0 1SM(i, j) represents the similarity measure between users u i and u j (1 ≤ i, j ≤ m). The greaterthe value of SM(i, j), the closer the two users u i and u j is related. Note that SM is a symmetricmatrix and elements along the main diagonal are all the same (i.e., SM(i,i) =1, forall 1 ≤ i ≤ m). Thus only those elements in the upper triangular matrix need to be stored inimplementation.Clustering Web-users into groups is equivalent to decomposing their SM matrix into submatrices.The goal of clustering users is achieved by two steps: (1) permute rows and columnsof the matrix such that those ”closely related” elements are located closely in the matrix;and (2) find the dividing point that decomposes the matrix into sub-matrices. The next twosubsections discuss the two steps in details.Permutation of the matrixIn order to locate those closely related users in the matrix, the authors use affinity to measurehow close two users are related in the SM matrix, which is defined as: A(i, j) =∑ m p=1 SM (i, p) ∗ SM (p, j). For users u i, u j ∈ U, they contribute to the affinity A(i, j) ifSM (i, j) ̸=0, or if there exists p,1 ≤ p ≤ m, such that SM (i, p) ̸=0 and SM (p, j) ̸=0. Twousers with higher affinity should have a higher chance to be put in the same cluster.To measure how closely those users with high affinity are located together in the matrix,we define the global affinity of a matrix as:GA(SM)=∑ m A(i,i − 1)+A(i,i + 1) (6.5)i=1A(i,i − l) is the affinity of u i with its preceding user, and A(i,i + 1) is the affinity of u i , withits succeeding user, in the matrix. For u 1 , and u k , th authors assume that A(O,1)=A(1,O)=A(m + 1,m) =A(m,re + 1) =0. GA(SM) represents the global affinity of each user in thematrix with its neighboring users. The higher the GA(SM) is, the closer the elements of greatervalues get together, which is the case where the users with higher similar interests are locatedtogether in the matrix.In order to get a higher global affinity, we permute the rows and columns of the matrix.The permutation procedure starts from the first column. It compares the GAs by swapping thepositions of every pair of columns. If the GA becomes higher after swapping, the two columnsswap their positions (the rows should be swapped accordingly to maintain the same relativepositions as columns); otherwise the positions of the two columns remain unchanged.When the permutation is complete, the global affinity of the matrix is maximized. That is,those closely related users are located closely to each other in the matrix.
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Web Mining and Social Networking
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Guandong Xu • Yanchun Zhang • L
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VIIIPrefacefollowing characteristic
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Acknowledgements: We would like to
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XIVContents3.1.2 Basic Algorithms f
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XVIContentsPart III Social Networki
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Part IFoundation
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4 1 Introduction(3). Learning usefu
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6 1 Introductioncalled computationa
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8 1 Introduction• The data on the
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10 1 Introductionin a broad range t
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2Theoretical BackgroundsAs discusse
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2.2 Textual, Linkage and Usage Expr
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2.4 Eigenvector, Principal Eigenvec
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2.5 Singular Value Decomposition (S
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2.6 Tensor Expression and Decomposi
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2.7 Information Retrieval Performan
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2.8 Basic Concepts in Social Networ
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2.8 Basic Concepts in Social Networ
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30 3 Algorithms and TechniquesTable
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32 3 Algorithms and TechniquesSpeci
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Page 93 and 94: 4.2 Web Search 75algorithm. The Web
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Page 126 and 127: 6Web Usage MiningIn previous chapte
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162 7 Extracting and Analyzing Web
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170 8 Web Mining and Recommendation
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190 9 Conclusionsries commonly used
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192 9 Conclusionsas computer scienc
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194 9 Conclusionsresearches have de
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196 References14. J. Ayres, J. Gehr
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198 References49. D. Chakrabarti, R
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200 References82. C. Dwork, R. Kuma
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202 References119. J. Hou and Y. Zh
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204 References151. A. N. Langville
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206 References186. J. K. Mui and K.
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208 References223. C. Shahabi, A. M
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