Randomized algorithm to determine the eigenvector of a stochastic matrix with application to the PageRank problem |
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Authors: | A V Nazin B T Polyak |
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Affiliation: | (3) Department Math., University Wisconsin, Madison, USA; |
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Abstract: | Consideration was given to estimation of the eigenvector corresponding to the greatest eigenvalue of a stochastic matrix.
There exist numerous applications of this problem arising at ranking the results of search, coordination of the multiagent
system actions, network control, and data analysis. The standard technique for its solution comes to the power method with
an additional regularization of the original matrix. A new randomized algorithm was proposed, and a uniform—over the entire
class of the stochastic matrices of a given size—upper boundary of the convergence rate was validated. It is given by {ie342-1},
where C is an absolute constant, N is size, and n is the number of iterations. This boundary seems promising because ln(N) is smallish even for a very great size. The algorithm relies on the mirror descent method for the problems of convex stochastic
optimization. Applicability of the method to the PageRank problem of ranking the Internet pages was discussed. |
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Keywords: | |
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