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Why doesn't your home page appear on the first page of search results, even when you query your own name? How do other web pages always appear at the top? What creates these powerful rankings? And how? The first book ever about the science of web page rankings, Google's PageRank and Beyond supplies the answers to these and other questions and more.
The book serves two very different audiences: the curious science reader and the technical computational reader. The chapters build in mathematical sophistication, so that the first five are accessible to the general academic reader. While other chapters are much more mathematical in nature, each one contains something for both audiences. For example, the authors include entertaining asides such as how search engines make money and how the Great Firewall of China influences research.
The book includes an extensive background chapter designed to help readers learn more about the mathematics of search engines, and it contains several MATLAB codes and links to sample web data sets. The philosophy throughout is to encourage readers to experiment with the ideas and algorithms in the text.
Any business seriously interested in improving its rankings in the major search engines can benefit from the clear examples, sample code, and list of resources provided.
1.1 A SHORT HISTORY OF INFORMATION RETRIEVAL
Today we have museums for everything-the museum of baseball, of baseball players, of crazed fans of baseball players, museums for world wars, national battles, legal fights, and family feuds. While there's no shortage of museums, we have yet to find a museum dedicated to this book's field, a museum of information retrieval and its history. Of course, there are related museums, such as the Library Museum in Boras, Sweden, but none concentrating on information retrieval. Information retrieval is the process of searching within a document collection for a particular information need (called a query). Although dominated by recent events following the invention of the computer, information retrieval actually has a long and glorious tradition. To honor that tradition, we propose the creation of a museum dedicated to its history. Like all museums, our museum of information retrieval contains some very interesting artifacts. Join us for a brief tour.
The earliest document collections were recorded on the painted walls of caves. A cavedweller interested in searching a collection of cave paintings to answer a particular information query had to travel by foot, and stand, staring in front of each painting. Unfortunately, it's hard to collect an artifact without being gruesome, so let's fast forward a bit.
Before the invention of paper, ancient Romans and Greeks recorded information on papyrus rolls. Some papyrus artifacts from ancient Rome had tags attached to the rolls. These tags were an ancient form of today's Post-it Note, and make an excellent addition to our museum. A tag contained a short summary of the rolled document, and was attached in order to save readers from unnecessarily unraveling a long irrelevant document. These abstracts also appeared in oral form. At the start of Greek plays in the fifth century B.C., the chorus recited an abstract of the ensuing action. While no actual classification scheme has survived from the artifacts of Greek and Roman libraries, we do know that another elementary information retrieval tool, the table of contents, first appeared in Greek scrolls from the second century B.C. Books were not invented until centuries later, when necessity required an alternative writing material. As the story goes, the Library of Pergamum (in what is now Turkey) threatened to overtake the celebrated Library of Alexandria as the best library in the world, claiming the largest collection of papyrus rolls. As a result, the Egyptians ceased the supply of papyrus to Pergamum, so the Pergamenians invented an alternative writing material, parchment, which is made from thin layers of animal skin. (In fact, the root of the word parchment comes from the word Pergamum.) Unlike papyrus, parchment did not roll easily, so scribes folded several sheets of parchment and sewed them into books. These books outlasted scrolls and were easier to use. Parchment books soon replaced the papyrus rolls.
The heights of writing, knowledge, and documentation of the Greek and Roman periods were contrasted with their lack during the Dark and Middle Ages. Precious few documents were produced during this time. Instead, most information was recorded orally. Document collections were recorded in the memory of a village's best storyteller. Oral traditions carried in poems, songs, and prayers were passed from one generation to the next. One of the most legendary and lengthy tales is Beowulf, an epic about the adventures of a sixth-century Scandinavian warrior. The tale is believed to have originated in the seventh century and been passed from generation to generation through song. Minstrels often took poetic license, altering and adding verses as the centuries passed. An inquisitive child wishing to hear stories about the monster Grendel waited patiently while the master storyteller searched his memory to find just the right part of the story. Thus, the result of the child's search for information was biased by the wisdom and judgement of the intermediary storyteller. Fortunately, the invention of paper, the best writing medium yet, superior to even parchment, brought renewed acceleration to the written record of information and collections of documents. In fact, Beowulf passed from oral to written form around A.D. 1000, a date over which scholars still debate. Later, monks, the possessors of treasured reading and writing skills, sat in scriptoriums working as scribes from sunrise to sunset. The scribes' works were placed in medieval libraries, which initially were so small that they had no need for classification systems. Eventually the collections grew, and it became common practice to divide the holdings into three groups: theological works, classical authors of antiquity, and contemporary authors on the seven arts. Lists of holdings and tables of contents from classical books make nice museum artifacts from the medieval period.
Other document collections sprung up in a variety of fields. This dramatically accelerated with the re-invention of the printing press by Johann Gutenberg in 1450. The wealthy proudly boasted of their private libraries, and public libraries were instituted in America in the 1700s at the prompting of Benjamin Franklin. As library collections grew and became publicly accessible, the desire for focused search became more acute. Hierarchical classification systems were used to group documents on like subjects together. The first use of a hierarchical organization system is attributed to the Roman author Valerius Maximus, who used it in A.D. 30 to organize the topics in his book, Factorum ac dictorum memorabilium libri IX (Nine Books of Memorable Deeds and Sayings). Despite these rudimentary organization systems, word of mouth and the advice of a librarian were the best means of obtaining accurate quality information for a search. Of course, document collections and their organization expanded beyond the limits of even the best librarian's memory. More orderly ways of maintaining records of a collection's holdings were devised. Notable artifacts that belong in our information retrieval museum are a few lists of individual library holdings, sorted by title and also author, as well as examples of the Dewey decimal system (1872), the card catalog (early 1900s), microfilm (1930s), and the MARC (MAchine Readable Cataloging) system (1960s).
These inventions were progress, yet still search was not completely in the hands of the information seeker. It took the invention of the digital computer (1940s and 1950s) and the subsequent inventions of computerized search systems to move toward that goal. The first computerized search systems used special syntax to automatically retrieve book and article information related to a user's query. Unfortunately, the cumbersome syntax kept search largely in the domain of librarians trained on the systems. An early representative of computerized search such as the Cornell SMART system (1960s) [146] deserves a place in our museum of information retrieval.
In 1989 the storage, access, and searching of document collections was revolutionized by an invention named the World Wide Web by its founder Tim Berners-Lee [79]. Of course, our museum must include artifacts from this revolution such as a webpage, some HTML, and a hyperlink or two. The invention of linked document collections was truly original at this time, despite the fact that Vannevar Bush, once Director of the Office of Scientific Research and Development, foreshadowed its coming in his famous 1945 essay, "As We May Think" [43]. In that essay, he describes the memex, a futuristic machine (with shocking similarity to today's PC and Web) that mirrors the cognitive processes of humans by leaving "trails of association" throughout document collections. Four decades of progress later, remnants of Bush's memex formed the skeleton of Berners-Lee's Web. A drawing of the memex (Figure 1.1) by a graphic artist and approved by Bush was included in LIFE magazine's 1945 publishing of Bush's prophetic article.
The World Wide Web became the ultimate signal of the dominance of the Information Age and the death of the Industrial Age. Yet despite the revolution in information storage and access ushered in by the Web, users initiating web searches found themselves floundering. They were looking for the proverbial needle in an enormous, ever-growing information haystack. In fact, users felt much like the men in Jorge Luis Borges' 1941 short story [35], "The Library of Babel", which describes an imaginary, infinite library.
When it was proclaimed that the Library contained all books, the first impression was one of extravagant happiness. All men felt themselves to be the masters of an intact and secret treasure. There was no personal or world problem whose eloquent solution did not exist in some hexagon.
... As was natural, this inordinate hope was followed by an excessive depression. The certitude that some shelf in some hexagon held precious books and that these precious books were inaccessible seemed almost intolerable.
Much of the information in the Library of the Web, like that in the fictitious Library of Babel, remained inaccessible. In fact, early web search engines did little to ease user frustration; search could be conducted by sorting through hierarchies of topics on Yahoo, or by sifting through the many (often thousands of) webpages returned by the search engine, clicking on pages to personally determine which were most relevant to the query. Some users resorted to the earliest search techniques used by ancient queriers-word of mouth and expert advice. They learned about valuable websites from friends and linked to sites recommended by colleagues who had already put in hours of search effort.
All this changed in 1998 when link analysis hit the information retrieval scene [40, 106]. The most successful search engines began using link analysis, a technique that exploited the additional information inherent in the hyperlink structure of the Web, to improve the quality of search results. Web search improved dramatically, and web searchers religiously used and promoted their favorite engines like Google and AltaVista. In fact, in 2004 many web surfers freely admit their obsession with, dependence on, and addiction to today's search engines. Below we include the comments [117] of a few Google fans to convey the joy caused by the increased accessibility of the Library of the Web made possible by the link analysis engines. Incidentally, in May 2004 Google held the largest share of the search market with 37% of searchers using Google, followed by 27% using the Yahoo conglomerate, which includes AltaVista, AlltheWeb, and Overture.
"It's not my homepage, but it might as well be. I use it to ego-surf. I use it to read the news. Anytime I want to find out anything, I use it."-Matt Groening, creator and executive producer, The Simpsons "I can't imagine life without Google News. Thousands of sources from around the world ensure anyone with an Internet connection can stay informed. The diversity of viewpoints available is staggering."-Michael Powell, chair, Federal Communications Commission "Google is my rapid-response research assistant. On the run-up to a deadline, I may use it to check the spelling of a foreign name, to acquire an image of a particular piece of military hardware, to find the exact quote of a public figure, check a stat, translate a phrase, or research the background of a particular corporation. It's the Swiss Army knife of information retrieval."-Garry Trudeau, cartoonist and creator, Doonesbury
Nearly all major search engines now combine link analysis scores, similar to those used by Google, with more traditional information retrieval scores. In this book, we record the history of one aspect of web information retrieval. That aspect is the link analysis or ranking algorithms underlying several of today's most popular and successful search engines, including Google and Teoma. Incidentally, we'll add the PageRank link analysis algorithm [40] used by Google (see Chapters 4-10) and the HITS algorithm [106] used by Teoma (see Chapter 11) to our museum of information retrieval.
1.2 AN OVERVIEW OF TRADITIONAL INFORMATION RETRIEVAL
To set the stage for the exciting developments in link analysis to come in later chapters, we begin our story by distinguishing web information retrieval from traditional information retrieval. Web information retrieval is search within the world's largest and linked document collection, whereas traditional information retrieval is search within smaller, more controlled, nonlinked collections. The traditional nonlinked collections existed before the birth of the Web and still exist today. Searching within a university library's collection of books or within a professor's reserve of slides for an art history course-these are examples of traditional information retrieval.
These document collections are nonlinked, mostly static, and are organized and categorized by specialists such as librarians and journal editors. These documents are stored in physical form as books, journals, and artwork as well as electronically on microfiche, CDs, and webpages. However, the mechanisms for searching for items in the collections are now almost all computerized. These computerized mechanisms are referred to as search engines, virtual machines created by software that enables them to sort through virtual file folders to find relevant documents. There are three basic computer-aided techniques for searching traditional information retrieval collections: Boolean models, vector space models, and probabilistic models. These search models, which were developed in the 1960s, have had decades to grow, mesh, and morph into new search models. In fact, as of June 2000, there were at least 3,500 different search engines (including the newer web engines), which means that there are possibly 3,500 different search techniques. Nevertheless, since most search engines rely on one or more of the three basic models, we describe these in turn.
1.2.1 Boolean Search Engines
The Boolean model of information retrieval, one of the earliest and simplest retrieval methods, uses the notion of exact matching to match documents to a user query. Its more refined descendents are still used by most libraries. The adjective Boolean refers to the use of Boolean algebra, whereby words are logically combined with the Boolean operators AND, OR, and NOT. For example, the Boolean AND of two logical statements xand ymeans that both xAND ymust be satisfied, while the Boolean OR of these two statements means that at least one of these statements must be satisfied. Any number of logical statements can be combined using the three Boolean operators. The Boolean model of information retrieval operates by considering which keywords are present or absent in a document. Thus, a document is judged as relevant or irrelevant; there is no concept of a partial match between documents and queries. This can lead to poor performance [14]. More advanced fuzzy set theoretic techniques try to remedy this black-white Boolean logic by introducing shades of gray. For example, a title search for car AND maintenance on a Boolean engine causes the virtual machine to return all documents that use both words in the title. A relevant document entitled "Automobile Maintenance" will not be returned. Fuzzy Boolean engines use fuzzy logic to categorize this document as somewhat relevant and return it to the user.
(Continues...)
Excerpted from Google's PageRank and Beyond by Amy N. Langville Carl D. Meyer Copyright © 2006 by Princeton University Press. Excerpted by permission.
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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 α 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 α 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 — αS) 71
7.2 Properties of (I — αH) 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
Anonymous
Posted July 25, 2008
For everyone who really wants to know the basics behind PageRank and how it is implemented. It does have a fair amount of mathematics. Great buy for people who like math, algorithms and their practical applications.
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Posted March 26, 2009
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Posted May 9, 2009
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Overview
Why doesn't your home page appear on the first page of search results, even when you query your own name? How do other web pages always appear at the top? What creates these powerful rankings? And how? The first book ever about the science of web page rankings, Google's PageRank and Beyond supplies the answers to these and other questions and more.
The book serves two very different audiences: the curious science reader and the technical computational reader. The chapters build ...