Page Rank Seminar: Link mining

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Page RankSeminar Link mining
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Contents

• Introduction
• PageRank
• Random Surfer Model
• Implementation
• General principle
• Algorithm
• Examples
• Convergence
• Applications and Areas of Research
• Conclusion
• References

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Introduction

• Search engines as an important tool.
• 1.- Find all pages which fit the searched
  query.
• 2.- Rank all pages by some sort of criterion
• Google is one of the most used because
• High performance
• Ease of use
• Quality of the search results.

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PageRank

• Method to rank web pages giving to it a numeric
  value that represent their importance
• Lawrence Page and Sergey Brin ( 1998).
• Based on the link structure of the web.
• Developed to provide a ranking on the search
  results.

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Random Surfer Model

• The random surfer picks a web page and keeps
  clicking on links, this probability is called
  damping factor.
• The PageRank value of a page reflects the
  frequency of hits on that page by the random
  surfer.
• If the random surfer arrives to a sink page o
  gets bored then will pick another URL at random.

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Implementation

• 1.- URL ? id
• 2.- Store each hyperlink in a database.
• 3.- Sort link structure by Parent id.
• 4.- Remove dangling links.
• 5.- Calculate the PR giving each page an initial
  value.
• 6.- Iterate until convergence.
• 7.- Add the dangling links.

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General Principle

• Every page has some number of Outbounds links
  (forward links) and Inbounds links (backlinks).
• A page X has a high rank if
• It has many Inbounds links
• It has highly ranked Inbounds links
• Page linking to has few Outbounds links.

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Algorithm

• PR(A) PR of site A
• PR(Ti) PR of sites linking A
• N(Ti) Outbound links of Ti
• d dumping-factor (usually set on .85)
• (1-d) prob. that the random surfer get bored.

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PageBrin Algorithm

• R(u) PR of site u
• c factor used for normalization (lt1)
• Bu Set of pages that point to u
• Nv Outbound links of v
• R(v) PR of site v which point to site u
• E(u) distribution of web pages that a random
  surfer periodically jumps (set to 0.15).

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Examples

• PR(A) .15.85(PR(B)/1) 1
• PR(B) .15.85(PR(A)/1) 1
• All pages PR of pages

PR1(A).15.85(1/2) .575 PR1(B).15.85(1/1)
1 PR1(C).15.85(1/2) .575
PR2(A).15.85(1/2) .575 PR2(B).15.85(11)
1.85 PR2(C).15.85(1/2) .575
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with d 0.5 Pr(A) PR(B)
PR(C)
0 1 2 3 . . . . 11 12
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Convergence

• PageRank will scale very well even for extremely
  large collections of links.

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Applications and Areas of research

• Some other Applications
• - Find an optimal order.
• - Help user to decide if a site is trustworthy
  or not.
• - Estimate web traffic.
• Areas of Research
• Computational cost.
• Updating problem.
• Dynamic growth of the web.
• Spam detection and prevention.

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Conclusion

• Global ranking based on the webs graph
  structure.
• Represent how important a page is on the web.
• Inbound links information to bring order to the
  web.
• Can be thought as a model of the random surfer
  behaviour.

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References

• http//pr.efactory.de/d-index.shtml
• http//www.webworkshop.net/pagerank.html
• http//www.iprcom.com/papers/pagerank/
• http//www.at-web.de/suchmaschinenoptimierung/page
  rank.htm
• http//www-db.stanford.edu/backrub/google.html
• L.Pager S. Brin,The PageRank citation ranking
  Bringing order to the web , Stanford Digital
  Library Technique, Working paper 1999-0120, 1998.
• Monika Henzinger, Link Analysis in Web
  Information Retrieval, 2000.
• Amy N. Langville Carl D. Meyer, Depper Inside
  PageRank, 2003.