The document proposes methods to accelerate PageRank computations by extrapolating from successive PageRank iterates. It presents the power method for computing PageRank and its convergence properties. The key idea is to estimate components of the current iterate using the next few iterates, eliminating coefficients of less dominant eigenvectors to isolate the principal eigenvector corresponding to PageRank. Empirical results show quadratic extrapolation can speed up convergence, making the approach useful for related problems requiring rapidly computed principal eigenvectors.
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Extrapolation
1. Extrapolation Methods for Accelerating PageRank Computations Sepandar D. Kamvar Taher H. Haveliwala Christopher D. Manning Gene H. Golub Stanford University
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4. Link Counts Linked by 2 Important Pages Linked by 2 Unimportant pages Sep’s Home Page Taher’s Home Page Yahoo! CNN DB Pub Server CS361
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6. Definition of PageRank Yahoo! CNN DB Pub Server Taher Sep 1/2 1/2 1 1 0.1 0.1 0.1 0.05 0.25
27. Power Method u 1 1 u 2 2 u 3 3 u 4 4 u 5 5 u 1 1 u 2 2 2 u 3 3 3 u 4 4 4 u 5 5 5 u 1 1 u 2 2 2 2 u 3 3 3 2 u 4 4 4 2 u 5 5 5 2
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29. Our Approach u 1 u 2 u 3 u 4 u 5 Estimate components of current iterate in the directions of second two eigenvectors, and eliminate them.
Assume that lambda 1 is less than 1 and all other eigenvalues are strictly less than 1.
Here, talk about in the past, how lambda 2 is often close to 1, so the power method is not useful. However, in our case,
Note : derivation given here is slightly different from what’s in the paper the one here is perhaps more intuitive the one in the paper is more compact