1. What is page importance? Page importance is hard to define unilaterally such that it satisfies everyone. There are however some desiderata: –It should be sensitive to The query –Or at least the topic of the query.. The user –Or at least the user population The link structure of the web The amount of accesses the page gets –It should be stable w.r.t. small random changes in the network link structure –It shouldn’t be easy to subvert with intentional changes to link structure How about: “Eloquence” of the page “informativeness” of the page

2. Desiderata for link-based ranking A page that is referenced by lot of important pages (has more back links) is more important (Authority) –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 (Hub) “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 Qn: Can we assign consistent authority/hub values to pages?

3. Authorities and Hubs as mutually reinforcing properties Authorities and hubs related to the same query tend to form a bipartite subgraph of the web graph. Suppose each page has an authority score a(p) and a hub score h(p) hubsauthorities

4. Authority and Hub Pages I: Authority Computation: for each page p: a(p) =  h(q) q: (q, p)  E O: Hub Computation: for each page p: h(p) =  a(q) q: (p, q)  E q1q1 q2q2 q3q3 p q3q3 q2q2 q1q1 p A set of simultaneous equations… Can we solve these?

5. 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 Normalize after every multiplication

6. 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

7. 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

8. What happens if you multiply a vector by a matrix? In general, when you multiply a vector by a matrix, the vector gets “scaled” as well as “rotated” –..except when the vector happens to be in the direction of one of the eigen vectors of the matrix –.. in which case it only gets scaled (stretched) A (symmetric square) matrix has all real eigen values, and the values give an indication of the amount of stretching that is done for vectors in that direction The eigen vectors of the matrix define a new ortho-normal space –You can model the multiplication of a general vector by the matrix in terms of First decompose the general vector into its projections in the eigen vector directions –..which means just take the dot product of the vector with the (unit) eigen vector Then multiply the projections by the corresponding eigen values—to get the new vector. –This explains why power method converges to principal eigen vector....since if a vector has a non-zero projection in the principal eigen vector direction, then repeated multiplication will keep stretching the vector in that direction, so that eventually all other directions vanish by comparison.. Optional

9. (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”

10. Can we power iterate to get other (secondary) eigen vectors? Yes—just find a matrix M 2 such that M 2 has the same eigen vectors as M, but the eigen value corresponding to the first eigen vector e 1 is zeroed out.. Now do power iteration on M 2 Alternately start with a random vector v, and find a new vector v’ = v – (v.e 1 )e 1 and do power iteration on M with v’ Why? 1. M 2 e 1 = 0 2. If e 2 is the second eigen vector of M, then it is also an eigen vector of M 2

11. Authority and Hub Pages 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 & hub scores;

13. Base set computation 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

14. 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.

15. 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).

16. 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.

17. 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.

18. 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

20. 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.

21. 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.

22. 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.

23. 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 

24. 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)

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

26. 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  Can be fixed by putting a weak link between any two pages.. (saying in essence that you expect every page to be reached from every other page)

27. Finding minority Communities 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.

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

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

30. PageRank

31. The importance of publishing.. A/H algorithm was published in SODA as well as JACM –Kleinberg became very famous in the scientific community (and got a McArthur Genius award) Pagerank algorithm was rejected from SIGIR and was never explicitly published –Larry Page never got a genius award or even a PhD `(and had to be content with being a mere billionaire)

32. PageRank (Importance 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!

33. Markov Chains & Random Surfer Model Markov Chains & Stationary distribution –Necessary conditions for existence of unique steady state distribution: Aperiodicity and Irreducibility –Irreducibility: Each node can be reached from every other node with non-zero probability Must not have sink nodes (which have no out links) »Because we can have several different steady state distributions based on which sink we get stuck in –If there are sink nodes, change them so that you can transition from them to every other node with low probability Must not have disconnected components »Because we can have several different steady state distributions depending on which disconnected component we get stuck in –Sufficient to put a low probability link from every node to every other node (in addition to the normal weight links corresponding to actual hyperlinks) The parameters of random surfer model –c the probability that surfer follows the page The larger it is, the more the surfer sticks to what the page says –M the way link matrix is converted to markov chain Can make the links have differing transition probability –E.g. query specific links have higher prob. Links in bold have higher prop etc –K the reset distribution of the surfer  great thing to tweak It is quite feasible to have m different reset distributions corresponding to m different populations of users (or m possible topic-oriented searches) It is also possible to make the reset distribution depend on other things such as –trust of the page [TrustRank] –Recency of the page [Recency- sensitive rank]

34. 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=

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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.

41. 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

42. 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

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

44. 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?

45. We can pick and choose Two alternate ways of computing page importance –I1. As authorities/hubs –I2. As stationary distribution over the underlying markov chain Two alternate ways of combining importance with similarity –C1. Compute importance over a set derived from the top-100 similar pages –C2. Combine apples & organges a*importance + b*similarity We can pick any pair of alternatives (even though I1 was originally proposed with C1 and I2 with C2)

46. Efficient computation: Prioritized Sweeping We can use asynchronous iterations where the iteration uses some of the values updated in the current iteration

47. Efficient Computation: Preprocess Remove ‘dangling’ nodes –Pages w/ no children Then repeat process –Since now more danglers Stanford WebBase –25 M pages –81 M URLs in the link graph –After two prune iterations: 19 M nodes

48. Representing ‘Links’ Table Stored on disk in binary format Size for Stanford WebBase: 1.01 GB –Assumed to exceed main memory 0 1 2 4 3 5 12, 26, 58, 94 5, 56, 69 1, 9, 10, 36, 78 Source node (32 bit int) Outdegree (16 bit int) Destination nodes (32 bit int)

49. Algorithm 1 =  DestLinks (sparse)Source source node dest node  s Source[s] = 1/N while residual >  {  d Dest[d] = 0 while not Links.eof() { Links.read(source, n, dest 1, … dest n ) for j = 1… n Dest[dest j ] = Dest[dest j ]+Source[source]/n }  d Dest[d] = c * Dest[d] + (1-c)/N /* dampening */ residual =  Source – Dest  /* recompute every few iterations */ Source = Dest }

50. Analysis of Algorithm 1 If memory is big enough to hold Source & Dest –IO cost per iteration is | Links| –Fine for a crawl of 24 M pages –But web ~ 800 M pages in 2/99 [NEC study] –Increase from 320 M pages in 1997 [same authors] If memory is big enough to hold just Dest –Sort Links on source field –Read Source sequentially during rank propagation step –Write Dest to disk to serve as Source for next iteration –IO cost per iteration is | Source| + | Dest| + | Links| If memory can’t hold Dest –Random access pattern will make working set = | Dest| –Thrash!!!

51. Block-Based Algorithm Partition Dest into B blocks of D pages each –If memory = P physical pages –D < P-2 since need input buffers for Source & Links Partition Links into B files –Links i only has some of the dest nodes for each source –Links i only has dest nodes such that DD*i <= dest < DD*(i+1) Where DD = number of 32 bit integers that fit in D pages =  Dest Links (sparse)Source source node dest node

52. 3 Partitioned Link File 0 1 2 4 3 5 12, 26 5 1, 9, 10 Source node (32 bit int) Outdegr (16 bit) Destination nodes (32 bit int) 2 1 Num out (16 bit) 1 0 1 2 4 3 5 58 56 36 1 1 1 0 1 2 4 3 5 94 69 78 1 1 Buckets 0-31 Buckets 32-63 Buckets 64-95

53. Block-based Page Rank algorithm

54. Analysis of Block Algorithm IO Cost per iteration = –B*| Source| + | Dest| + | Links|*(1+e) –e is factor by which Links increased in size Typically 0.1-0.3 Depends on number of blocks Algorithm ~ nested-loops join

55. Comparing the Algorithms

56. 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..

59. Use of Link Information 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

60. 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

61. 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. )

63. 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..

64. 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).

66. 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

67. 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…)

68. 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..

69. Summary of Key Points PageRank Iterative Algorithm Rank Sinks Efficiency of computation – Memory! –Single precision Numbers. –Don’t represent M* explicitly. –Break arrays into Blocks. –Minimize IO Cost. Number of iterations of PageRank. Weighting of PageRank vs. doc similarity.

70. Beyond Google (and Pagerank) Are backlinks reliable metric of importance? –It is a “one-size-fits-all” measure of importance… Not user specific Not topic specific –There may be discrepancy between back links and actual popularity (as measured in hits) »The “sense” of the link is ignored (this is okay if you think that all publicity is good publicity) Mark Twain on Classics –“A classic is something everyone wishes they had already read and no one actually had..” (paraphrase) Google may be its own undoing…(why would I need back links when I know I can get to it through Google?) Customization, customization, customization… –Yahoo sez about their magic bullet.. (NYT 2/22/04) –"If you type in flowers, do you want to buy flowers, plant flowers or see pictures of flowers?"

71. Challenges in Web Search Engines Spam –Text Spam –Link Spam –Cloaking Content Quality –Anchor text quality Quality Evaluation –Indirect feedback Web Conventions –Articulate and develop validation Duplicate Hosts –Mirror detection Vaguely Structured Data –Page layout –The advantage of making rendering/content language be same

72. Spam is a serious problem… We have Spam Spam Spam Spam Spam with Eggs and Spam –in Email Most mail transmitted is junk –web pages Many different ways of fooling search engines This is an open arms race –Annual conference on Email and Anti-Spam Started 2004 –Intl. workshop on AIR-Web (Adversarial Info Retrieval on Web) Started in 2005 at WWW

73. Trust & Spam (Knock-Knock. Who is there?) A powerful way we avoid spam in our physical world is by preferring interactions only with “trusted” parties –Trust is propagated over social networks When knocking on the doors of strangers, the first thing we do is to identify ourselves as a friend of a friend of friend … –So they won’t train their dogs/guns on us.. Knock-knock. Who is there? Aardwark. Okay (door opened)  not funny –Aardwark who? Aardwark a million miles for one of your smiles.  FUNNY We can do it in cyber world too Accept product recommendations only from trusted parties –E.g. Epinions Accept mails only from individuals who you trust above a certain threshold Bias page importance computation so that it counts only links from “trusted” sites.. –Sort of like discounting links that are “off topic”

74. Trust Propagation Trust is “transitive” so easy to propagate –..but attenuates as it traverses as a social network If I trust you, I trust your friend (but a little less than I do you), and I trust your friend’s friend even less Trust may not be symmetric.. Trust is normally additive –If you are friend of two of my friends, may be I trust you more.. Distrust is difficult to propagate –If my friend distrusts you, then I probably distrust you –…but if my enemy distrusts you? …is the enemy of my enemy automatically my friend? Trust vs. Reputation –“Trust” is a user-specific metric Your trust in an individual may be different from someone else’s –“Reputation” can be thought of as an “aggregate” or one-size-fits-all version of Trust Most systems such as EBay tend to use Reputation rather than Trust –Sort of the difference between User-specific vs. Global page rank

75. Case Study: Epinions Users can write reviews and also express trust/distrust on other users –Reviewers get royalties –…so some tried to game the system –So, distrust measures introduced Out degree Num nodes [Guha et. Al. WWW 2004] compares some 81 different ways of propagating trust and distrust on the Epinion trust matrix

76. Evaluating Trust Propagation Approaches Given n users, and a sparsely populated nxn matrix of trusts between the users –And optionally an nxn matrix of distrusts between the users –Start by “erasing” some of the entries (but remember the values you erased) –For each trust propagation method Use it to fill the nxn matrix Compare the predicted values to the erased values

77. Fighting Page Spam We saw discussion of these in the Henzinger et. Al. paper Can social networks, which gave rise to the ideas of page importance computation, also rescue these computations from spam?

78. TrustRank idea  Tweak the “default” distribution used in page rank computation (the distribution that a bored user uses when she doesn’t want to follow the links) From uniform To “Trust based”  Very similar in spirit to the Topic-sensitive or User- sensitive page rank Where too you fiddle with the default distribution  Sample a set of “seed pages” from the web  Have an oracle (human) identify the good pages and the spam pages in the seed set Expensive task, so must make seed set as small as possible  Propagate Trust (one pass)  Use the normalized trust to set the initial distribution Slides modified from Anand Rajaraman’s lecture at Stanford [Gyongyi et al, VLDB 2004]

79. Example 1 4 7 2 5 3 6 good bad

80. Rules for trust propagation  Trust attenuation The degree of trust conferred by a trusted page decreases with distance  Trust splitting The larger the number of outlinks from a page, the less scrutiny the page author gives each outlink Trust is “split” across outlinks  Combining splitting and damping, each out link of a node p gets a propagated trust of: t(p)/|O(p)| O(p) is the out degree and t(p) is the trust of p  Trust additivity Propagated trust from different directions is added up

81. Simple model  Suppose trust of page p is t(p) Set of outlinks O(p)  For each q 2 O(p), p confers the trust t(p)/|O(p)| for 0<<1  Trust is additive Trust of p is the sum of the trust conferred on p by all its inlinked pages  Note similarity to Topic-Specific Page Rank Within a scaling factor, trust rank = biased page rank with trusted pages as teleport set

82. Picking the seed set  Two conflicting considerations Human has to inspect each seed page, so seed set must be as small as possible Must ensure every “good page” gets adequate trust rank, so need make all good pages reachable from seed set by short paths

83. Approaches to picking seed set  Suppose we want to pick a seed set of k pages  The best idea would be to pick them from the top-k hub pages. Note that “trustworthiness” is subjective  Aljazeera may be considered more trustworthy than NY Times by some (and the reverse by others)  PageRank Pick the top k pages by page rank Assume high page rank pages are close to other highly ranked pages We care more about high page rank “good” pages

84. Inverse page rank  Pick the pages with the maximum number of outlinks  Can make it recursive Pick pages that link to pages with many outlinks  Formalize as “inverse page rank” Construct graph G’ by reversing each edge in web graph G Page Rank in G’ is inverse page rank in G  Pick top k pages by inverse page rank

85. Anatomy of Google (circa 1999) Slides from http://www.cs.huji.ac.il/~sdbi/2000/google/index.htm

86. Some points… Fancy hits? Why two types of barrels? How is indexing parallelized? How does Google show that it doesn’t quite care about recall? How does Google avoid crawling the same URL multiple times? What are some of the memory saving things they do? Do they use TF/IDF? Do they normalize? (why not?) Can they support proximity queries? How are “page synopses” made?

87. Types of Web Queries Navigational –User is looking for the address of a specific page (so the “relevant” set is a singleton!) Success on these is responsible for much of the “OOooo” appeal of search engines.. Informational –User is trying to learn information about a specific topic (so the relevant set can be non-singleton) Transactional –The user is searching with the final aim of conducting a transaction on that page.. E.g. comparison shopping

88. Information from searchenginewatch.com Number of indexed pages, self-reported Google: 50% of the web? Search Engine Size over Time The “google” paper Discusses google’s Architecture circa 99

89. System Anatomy High Level Overview

90. Google Search Engine Architecture SOURCE: BRIN & PAGE URL Server- Provides URLs to be fetched Crawler is distributed Store Server - compresses and stores pages for indexing Repository - holds pages for indexing (full HTML of every page) Indexer - parses documents, records words, positions, font size, and capitalization Lexicon - list of unique words found HitList – efficient record of word locs+attribs Barrels hold (docID, (wordID, hitList*)*)* sorted: each barrel has range of words Anchors - keep information about links found in web pages URL Resolver - converts relative URLs to absolute Sorter - generates Doc Index Doc Index - inverted index of all words in all documents (except stop words) Links - stores info about links to each page (used for Pagerank) Pagerank - computes a rank for each page retrieved Searcher - answers queries

91. Major Data Structures Big Files –virtual files spanning multiple file systems –addressable by 64 bit integers –handles allocation & deallocation of File Descriptions since the OS’s is not enough –supports rudimentary compression

92. Major Data Structures (2) Repository –tradeoff between speed & compression ratio –choose zlib (3 to 1) over bzip (4 to 1) –requires no other data structure to access it

93. Major Data Structures (3) Document Index –keeps information about each document –fixed width ISAM (index sequential access mode) index –includes various statistics pointer to repository, if crawled, pointer to info lists –compact data structure –we can fetch a record in 1 disk seek during search

94. Major Data Structures (4) URL’s - docID file –used to convert URLs to docIDs –list of URL checksums with their docIDs –sorted by checksums –given a URL a binary search is performed –conversion is done in batch mode

95. Major Data Structures (4) Lexicon –can fit in memory for reasonable price currently 256 MB contains 14 million words 2 parts –a list of words –a hash table

96. Major Data Structures (4) Hit Lists –includes position font & capitalization –account for most of the space used in the indexes –3 alternatives: simple, Huffman, hand- optimized –hand encoding uses 2 bytes for every hit

97. Major Data Structures (4) Hit Lists (2)

98. Major Data Structures (5) Forward Index –partially ordered –used 64 Barrels –each Barrel holds a range of wordIDs –requires slightly more storage –each wordID is stored as a relative difference from the minimum wordID of the Barrel –saves considerable time in the sorting

99. Major Data Structures (6) Inverted Index –64 Barrels (same as the Forward Index) –for each wordID the Lexicon contains a pointer to the Barrel that wordID falls into –the pointer points to a doclist with their hit list – the order of the docIDs is important by docID or doc word-ranking –Two inverted barrels—the short barrel/full barrel

100. Major Data Structures (7) Crawling the Web –fast distributed crawling system –URLserver & Crawlers are implemented in phyton –each Crawler keeps about 300 connection open –at peek time the rate - 100 pages, 600K per second –uses:internal cached DNS lookup –synchronized IO to handle events –number of queues –Robust & Carefully tested

101. Major Data Structures (8) Indexing the Web –Parsing should know to handle errors –HTML typos –kb of zeros in a middle of a TAG –non-ASCII characters –HTML Tags nested hundreds deep Developed their own Parser –involved a fair amount of work –did not cause a bottleneck

102. Major Data Structures (9) Indexing Documents into Barrels –turning words into wordIDs –in-memory hash table - the Lexicon –new additions are logged to a file –parallelization shared lexicon of 14 million pages log of all the extra words

103. Major Data Structures (10) Indexing the Web –Sorting creating the inverted index produces two types of barrels –for titles and anchor (Short barrels) –for full text (full barrels) sorts every barrel separately running sorters at parallel the sorting is done in main memory Ranking looks at Short barrels first And then full barrels

104. Searching Algorithm –1. Parse the query –2. Convert word into wordIDs –3. Seek to the start of the doclist in the short barrel for every word –4. Scan through the doclists until there is a document that matches all of the search terms –5. Compute the rank of that document –6. If we’re at the end of the short barrels start at the doclists of the full barrel, unless we have enough –7. If were not at the end of any doclist goto step 4 –8. Sort the documents by rank return the top K (May jump here after 40k pages)

105. The Ranking System The information –Position, Font Size, Capitalization –Anchor Text –PageRank Hits Types –title,anchor, URL etc.. –small font, large font etc..

106. The Ranking System (2) Each Hit type has it’s own weight –Counts weights increase linearly with counts at first but quickly taper off this is the IR score of the doc –(IDF weighting??) the IR is combined with PageRank to give the final Rank For multi-word query –A proximity score for every set of hits with a proximity type weight 10 grades of proximity

107. Feedback A trusted user may optionally evaluate the results The feedback is saved When modifying the ranking function we can see the impact of this change on all previous searches that were ranked

108. Results Produce better results than major commercial search engines for most searches Example: query “bill clinton” –return results from the “Whitehouse.gov” –email addresses of the president –all the results are high quality pages –no broken links –no bill without clinton & no clinton without bill

109. Storage Requirements Using Compression on the repository about 55 GB for all the data used by the SE most of the queries can be answered by just the short inverted index with better compression, a high quality SE can fit onto a 7GB drive of a new PC

110. Storage Statistics Web Page Statistics

111. System Performance It took 9 days to download 26million pages 48.5 pages per second The Indexer & Crawler ran simultaneously The Indexer runs at 54 pages per second The sorters run in parallel using 4 machines, the whole process took 24 hours