1 / 21

Recitation 3

Recitation 3. Steve Gu Jan 31 2008. 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. Part I. Review of LDSDDS. Review of LDSDDS. For example:.

steel-bridges
Download Presentation

Recitation 3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related