Google's PageRank and Beyond

Preface ix

Chapter 1: Introduction to Web Search Engines 1
1.1 A Short History of Information Retrieval 1
1.2 An Overview of Traditional Information Retrieval 5
1.3 Web Information Retrieval 9

Chapter 2: Crawling, Indexing, and Query Processing 15
2.1 Crawling 15
2.2 The Content Index 19
2.3 Query Processing 21

Chapter 3: Ranking Webpages by Popularity 25
3.1 The Scene in 1998 25
3.2 Two Theses 26
3.3 Query-Independence 30

Chapter 4: The Mathematics of Google's PageRank 31
4.1 The Original Summation Formula for PageRank 32
4.2 Matrix Representation of the Summation Equations 33
4.3 Problems with the Iterative Process 34
4.4 A Little Markov Chain Theory 36
4.5 Early Adjustments to the Basic Model 36
4.6 Computation of the PageRank Vector 39
4.7 Theorem and Proof for Spectrum of the Google Matrix 45

Chapter 5: Parameters in the PageRank Model 47
5.1 The a Factor 47
5.2 The Hyperlink Matrix H 48
5.3 The Teleportation Matrix E 49

Chapter 6: The Sensitivity of PageRank 57
6.1 Sensitivity with respect to a 57
6.2 Sensitivity with respect to H 62
6.3 Sensitivity with respect to vT 63
6.4 Other Analyses of Sensitivity 63
6.5 Sensitivity Theorems and Proofs 66

Chapter 7: The PageRank Problem as a Linear System 71
7.1 Properties of (I -- aS) 71
7.2 Properties of (I -- aH) 72
7.3 Proof of the PageRank Sparse Linear System 73

Chapter 8: Issues in Large-Scale Implementation of PageRank 75
8.1 Storage Issues 75
8.2 Convergence Criterion 79
8.3 Accuracy 79
8.4 Dangling Nodes 80
8.5 Back Button Modeling 84

Chapter 9: Accelerating the Computation of PageRank 89
9.1 An Adaptive Power Method 89
9.2 Extrapolation 90
9.3 Aggregation 94
9.4 Other Numerical Methods 97

Chapter 10: Updating the PageRank Vector 99
10.1 The Two Updating Problems and their History 100
10.2 Restarting the Power Method 101
10.3 Approximate Updating Using Approximate Aggregation 102
10.4 Exact Aggregation 104
10.5 Exact vs. Approximate Aggregation 105
10.6 Updating with Iterative Aggregation 107
10.7 Determining the Partition 109
10.8 Conclusions 111

Chapter 11: The HITS Method for Ranking Webpages 115
11.1 The HITS Algorithm 115
11.2 HITS Implementation 117
11.3 HITS Convergence 119
11.4 HITS Example 120
11.5 Strengths and Weaknesses of HITS 122
11.6 HITS's Relationship to Bibliometrics 123
11.7 Query-Independent HITS 124
11.8 Accelerating HITS 126
11.9 HITS Sensitivity 126

Chapter 12: Other Link Methods for Ranking Webpages 131
12.1 SALSA 131
12.2 Hybrid Ranking Methods 135
12.3 Rankings based on Traffic Flow 136

Chapter 13: The Future of Web Information Retrieval 139
13.1 Spam 139
13.2 Personalization 142
13.3 Clustering 142
13.4 Intelligent Agents 143
13.5 Trends and Time-Sensitive Search 144
13.6 Privacy and Censorship 146
13.7 Library Classification Schemes 147
13.8 Data Fusion 148

Chapter 14: Resources for Web Information Retrieval 149
14.1 Resources for Getting Started 149
14.2 Resources for Serious Study 150

Chapter 15: The Mathematics Guide 153
15.1 Linear Algebra 153
15.2 Perron-Frobenius Theory 167
15.3 Markov Chains 175
15.4 Perron Complementation 186
15.5 Stochastic Complementation 192
15.6 Censoring 194
15.7 Aggregation 195
15.8 Disaggregation 198

Chapter 16: Glossary 201

Bibliography 207
Index 219