1. CMU SCS PageRank Brin, Page description: C. Faloutsos, CMU

2. CMU SCS ICDM'06 PanelC. Faloutsos2 Problem definition: Given a directed graph which are the most important nodes? 1 2 3 4 5

3. CMU SCS ICDM'06 PanelC. Faloutsos3 google/Page-rank algorithm Imagine a particle randomly moving along the edges (*) compute its steady-state probabilities (*) with occasional random jumps

4. CMU SCS ICDM'06 PanelC. Faloutsos4 google/Page-rank algorithm that is: given a Markov Chain, compute the steady state probabilities p1... p5 1 2 3 4 5

5. CMU SCS ICDM'06 PanelC. Faloutsos5 (Simplified) PageRank algorithm Let W be the transition matrix (= adjacency matrix); let A be W T, and column-normalized - then 1 2 3 4 5 = To From A

6. CMU SCS ICDM'06 PanelC. Faloutsos6 (Simplified) PageRank algorithm A p = p 1 2 3 4 5 =

7. CMU SCS ICDM'06 PanelC. Faloutsos7 (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 )

8. CMU SCS ICDM'06 PanelC. Faloutsos8 (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

9. CMU SCS ICDM'06 PanelC. Faloutsos9 Full Algorithm With probability 1-c, fly-out to a random node Then, we have p = c A p + (1-c)/n 1 => p = (1-c)/n [I - c A] -1 1

10. CMU SCS ICDM'06 PanelC. Faloutsos10 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+]...

11. CMU SCS ICDM'06 PanelC. Faloutsos11 References Brin, S. and L. Page (1998). Anatomy of a Large- Scale Hypertextual Web Search Engine. 7th Intl World Wide Web Conf.