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Lecture #10 PageRank

Lecture #10 PageRank. CS492 Special Topics in Computer Science: Distributed Algorithms and Systems. Origin of “Google”. Hostnames Active. http://news.netcraft.com. Googol 10^100 Motivation behind Human maintained indices such as Yahoo! Explosive growth. Design Goals of Google.

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Lecture #10 PageRank

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  1. Lecture #10PageRank CS492 Special Topics in Computer Science: Distributed Algorithms and Systems

  2. Origin of “Google” Hostnames Active http://news.netcraft.com • Googol • 10^100 • Motivation behind • Human maintained indices such as Yahoo! • Explosive growth

  3. Design Goals of Google • Improved search quality • In 1997, 1 out of 4 top search engines found itself • High precision in finding relevant document was necessary • Academic search engine research • Search engine technology went commercial: an black art • To build systems that a good number of people could use • To build an architecture to support novel research on large-scale Web data

  4. Weakness of Existing Approaches • Calculate similarities • Based on flat, vector-space model of each page • Prone to cheating (Web spamming or search engine persuasion)

  5. Basic Idea of PageRank Exploit the topological structure of hypertextual systems

  6. Simple Example A 0.4 C 0.4 B 0.2

  7. Related Work • Academic citation analysis • Similarities • Graph structure; paper = node, web page = node citation = link, URL = link • “node” authority independent of “node” content • Differences • Uniform unit of info (paper) versus great variability in quality, usage, citations, and length • Equal link weight vs variable importance A backlink from Yahoo! vs. from a friend

  8. Which Page Should Be Ranked Higher? JohnDoe A B

  9. Simple Expression page rank of set of pages pointing at out-degree of Question: role of c? Answer: total rank of all web pages constant

  10. Dangling links • Pages without outgoing pointers • Example: Pages not yet downloaded • Do not affect the calculation much • Remove them, calculate ranks, and add them back

  11. Loop A C B Question: ranks of A, B, and C? Answer: infinite! (rank sink)

  12. Basic Algorithm page rank of set of pages pointing at out-degree of dumping factor

  13. Matrix Representation where and Question: Where to start?

  14. Iterative Algorithm where and Question: Will it converge?

  15. Example [LM04]

  16. Turn the Problem into a Markov Process [LM04]

  17. Evenly Split Rank of Dangling Links [LM04]

  18. Final Solution Eigenvector of P = steady state rank

  19. Spam Rank [BGS05]

  20. Questions • Where to start? • Find a nondegenerate start vector • What if there are two pages that point to each other and no one else and there is a page that points to one of them? • Role of dumping factor guarantees no rank sink

  21. References [PBMW] L. Page, S. Brin, R. Motwani, T. Winograd, “The PageRank citation ranking: bringing order to the web,” WWW 1998 [BP98] Sergey Brin, Lawrence Page, “The anatomy of a large-scale hypertextual Web search engine,” Computer Networks and ISDN Systems, Vol. 30, 1998. [BGS05] Monica Bianchini, Marco Gori, Franco Scarselli, “Inside PageRank,” ACM Transactions on Internet Technology, Vol. 5, No. 1, Feb. 2005. [LM04] Amy N. Langville, Carl Meyer, “Deeper inside PageRank,” Internet Mathematics, Vol. I, No. 3, 2004. [K99] Jon Kleinberg, “Authoritative sources in a Hyperlinked Environment,” Journal of the ACM 46:5 (1999).

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