PageRank The PageRank

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					The PageRank Citation Ranking:
  Bringing Order to the Web

   L Page, S Brin, R Motwani, T Winograd
            Stanford University

             January 29, 1998

        Presented by Ruoran Zhou
                                           1
                  Outline
•   Motivation
•   Backlink
•   PageRank
•   Applications
•   Conclusion
•   Comments
•   Relate to our project
                            2
               Motivation
• Web:
  • Information is large and heterogeneous
  • Profit seeking ventures
  • Free of quality control
• Search engines face:
  • Inexperienced users
  • Manipulations
• PageRank
  • Better than simple citation count
                                             3
                     Backlink
• Backlink
  A and B are back
  links of C




• Intuition
  • Pages with lots of backlinks are important
  • Backlinks coming from important pages convey
    more importance to a page                   4
               PageRank I
• Simplified version



  •   u, v—web page
  •   Bu—the set of pages that point to u
  •   Nv—number of links from v
  •   c—a factor used for normalization, c<1
                                               5
              PageRank I (cont)
• Example



•   c=0.85
•   Initially RA=RB=RC=RD=1
•   After first iteration:
•   RA =RC*0.85=1*0.85=0.85
•   RB=(RA/2)*0.85=0.5*0.85=0.425
•   RC=((RA /2)+ RB + RD)*0.85=(0. 5+1+1)*0.85=2.125
                                                       6
                PageRank II
• Problem: rank sink



• Intuitive basis:
   – Probability of a click
   by a random surfer
   – Random surfer keeps
   clicking on successive links at random
                                            7
         PageRank II (cont)
• Rank source E(u)




  – Let E(u) be some vector over the Web pages that
    corresponds to a source of rank
  – E(u) help the surfer jumps out of the sink,
    personalization

                                                      8
• c=0.85, cE(u)=0.15
• Ranks converge after 48th iteration




   http://en.wikipedia.org/wiki/PageRank “PageRank Uncovered”   9
                      PageRank III
• Scalability




•   PageRank computation terminates in logarithmic time in the size of the
    graph.                                                                   10
                PageRank IV
• Personalized PageRank
  – Rank source E(u)
     • Intuition: distribution of web pages a random surfer
       periodically jumps to
     • uniformly over all pages
     • total weight on a single page
     • Between the two extremes


  – Immune to commercial manipulation
     • Having important link as its backlink
     • Many backlinks

                                                              11
               Application I
• Estimating Web Traffic
  – PageRank vs. Usage, e.g. Porn sites: high
    usage, low pagerank

• Backlink predictor
  – PageRank vs. Citation Count
     • Better at mapping the citation structure of the
       web completely
     • Avoid the local maxima that citation counts get
       stuck in and more efficient
                                                     12
            Application II
• PageRank Proxy




                             13
             Conclusion
• PageRank is a global ranking based on
  the link structure of the web
  – Backlinks: indicate importance
  – Rank Source: escape rank sink;
    personalization


• Plenty of applications

                                          14
                    Comments
• Good
  –   PageRank: make use of link structures
  –   Google
  –   Give intuitions for algorithms
  –   All kinds of possible applications


• Shortcoming
  – Some points need more explanation
       • Computing algorithm of PageRank (section 2.7)
  – A little stray away
       • Section 5: Introduction of Google               15
       Relate to the project
• Our project
  – Goal: produce playlists for customers
  – Techniques: compression


• Relates
  – User navigation: rankings in the playlist
  – Collaborative filtering: rank; preprocessing

                                                   16
Thank you




            17

				
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