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# Page rank algorithm

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Page Rank, PR algorithm, page rank algorithm

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### Page rank algorithm

1. 1. Jung Hoon Kim N5, Room 2239 E-mail: junghoon.kim@kaist.ac.kr 2014.01.14 KAIST Knowledge Service Engineering Data Mining Lab. 1
2. 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 KAIST Knowledge Service Engineering Data Mining Lab. 2
3. 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 KAIST Knowledge Service Engineering Data Mining Lab. 3
4. 4. principle  hyperlink trick  many incident node means more important KAIST Knowledge Service Engineering Data Mining Lab. 4
5. 5. Authority  more authority people say .. is more important  John is computer scientist  Alice is cooker KAIST Knowledge Service Engineering Data Mining Lab. 5
6. 6. Big picture  big picture  famous person is means having many incident edges KAIST Knowledge Service Engineering Data Mining Lab. 6
7. 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 KAIST Knowledge Service Engineering Data Mining Lab. 7
8. 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 KAIST Knowledge Service Engineering Data Mining Lab. 8
9. 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 KAIST Knowledge Service Engineering Data Mining Lab. 9
10. 10.  Example KAIST Knowledge Service Engineering Data Mining Lab. 10
11. 11. Solve cycle problem  Solve cycle problem KAIST Knowledge Service Engineering Data Mining Lab. 11
12. 12. Formula  a 1 i b 3 c 2 KAIST Knowledge Service Engineering Data Mining Lab. 12
13. 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 KAIST Knowledge Service Engineering Data Mining Lab. 13
14. 14. Example KAIST Knowledge Service Engineering Data Mining Lab. 14
15. 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 KAIST Knowledge Service Engineering Data Mining Lab. 15
16. 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 KAIST Knowledge Service Engineering Data Mining Lab. 16
17. 17. Modified version KAIST Knowledge Service Engineering Data Mining Lab. 17
18. 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 KAIST Knowledge Service Engineering Data Mining Lab. 18
19. 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 KAIST Knowledge Service Engineering Data Mining Lab. 19
20. 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. KAIST Knowledge Service Engineering Data Mining Lab. 20
21. 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 KAIST Knowledge Service Engineering Data Mining Lab. 21
22. 22. Thank you KAIST Knowledge Service Engineering Data Mining Lab. 22