1. The $25 Billion Eigenvector How does Google do Pagerank?

2. The Imaginary Web Surfer: Starts at any page, Randomly goes to a page linked from the current page, Randomly goes to any web page from a dangling page, … except sometimes (e.g. 15% of the time), goes to a purely random page.

3. A tiny web: who should get the highest rank? JA B IC DH G FE

4. The associated stochastic matrix: 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.4400 0.0150 0.0150 0.2983 0.4400 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.2983 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.2983 0.8650 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.4400 0.0150 0.0150 0.8650 0.0150 0.8650 0.0150 0.0150 0.0150 0.0150 0.0150 0.2983 0.0150 0.0150 0.8650 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.8650 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.8650 0.2983 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.2983 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.4400 0.0150 0.0150 0.0150

5. How is y k+1 =Ax k performed? JA B IC DH G FE connection = [2 5 3 4 6 4 5 6 5 1 10 7 8 1 8 9] end = [2 5 6 7 8 9 11 12 13 16]

6. How is y k+1 =Ax k performed? 1.y k+1 =.15/n e, (where e is all 1’s) 2.start = 1 3.for j = 1,…, n a)col_tot = end j -start b)for i = start,…, end j ii = connection i y k+1 ii = y k+1 ii +.85/col_tot*y k i c) start =end j +1

7. Start with equal components

8. One iteration

9. Two iterations

10. Three iterations

11. Four iterations

12. Five iterations

13. Six iterations

14. Seven iterations

15. Eight iterations

16. Nine iterations

17. Ten iterations

18. The Eigenvector

19. The Imaginary Web Surfer: Starts at any page, Randomly goes to a page linked from the current page, Randomly goes to any web page from a dangling page, … except sometimes (e.g. 15% of the time), goes to a purely random page.

20. [U,G] = surfer (‘http://google.com’, 100)

21. Pagerank Power Iteration 1 step

22. Pagerank Power Iteration 2 steps

23. Pagerank Power Iteration 3 steps

24. Pagerank Power Iteration 4 steps

25. Pagerank Power Iteration 5 steps

26. Pagerank Power Iteration the limit

27. And the winners are… 'http://www.loc.gov/standards/iso639-2' 'http://www.sil.org/iso639-3' 'http://www.loc.gov/standards/iso639-5' 'http://purl.org/dc/elements/1.1' 'http://purl.org/dc/terms' 'http://purl.org/dc' 'http://creativecommons.org/licenses/by/3.0' 'http://i.creativecommons.org/l/by/3.0/88x31.png' 'http://www.nlb.gov.sg' 'http://purl.org/dcpapers' 'http://www.nl.go.kr' 'http://purl.org/dcregistry' 'http://www.kc.tsukuba.ac.jp/index_en.html'