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Topic-Sensitive PageRank Reference: Taher H. Haveliwala, Topic-Sensitive PageRank: A context-sensitive ranking algorithm for websearch, IEEE Trans. On.

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Presentation on theme: "Topic-Sensitive PageRank Reference: Taher H. Haveliwala, Topic-Sensitive PageRank: A context-sensitive ranking algorithm for websearch, IEEE Trans. On."— Presentation transcript:

1 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 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.

2 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: 16 top level topics

3 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 M i,j =1/N j, where N j is the number of out-links of page j.

4 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. – d i =1 if page i has no out links. Otherwise, d i =0. D=p p T, and E=p [1] 1 n M=(1- )(M+D) + E. Rank=M Rank=(1- )(M+D) Rank + P.

5 Topic sensitive Page Rank Let T j be the set of URLs in the ODP category c j. P=vj, where –V j,i =1/|T j | if page j points to page i. Otherwisr v j,i =0. The pageRank vector for topic c j is PR(, v j ). Compute the pageRAnk for all pages related to topic c j as if for the original PageRank by considering T j.

6 The Retrieval Score Let r j, d be the PageRank of document d given by the rank PR(, v j ). S q,d = j P(c j |q)r j,d, P(c j |q) is the score that topic is related to q.

7 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).

8 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) =I u / p R(v) I p, I u number of inlinks of page u. R(v)-the set of all pages that v points to.

9 Weighted PageRank w out (v, u) =O u / p R(v) O p, O u 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 2 nd Annual Conference on Communication Networks and Services Research (CNSR04), 2004.

10 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.

11 GOOGLE: City University 1.City University London - the University for business and the The University for business and the professions. Contact Us | About City University | Maps & Directions, AZ Index | Site Map | Help. Prospective Students.... Description: Official site with information about courses, research, schools, and departments. Includes details...City University London - the University for business and the... 2.City University Home A University which believes in forward-thinking business and leadership skills, exposing students to the latest technology in all courses of study. Description: A private, nonprofit institution founded to serve working adults wanting to pursue educational opportunit...City University Home 3.Welcome to Dublin City University... here... Dublin City University, Dublin 9, Ireland. Tel (0) , Fax (0) Page updated: 02/09/03 legal.... Description: Information on facilities, services, degree courses, research, the campus, student life, the library...Welcome to Dublin City University 4.The City University of New York Description: The University's Main Website.The City University of New York 5.City University of Hong Kong AD Working Group lends staff, students an ear. Several issues still evoked strong emotions as staff members and students voiced their... Description: Formerly the City Polytechnic of Hong Kong. Includes information on university, links to learning...City University of Hong Kong 6.Welcome to Oklahoma City University... At Oklahoma City University, our students come first. Our... Oklahoma City University offers a quality, values-centered education. United... Description: Admissions, academic programs and alumni relations, sports, services, news, calendar of events and...Welcome to Oklahoma City University

12 YAHOO 1.City University London - the University for business and the The University for business and the professions. Contact Us | About City University | Maps & Directions, AZ Index | Site Map | Help. Prospective Students....City University London - the University for business and the... 2.City University A University which believes in forward-thinking business and leadership skills, exposing students to the latest technology in all courses of study. - 3k - Cached - More pages from this siteCity UniversityCachedMore pages from this site 3.Dublin City University... here... Dublin City University, Dublin 9, Ireland. Tel (0) , Fax (0) Page updated: 02/09/03 legal k - Cached - More pages from this siteDublin City UniversityCachedMore pages from this site 4.City University of New York The University's Main Website. - More pages from this siteCity University of New YorkMore pages from this site 5.City University of Hong Kong AD Working Group lends staff, students an ear. Several issues still evoked strong emotions as staff members and students voiced their k - Cached - More pages from this siteCity University of Hong KongCachedMore pages from this site 6.Oklahoma City University... At Oklahoma City University, our students come first. Our... Oklahoma City University offers a quality, values-centered education. United k - Cached - More pages from this siteOklahoma City UniversityCachedMore pages from this site

13 AllTheWeb 1.Apartment Listings in University City (sponsored) St. Louis, Missouri area apartment listings at Apartments.com. Free nationwide apartment search with visual rental listings online. Listings in University City 2.City University - Washington (sponsored) Contact information and resources such as yellow page information, phone number, address, maps and directions as provided by QwestDex. University - Washington 3.City University Apartments - Rent.com (sponsored) Rent.com has millions of free apartment listings nationwide. Get $100 when you sign a lease near your school - it's easy. University Apartments - Rent.com 4.City University London - the University for business and the professions... Contact Us | About City University | Maps & Directions A-Z Index | Site Map | Help... Description: Official site with information about courses, research, schools, and departments. Includes details of news and events. more hits from: KBCity University London - the University for business and the professions more hits from: 5.Flash Upgrade Description: A University which believes in forward-thinking business and leadership skills, exposing students to the latest technology in all courses of study KBFlash Upgrade 6.Welcome to Dublin City University... KnowledgeWorks, wins DCU Mallin-invent award Full text you can go anywhere in the world from here... Dublin City University, Dublin 9, Ireland. Tel (0) , Fax (0) Page updated: 02/09/03 legal search... Description: Information on facilities, services, degree courses, research, the campus, student life, the library and DCU news.Welcome to Dublin City University

14 MSN Search 1.City University of New York Details the CUNY system's campuses and admissions requirements. Eye photos of notable graduates such as actor Judd Hirsch. University of New York 2.City University Offers prospectus, admissions, academic calendar, courses and degrees, and news. University 3.City University Private, nonprofit institution located in Belleview, Washington, offers higher education opportunities to working professionals and lifelong learners. University 4.Valley City University Admissions Site covers financial aid and tuition and offers a virtual campus tour. Site also provides access to an online application. City University Admissions 5.Oklahoma City University The Oklahoma City University site contains information about admissions, academic departments and student life. The site also provides library resources, faculty information and news. frodo.okcu.eduOklahoma City University 6.Dublin City University, Dublin - TripAdvisor Browse reviews of the Dublin City University in Dublin, County Dublin, Ireland. Check consumer reviews, articles and opinions about the Dublin City University. City University, Dublin - TripAdvisor

15 AOL Search 1.City University London - the University for business and the The University for business and the professions. Contact Us | About City University | Maps & Directions, AZ Index | Site Map | Help. Prospective Students.... University London - the University for business and the... 2.City University Home - A University which believes in forward-thinking business and leadership skills, exposing students to the latest technology in all courses of study. University Home 3.Welcome to Dublin City University -... here... Dublin City University, Dublin 9, Ireland. Tel (0) , Fax (0) Page updated: 02/09/03 legal.... to Dublin City University 4.http://www.cuny.edu/ - The University's Main Website. 5.City University of Hong Kong - AD Working Group lends staff, students an ear. Several issues still evoked strong emotions as staff members and students voiced their... University of Hong Kong 6.Welcome to Oklahoma City University -... At Oklahoma City University, our students come first. Our... Oklahoma City University offers a quality, values-centered education. United... to Oklahoma City University

16 Ask Jeeves 1.City University of Hong Kong Formerly the City Polytechnic of Hong Kong. Includes information on university, links to learning resources, research and departmental information.....From:www.cityu.edu.hk/City University of Hong Kong 2.City University Text Version. The University for business and the professions... Contact Us | About City University | Maps & Directions A-Z Index | Site Map | Help...From:www.city.ac.uk/City University 3.New Jersey City University Official site includes graduate and undergraduate information, news, events, online learning, calendars, and athletics.From:www.njcu.edu/New Jersey City University 4.Elizabeth City State University Admission Application Introduction APPLICATION FOR ADMISSION. Welcome to the Elizabeth City State University Online Application. New Freshmen...From:www.ncmentor.org/applications/unc/apply/elizabeth_city _state_univ...Elizabeth City State University Admission Application Introduction 5.City University A University which believes in forward-thinking business and leadership skills, exposing students to the latest technology in all courses of study.From:www.cityu.edu/City University 6.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...From:www.ccny.cuny.edu/The City College of New York City College of New York (CUNY)

17 HotBot 1. City University of New York Details the CUNY system's campuses and admissions requirements. Eye photos of notable graduates such as actor Judd Hirsch. - August 10, KB City University of New York 2. City University Private, nonprofit institution located in Belleview, Washington, offers higher education opportunities to working professionals and lifelong learners. - August 23, KB City University 3. New Jersey City University Explore the course requirements for this liberal arts institution. Link to admissions and financial aid information.... New Jersey City University Kennedy Boulevard Jersey City, New Jersey November 1, KB New Jersey City University 4. City University London - the University for business and the Contact Us | About City University | Maps & Directions. A-Z Index | Site Map | Help September 28, KB City University London - the University for business and the Oklahoma City University Take a tour of the campus, and explore a roster of academic programs.... At Oklahoma City University, our students come first October 26, KB Oklahoma City University 6. University of Missouri, Kansas City University based in Kansas City, Missouri, presents and overview of its academic programs, and offers campus news.... UNIVERSITY OF MISSOURI-KANSAS CITY. Bulletin. Winter 2004 Fee Update, more October 23, KB University of Missouri, Kansas City

18 Lycos 1. City University London - the University for business and the... … Contact Us | About City University | Maps & Directions A-Z Index | Site Map | Help … More results from: September 16, KB City University London - the University for business and the... More results from 2. Flash Upgrade A University which believes in forward-thinking business and leadership skills, exposing students to the latest technology in all courses of study. November 1, KB Flash Upgrade 3. The City University of New York The University's Main Website. December 31, B The City University of New York 4. Welcome to Dublin City University … KnowledgeWorks, wins DCU Mallin-invent award Full text you can go anywhere in the world from here... Dublin City University, Dublin 9, Ireland. Tel (0) , Fax (0) More results from: October 29, KB Welcome to Dublin City University More results from 5. City University of Hong Kong Formerly the City Polytechnic of Hong Kong. Includes information on university, links to learning resources, research and departmental information and student information. More results from: October 29, KB City University of Hong Kong More results from 6. HCU HomePage -English- … contact us For any suggestion and requests to this web site, cu.ac.jp Feel free to link this web site. Hiroshima City University More results from: May 11, KB HCU HomePage -English- More results from

19 Teoma 1.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 University of Hong KongRelated PagesMore Results from 2.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 UniversityMore Results from 3.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 Jersey City UniversityRelated PagesMore Results from 4.Elizabeth City State University Admission Application Introduction APPLICATION FOR ADMISSION. Welcome to the Elizabeth City State University Online Application. New Freshmen...www.ncmentor.org/applications/unc/apply/el...Elizabeth City State University Admission Application Introduction 5.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/City University 6.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 City College of New York City College of New York (CUNY)More Results from

20 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.

21 Longest common subsequence Definition 1: Given a sequence X=x 1 x 2...x m, another sequence Z=z 1 z 2...z k is a subsequence of X if there exists a strictly increasing sequence i 1 i 2...i k of indices of X such that for all j=1,2,...k, we have x ij =z j. Example 1: If X=abcdefg, Z=abdg is a subsequence of X. X=abcdefg, Z=ab d g

22 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

23 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.

24 Longest common subsequence problem Input: Two sequences X=x 1 x 2...x m, and Y=y 1 y 2...y n. Output: a longest common subsequence of X and Y. A brute-force approach Suppose that m n. Try all subsequence of X (There are 2 m subsequence of X), test if such a subsequence is also a subsequence of Y, and select the one with the longest length.

25 Charactering a longest common subsequence Theorem (Optimal substructure of an LCS) Let X=x 1 x 2...x m, and Y=y 1 y 2...y n be two sequences, and Z=z 1 z 2...z k be any LCS of X and Y. 1. If x m =y n, then z k =x m =y n and Z[1..k-1] is an LCS of X[1..m-1] and Y[1..n-1]. 2. If x m y n, then z k x m implies that Z is an LCS of X[1..m-1] and Y. 2. If x m y n, then z k y n implies that Z is an LCS of X and Y[1..n-1].

26 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 x i =y j, max{c[i,j-1],c[i-1,j]} if i,j>0 and x i y j. Computing the length of an LCS There are n m c[i,j]s. So we can compute them in a specific order.

27 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. else if 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 }

28 Example 3: X=BDCABA and Y=ABCBDAB.

29 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).

30 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.

31 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 x i =y j, min{c[i,j-1]+1,c[i-1,j]+1} if i,j>0 and x i y j.

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