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Topic-Sensitive PageRank. Reference: Taher H. Haveliwala, “Topic-Sensitive PageRank: A context-sensitive ranking algorithm for websearch”, IEEE Trans. On Knowledge and Data Engineering, vol. 15, No. 4, PP. 784-796. The original PageRank: purely based on the hyperlinks of web pages.

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topic sensitive pagerank
Topic-Sensitive PageRank

Reference: Taher H. Haveliwala, “Topic-Sensitive PageRank: A context-sensitive ranking algorithm for websearch”, IEEE Trans. On Knowledge and Data Engineering, vol. 15, No. 4, PP. 784-796.

The original PageRank:

  • purely based on the hyperlinks of web pages.
  • Contents are not considered.
  • A vector of PageRank is used for all web pages.

Topic-Sensitive PageRank

  • For each topic, a vector of PageRank is created.
  • Each page has several PageRank values. One for each topic.
creating a page rank vector for each topic
Creating a Page Rank vector for each topic
  • How to select topics?
    • Using a small set of topics is important for low computation cost and quick response time.
    • Open Directory: http://www.dmoz.org
      • 16 top level topics
original pagerank
Original PageRank
  • Rank=MRank
    • Rank is a vector, one element for each web page.
    • M is a nn matric
      • If there is a link from page j to page I, then

Mi,j =1/Nj, where Nj is the number of out-links of page j.

another version
Another Version
  • Let n be the total number of web pages.

P=[1/n] n1 be a vector.

  • d is a n1 matrix.
    • di=1 if page i has no out links. Otherwise, di=0.
  • D=ppT, and E=p[1] 1n
  • M’=(1-)(M+D) +E.
  • Rank=M’Rank=(1-)(M+D) Rank +P.
topic sensitive page rank
Topic sensitive Page Rank
  • Let Tj be the set of URLs in the ODP category cj.
  • P=vj, where
    • Vj,i =1/|Tj| if page j points to page i. Otherwisr vj,i=0.
  • The pageRank vector for topic cj is PR(, vj).
  • Compute the pageRAnk for all pages related to topic cj as if for the original PageRank by considering Tj.
the retrieval score
The Retrieval Score
  • Let r j, d be the PageRank of document d given by the rank PR( , vj).
  • Sq,d=  j P(cj|q)•r j,d ,
  • P(cj|q) is the score that topic is related to q.
similarity measures for induced rankings another version
Similarity Measures for Induced Rankings Another Version
  • Let 1 and 2 be two rankings of documents.
  • OSim(1,2) indicates the degree of overlap between the top k URLs of the two rankings.
  • OSim (1,2) =|AB|/k.
  • KSimn (1,2) =

|(u, v): 1 and 2 agree on order of (u, v)|/(|U|)(|U|-1)

Let  be the true ranking given by user. To compare 1 and 2, we can use OSim (1,2) or KSimn (1,2) .

weighted pagerank
Weighted PageRank
  • Assign larger rank values to more important pages.
  • Each outlink page gets its value proportional to it popularity.
  • W in(v, u) is the weight of link(v, u) calculated based on the number of inlinks of page u and the number of inlinks of all reference pages of page v.

w in(v, u) =Iu/pR(v) Ip,

Iu—number of inlinks of page u.

R(v)-the set of all pages that v points to.

weighted pagerank1
Weighted PageRank
  • w out(v, u) =Ou/pR(v) Op,

Ou—number of outlinks of page u.

Let B(u) be the set of pages that points to v.

PR(u)=(1-d) +d  vB(u) PR(v) w in(v, u) w out(v, u)

Reference: Wenpu Xing and Ali Ghorbani, Weighted PageRank Algorithm, Proceedings of the 2nd Annual Conference on Communication Networks and Services Research (CNSR’04), 2004.

choices of search engines
Choices of Search Engines
  • Many search engines exist to compete for users
    • The results are not necessarily the same
    • Different users prefer different search engines
    • Search results may, in the future, be biased towards paid advertisements.
google city university
GOOGLE: City University
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yahoo
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alltheweb
AllTheWeb
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msn search
MSN Search
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aol search
AOL Search
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ask jeeves
Ask Jeeves
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hotbot
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teoma
Teoma
  • City University of Hong Kong Formerly the City Polytechnic of Hong Kong. Includes information on university, links to learning resources, research and departmental information...www.cityu.edu.hk/[Related Pages][More Results from www.cityu.edu.hk]
  • City University Text Version. The University for business and the professions ... Contact Us | About City University | Maps & Directions A-Z Index | Site Map | Help...www.city.ac.uk/[More Results from www.city.ac.uk]
  • New Jersey City University Official site includes graduate and undergraduate information, news, events, online learning, calendars, and athletics.www.njcu.edu/[Related Pages][More Results from www.njcu.edu]
  • Elizabeth City State University Admission Application Introduction 2004-2005 APPLICATION FOR ADMISSION. Welcome to the Elizabeth City State University Online Application. New Freshmen...www.ncmentor.org/applications/unc/apply/el...
  • City University A University which believes in forward-thinking business and leadership skills, exposing students to the latest technology in all courses of study.www.cityu.edu/
  • The City College of New York City College of New York (CUNY) A senior college of The City University of New York. Located in Manhattan. 138th Street at Convent Avenue. A Harlem masterpiece in the neo-Gothic...www.ccny.cuny.edu/[More Results from www.ccny.cuny.edu]
metasearch engine
MetaSearch Engine
  • Metasearch Engines are designed to increase the coverage of web by forwarding users’ queries to multiple search engines
    • Users’ requests are sent to multiple search engines such as AlltheWeb, Google, MSN.
  • Then the results from the individual search engine are combined into a single result set to present to users.
longest common subsequence
Longest common subsequence
  • Definition 1: Given a sequence X=x1x2...xm, another sequence Z=z1z2...zk is a subsequence of X if there exists a strictly increasing sequence i1i2...ik of indices of X such that for all j=1,2,...k, we have xij=zj.
  • Example 1: If X=abcdefg, Z=abdg is a subsequence of X. X=abcdefg,Z=ab d g
slide22
Definition 2: Given two sequences X and Y, a sequence Z is a common subsequence of X and Y if Z is a subsequence of both X and Y.
  • Example 2: X=abcdefg and Y=aaadgfd. Z=adf is a common subsequence of X and Y.

X=abc defg

Y=aaaadgfd

Z=a d f

slide23
Definition 3: A longest common subsequence of X and Y is a common subsequence of X and Y with the longest length. (The length of a sequence is the number of letters in the seuqence.)
  • Longest common subsequence may not be unique.
  • Example: abcd

acbd

Both acd and abd are LCS.

longest common subsequence problem
Longest common subsequence problem
  • Input: Two sequences X=x1x2...xm, and

Y=y1y2...yn.

  • Output:a longest common subsequence of X and Y.
  • A brute-force approach

Suppose that mn. Try all subsequence of X (There are 2m subsequence of X), test if such a subsequence is also a subsequence of Y, and select the one with the longest length.

charactering a longest common subsequence
Charactering a longest common subsequence
  • Theorem (Optimal substructure of an LCS)
  • Let X=x1x2...xm, and Y=y1y2...yn be two sequences, and
  • Z=z1z2...zk be any LCS of X and Y.
  • 1. If xm=yn, then zk=xm=yn and Z[1..k-1] is an LCS of X[1..m-1] and Y[1..n-1].
  • 2. If xmyn, then zkxm implies that Z is an LCS of X[1..m-1] and Y.
  • 2. If xmyn, then zkyn implies that Z is an LCS of X and Y[1..n-1].
the recursive equation
The recursive equation
  • Let c[i,j] be the length of an LCS of X[1...i] and X[1...j].
  • c[i,j] can be computed as follows:

0 if i=0 or j=0,

c[i,j]= c[i-1,j-1]+1 if i,j>0 and xi=yj,

max{c[i,j-1],c[i-1,j]} if i,j>0 and xiyj.

Computing the length of an LCS

  • There are nm c[i,j]’s. So we can compute them in a specific order.
the algorithm to compute an lcs
The algorithm to compute an LCS
  • 1. for i=1 to m do
  • 2. c[i,0]=0;
  • 3. for j=0 to n do
  • 4. c[0,j]=0;
  • 5. for i=1 to m do
  • 6. for j=1 to n do
  • 7. {
  • 8. if x[I] ==y[j] then
  • 9. c[i,j]=c[i-1,j-1]=1;
  • 10 b[i,j]=1;
  • 11. elseif c[i-1,j]>=c[i,j-1] then
  • 12. c[i,j]=c[i-1,j]
  • 13. b[i,j]=2;
  • 14. else c[i,j]=c[i,j-1]
  • 15. b[i,j]=3;
  • 14 }
constructing an lcs back tracking
Constructing an LCS (back-tracking)
  • We can find an LCS using b[i,j]’s.
  • We start with b[n,m] and track back to some cell b[0,i] or b[i,0].
  • The algorithm to construct an LCS

1. i=m

2. j=n;

3. if i==0 or j==0 then exit;

4. if b[i,j]==1 then

{

i=i-1;

j=j-1;

print “xi”;

}

5. if b[i,j]==2 i=i-1

6. if b[i,j]==3 j=j-1

7. Goto Step 3.

  • The time complexity: O(nm).
shortest common supersequence
Shortest common supersequence
  • Definition:Let X and Y be two sequences. A sequence Z is a supersequence of X and Y if both X and Y are subsequence of Z.
  • Shortest common supersequence problem:

Input: Two sequences X and Y.

Output: a shortest common supersequence of X and Y.

  • Example: X=abc and Y=abb. Both abbc and abcb are the shortest common supersequences for X and Y.
slide31
Recursive Equation:
  • Let c[i,j] be the length of an LCS of X[1...i] and X[1...j].
  • c[i,j] can be computed as follows:

j if i=0

i if j=0,

c[i,j]= c[i-1,j-1]+1 if i,j>0 and xi=yj,

min{c[i,j-1]+1,c[i-1,j]+1} if i,j>0 and xiyj.