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- 1. Numerical computing &Google’s PageRankDAVID F. GLEICH, CS 197 PRESENTATION
- 2. Hey Katie, do you have a date for Valentine’s Day? It was1234567890in 2009.
- 3. Thanks Internet! http://school.discoveryeducation.com/clipart/clip/stk-fgr6.html http://listsoplenty.com/pix/tag/cartoon https://www.facebook.com/ProgrammersJokeshttp://www.feld.com/wp/archives/2009/02/unix-time-1234567890- on-valentines-day.html
- 4. og le Go Thanks Internet! n ks ha http://school.discoveryeducation.com/clipart/clip/stk-fgr6.htmlT http://listsoplenty.com/pix/tag/cartoon https://www.facebook.com/ProgrammersJokeshttp://www.feld.com/wp/archives/2009/02/unix-time-1234567890- on-valentines-day.html
- 5. How did Google get started?
- 6. How did Google get started?… with an idea … … on the shoulders of giants!
- 7. LEO KATZ
- 8. Vannevar Bush“wholly new forms ofencyclopedias will appear,ready made with a mesh ofassociative trails runningthrough them, ready to bedropped into the memex andthere ampliﬁed” -- “As we may think” The Atlantic, July 1945
- 9. Sir Tim Berners-Lee“We should work towards auniversal linked informationsystem … to allow a place forany information or referenceone felt was important and away of ﬁnding it afterwards.” -- Founding proposal for “the mesh”, 1989
- 10. … the mesh became the web … the web became a mess... “ﬁnding it afterwards”? Hah!
- 11. Larry Page "Sergey Brin• Grad students at Stanford• Worked with Terry Winograd (artiﬁcial intelligence)• Created a web-search algorithm called “backrub”• Spun-off a company “Googol”• Worth about $20 billion each
- 12. A cartoon websearch primer1. Crawl webpages2. Analyze webpage text (information retrieval)3. Analyze webpage links4. Fit measures to human evaluations5. Produce rankings6. Continuously update
- 13. SportsIllustrated.comBobsPortsIllustrated.com
- 14. 1 2to 3
- 15. What pages areimportant?Those that people visit a lot!How to we check?Create a model of how peoplevisit the web.
- 16. What pages areimportant?The Google random surfer• Follows a random link with probability alpha" “random clicks”• Goes anywhere with probability (1-alpha)" “random jumps”
- 17. This is a Markov chain!
- 18. Andrei Markov• Studied sequences of random variables.• The probability that the random variable takes a particular value only depends on it’s current value.• The “page id” is the “random variable” in the Markov chain!
- 19. Oskar Perron"Georg Frobenius• Simultaneously discovered when a Markov chain has an “average” • The “average” of the web? It’s the probability of ﬁnding the random surfer at a page.• In 1907
- 20. What pages areimportant?Perron and Frobenius proved thefollowing algorithm alwaysconverges to a solution…set prob[i] = 0 for all pagesset p to a random pagefor t = 1 to ... increment prob[p] if rand() < alpha, set p to a random neighbor of p else, set p to a random page
- 21. Richard von Mises• Created “the power method”• An efﬁcient algorithm to “average” a Markov chain• It updated the probabilities of all pages at once.“Praktische Verfahren der Gleichungsauﬂösung”"R. von Mises and H. Pollaczek-Geiringer, 1929
- 22. What pages areimportant?Using the von Mises method …set prob[i] = 1/n for all pagesfor t = 1 to about 80 set newprob[i] = 0 for all pages for all links from page i to page j set newprob[j] += prob[i]/deg[i] for all pages I set prob[i] = alpha*newprob[i] + (1-alpha)/n
- 23. That algorithm underlyingGoogle’s analysis of the web isfrom 1929!
- 24. Leo Katz
- 25. That’s not qu right W ite ikipedi a!Leo Katz
- 26. A new status index (1953)"Leo KatzA paper about how information spreads in groups … “For example, the information that the new high-school principal is unmarried and handsome mightoccasion a violent reaction in a ladies garden cluband hardly a ripple of interest in a luncheon group ofthe local chamber of commerce. On the other hand,the luncheon group might be anything but apatheticin its response to information concerning a fractionalchange in credit buying restrictions announced by thefederal government.”
- 27. … there were many other shoulders too …
- 28. Gene Golub Popularized numerical computing with matrices via the informal “Golub thesis” “anything worth computing can be stated as a matrix problem” William Kahan Formalized IEEE-754 ﬂoating point arithmetic. Make it possible to compute with probabilities as “real numbers” instead of discrete counts.
- 29. CreditsMost pictures taken from Google image search.Original idea from Massimo Franceschet.“PageRank: Standing on the shoulders of giants”

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