The $25 Billion Eigenvector
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Transcript of The $25 Billion Eigenvector
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.
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
How is yk+1=Axk performed?
J A B
I C
DH
G F E
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]
How is yk+1=Axk performed?
1. yk+1 = .15/n e, (where e is all 1’s)2. start = 13. for j = 1,…, n
a) col_tot = endj-startb) for i = start,…, endj
• ii = connectioni
• yk+1ii = yk+1
ii+.85/col_tot*yki
c) start =endj+1
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.
0 20 40 60 80 100 1200
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09 Pagerank Power Iteration the limit
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'