Page Rank, PR algorithm, page rank algorithm

1. Jung Hoon Kim
N5, Room 2239
E-mail: junghoon.kim@kaist.ac.kr
2014.01.14
KAIST Knowledge Service Engineering
Data Mining Lab.
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2. Introduction
 First introduced by Sergey Brin & Larry Page in 1998
 Original ranking algorithm didn’t suitable for web in 1996
 # of Web pages grew rapidly

in 1996, query “classification technique” => 10 million relevant
page searched!
 content similarity method are easily spammed

vulnerable for spam page
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3. Basic
 page rank algorithm has two principle
 A hyperlink from a page pointing to another page is an
implicit conveyance of authority to the target page.
thus, the more in-links that a page i receives, the more
prestige the page i has
 Pages that point to page i also have their own prestige
score. A page with higher prestige score pointing to i is
more important than a page with a lower prestige score
pointing to i
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4. principle
 hyperlink trick
 many incident node means more important
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5. Authority
 more authority people say .. is more important
 John is computer scientist
 Alice is cooker
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6. Big picture
 big picture
 famous person is means having many incident edges
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7. Cyclic problem
 In web, there are many cycles like this
 this matrix has cycle A->B->E
 it means the score is increased by infinitely
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8. Random suffer trick
 To avoid many problem and many reason
 they adapted random surfer




each node can ability to move any node
it can solve cycle problem
high incident node can have high rank
sometimes it called as damping factor(d)
 by google initial model, d = 0.15
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9. Test
 1000 times test result
 nearly correct ;
 D, A has high rank

A has only one incident link
 To easily identify rank, to
express percentage is good
methods
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10.  Example
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11. Solve cycle problem
 Solve cycle problem
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12. Formula

a
1
i
b
3
c
2
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13. Formula
 in mathematically, we have a system of n linear
equations.
 P=(P1, P2, P3 , … Pn)
 A is adjacent matrix, so we can make this formula
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14. Example
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15. Linear Algebra
 formula
 P is an eigenvector with the corresponding eigenvalue of 1.
 1 is the largest eigenvalue and the PageRank vector P is the
principle eigenvector

to calculate P, we can use power iteration algorithm
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16. Condition
 but the conditions are that A is a stochastic matrix and
that it is irreducible and aperiodic
 We can see the graph model as markov model
 each web page is node and hyperlink is transition
 A is not a stochastic matrix, because there are zero
row(5). zero row means no out-link.
 So we fix the problem by adding a complete set of outgoing
links from each such page i to all the pages on the Web
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17. Modified version
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18. irreducible
 if there is no path from u to v, A is not irreducible because
of some pair of nodes u and v.
 if there are path u to v, A is irreducible!
 A state i is periodic with period k > 1 if k is the smallest
number such that all paths leading from state i back to
state i have a length that is a multiple of k. If a state is not
periodic, A markov chain is aperiodic if all states are
aperiodic
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19. Page Rank
 It is easy to deal with the above two problems with a
single strategy
 We add a link from each page to every page and give each
link a small transition probability controlled by a parameter
d
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20. Page Rank
 The computation of pagerank values of the Web pages can
be done using the power iteration method, which produces
the principal eigenvector with an eigenvalue of 1
 The iteration ends when the PageRank values do not
change much or converge.
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21. Real Page rank
 To deal with web spam is most important thing
 give equal random surfer constants and calculate all the
page needs to many times to calculate it
 Currently, Google use more 200 factors to calculate
ranking in web
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22. Thank you
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