1. Web Information retrieval (Web IR)
Handout #9: Connectivity Ranking
Ali Mohammad Zareh Bidoki
ECE Department, Yazd University
Autumn 2011

2. Outline PageRank HITS Personalized PageRank HostRank Distance Rank
Autumn 2011

3. Ranking : Definition
Ranking is the process which estimates the quality of a set of results retrieved by a search engine
Ranking is the most important part of a search engine
Autumn 2011

4. Ranking Types Content-based Connectivity based (web)
Classical IR
Connectivity based (web)
Query independent
Query dependent
User-behavior based
Autumn 2011

5. Web information retrieval
Queries are short: 2.35 terms in avg.
Huge variety in documents: language, quality, duplication
Huge vocabulary: 100s millions terms
Deliberate misinformation
Spamming!
Its rank is completely under the control of Web page’s author
Autumn 2011

6. Ranking in Web IR
Words
Docs 1 2 w n
Web graph
Query
Ranking is a function of the query terms and of the hyperlink structure
Using content of other pages to rank current pages
It is out of the control of the page’s author
Spamming is hard
Autumn 2011

7. Connectivity-based Ranking
Query independent
PageRank
Query dependent
HITS
Autumn 2011

8. Google’s PageRank Algorithm
Idea: Mine structure of the web graph
Each web page is a node
Each hyperlink is a directed edge
Autumn 2011

9. PageRank
Assumption: A link from page A to page B is a recommendation of page B by the author of A (we say B is successor of A)
Quality of a page is related to its in-degree
Recursion: Quality of a page is related to
its in-degree, and to
the quality of pages linking to it
PageRank A B
Successor
Autumn 2011

10. Definition of PageRank
Consider the following infinite random walk (surf):
Initially the surfer is at a random page
At each step, the surfer proceeds to a randomly chosen successor of the current page (With probability 1/outdegree)
The PageRank of a page p is the fraction of steps the surfer spends at p in the limit.
Random surfer model p s
Surfer
Autumn 2011

11. PageRank (cont.) By previous theorem:
PageRank = stationary probability for this Markov chain, i.e.
Autumn 2011

12. PageRank (cont.) B A P
PageRank of P is
P(A)/4 + P(B)/3
Autumn 2011

13. PageRank (cont.)
Autumn 2011

14. Damping Factor (d) where n is the total number of nodes in the graph
Web graph is not strongly connected
Convergence of PageRank is not guaranteed
Effects of sinking web pages
Pages without outputs
Trapping pages
Damping factor (d)
Surfer proceeds to a randomly chosen successor of the current page with probability d or to a randomly chosen web page with probability (1-d)
where n is the total number of nodes in the graph
Autumn 2011

15. PageRank Vector (Linear Algebra)
R is the rank vector (eigen vector)
ri is rank value of page i
P is a matrix in that pij=1/O(i) if i points to j then else pij=0
Goal is to find eigen vector of matrix P with eigen value one
It iterates to converge (power method)
Using damping factor we have (ei=1/n)
Autumn 2011

16. PageRank Properties Advantages Disadvantages Finds popularity
It is offline
Disadvantages
It is query independent
All of pages will compete together
Unfairness
Autumn 2011

17. HITS (An online query dependent)
Hypertext Induced Topic Search
By Kleinberg
Autumn 2011

18. HITS (Hypertext Induced Topic Selection)
The algorithm produces two types of pages:
- Authority: A page is very authoritative if it receives many citations. Citation from important pages weight more than citations from less-important pages
- Hub: Hubness shows the importance of a page. A good hub is a page that links to many authoritative sites
For each vertex v Є V in a graph of interest:
a(v) - the authority of v
h(v) - the hubness of v
Autumn 2011

19. HITS 2 5 3 1 1 6 4 7
a(1) = h(2) + h(3) + h(4)
h(1) = a(5) + a(6) + a(7)
Autumn 2011

20. Authority and Hubness Convergence
Authorities and hubs exhibit a mutually reinforcing relationship: a better hub points to many good authorities, and a better authority is pointed to by many good hubs
Autumn 2011

21. HITS Example Find a base subgraph:
Start with a root set R {1, 2, 3, 4}
{1, 2, 3, 4} - nodes relevant to the topic
Expand the root set R to include all the children and a fixed number of parents (d) of nodes in R
A new set S (base subgraph)
Real version of HITS is based on site relations
Autumn 2011

22. Topic Sensitive PageRank (TSPR)
It precomputes the importance scores online, as with ordinary PageRank.
However, it compute multiple importance scores for each page;
It computes a set of scores of the importance of
a page with respect to various topics.
At query time, these importance scores are combined based on the topics of the query to form a composite PageRank score for those pages matching the query.
Autumn 2011

23. TSPR (Cont.)
We have n topics on the web, The rank of page v in topic t
Difference with original PageRank is in E vector (it is not uniform and we have n E vectors)
The are n ranking values for each page
Problem: finding the topic of a page and a query (we do not know user interest)
Autumn 2011

24. TSPR (Cont.) Cj = category j
Given a query q, let q’ be the context of q (here q’=q)
P(q’|cj) is computed from the class term-vector Dj (number of the terms in the documents below each of the 16 top-level categories, Djt simply gives the total number of occurrences of term t in documents listed below class cj)
Autumn 2011

25. TSPR (Cont.)
The quantity P(cj ) is not as straightforward. It is used uniformly, although we could personalize the query results for deferent users by varying this distribution.
In other words, for some user k, we can use a prior distribution Pk(cj ) that reflects the interests of user k.
This method provides an alternative framework for user-based personalization, rather than directly varying the damping vector E
Autumn 2011

26. TrustRank Spamming in Web TrustRank is used to overcome Spamming
Good and bad pages
TrustRank is used to overcome Spamming
It proposes techniques to semi-automatically separate reputable, good pages from spam.
It first selects a small set of seed pages to be evaluated by an expert.
Once it manually identifies the reputable seed pages, then it uses the link structure of the web to discover other pages that are likely to be good.
Autumn 2011

27. TrustRank (cont.)
Idea: Good page links to other Good page and bad pages link to other bad pages
Autumn 2011

28. TrustRank (cont.)
It formalizes the notion of a human checking a page for spam by a binary oracle function O over all pages p :
Autumn 2011

29. Trust damping and Trust Splitting
Autumn 2011

30. Computing Trustiness of each page
Goal:
Trust Propagation (E(i) is computed from Normalized Oracle vector for example if O(5)=O(10)=O(15)=1 then E(5)=E(10)=E(15)=0.33 ):
Autumn 2011

31. HostRank
Pervious link analysis algorithms generally work on a flat link graph, ignoring the hierarchal structure of the Web graph.
They suffer from two problems: the sparsity of link graph and biased ranking of newly-emerging pages.
HostRank considers both the hierarchical structure and the link structure of the Web.
Autumn 2011

32. Example of Domain, Host, Directory
Autumn 2011

33. Supper node & Hierarchical Structure of a Web Graph
Tupper-layer is an aggregated link graph which consists with supernodes (such as domain, host and directory).
The lower-layer graph is the hierarchical tree structure, in which each node is the individual Web page in the supernode, and the edges are the hierarchical links between the pages.
Autumn 2011

34. Hierarchical Random Walk Model
At the beginning of each browsing session, a user randomly selects the supernode.
2. After the user finished reading a page in a supernode, he may select one of the following three actions with a certain probability:
Going to another page within current supernode.
Jumping to another supernode that is linked by current supernode.
Ending the browsing.
Autumn 2011

35. Two stages in HostRank
First computing score of each suppernode by random walk (PageRank)
Second propagating score among pages inside a supernode
Dissipative Heat Conductance (DHC) model
Autumn 2011

36. Ranking & Crawling Challenges
Rich-get-richer problem
Unfairness
Low precision
Spamming phenomenon
Autumn 2011

37. Popularity and Quality
Definition 1:We define the popularity of page p at time t, P(p; t), as the fraction of Web users who like the page
We can interpret the PageRank of page as its popularity on the web
Definition 2 : We define the quality of a page p, Q(p), as the probability that an average user will like the page when user sees the page for the first time
Autumn 2011

38. Rich-get-richer Problem
It causes young high quality pages receive less popularity
It is from search-engine bias
Entrenchment Effect
Autumn 2011

39. Entrenchment Effect
Search engines show entrenched (already-popular) pages at the top
Users discover pages via search engines; tend to focus on top results …
entrenched pages
user attention
new unpopular pages
Autumn 2011

40. Popularity as a Surrogate for Quality
Search engines want to measure the “quality” of pages
Quality is hard to define and measure
Various “popularity” measures are used in ranking
e.g., in-links, PageRank, user traffic
Autumn 2011

41. Measuring Search-Engine Bias
Random-surfer model
Users follow links randomly
Never use search engines
Search-dominant model
Users always start with a search engine
Only visit pages returned by search engines
It has been found that it takes 60 times longer for a new page to become popular under Search-Dominant than Random-Surfer model.
Autumn 2011

42. Popularity Evaluation
Random Surfer
Search Dominant
Autumn 2011

43. Some Definitions
Autumn 2011

44. Relation between Popularity & Visit rate in Random Surfer Model
r1 is constant
We can consider PageRank as Popularity (the current PageRank of a page represents the probability that a person arrives at the page if the person follows links on the Web randomly)
Autumn 2011

45. Popularity evolution
Autumn 2011

46. Popularity evolution (Q(p)=1)
Autumn 2011

47. Relation in Search Dominant Model
Autumn 2011

48. Random Surfer vs. Search Dominant
Autumn 2011

49. Search Dominant Formula Detail (Found from AltaVista log-power law)
Autumn 2011

50. Rank Promotion (by Pandey)
Autumn 2011

51. Relationship Between Popularity and Quality
aware of
page p
Users
like page p
Popularity : depends on the number of users who “like” a page
relies on both quality and awareness of the page
Popularity is different from quality
But strongly correlated when awareness is large
P(p,t) = A(p,t)*Q(p)
Autumn 2011

52. Exploitation vs. Exploration
Popular
pages
High quality +
Others
Opportunity for no-popular pages
Autumn 2011

53. An Intelligent Ranking Algorithm for Web Pages
DistanceRank:
An Intelligent Ranking Algorithm for Web Pages
Autumn 2011

54. DistanceRank Goals
A Ranking algorithm based on connectivity with less sensitivity to Rich-get-richer problem in addition to the better ranking
Autumn 2011

55. Definitions
Definition 1. If page i points to page j then the weight of link between i and j is equal to Log10O(i) j i
logO(i)
Definition 2. The distance between two pages i and j is the weight of the shortest path from i to j. We call this logarithmic distance and denote it with dij i j
dij
Autumn 2011

56. An Example
log4 s q t
log3 p
log2 r
The distance between p and t is equal to log(2)+log(3) if the path p-r-t was the shortest path between p and q
The distance between p and s is log(2)+log(4)
Autumn 2011

57. Distance as a Random Surfer Model
If distance between i and j was less than between i and k (dij<dik ) the probability that a random surfer from i reach to j is more than k j
dij i
dik k
Autumn 2011

58. Definition 3
If dij shows the (logarithmic) distance between two page i and j as definition 2, then dj denotes the average distance of page j and is defined as the following (N shows number of web pages):
Autumn 2011

59. Distance as Ranking Criterion
Each page that has less average distance from others has a higher rank
A page having many input links should have low average distance
If pages pointing to this page have low distance then this page should have a low average distance
Autumn 2011

60. Disadvantage of Average Distance
The main problem of the average distance is its complexity, O(|V|*|E|)
So the implementation of average distance is not practical in real web with 25 billion pages
Autumn 2011

61. The DistanceRank
In general, suppose O(i) denotes the number of forwarding (outgoing) links from i and B(j) denotes the set of pages that point to page j. The DistanceRank of page j, denoted by dj , is given by:
Min i
di+logO(i) j
dk+logO(k) k
Low complexity!
B(j)
Autumn 2011

62. Intelligent Surfer
Intuitively, when a user start browsing from a random page, s/he does not have any background about the web
Then, by surfing and visiting web pages, s/he clicks links based on both his/her pervious experiences and the current status (content) of web pages
Continuously, s/he accumulates knowledge that causing to reach his/her goal and suitable pages faster
Autumn 2011

63. DistanceRank based on Reinforcement Learning
State: Web pages (V)
Action: Move from i to j (click j)
Punishment: logO(i)
Minimize punishments (distance)
First: Definition of RL
در محيط يادگيري تقويتي يادگيري با استفاده از تعامل صورت مي‌گيرد كه يادگيرنده يا تصميم‌گيرنده عامل ناميده مي‌شود. چيزهايي كه عامل با آنها تعامل مي‌كند شامل همه شرايط خارج از كنترل عامل مي‌باشد كه اصطلاحاً محيط ناميده مي‌شود. عامل با انجام يك سري عمل با محيط تعامل كرده و محيط در پاسخ به هر عمل به عامل، پاداش يا توبيخارائه مي‌كند. عامل و محيط با يكديگر در بازه‌هاي زماني متوالي t=0,1,2,… تعامل خواهند كرد. در هر مرحله‌ي زماني عامل تصويري از حالت محيط دريافت مي‌كند كه S شامل همه حالتهاي ممكن مي‌باشد، و عمل را براي رسيدن به حالت جديد انتخاب مي‌كند. هدف اصلي عامل بيشينه (كمينه) كردن پاداش(توبيخ)هاي دريافتي در طي زمان مي‌باشد. i
logO(i) j
logO(j)
Autumn 2011

64. DistanceRank is similar to Q-Learning
The learning rate:
log(O(i)) is the instantaneous punishment it receives in transition state from i to j
djt and dit show average distance value of page j and i in time t respectively
djt+1 is average distance of page j at time t+1
It is mapped on Intelligent surfer
First alpha is one and then decreases in time
Gamma is discount factor
It is iterative
Finally distances are sorted in increasing order
Autumn 2011

65. DistanceRank example 1 2 3 4 5 Autumn 2011 Iteration 4 Iteration 3
Distnace Formula
Node
log2
d1=0.5*d4+log2 1
0.25log2
d2=0.5*Min(d3,d1) 2
0.5log2
d3=0.5*d5 3
0.12log2
d4=0.5*d2 4
d5=0.5*d4+log2 5
Autumn 2011

66. Experimental Results
We used University of California, Berkeley’s Web site which includes 5 millions web pages to evaluate DistanceRank
Three scenarios were used:
Crawling scheduling
The goal was to find more important pages faster in the crawling process
Rank ordering
We compared the ordering of DistanceRank with PageRank and found their similarity
Comparison with Google
Autumn 2011

67. Rank Ordering
We used Kendall's metric for correlation between two rank lists
Ideal is PageRank
Algorithm
Kendall's Tau
Breadth-first
0.11
Back Link
0.40
OPIC
0.62
DistanceRank
0.75
Autumn 2011

68. Rich-get-richer Problem
It is proved that the popularity of each page is computed as the following. Pp and Pc are pervious and current popularity respectively
There is a relation between popularity and quality (Q=0.80, ):
Autumn 2011

69. Popularity growth in DistanceRank (Q=0.8)
DistanceRank is closer to the page quality
Autumn 2011

70. Experimental result
DistanceRank is less sensitive to the "rich get richer" problem in in comparison with PageRank
dj=Alpha*(difference between current and previous distance) + pervious distance
DistanceRank is closer to the page quality
Autumn 2011

71. DistanceRank Convergence
The ordering obtained by only 5 iterations agree closely with ordering of 20 iterations for 5 million pages
the time complexity of algorithm reduces to O(p*|E|) where p<<N in that p shows number of iterations for convergence
Autumn 2011

72. Different learning rates
Autumn 2011