PageRank: Splitting Homogeneous Singular Linear Systems of Index One

  title={PageRank: Splitting Homogeneous Singular Linear Systems of Index One},
  author={Douglas Vincent de Jager and Jeremy T. Bradley},
The PageRank algorithm is used today within web information retrieval to provide a content-neutral ranking metric over web pages. It employs power method iterations to solve for the steady-state vector of a DTMC. The defining one-step probability transition matrix of this DTMC is derived from the hyperlink structure of the web and a model of web surfing behaviour which accounts for user bookmarks and memorised URLs. In this paper we look to provide a more accessible, more broadly applicable… 

Efficient Methodologies to Determine the Relevancy of Hanging Pages Using Stability Analysis

An algorithm to determine the relevancy of hanging pages in the link-structure-based ranking algorithms is presented and it is shown that rank results are consistent before and after altering the link structure.

Review of Link Structure Based Ranking Algorithms and Hanging Pages

This chapter addresses the issues caused by hanging pages in Web computing and compares and review the different types of link structure based ranking algorithms in ranking Web pages.

A new algorithm for detection of link spam contributed by zero-out link pages

This paper proposed a methodology to detect link spam contributed by zero-out link or dangling pages using eigenvectors and eigenvalues and found that there was a considerable improvement in their PageRank after the link spam was induced.

Solving hanging relevancy using genetic algorithm

This paper proposes a method to include the relevant hanging pages in the ranking of IR ranking algorithms by application of Genetic Algorithm.

Collecte orientée sur le Web pour la recherche d'information spécialisée. (Focused document gathering on the Web for domain-specific information retrieval)

Un coeur de tout robot d'exploration orientee se trouve une strategie de crawl qui lui permet de maximiser le rapatriement de pages pertinentes pour un theme, tout en minimisant le nombre de pages visitees qui ne sont pas en rapport avec le theme.

Towards ab initio assisted materials design: DFT based thermodynamics up to the melting point

A systematic and with respect to numerical accuracy fully controlled DFT study of thermodynamic properties for an extensive set of metals is provided, and it is shown that a high quality prediction of its temperature and volume dependence is crucial to guarantee an unbiased description of derived materials properties.



A Survey on PageRank Computing

  • P. Berkhin
  • Computer Science, Mathematics
    Internet Math.
  • 2005
The theoretical foundations of the PageRank formulation are examined, the acceleration of PageRank computing, in the effects of particular aspects of web graph structure on the optimal organization of computations, and in PageRank stability.

Extrapolation methods for accelerating PageRank computations

In Quadratic Extrapolation, the first eigenvalue of a Markov matrix is known to be 1 to compute the nonprincipal eigenvectors using successive iterates of the Power Method, a fast method for determining the dominant eigenvector of a matrix that is too large for standard fast methods to be practical.

Ranking the web frontier

This paper analyzes features of the rapidly growing "frontier" of the web, namely the part of theweb that crawlers are unable to cover for one reason or another, and suggests ways to improve the quality of ranking by modeling the growing presence of "link rot" on the web as more sites and pages fall out of maintenance.

Hypergraph Partitioning for Faster Parallel PageRank Computation

The PageRank algorithm is used by search engines such as Google to order web pages. It uses an iterative numerical method to compute the maximal eigenvector of a transition matrix derived from the

Decomposition of the Google PageRank and Optimal Linking Strategy

It is shown that there exists an optimal linking strategy that benefits a user with links inside its Web community and in contrast inappropriate links penalize the Web users and their Web communities.

On computing PageRank via lumping the Google matrix

A Web-Site-Based Partitioning Technique for Reducing Preprocessing Overhead of Parallel PageRank Computation

A power method formulation, which efficiently handles the problem of dangling pages, is investigated and an efficient parallelization scheme for matrix-vector multiplies is proposed in order to avoid possible communication due to the pages without in-links.

PageRank Computation, with Special Attention to Dangling Nodes

A Jordan decomposition of the Google matrix for the (theoretical) extreme case when all Web pages are dangling nodes, when it is required to distinguish among different classes of dangling nodes.

The PageRank Citation Ranking : Bringing Order to the Web

This paper describes PageRank, a mathod for rating Web pages objectively and mechanically, effectively measuring the human interest and attention devoted to them, and shows how to efficiently compute PageRank for large numbers of pages.

Matrix Computations, 3rd Edition