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Recitation 3

Learn about the Linear Deterministic Stationary Discrete Dynamic System, with focus on Google's PageRank as an example. Explore the shift from deterministic to stochastic systems, randomness, and common histograms.

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Recitation 3

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  1. Recitation 3 Steve Gu Jan 31 2008

  2. Outline • Part I: Review of LDSDDS • Linear, Deterministic, Stationary, Discrete, Dynamic System • Example: Google’s PageRank • Part II: From Deterministic to Stochastic • Randomness • Some histograms

  3. Part I

  4. Review of LDSDDS

  5. Review of LDSDDS For example:

  6. Review of LDSDDS • Interested? • Confused? • Doubted? • Bored? • Hey! Let’s take a real example

  7. PageRank • PageRank was developed at Stanford University by Larry Page (hence the name Page-Rank[1]) and later Sergey Brin as part of a research project about a new kind of search engine. The project started in 1995 and led to a functional prototype, named Google, in 1998

  8. PageRank How to rank the importance of web pages?

  9. PageRank http://en.wikipedia.org/wiki/Image:PageRanks-Example.svg

  10. PageRank: Modelling Votes PR(v) is the PageRank of v L(v) is the number of pages linked to v PR(u) is a collection of votes by pages linked to it!

  11. PageRank • For example: A receives 3 votes B receives 1 votes C receives 1 votes D receives none B C A D

  12. PageRank: Dynamic Systems? For N pages, say p1,…,pN Write the Equation to compute PageRank as: where l(i,j) is define to be:

  13. PageRank: Dynamic Systems? • Written in Matrix Form: F Look familiar?

  14. PageRank: Dynamic Systems? • Usually there is a damping factor d, which is used to guarantee convergence, that is:

  15. PageRank: Dynamic Systems! • PageRank is fully described by a LDSDDS • There is no magic here! • Ideas change the world (e.g. Google) • LDSDDS is simple • LDSDDS is powerful • LDSDDS is useful • LDSDDS is beautiful

  16. Part II From Deterministic to Stochastic

  17. Randomness

  18. Randomness • Stock Prices • Games (Poker, Casino, etc) • Biology: Evolution, Mutation • Physics: Quantum Mechanics • … • Is the world deterministic or stochastic?

  19. Some Common Histograms

  20. Review • LDSDDS • Uncover the secret: Google’s PageRank • DeterministicStochastic • That’s more fascinating • Welcome to the Stochastic World!

  21. The End • Thank you • Q&A

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