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PageRank. Brin, Page description: C. Faloutsos, CMU. Problem definition:. Given a directed graph which are the most ‘important’ nodes?. 2. 1. 3. 4. 5. google/Page-rank algorithm. Imagine a particle randomly moving along the edges (*) compute its steady-state probabilities

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Presentation Transcript
pagerank

PageRank

Brin, Page

description: C. Faloutsos, CMU

problem definition
Problem definition:
  • Given a directed graph
  • which are the most ‘important’ nodes?

2

1

3

4

5

C. Faloutsos

google page rank algorithm
google/Page-rank algorithm
  • Imagine a particle randomly moving along the edges (*)
  • compute its steady-state probabilities

(*) with occasional random jumps

C. Faloutsos

google page rank algorithm4
google/Page-rank algorithm
  • that is: given a Markov Chain, compute the steady state probabilities p1 ... p5

2

1

3

4

5

C. Faloutsos

simplified pagerank algorithm
2

1

3

4

5

(Simplified) PageRank algorithm
  • Let W be the transition matrix (= adjacency matrix); let A be WT, and column-normalized - then

From

A

To

=

C. Faloutsos

simplified pagerank algorithm6
(Simplified) PageRank algorithm
  • A p = p

A p = p

2

1

3

=

4

5

C. Faloutsos

simplified pagerank algorithm7
(Simplified) PageRank algorithm
  • A p = 1 * p
  • thus, p is the eigenvector that corresponds to the highest eigenvalue(=1, since the matrix is column-normalized)

C. Faloutsos

simplified pagerank algorithm8
(Simplified) PageRank algorithm
  • In short: imagine a particle randomly moving along the edges
  • compute its steady-state probabilities

Full version of algo: with occasional random jumps

C. Faloutsos

full algorithm
Full Algorithm
  • With probability 1-c, fly-out to a random node
  • Then, we have

p = c Ap + (1-c)/n 1 =>

p = (1-c)/n [I - c A] -1 1

C. Faloutsos

impact current research
Impact - current research
  • multi-billion $ company
  • over 2,500 citations (Google scholar)
  • Topic-Sensitive PageRank [Haveliwala+]
  • TrustRank [Gyongyi+]
  • Efficient computation
  • ObjectRank [Papakonstantinou+]
  • centerPiece subgraphs [Tong+]
  • ...

C. Faloutsos

references
Brin, S. and L. Page (1998). Anatomy of a Large-Scale Hypertextual Web Search Engine. 7th Intl World Wide Web Conf.References

C. Faloutsos

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