Google's PageRank and Beyond

Amy N. Langville is Assistant Professor of Mathematics at the College of Charleston in Charleston, South Carolina. She studies mathematical algorithms for information retrieval and text and data mining applications. Carl D. Meyer is Professor of Mathematics at North Carolina State University. In addition to information retrieval, his research areas include numerical analysis, linear algebra, and Markov chains. He is the author of "Matrix Analysis and Applied Linear Algebra".

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 alpha 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 alpha 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 -- alphaS) 71 7.2 Properties of (I -- alphaH) 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