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2 1998: enter Link Analysis uses hyperlink structure to focus the relevant set combine traditional IR score with popularity score Page and Brin 1998 Kleinberg

3 Web Information Retrieval IR before the Web = traditional IR IR on the Web = web IR

4 Web Information Retrieval IR before the Web = traditional IR IR on the Web = web IR How is the Web different from other document collections?

5 Web Information Retrieval IR before the Web = traditional IR IR on the Web = web IR How is the Web different from other document collections? It s huge. over 10 billion pages, average page size of 500KB 20 times size of Library of Congress print collection Deep Web X bigger than Surface Web

6 Web Information Retrieval IR before the Web = traditional IR IR on the Web = web IR How is the Web different from other document collections? It s huge. over 10 billion pages, average page size of 500KB 20 times size of Library of Congress print collection Deep Web X bigger than Surface Web It s dynamic. content changes: 40% of pages change in a week, 23% of.com change daily size changes: billions of pages added each year

7 Web Information Retrieval IR before the Web = traditional IR IR on the Web = web IR How is the Web different from other document collections? It s huge. over 10 billion pages, average page size of 500KB 20 times size of Library of Congress print collection Deep Web X bigger than Surface Web It s dynamic. content changes: 40% of pages change in a week, 23% of.com change daily size changes: billions of pages added each year It s self-organized. no standards, review process, formats errors, falsehoods, link rot, and spammers!

8 Web Information Retrieval IR before the Web = traditional IR IR on the Web = web IR How is the Web different from other document collections? It s huge. over 10 billion pages, average page size of 500KB 20 times size of Library of Congress print collection Deep Web X bigger than Surface Web It s dynamic. content changes: 40% of pages change in a week, 23% of.com change daily size changes: billions of pages added each year It s self-organized. no standards, review process, formats errors, falsehoods, link rot, and spammers! A Herculean Task!

9 Web Information Retrieval IR before the Web = traditional IR IR on the Web = web IR How is the Web different from other document collections? It s huge. over 10 billion pages, each about 500KB 20 times size of Library of Congress print collection Deep Web X bigger than Surface Web It s dynamic. content changes: 40% of pages change in a week, 23% of.com change daily size changes: billions of pages added each year It s self-organized. no standards, review process, formats errors, falsehoods, link rot, and spammers! Ah, but it s hyperlinked! Vannevar Bush s 1945 memex

10 Elements of a Web Search Engine WWW Crawler Module Page Repository User Indexing Module Results Queries query-independent Indexes Ranking Module Query Module Special-purpose indexes Content Index Structure Index

11 The Ranking Module (generates popularity scores) Measure the importance of each page

12 The Ranking Module (generates popularity scores) Measure the importance of each page The measure should be Independent of any query Primarily determined by the link structure of the Web Tempered by some content considerations

13 The Ranking Module (generates popularity scores) Measure the importance of each page The measure should be Independent of any query Primarily determined by the link structure of the Web Tempered by some content considerations Compute these measures off-line long before any queries are processed

14 The Ranking Module (generates popularity scores) Measure the importance of each page The measure should be Independent of any query Primarily determined by the link structure of the Web Tempered by some content considerations Compute these measures off-line long before any queries are processed Google s PageRank c technology distinguishes it from all competitors

15 The Ranking Module (generates popularity scores) Measure the importance of each page The measure should be Independent of any query Primarily determined by the link structure of the Web Tempered by some content considerations Compute these measures off-line long before any queries are processed Google s PageRank c technology distinguishes it from all competitors Google s PageRank = Google s $$$$$

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21 Google s PageRank (Lawrence Page & Sergey Brin 1998) The Google Goals Create a PageRank r(p ) that is not query dependent Off-line calculations No query time computation Let the Web vote with in-links But not by simple link counts One link to P from Yahoo! is important Many links to P from me is not Share The Vote Yahoo! casts many votes value of vote from Y ahoo! is diluted If Yahoo! votes for n pages Then P receives only r(y )/n credit from Y

22 Google s PageRank (Lawrence Page & Sergey Brin 1998) The Google Goals Create a PageRank r(p ) that is not query dependent Off-line calculations No query time computation Let the Web vote with in-links But not by simple link counts One link to P from Yahoo! is important Many links to P from me is not Share The Vote Yahoo! casts many votes value of vote from Y ahoo! is diluted If Yahoo! votes for n pages Then P receives only r(y )/n credit from Y

23 Google s PageRank (Lawrence Page & Sergey Brin 1998) The Google Goals Create a PageRank r(p ) that is not query dependent Off-line calculations No query time computation Let the Web vote with in-links But not by simple link counts One link to P from Yahoo! is important Many links to P from me is not Share The Vote Yahoo! casts many votes value of vote from Y ahoo! is diluted If Yahoo! votes for n pages Then P receives only r(y )/n credit from Y

24 Google s PageRank (Lawrence Page & Sergey Brin 1998) The Google Goals Create a PageRank r(p ) that is not query dependent Off-line calculations No query time computation Let the Web vote with in-links But not by simple link counts One link to P from Yahoo! is important Many links to P from me is not Share The Vote Yahoo! casts many votes value of vote from Y ahoo! is diluted If Yahoo! votes for n pages Then P receives only r(y )/n credit from Y

25 The Definition r(p )= r(p ) P P B P PageRank B P = {all pages pointing to P } P = number of out links from P

26 The Definition r(p )= r(p ) P P B P PageRank B P = {all pages pointing to P } P = number of out links from P Successive Refinement Start with r 0 (P i )=1/n for all pages P 1,P 2,...,P n

27 The Definition r(p )= r(p ) P P B P Successive Refinement Start with r 0 (P i )=1/n PageRank B P = {all pages pointing to P } P = number of out links from P for all pages P 1,P 2,...,P n Iteratively refine rankings for each page r 1 (P i )= r 0 (P ) P P B Pi

28 The Definition r(p )= r(p ) P P B P Successive Refinement Start with r 0 (P i )=1/n PageRank B P = {all pages pointing to P } P = number of out links from P for all pages P 1,P 2,...,P n Iteratively refine rankings for each page r 1 (P i )= r 0 (P ) P P B Pi r 2 (P i )= r 1 (P ) P P B Pi

29 The Definition r(p )= r(p ) P P B P Successive Refinement Start with r 0 (P i )=1/n PageRank B P = {all pages pointing to P } P = number of out links from P for all pages P 1,P 2,...,P n Iteratively refine rankings for each page r 1 (P i )= r 0 (P ) P P B Pi r 2 (P i )= r 1 (P ) P P B Pi... r j+1 (P i )= r j (P ) P P B Pi

30 In Matrix Notation After Step k π T k = [r k(p 1 ),r k (P 2 ),...,r k (P n )]

31 In Matrix Notation After Step k π T k = [r k(p 1 ),r k (P 2 ),...,r k (P n )] π T k+1 = πt k H where h ij = { 1/ Pi if i j 0 otherwise

32 In Matrix Notation After Step k π T k = [r k(p 1 ),r k (P 2 ),...,r k (P n )] π T k+1 = πt k H where h ij = { 1/ Pi if i j 0 otherwise PageRank vector = π T = lim k π T k = eigenvector for H Provided that the limit exists

33 Tiny Web 1 2 P 1 P 2 P 3 P 4 P 5 P H = P 1 P 2 P 3 P 4 P 5 P 6 4

34 H = Tiny Web P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P 2 P 3 P 4 P 5 P 6 4

35 H = Tiny Web P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 P 4 P 5 P 6 4

36 H = Tiny Web P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P 4 P 5 P 6 4

37 Tiny Web H = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P /2 1/2 P 5 P 6 4

38 Tiny Web H = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P 6 4

39 Tiny Web H = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P

40 Tiny Web H = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P A random walk on the Web Graph

41 Tiny Web H = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P A random walk on the Web Graph PageRank = π i = amount of time spent at P i

42 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote 2 3 Markov chain 6 5 4

43 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

44 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

45 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

46 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

47 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

48 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

49 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

50 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

51 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote

52 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote 2 page 2 is a dangling node

53 Tiny Web H = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P A random walk on the Web Graph PageRank = π i = amount of time spent at P i Dead end page (nothing to click on) a dangling node

54 Tiny Web H = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P A random walk on the Web Graph PageRank = π i = amount of time spent at P i Dead end page (nothing to click on) a dangling node π T =(0, 1, 0, 0, 0, 0) = e-vector = Page P 2 is a rank sink

55 The Fix Allow Web Surfers To Make Random Jumps

56 Ranking with a Random Surfer Rank each page corresponding to a search term by number and quality of votes cast for that page. Hyperlink as vote 2 surfer teleports

57 The Fix Allow Web Surfers To Make Random Jumps ( 1 Replace zero rows with et n = n, 1 n,..., 1 ) n S = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P 2 1/6 1/6 1/6 1/6 1/6 1/6 P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P

58 The Fix Allow Web Surfers To Make Random Jumps ( 1 Replace zero rows with et n = n, 1 n,..., 1 ) n S = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P 2 1/6 1/6 1/6 1/6 1/6 1/6 P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P S = H + aet 6 is now row stochastic = ρ(s) = 1

59 The Fix Allow Web Surfers To Make Random Jumps ( 1 Replace zero rows with et n = n, 1 n,..., 1 ) n S = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P 2 1/6 1/6 1/6 1/6 1/6 1/6 P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P S = H + aet 6 is now row stochastic = ρ(s) = 1 Perron says π T 0 s.t. π T = π T S with i π i = 1

60 Nasty Problem The Web Is Not Strongly Connected

61 Nasty Problem The Web Is Not Strongly Connected S is reducible S = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P 2 1/6 1/6 1/6 1/6 1/6 1/6 P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P

62 Nasty Problem The Web Is Not Strongly Connected S is reducible S = P 1 P 2 P 3 P 4 P 5 P 6 P 1 0 1/2 1/ P 2 1/6 1/6 1/6 1/6 1/6 1/6 P 3 1/3 1/ /3 0 P /2 1/2 P /2 0 1/2 P Reducible = PageRank vector is not well defined Frobenius says S needs to be irreducible to ensure a unique π T > 0 s.t. π T = π T S with i π i = 1

63 Irreducibility Is Not Enough Could Get Trapped Into A Cycle (P i P j P i )

64 Irreducibility Is Not Enough Could Get Trapped Into A Cycle (P i P j P i ) The powers S k fail to converge

65 Irreducibility Is Not Enough Could Get Trapped Into A Cycle (P i P j P i ) The powers S k fail to converge π T k+1 = πt k S fails to convergence

66 Irreducibility Is Not Enough Could Get Trapped Into A Cycle (P i P j P i ) The powers S k fail to converge π T k+1 = πt k S fails to convergence Convergence Requirement Perron Frobenius requires S to be primitive

67 Irreducibility Is Not Enough Could Get Trapped Into A Cycle (P i P j P i ) The powers S k fail to converge π T k+1 = πt k S fails to convergence Convergence Requirement Perron Frobenius requires S to be primitive No eigenvalues other than λ = 1 on unit circle

68 Irreducibility Is Not Enough Could Get Trapped Into A Cycle (P i P j P i ) The powers S k fail to converge π T k+1 = πt k S fails to convergence Convergence Requirement Perron Frobenius requires S to be primitive No eigenvalues other than λ = 1 on unit circle Frobenius proved S is primitive S k > 0 for some k

69 The Google Fix Allow A Random Jump From Any Page G = αs +(1 α)e > 0, E = ee T /n, 0 <α<1

70 The Google Fix Allow A Random Jump From Any Page G = αs +(1 α)e > 0, E = ee T /n, 0 <α<1 G = αh + uv T > 0 u = αa +(1 α)e, v T = e T /n

71 The Google Fix Allow A Random Jump From Any Page G = αs +(1 α)e > 0, E = ee T /n, 0 <α<1 G = αh + uv T > 0 u = αa +(1 α)e, v T = e T /n PageRank vector π T = left-hand Perron vector of G

72 Ranking with a Random Surfer If a page is important, it gets lots of votes from other important pages, which means the random surfer visits it often. Simply count the number of times, or proportion of time, the surfer spends on each page to create ranking of webpages.

73 Ranking with a Random Surfer If a page is important, it gets lots of votes from other important pages, which means the random surfer visits it often. Simply count the number of times, or proportion of time, the surfer spends on each page to create ranking of webpages. Proportion of Time Page 1 =.04 Page 2 =.05 Page 3 =.04 Page 4 =.38 Page 5 =.20 Page 6 = Ranked List of Pages Page 4 Page 6 Page 5 Page 2 Page 1 Page 3

74 The Google Fix Allow A Random Jump From Any Page G = αs +(1 α)e > 0, E = ee T /n, 0 <α<1 G = αh + uv T > 0 u = αa +(1 α)e, v T = e T /n PageRank vector π T = left-hand Perron vector of G Some Happy Accidents x T G = αx T H + βv T Sparse computations with the original link structure

75 The Google Fix Allow A Random Jump From Any Page G = αs +(1 α)e > 0, E = ee T /n, 0 <α<1 G = αh + uv T > 0 u = αa +(1 α)e, v T = e T /n PageRank vector π T = left-hand Perron vector of G Some Happy Accidents x T G = αx T H + βv T Sparse computations with the original link structure λ 2 (G) =α Convergence rate controllable by Google engineers

76 The Google Fix Allow A Random Jump From Any Page G = αs +(1 α)e > 0, E = ee T /n, 0 <α<1 G = αh + uv T > 0 u = αa +(1 α)e, v T = e T /n PageRank vector π T = left-hand Perron vector of G Some Happy Accidents x T G = αx T H + βv T Sparse computations with the original link structure λ 2 (G) =α Convergence rate controllable by Google engineers v T can be any positive probability vector in G = αh + uv T

77 The Google Fix Allow A Random Jump From Any Page G = αs +(1 α)e > 0, E = ee T /n, 0 <α<1 G = αh + uv T > 0 u = αa +(1 α)e, v T = e T /n PageRank vector π T = left-hand Perron vector of G Some Happy Accidents x T G = αx T H + βv T Sparse computations with the original link structure λ 2 (G) =α Convergence rate controllable by Google engineers v T can be any positive probability vector in G = αh + uv T The choice of v T allows for personalization

78 PageRank Issues Compu'ng PageRank: simula'on, eigensystem, linear system; accuracy power law distribu'on: sensi'vity, spamming link strategies overuse

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