Download presentation

Presentation is loading. Please wait.

Published byDonavan Serviss Modified over 2 years ago

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?

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... p

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 = To From A

6
CMU SCS ICDM'06 PanelC. Faloutsos6 (Simplified) PageRank algorithm A p = p =

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.

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google