# PageRank The PageRank

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```					The PageRank Citation Ranking:
Bringing Order to the Web

L Page, S Brin, R Motwani, T Winograd
Stanford University

January 29, 1998

Presented by Ruoran Zhou
1
Outline
•   Motivation
•   PageRank
•   Applications
•   Conclusion
•   Relate to our project
2
Motivation
• Web:
• Information is large and heterogeneous
• Profit seeking ventures
• Free of quality control
• Search engines face:
• Inexperienced users
• Manipulations
• PageRank
• Better than simple citation count
3
A and B are back

• Intuition
• Pages with lots of backlinks are important
• Backlinks coming from important pages convey
more importance to a page                   4
PageRank I
• Simplified version

•   u, v—web page
•   Bu—the set of pages that point to u
•   Nv—number of links from v
•   c—a factor used for normalization, c<1
5
PageRank I (cont)
• Example

•   c=0.85
•   Initially RA=RB=RC=RD=1
•   After first iteration:
•   RA =RC*0.85=1*0.85=0.85
•   RB=(RA/2)*0.85=0.5*0.85=0.425
•   RC=((RA /2)+ RB + RD)*0.85=(0. 5+1+1)*0.85=2.125
6
PageRank II
• Problem: rank sink

• Intuitive basis:
– Probability of a click
by a random surfer
– Random surfer keeps
clicking on successive links at random
7
PageRank II (cont)
• Rank source E(u)

– Let E(u) be some vector over the Web pages that
corresponds to a source of rank
– E(u) help the surfer jumps out of the sink,
personalization

8
• c=0.85, cE(u)=0.15
• Ranks converge after 48th iteration

http://en.wikipedia.org/wiki/PageRank “PageRank Uncovered”   9
PageRank III
• Scalability

•   PageRank computation terminates in logarithmic time in the size of the
graph.                                                                   10
PageRank IV
• Personalized PageRank
– Rank source E(u)
• Intuition: distribution of web pages a random surfer
periodically jumps to
• uniformly over all pages
• total weight on a single page
• Between the two extremes

– Immune to commercial manipulation

11
Application I
• Estimating Web Traffic
– PageRank vs. Usage, e.g. Porn sites: high
usage, low pagerank

– PageRank vs. Citation Count
• Better at mapping the citation structure of the
web completely
• Avoid the local maxima that citation counts get
stuck in and more efficient
12
Application II
• PageRank Proxy

13
Conclusion
• PageRank is a global ranking based on
the link structure of the web
– Rank Source: escape rank sink;
personalization

• Plenty of applications

14
• Good
–   PageRank: make use of link structures
–   Give intuitions for algorithms
–   All kinds of possible applications

• Shortcoming
– Some points need more explanation
• Computing algorithm of PageRank (section 2.7)
– A little stray away
• Section 5: Introduction of Google               15
Relate to the project
• Our project
– Goal: produce playlists for customers
– Techniques: compression

• Relates
– User navigation: rankings in the playlist
– Collaborative filtering: rank; preprocessing

16
Thank you

17

```
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