Ranking

• Authorities and Hubs (Kleinberg' 1998)
• A Web page is a good authority -> pointed to by many good hubs
• A Web page is a good hub -> points to many good authorities
• Good hubs and authorities reinforce each other
• Authorities & Hubs form a bipartite sub-graph of the Web
• Rank(p) -> weight of Web page p
• $N_u$ -> outdegree of Web page u
• Edge u -> v gives $Rank(u) / N_u$ to webpage v
• $B_v$ -> Web pages pointing to v
• Rank(v) on the next iteration (i+1)

$$ \forall v, Rank_{i + 1}(V) = \sum _{u \epsilon B_v}{\frac{Rank_i(u)}{N_u}} $$

• Fixpoint algorithm
  • For N pages initialize the rank to 1/N
• Iteratively compute the Page rank equation
• Can be expressed as computing eigenvectors for a matrix
• Ranking Web pages by relevance to the Query
  • (page, query, rank)
• Ranking Function
  • Features (of a webpage)
    • Affect rank of webpage
  • Static features
    • precompiled
  • Dynamic features
    • At query time
• Algorithms
  • A big if statement
  • Machine learning algorithm
• Fixpoint algorithm
  • For N pages initialize the rank to 1/N
• Iteratively compute the Pagerank equation
• Can be expressed as computing eigenvectors for a matrix
• Page rank really has nothing to do with the user query. It is just the ranking of a certain webpage.
  • Means we need features for the ranking function. This is why we have Dynamic Features