The document discusses the development of Google's PageRank algorithm, tracing its origins to concepts in mathematical theory and artificial intelligence used by its founders Larry Page and Sergey Brin. It highlights the importance of web page ranking, the Markov chain model used to analyze link structure, and historical contributions from figures like Andrei Markov and Richard von Mises. Additionally, it references the impact of other theorists on the information spread and numerical computing landscape.

1. Numerical computing &
Google’s PageRank
DAVID F. GLEICH, CS 197 PRESENTATION

2. Hey Katie, do you have a
date for Valentine’s Day?
It was
1234567890
in 2009.

3. Thanks Internet!
http://school.discoveryeducation.com/clipart/clip/stk-fgr6.html
http://listsoplenty.com/pix/tag/cartoon
https://www.facebook.com/ProgrammersJokes
http://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.html
T
http://listsoplenty.com/pix/tag/cartoon
https://www.facebook.com/ProgrammersJokes
http://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 of
encyclopedias will appear,
ready made with a mesh of
associative trails running
through them, ready to be
dropped into the memex and
there amplified”
-- “As we may think” The Atlantic, July 1945

9. Sir Tim Berners-Lee
“We should work towards a
universal linked information
system … to allow a place for
any information or reference
one felt was important and a
way 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 primer
1. Crawl webpages
2. Analyze webpage text (information retrieval)
3. Analyze webpage links
4. Fit measures to human evaluations
5. Produce rankings
6. Continuously update

13. SportsIllustrated.com
BobsPortsIllustrated.com

14. 1
2
to
3

15. What pages are
important?
Those that people visit a lot!
How to we check?
Create a model of how people
visit the web.

16. What pages are
important?
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 are
important?
Perron and Frobenius proved the
following algorithm always
converges to a solution…
set prob[i] = 0 for all pages
set p to a random page
for 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 are
important?
Using the von Mises method …
set prob[i] = 1/n for all pages
for 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 underlying
Google’s analysis of the web is
from 1929!

24. Leo Katz

25. That’s
not qu
right W ite
ikipedi
a!
Leo Katz

26. A new status index (1953)"
Leo Katz
A paper about how information spreads in groups …
“For example, the information that the new high-
school principal is unmarried and handsome might
occasion a violent reaction in a ladies' garden club
and hardly a ripple of interest in a luncheon group of
the local chamber of commerce. On the other hand,
the luncheon group might be anything but apathetic
in its response to information concerning a fractional
change in credit buying restrictions announced by the
federal 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. Credits
Most pictures taken from Google image search.
Original idea from Massimo Franceschet.
“PageRank: Standing on the shoulders of giants”