1. Search Engine Technology Slides are revised version of the ones taken from http://panda.cs.binghamton.edu/~meng/

2. Search Engine Technology Two general paradigms for finding information on Web: Browsing: From a starting point, navigate through hyperlinks to find desired documents. –Yahoo’s category hierarchy facilitates browsing. Searching: Submit a query to a search engine to find desired documents. –Many well-known search engines on the Web: AltaVista, Excite, HotBot, Infoseek, Lycos, Google, Northern Light, etc.

3. Browsing Versus Searching Category hierarchy is built mostly manually and search engine databases can be created automatically. Search engines can index much more documents than a category hierarchy. Browsing is good for finding some desired documents and searching is better for finding a lot of desired documents. Browsing is more accurate (less junk will be encountered) than searching.

4. Search Engine A search engine is essentially a text retrieval system for web pages plus a Web interface. So what’s new???

5. Some Characteristics of the Web Web pages are –very voluminous and diversified –widely distributed on many servers. –extremely dynamic/volatile. Web pages have –more structures (extensively tagged). –are extensively linked. –may often have other associated metadata Web users are –ordinary folks (“dolts”?) without special training they tend to submit short queries. –There is a very large user community. Use the links and tags and Meta-data! Use the social structure of the web Standard content-based IR Methods may not work

6. Overview Discuss how to take the special characteristics of the Web into consideration for building good search engines. Specific Subtopics: The use of tag information The use of link information Robot/Crawling Clustering/Collaborative Filtering

7. Use of TAG information Class of 9/18 Starts

8. Use of Tag Information (1) Web pages are mostly HTML documents (for now). HTML tags allow the author of a web page to –Control the display of page contents on the Web. –Express their emphases on different parts of the page. HTML tags provide additional information about the contents of a web page. Can we make use of the tag information to improve the effectiveness of a search engine?

9. Use of Tag Information (2) Two main ideas of using tags: Associate different importance to term occurrences in different tags. Use anchor text to index referenced documents....... airplane ticket and hotel...... Page 1 Page 2: http://travelocity.com/

10. Use of Tag Information (3) Many search engines are using tags to improve retrieval effectiveness. Associating different importance to term occurrences is used in Altavista, HotBot, Yahoo, Lycos, LASER, SIBRIS. WWWW and Google use terms in anchor tags to index a referenced page. Qn: what should be the exact weights for different kinds of terms?

11. Use of Tag Information (4) The Webor Method (Cutler 97, Cutler 99) Partition HTML tags into six ordered classes: –title, header, list, strong, anchor, plain Extend the term frequency value of a term in a document into a term frequency vector (TFV). Suppose term t appears in the i th class tf i times, i = 1..6. Then TFV = (tf 1, tf 2, tf 3, tf 4, tf 5, tf 6 ). Example: If for page p, term “binghamton” appears 1 time in the title, 2 times in the headers and 8 times in the anchors of hyperlinks pointing to p, then for this term in p: TFV = (1, 2, 0, 0, 8, 0).

12. Use of Tag Information (5) The Webor Method (Continued) Assign different importance values to term occurrences in different classes. Let civ i be the importance value assigned to the ith class. We have CIV = (civ 1, civ 2, civ 3, civ 4, civ 5, civ 6 ) Extend the tf term weighting scheme –tfw = TFV  CIV = tf 1  civ 1 + … + tf 6  civ 6 When CIV = (1, 1, 1, 1, 0, 1), the new tfw becomes the tfw in traditional text retrieval. How to find Optimal CIV?

13. Use of Tag Information (6) The Webor Method (Continued) Challenge: How to find the (optimal) CIV = (civ 1, civ 2, civ 3, civ 4, civ 5, civ 6 ) such that the retrieval performance can be improved the most? One Solution: Find the optimal CIV experimentally using a hill-climbing search in the space of CIV Details Skipped

14. Use of Tag Information (7) The Webor Method (Continued) Creating a test bed: Web pages: A snap shot of the Binghamton University site in Dec. 1996 (about 4,600 pages; after removing duplicates, about 3,000 pages). Queries: 20 queries were created (see next page). For each query, (manually) identify the documents relevant to the query.

15. Use of Tag Information (8) The Webor Method (Continued): 20 test bed queries: web-based retrieval concert and music neural network intramural sports master thesis in geology cognitive science prerequisite of algorithm campus dining handicap student help career development promotion guideline non-matriculated admissions grievance committee student associations laboratory in electrical engineering research centers anthropology chairman engineering program computer workshop papers in philosophy and computer and cognitive system

16. Use of Tag Information (9) The Webor Method (Continued) Use a Genetic Algorithm Use a Genetic Algorithm to find the optimal CIV. The initial population has 30 CIVs. –25 are randomly generated (range [1, 15]) –5 are “good” CIVs from manual screening. Each new generation of CIVs is produced by executing: crossover, mutation, and reproduction.

17. Use of Tag Information (10) The Genetic Algorithm (continued) Crossover –done for each consecutive pair CIVs, with probability 0.75. –a single random cut for each selected pair Example: old pair new pair (1, 4, 2, 1, 2, 1) (2, 3, 2, 1, 2, 1) (2, 3, 1, 2, 5, 1) (1, 4, 1, 2, 5, 1) cut

18. Use of Tag Information (11) The Genetic Algorithm (continued) Mutation –performed on each CIV with probability 0.1. –When mutation is performed, each CIV component is either decreased or increased by one with equal probability, subject to range conditions of each component. Example: If a component is already 15, then it cannot be increased.

19. Use of Tag Information (12) The Genetic Algorithm (continued) The fitness functionThe fitness function –A CIV has an initial fitness of 0 when the 11-point average precision is less than 0.22. (11-point average precision - 0.22), otherwise. –The final fitness is its initial fitness divided by the sum of the initial fitnesses of all the CIVs in the current generation. each fitness is between 0 and 1 the sum of all fitnesses is 1

20. Use of Tag Information (13) The Genetic Algorithm (continued) Reproduction –Wheel of fortune scheme to select the parent population. –The scheme selects fit CIVs with high probability and unfit CIVs with low probability. –The same CIV may be selected more than once. The algorithm terminates after 25 generations and the best CIV obtained is reported as the optimal CIV. The 11-point average precision by the optimal CIV is reported as the performance of the CIV.

21. Use of Tag Information (14) The Webor Method (continued): Experimental Results Classes: title, header, list, strong, anchor, plain Queries Opt. CIV Normal New Improvement 1 st 10 281881 0.182 0.254 39.6% 2 nd 10 271881 0.172 0.255 48.3% all 251881 0.177 0.254 43.5% Conclusions: anchor and strong are most important header is also important title is only slightly more important than list and plain

22. Use of Tag Information (15) The Webor Method (continued): Summary The Webor method has the potential to substantially improve the retrieval effectiveness. But be cautious to draw any definitive conclusions as the results are too preliminary. Need to –Expand the set of queries in the test bed –Use other Web page collections

23. Use of LINK information

24. Use of Link Information (1) Hyperlinks among web pages provide new document retrieval opportunities. Selected Examples: Anchor texts can be used to index a referenced page (e.g., Webor, WWWW, Google). The ranking score (similarity) of a page with a query can be spread to its neighboring pages. Links can be used to compute the importance of web pages based on citation analysis. Links can be combined with a regular query to find authoritative pages on a given topic.

25. Connection to Citation Analysis Mirror mirror on the wall, who is the biggest Computer Scientist of them all? –The guy who wrote the most papers That are considered important by most people –By citing them in their own papers »“Science Citation Index” –Should I write survey papers or original papers? Infometrics; Bibliometrics

26. What Citation Index says About Rao’s papers

27. Desiderata for ranking A page that is referenced by lot of important pages (has more back links) is more important –A page referenced by a single important page may be more important than that referenced by five unimportant pages A page that references a lot of important pages is also important “Importance” can be propagated – Your importance is the weighted sum of the importance conferred on you by the pages that refer to you –The importance you confer on a page may be proportional to how many other pages you refer to (cite) (Also what you say about them when you cite them!) Different Notions of importance

28. Use of Link Information (2) Vector spread activation (Yuwono 97) The final ranking score of a page p is the sum of its regular similarity and a portion of the similarity of each page that points to p. Rationale: If a page is pointed to by many relevant pages, then the page is also likely to be relevant. Let sim(q, d i ) be the regular similarity between q and d i ; rs(q, d i ) be the ranking score of d i with respect to q; link(j, i) = 1 if d j points to d i, = 0 otherwise. rs(q, di) = sim(q, di) +   link(j, i)  sim(q, dj)  = 0.2 is a constant parameter.

29. Authority and Hub Pages (1) The basic idea: A page is a good authoritative page with respect to a given query if it is referenced (i.e., pointed to) by many (good hub) pages that are related to the query. A page is a good hub page with respect to a given query if it points to many good authoritative pages with respect to the query. Good authoritative pages (authorities) and good hub pages (hubs) reinforce each other.

30. Authority and Hub Pages (2) Authorities and hubs related to the same query tend to form a bipartite subgraph of the web graph. A web page can be a good authority and a good hub. hubsauthorities

31. Authority and Hub Pages (3) Main steps of the algorithm for finding good authorities and hubs related to a query q. 1.Submit q to a regular similarity-based search engine. Let S be the set of top n pages returned by the search engine. (S is called the root set and n is often in the low hundreds). 2.Expand S into a large set T (base set): Add pages that are pointed to by any page in S. Add pages that point to any page in S. If a page has too many parent pages, only the first k parent pages will be used for some k.

32. Authority and Hub Pages (4) 3. Find the subgraph SG of the web graph that is induced by T. S T

34. Authority and Hub Pages (5) Steps 2 and 3 can be made easy by storing the link structure of the Web in advance Link structure table (during crawling) --Most search engines serve this information now. (e.g. Google’s link: search) parent_url child_url url1 url2 url1 url3

35. USER(41): aaa ;;an adjacency matrix #2A((0 0 1) (0 0 1) (1 0 0)) USER(42): x ;;an initial vector #2A((1) (2) (3)) USER(43): (apower-iteration aaa x 2) ;;authority computation—two iterations [1] USER(44): (apower-iterate aaa x 3) ;;after three iterations #2A((0.041630544) (0.0) (0.99913305)) [1] USER(45): (apower-iterate aaa x 15) ;;after 15 iterations #2A((1.0172524e-5) (0.0) (1.0)) [1] USER(46): (power-iterate aaa x 5) ;;hub computation 5 iterations #2A((0.70641726) (0.70641726) (0.04415108)) [1] USER(47): (power-iterate aaa x 15) ;;15 iterations #2A((0.7071068) (0.7071068) (4.3158376e-5)) [1] USER(48): Y ;; a new initial vector #2A((89) (25) (2)) [1] USER(49): (power-iterate aaa Y 15) ;;Magic… same answer after 15 iter #2A((0.7071068) (0.7071068) (7.571644e-7)) A B C

36. Authority and Hub Pages (6) 4.Compute the authority score and hub score of each web page in T based on the subgraph SG(V, E). Given a page p, let a(p) be the authority score of p h(p) be the hub score of p (p, q) be a directed edge in E from p to q. Two basic operations: Operation I: Update each a(p) as the sum of all the hub scores of web pages that point to p. Operation O: Update each h(p) as the sum of all the authority scores of web pages pointed to by p.

37. Authority and Hub Pages (7) Operation I: for each page p: a(p) =  h(q) q: (q, p)  E Operation O: for each page p: h(p) =  a(q) q: (p, q)  E q1q1 q2q2 q3q3 p q3q3 q2q2 q1q1 p

38. Authority and Hub Pages (8) Matrix representation of operations I and O. Let A be the adjacency matrix of SG: entry (p, q) is 1 if p has a link to q, else the entry is 0. Let A T be the transpose of A. Let h i be vector of hub scores after i iterations. Let a i be the vector of authority scores after i iterations. Operation I: a i = A T h i-1 Operation O: h i = A a i

39. The class of 9/23

40. Authority and Hub Pages (10) Algorithm (summary) submit q to a search engine to obtain the root set S; expand S into the base set T; obtain the induced subgraph SG(V, E) using T; initialize a(p) = h(p) = 1 for all p in V; for each p in V until the scores converge { apply Operation I; apply Operation O; normalize a(p) and h(p); } return pages with top authority scores;

41. Authority and Hub Pages (9) After each iteration of applying Operations I and O, normalize all authority and hub scores. Repeat until the scores for each page converge (the convergence is guaranteed). 5. Sort pages in descending authority scores. 6. Display the top authority pages.

42. Authority and Hub Pages (11) Example: Initialize all scores to 1. 1 st Iteration: I operation: a(q 1 ) = 1, a(q 2 ) = a(q 3 ) = 0, a(p 1 ) = 3, a(p 2 ) = 2 O operation: h(q 1 ) = 5, h(q 2 ) = 3, h(q 3 ) = 5, h(p 1 ) = 1, h(p 2 ) = 0 Normalization: a(q 1 ) = 0.267, a(q 2 ) = a(q 3 ) = 0, a(p 1 ) = 0.802, a(p 2 ) = 0.535, h(q 1 ) = 0.645, h(q 2 ) = 0.387, h(q 3 ) = 0.645, h(p 1 ) = 0.129, h(p 2 ) = 0 q1q1 q2q2 q3q3 p1p1 p2p2

43. Authority and Hub Pages (12) After 2 Iterations: a(q 1 ) = 0.061, a(q 2 ) = a(q 3 ) = 0, a(p 1 ) = 0.791, a(p 2 ) = 0.609, h(q 1 ) = 0.656, h(q 2 ) = 0.371, h(q 3 ) = 0.656, h(p 1 ) = 0.029, h(p 2 ) = 0 After 5 Iterations: a(q 1 ) = a(q 2 ) = a(q 3 ) = 0, a(p 1 ) = 0.788, a(p 2 ) = 0.615 h(q 1 ) = 0.657, h(q 2 ) = 0.369, h(q 3 ) = 0.657, h(p 1 ) = h(p 2 ) = 0 q1q1 q2q2 q3q3 p1p1 p2p2

44. (why) Does the procedure converge? x x2x2 xkxk As we multiply repeatedly with M, the component of x in the direction of principal eigen vector gets stretched wrt to other directions.. So we converge finally to the direction of principal eigenvector Necessary condition: x must have a component in the direction of principal eigen vector (c 1 must be non-zero) The rate of convergence depends on the “eigen gap”

45. (why) Does the procedure converge? x x2x2 xkxk As we multiply repeatedly with M, the component of x in the direction of principal eigen vector gets stretched wrt to other directions.. So we converge finally to the direction of principal eigenvector Necessary condition: x must have a component in the direction of principal eigen vector

46. Handling “spam” links Should all links be equally treated? Two considerations: Some links may be more meaningful/important than other links. Web site creators may trick the system to make their pages more authoritative by adding dummy pages pointing to their cover pages (spamming).

47. Handling Spam Links (contd) Transverse link: links between pages with different domain names. Domain name: the first level of the URL of a page. Intrinsic link: links between pages with the same domain name. Transverse links are more important than intrinsic links. Two ways to incorporate this: 1.Use only transverse links and discard intrinsic links. 2.Give lower weights to intrinsic links.

48. Handling Spam Links (contd) How to give lower weights to intrinsic links? In adjacency matrix A, entry (p, q) should be assigned as follows: If p has a transverse link to q, the entry is 1. If p has an intrinsic link to q, the entry is c, where 0 < c < 1. If p has no link to q, the entry is 0.

49. Considering link “context” For a given link (p, q), let V(p, q) be the vicinity (e.g.,  50 characters) of the link. If V(p, q) contains terms in the user query (topic), then the link should be more useful for identifying authoritative pages. To incorporate this: In adjacency matrix A, make the weight associated with link (p, q) to be 1+n(p, q), where n(p, q) is the number of terms in V(p, q) that appear in the query. Alternately, consider the “vector similarity” between V(p,q) and the query Q

51. Evaluation Sample experiments: Rank based on large in-degree (or backlinks) query: game Rank in-degree URL 1 13 http://www.gotm.orghttp://www.gotm.org 2 12 http://www.gamezero.com/team-0/http://www.gamezero.com/team-0/ 3 12 http://ngp.ngpc.state.ne.us/gp.htmlhttp://ngp.ngpc.state.ne.us/gp.html 4 12 http://www.ben2.ucla.edu/~permadi/http://www.ben2.ucla.edu/~permadi/ gamelink/gamelink.html 5 11 http://igolfto.net/http://igolfto.net/ 6 11 http://www.eduplace.com/geo/indexhi.html http://www.eduplace.com/geo/indexhi.html Only pages 1, 2 and 4 are authoritative game pages.

52. Evaluation Sample experiments (continued) Rank based on large authority score. query: game Rank Authority URL 1 0.613 http://www.gotm.orghttp://www.gotm.org 2 0.390 http://ad/doubleclick/net/jump/http://ad/doubleclick/net/jump/ gamefan-network.com/ 3 0.342 http://www.d2realm.com/http://www.d2realm.com/ 4 0.324 http://www.counter-strike.net 5 0.324 http://tech-base.com/ 6 0.306 http://www.e3zone.comhttp://www.e3zone.com All pages are authoritative game pages.

53. Authority and Hub Pages (19) Sample experiments (continued) Rank based on large authority score. query: free email Rank Authority URL 1 0.525 http://mail.chek.com/http://mail.chek.com/ 2 0.345 http://www.hotmail/com/http://www.hotmail/com/ 3 0.309 http://www.naplesnews.net/http://www.naplesnews.net 4 0.261 http://www.11mail.com/ 5 0.254 http://www.dwp.net/ 6 0.246 http://www.wptamail.com/http://www.wptamail.com/ All pages are authoritative free email pages.

54. Cora thinks Rao is Authoritative on Planning Citeseer has him down at 90 th position…  How come??? --Planning has two clusters --Planning & reinforcement learning --Deterministic planning --The first is a bigger cluster --Rao is big in the second cluster 

55. Tyranny of Majority 1 2 3 4 6 7 8 5 Which do you think are Authoritative pages? Which are good hubs? -intutively, we would say that 4,8,5 will be authoritative pages and 1,2,3,6,7 will be hub pages. BUT The power iteration will show that Only 4 and 5 have non-zero authorities [.923.382] And only 1, 2 and 3 have non-zero hubs [.5.7.5] The authority and hub mass Will concentrate completely Among the first component, as The iterations increase. (See next slide)

56. Tyranny of Majority (explained) p1 p2 pm p q1 qn q m n Suppose h0 and a0 are all initialized to 1 m>n

57. On Lincoln’s Gettysburg address (1863) The cheek of every american must tingle with shame as he reads the silly, flat dish-watery utterances, of the man who has to be pointed to intelligent foreigners as the President of the United States. -Chicago Times Class of 9/25

58. Agenda/Announcements Homework 1 due Monday in class Qn. Re: project 1 can be referred to –Slakshmi@asu.eduSlakshmi@asu.edu –Courtesy Office hrs: T/Th 1-2pm GWC 387 Online feedback survey in progress –Vote early (but not often) Class today –Pagerank –Comparison between Pagerank & A/H –Start “crawling” Next big topic – The Google paper

59. The cheek of every american must tingle with shame as he reads the silly, flat dish-watery utterances, of the man who has to be pointed to intelligent foreigners as the President of the United States -Chicago Times On Lincoln’s Gettysburg address (1863) Class of 9/25 In the modesty of his nature he said ‘the world will little note, nor long remember what we say here; but it can never forget what they did here.’ He was mistaken. The world at once noted what he said, and will never cease to remember it. The battle itself was less important than the speech. Ideas are always more [important] than battles." - Charles Sumner

60. Tyranny of Majority (explained) p1 p2 pm p q1 qn q m n Suppose h0 and a0 are all initialized to 1 m>n

61. Impact of Bridges.. 1 2 3 4 6 7 8 5 When the graph is disconnected, only 4 and 5 have non-zero authorities [.923.382] And only 1, 2 and 3 have non-zero hubs [.5.7.5]CV 9 When the components are bridged by adding one page (9) the authorities change only 4, 5 and 8 have non-zero authorities [.853.224.47] And o1, 2, 3, 6,7 and 9 will have non-zero hubs [.39.49.39.21.21.6] Bad news from stability point of view

62. Multiple Clusters on “House” Query: House (first community)

63. Authority and Hub Pages (26) Query: House (second community)

64. Authority and Hub Pages (20) For a given query, the induced subgraph may have multiple dense bipartite communities due to: multiple meanings of query terms multiple web communities related to the query ad page obscure web page

65. Authority and Hub Pages (21) Multiple Communities (continued) If a page is not in a community, then it is unlikely to have a high authority score even when it has many backlinks. Example: Suppose initially all hub and authority scores are 1. q’s p q’s p’s G1: G2: 1 st iteration for G1: a(q) = 0, a(p) = 5, h(q) = 5, h(p) = 0 1 st iteration for G2: a(q) = 0, a(p) = 3, h(q) = 9, h(p) = 0

66. Authority and Hub Pages (22) Example (continued): 1 st normalization (suppose normalization factors H 1 for hubs and A 1 for authorities): for pages in G1: a(q) = 0, a(p) = 5/A 1, h(q) = 5/H 1, h(p) = 0 for pages in G2: a(q) = 0, a(p) = 3/A 1, h(q) = 9/H 1, a(p) = 0 After the nth iteration (suppose H n and A n are the normalization factors respectively): for pages in G1: a(p) = 5 n / (H 1 …H n-1 A n ) ---- a for pages in G2: a(p) = 3*9 n-1 /(H 1 …H n-1 A n ) ---- b Note that a/b approaches 0 when n is sufficiently large, that is, a is much much smaller than b.

67. Authority and Hub Pages (23) Multiple Communities (continued) If a page is not in the largest community, then it is unlikely to have a high authority score. –The reason is similar to that regarding pages not in a community. larger community smaller community

68. Authority and Hub Pages (24) Multiple Communities (continued) How to retrieve pages from smaller communities? A method for finding pages in nth largest community: –Identify the next largest community using the existing algorithm. –Destroy this community by removing links associated with pages having large authorities. –Reset all authority and hub values back to 1 and calculate all authority and hub values again. –Repeat the above n  1 times and the next largest community will be the nth largest community.

69. PageRank

70. Use of Link Information (3) PageRank citation ranking (Page 98). Web can be viewed as a huge directed graph G(V, E), where V is the set of web pages (vertices) and E is the set of hyperlinks (directed edges). Each page may have a number of outgoing edges (forward links) and a number of incoming links (backlinks). Each backlink of a page represents a citation to the page. PageRank is a measure of global web page importance based on the backlinks of web pages.

71. PageRank (Authority as Stationary Visit Probability on a Markov Chain) Basic Idea: Think of Web as a big graph. A random surfer keeps randomly clicking on the links. The importance of a page is the probability that the surfer finds herself on that page --Talk of transition matrix instead of adjacency matrix Transition matrix M derived from adjacency matrix A --If there are F(u) forward links from a page u, then the probability that the surfer clicks on any of those is 1/F(u) (Columns sum to 1. Stochastic matrix) [M is the normalized version of A t ] --But even a dumb user may once in a while do something other than follow URLs on the current page.. --Idea: Put a small probability that the user goes off to a page not pointed to by the current page. Principal eigenvector Gives the stationary distribution!

72. Computing PageRank (1) PageRank is based on the following basic ideas: If a page is linked to by many pages, then the page is likely to be important. If a page is linked to by important pages, then the page is likely to be important even though there aren’t too many pages linking to it. The importance of a page is divided evenly and propagated to the pages pointed to by it. 10 5 5

73. Computing PageRank (2) PageRank Definition Let u be a web page, F u be the set of pages u points to, B u be the set of pages that point to u, N u = |F u | be the number pages in F u. The rank (importance) of a page u can be defined by: R(u) =  ( R(v) / N v ) v  B u

74. Computing PageRank (3) PageRank is defined recursively and can be computed iteratively. Initiate all page ranks to be 1/N, N is the number of vertices in the Web graph. In i th iteration, the rank of a page is computed using the ranks of its parent pages in (i-1)th iteration. Repeat until all ranks converge. Let R i (u) be the rank of page u in ith iteration and R 0 (u) be the initial rank of u. R i (u) =  ( R i-1 (v) / N v ) v  B u

75. Computing PageRank Matrix representation Let M be an N  N matrix and m uv be the entry at the u-th row and v-th column. m uv = 1/N v if page v has a link to page u m uv = 0 if there is no link from v to u Let R i be the N  1 rank vector for I-th iteration and R 0 be the initial rank vector. Then R i = M  R i-1

76. Computing PageRank If the ranks converge, i.e., there is a rank vector R such that R = M  R, R is the eigenvector of matrix M with eigenvalue being 1. Convergence is guaranteed only if M is aperiodic (the Web graph is not a big cycle). This is practically guaranteed for Web. M is irreducible (the Web graph is strongly connected). This is usually not true. Principal eigen value for A stochastic matrix is 1

77. Computing PageRank (10) Example: Suppose the Web graph is: M = A B C D 0 0 0 ½ 11 0 0 0 0 1 0 ABCDABCD A B C D 0 0 1 0 0 0 0 1 1 1 0 0 ABCDABCD A B C D A=

78. Class of 9/30 -- Homework 1 due today  -- Homework 2 assigned; due 10/14 -- Project 1 Task 2 (LSI is added) Completion dates for tasks specified help session on Tuesday (check mail) -- Mid-term will be in Mid-october Soon after hw 2 due-date. --Next class: Google paper discussion ** you are expected to read the paper before showing up in the class (hint: class participation credit)

79. Computing PageRank (6) Rank sink: A page or a group of pages is a rank sink if they can receive rank propagation from its parents but cannot propagate rank to other pages. Rank sink causes the loss of total ranks. Example: A B CD (C, D) is a rank sink

80. Computing PageRank (7) A solution to the non-irreducibility and rank sink problem. Conceptually add a link from each page v to every page (include self). If v has no forward links originally, make all entries in the corresponding column in M be 1/N. If v has forward links originally, replace 1/N v in the corresponding column by c  1/N v and then add (1-c)  1/N to all entries, 0 < c < 1. Motivation comes also from random-surfer model

81. Computing PageRank (8) M * = c (M + Z) + (1 – c) x K M* is irreducible. M* is stochastic, the sum of all entries of each column is 1 and there are no negative entries. Therefore, if M is replaced by M* as in R i = M*  R i-1 then the convergence is guaranteed and there will be no loss of the total rank (which is 1). Z will have 1/N For sink pages And 0 otherwise K will have 1/N For all entries

82. Computing PageRank (9) Interpretation of M* based on the random walk model. If page v has no forward links originally, a web surfer at v can jump to any page in the Web with probability 1/N. If page v has forward links originally, a surfer at v can either follow a link to another page with probability c  1/N v, or jumps to any page with probability (1-c)  1/N.

83. Computing PageRank (10) Example: Suppose the Web graph is: M = A B C D 0 0 0 ½ 11 0 0 0 0 1 0 ABCDABCD A B C D

84. Computing PageRank (11) Example (continued): Suppose c = 0.8. All entries in Z are 0 and all entries in K are ¼. M* = 0.8 (M+Z) + 0.2 K = Compute rank by iterating R := M*xR 0.05 0.05 0.05 0.45 0.85 0.85 0.05 0.05 0.05 0.05 0.85 0.05 MATLAB says: R(A)=.338 R(B)=.338 R(C)=.6367 R(D)=.6052

85. pagerank A/H Comparing PR & A/H on the same graph

86. Combining PR & Content similarity Incorporate the ranks of pages into the ranking function of a search engine. The ranking score of a web page can be a weighted sum of its regular similarity with a query and its importance. ranking_score(q, d) = w  sim(q, d) + (1-w)  R(d), if sim(q, d) > 0 = 0, otherwise where 0 < w < 1. –Both sim(q, d) and R(d) need to be normalized to between [0, 1]. Who sets w?

87. Use of Link Information (13) PageRank defines the global importance of web pages but the importance is domain/topic independent. We often need to find important/authoritative pages which are relevant to a given query. –What are important web browser pages? –Which pages are important game pages? Idea: Use a notion of topic-specific page rank –Involves using a non-uniform probability

88. Topic Specific Pagerank For each page compute k different page ranks –K= number of top level hierarchies in the Open Directory Project –When computing PageRank w.r.t. to a topic, say that with  probability we transition to one of the pages of the topic k When a query q is issued, –Compute similarity between q (+ its context) to each of the topics –Take the weighted combination of the topic specific page ranks of q, weighted by the similarity to different topics Haveliwala, WWW 2002

89. Stability of Rank Calculations The left most column Shows the original rank Calculation -the columns on the right are result of rank calculations when 30% of pages are randomly removed (From Ng et. al. )

91. Effect of collusion on PageRank A B C A B C Assuming  0.8 and K=[1/3] Rank(A)=Rank(B)=Rank(C)= 0.5774 Rank(A)=0.37 Rank(B)=0.6672 Rank(C)=0.6461 Moral: By referring to each other, a cluster of pages can artificially boost their rank (although the cluster has to be big enough to make an appreciable difference. Solution: Put a threshold on the number of intra-domain links that will count Counter: Buy two domains, and generate a cluster among those..

92. More stable because random surfer model allows low prob edges to every place.CV Can be done For base set too Can be done For full web too Query relevance vs. query time computation tradeoff Can be made stable with subspace-based A/H values [see Ng. et al.; 2001] See topic-specific Page-rank idea..

93. Novel uses of Link Analysis Link analysis algorithms—HITS, and Pagerank—are not limited to hyperlinks -Citeseer/Cora use them for analyzing citations (the link is through “citation”) -See the irony here—link analysis ideas originated from citation analysis, and are now being applied for citation analysis -Some new work on “keyword search on databases” uses foreign-key links and link analysis to decide which of the tuples matching the keyword query are most important (the link is through foreign keys) -[Sudarshan et. Al. ICDE 2002]Sudarshan et. Al. ICDE 2002 -Keyword search on databases is useful to make structured databases accessible to naïve users who don’t know structured languages (such as SQL).

95. Query complexity Complex queries (966 trials) –Average words 7.03 –Average operators ( +*–" ) 4.34 Typical Alta Vista queries are much simpler [Silverstein, Henzinger, Marais and Moricz] –Average query words 2.35 –Average operators ( +*–" ) 0.41 Forcibly adding a hub or authority node helped in 86% of the queries

96. What about non-principal eigen vectors? Principal eigen vector gives the authorities (and hubs) What do the other ones do? –They may be able to show the clustering in the documents (see page 23 in Kleinberg paper) The clusters are found by looking at the positive and negative ends of the secondary eigen vectors (ppl vector has only +ve end…)