Search Engine Technology

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.
• Yahoos 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 whats 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.

Standard content-based IR Methods may not work
Use the links and tags and Meta-data!
Use the social structure of the web
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.

Page 2 http//travelocity.com/
Page 1
. . . . . . airplane ticket and
hotel . . . . . .
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 ith class tfi
  times, i 1..6. Then TFV (tf1, tf2, tf3, tf4,
  tf5, tf6).
• 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 civi be the
  importance value assigned to the ith class. We
  have
• CIV (civ1, civ2, civ3, civ4, civ5, civ6)
• Extend the tf term weighting scheme
• tfw TFV ? CIV tf1?civ1 tf6 ?civ6
• 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 (civ1,
  civ2, civ3, civ4, civ5, civ6) 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 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 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
• 1st 10 281881 0.182
  0.254 39.6
• 2nd 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 Raos 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, di) be the regular similarity between
  q and di
• rs(q, di) be the ranking score of di with
  respect to q
• link(j, i) 1 if dj points to di, 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.

hubs
authorities
31
Authority and Hub Pages (3)

• Main steps of the algorithm for finding good
  authorities and hubs related to a query q.
• 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).
• 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.

33
(No Transcript)
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. Googles link search)
• parent_url child_url
• url1 url2
• url1 url3

35
B
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
computationtwo 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((0.70
71068) (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
C
36
Authority and Hub Pages (6)

• 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

q1
q2
p
q3
q1
q2
p
q3
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 AT be the transpose of A.
• Let hi be vector of hub scores after i
  iterations.
• Let ai be the vector of authority scores after i
  iterations.
• Operation I ai AT hi-1
• Operation O hi A ai

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.
• 1st Iteration
• I operation
• a(q1) 1, a(q2) a(q3) 0,
• a(p1) 3, a(p2) 2
• O operation h(q1) 5,
• h(q2) 3, h(q3) 5, h(p1) 1, h(p2) 0
• Normalization a(q1) 0.267, a(q2) a(q3)
  0,
• a(p1) 0.802, a(p2) 0.535, h(q1) 0.645,
  
• h(q2) 0.387, h(q3) 0.645, h(p1) 0.129,
  h(p2) 0

q1
p1
q2
p2
q3
43
Authority and Hub Pages (12)

• After 2 Iterations
• a(q1) 0.061, a(q2) a(q3) 0, a(p1)
  0.791,
• a(p2) 0.609, h(q1) 0.656, h(q2) 0.371,
• h(q3) 0.656, h(p1) 0.029, h(p2) 0
• After 5 Iterations
• a(q1) a(q2) a(q3) 0,
• a(p1) 0.788, a(p2) 0.615
• h(q1) 0.657, h(q2) 0.369,
• h(q3) 0.657, h(p1) h(p2) 0

q1
p1
q2
p2
q3
44
(why) Does the procedure converge?
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 (c1must be non-zero)
The rate of convergence depends on the eigen gap
45
(why) Does the procedure converge?
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
• Use only transverse links and discard intrinsic
  links.
• 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 lt c lt 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
  1n(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

50
(No Transcript)
51
Evaluation

• Sample experiments
• Rank based on large in-degree (or backlinks)
• query game
• Rank in-degree URL
• 1 13 http//www.gotm.org
• 2 12 http//www.gamezero.c
  om/team-0/
• 3 12 http//ngp.ngpc.state
  .ne.us/gp.html
• 4 12 http//www.ben2.ucla.
  edu/permadi/
• 
  gamelink/gamelink.html
• 5 11 http//igolfto.net/
• 6 11 http//www.eduplace.c
  om/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.org
• 2 0.390 http//ad/doubleclick/n
  et/jump/
• 
  gamefan-network.com/
• 3 0.342 http//www.d2realm.com/
  
• 4 0.324 http//www.counter-stri
  ke.net
• 5 0.324 http//tech-base.com/
• 6 0.306 http//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/
• 2 0.345 http//www.hotmail/com/
  
• 3 0.309 http//www.naplesnews.n
  et/
• 4 0.261 http//www.11mail.com/
• 5 0.254 http//www.dwp.net/
• 6 0.246 http//www.wptamail.com
  /
• All pages are authoritative free email pages.

54
Cora thinks Rao is Authoritative on Planning
Citeseer has him down at 90th 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
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.
1
6
8
2
4
7
3
5
The authority and hub mass Will concentrate
completely Among the first component, as The
iterations increase. (See next slide)
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
56
Tyranny of Majority (explained)
Suppose h0 and a0 are all initialized to 1
p1
q1
m
n
q
p2
p
qn
pm
mgtn
57
Class of 9/25

• 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

58
Agenda/Announcements

• Homework 1 due Monday in class
• Qn. Re project 1 can be referred to
• Slakshmi_at_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
Class of 9/25

• 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 Lincolns Gettysburg address (1863)
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)
Suppose h0 and a0 are all initialized to 1
p1
q1
m
n
q
p2
p
qn
pm
mgtn
61
Impact of Bridges..
1
6
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 .5CV
8
2
4
7
3
5
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

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. qs
  p qs ps
• G1
  G2
• 1st iteration for G1 a(q) 0, a(p) 5, h(q)
  5, h(p) 0
• 1st iteration for G2 a(q) 0, a(p) 3, h(q)
  9, h(p) 0

66
Authority and Hub Pages (22)

• Example (continued)
• 1st normalization (suppose normalization
  factors H1 for hubs and A1 for authorities)
• for pages in G1 a(q) 0, a(p) 5/A1, h(q)
  5/H1, h(p) 0
• for pages in G2 a(q) 0, a(p) 3/A1,
  h(q) 9/H1, a(p) 0
• After the nth iteration (suppose Hn and An are
  the normalization factors respectively)
• for pages in G1 a(p) 5n / (H1Hn-1An)
  ---- a
• for pages in G2 a(p) 39n-1
  /(H1Hn-1An) ---- 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 At
• --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 arent too many pages linking to it.
• The importance of a page is divided evenly and
  propagated to the pages pointed to by it.

5
10
5
73
Computing PageRank (2)

• PageRank Definition
• Let u be a web page,
• Fu be the set of pages u points to,
• Bu be the set of pages that point to u,
• Nu Fu be the number pages in Fu.
• The rank (importance) of a page u can be defined
  by
• R(u) ? ( R(v) / Nv )
• v ?Bu

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 ith 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 Ri(u) be the rank of page u in ith iteration
  and R0(u) be the initial rank of u.
• Ri(u) ? ( Ri-1(v) / Nv )
• v ?Bu

75
Computing PageRank

• Matrix representation
• Let M be an N?N matrix and muv be the entry at
  the u-th row and v-th column.
• muv 1/Nv if page v has a link to page
  u
• muv 0 if there is no link from v to u
• Let Ri be the N?1 rank vector for I-th
  iteration
• and R0 be the initial rank vector.
• Then Ri M ? Ri-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

D
C
A
B
A B C D
A B C D

• 0 0 0 ½
• 0 0 0 ½
• 1 0 0
• 0 0 1 0

A B C D
0 0 1 0 0 0 1 0 0 0 0 1 1 1
0 0
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
(C, D) is a rank sink
B
C
D
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/Nv
  in the corresponding column by c?1/Nv and then
  add (1-c) ?1/N to all entries, 0 lt c lt 1.

Motivation comes also from random-surfer model
81
Computing PageRank (8)
Z will have 1/N For sink pages And 0 otherwise
K will have 1/N For all entries

• 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
• Ri M ? Ri-1
• then the convergence is guaranteed and there
  will be no loss of the total rank (which is 1).

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/Nv, or jumps to any page
  with probability (1-c) ?1/N.

83
Computing PageRank (10)

• Example Suppose the Web graph is
• M

D
C
A
B
A B C D

• 0 0 0 ½
• 0 0 0 ½
• 1 0 0
• 0 0 1 0

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 (MZ) 0.2 K
• Compute rank by iterating
• R MxR

0.05 0.05 0.05 0.45 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
Comparing PR A/H on the same graph
pagerank
A/H
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) gt 0
• 0, otherwise
• where 0 lt w lt 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
Haveliwala, WWW 2002

• 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 e probability we transition to one of
  the pages of the topick
• 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

89
Stability of Rank Calculations
(From Ng et. al. )
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
90
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91
Effect of collusion on PageRank
C
C
A
A
B
B
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 made stable with subspace-based A/H values
see Ng. et al. 2001
93
Novel uses of Link Analysis

• Link analysis algorithmsHITS, and Pagerankare
  not limited to hyperlinks
• Citeseer/Cora use them for analyzing citations
  (the link is through citation)
• See the irony herelink 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
• Keyword search on databases is useful to make
  structured databases accessible to naïve users
  who dont know structured languages (such as
  SQL).

94
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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)