1. The PageRank Citation Ranking: Bringing Order to the Web
Dr. Yingwu Zhu

2. Overview Motivation Related work Page Rank & Random Surfer Model
Implementation
Conclusion

3. Motivation Web: heterogeneous and unstructured
Free of quality control on the web
Commercial interest to manipulate ranking

4. Related Work Academic citation analysis Link-based analysis
Clustering methods of link structure
Hubs & Authorities Model

5. Backlink Link Structure of the Web
Approximation of importance / quality

6. PageRank Pages with lots of backlinks are important
Backlinks coming from important pages convey more importance to a page

7. PageRank

8. Two Problems! Rank sink Dangling Links Introduce escape terms
Dangling links are simply links that point to any page with no outgoing links
They do not affect the rank of any other pages directly
Ignore first and add back later

9. Rank Sink Page cycles pointed by some incoming link
Problem: this loop will accumulate rank but never distribute any rank outside

10. Escape Term Solution: Rank Source c is maximized and = 1
E(u) is some vector over the web pages
– uniform, favorite page etc.

11. Matrix Notation
R is the dominant eigenvector and c is the dominant eigenvalue of because c is maximized

12. Computing PageRank - initialize vector over web pages loop:
- new ranks sum of normalized backlink ranks
- compute normalizing factor
- add escape term
- control parameter
while stop when converged

13. Random Surfer Model
PageRank corresponds to the probability distribution of a random walk on the web graphs
E(u) can be re-phrased as the random surfer gets bored periodically and jumps to a different page and not kept in a loop forever

14. Implementation Computing resources Memory and disk storage
— 24 million pages
— 75 million URLs
Memory and disk storage
Weight Vector
(4 byte float)
Matrix A
(linear access)

15. Implementation (Con't)
Dealing with dangling links
Unique integer ID for each URL
Sort and Remove dangling links
Rank initial assignment
Iteration until convergence
Add back dangling links and Re-compute

16. Convergence Properties (con't)
PageRank computation is O(log(|V|)) due to rapidly mixing graph G of the web.

17. Personalized PageRank
Rank Source E can be initialized :
– uniformly over all pages: e.g. copyright
warnings, disclaimers, mailing lists archives
 result in overly high ranking
– total weight on a single page, e.g. Netscape, McCarthy
 great variation of ranks under different single pages as rank source
– and everything in-between, e.g. server root pages
 allow manipulation by commercial interests

18. Issues Users are no random walkers Starting point distribution
– Content based methods
Starting point distribution
– Actual usage data as starting vector
Reinforcing effects/bias towards main pages
How about traffic to ranking pages?
No query specific rank
Linkage spam
– PageRank favors pages that managed to get other pages to link to
them
– Linkage not necessarily a sign of relevancy, only of promotion
(advertisement…)

19. Conclusion
PageRank is a global ranking based on the web's graph structure
PageRank use backlinks information to bring order to the web
PageRank can separate out representative pages as cluster center
A great variety of applications