Updating pagerank with iterative aggregation

23-Nov-2015 15:13

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An accelerated multilevel aggregation method is presented for calculating the stationary probability vector of an irreducible stochastic matrix in Page Rank computation, where the vector extrapolation method is its accelerator.

We show how to periodically combine the extrapolation method together with the multilevel aggregation method on the finest level for speeding up the Page Rank computation.

Detailed numerical results are given to illustrate the behavior of this method, and comparisons with the typical methods are also made.

Due to the large size of the web graph (over eight billion nodes [2]), computing Page Rank is faced with the big challenge of computational resources, both in terms of the space of CPU and RAM required and in terms of the speed of updating in time; that is, as a new crawl is completed, it can be soon available for searching.

Among all the numerical methods to compute Page Rank, the Power method is one of the standard ways for its stable and reliable performances [1], whereas the low rate of convergence is its fatal flaw.

Section 3 describes our main acceleration algorithm.

The Page Rank algorithm for assigning a rank of importance to web pages has been the key technique in web search [1].

The core of the Page Rank computation consists in the principal eigenvector of a stochastic matrix representing the hyperlink structure of the web.

Many accelerating techniques have been proposed to speed up the convergence of the Power method, including aggregation/disaggregation [3–5], vector extrapolation [6–10], multilevel [11–14], lumping [15, 16], Arnoldi-type [10, 17], and adaptive methods [4, 18].

To some extent, our work follows in this vein, that is, seeking a method to accelerate the convergence of Page Rank computation.

Section 3 describes our main acceleration algorithm.

The Page Rank algorithm for assigning a rank of importance to web pages has been the key technique in web search [1].

The core of the Page Rank computation consists in the principal eigenvector of a stochastic matrix representing the hyperlink structure of the web.

Many accelerating techniques have been proposed to speed up the convergence of the Power method, including aggregation/disaggregation [3–5], vector extrapolation [6–10], multilevel [11–14], lumping [15, 16], Arnoldi-type [10, 17], and adaptive methods [4, 18].

To some extent, our work follows in this vein, that is, seeking a method to accelerate the convergence of Page Rank computation.

Section 4 covers our numerical results and comparisons among the main Page Rank algorithms.