15 research outputs found
Random Surfing Without Teleportation
In the standard Random Surfer Model, the teleportation matrix is necessary to
ensure that the final PageRank vector is well-defined. The introduction of this
matrix, however, results in serious problems and imposes fundamental
limitations to the quality of the ranking vectors. In this work, building on
the recently proposed NCDawareRank framework, we exploit the decomposition of
the underlying space into blocks, and we derive easy to check necessary and
sufficient conditions for random surfing without teleportation.Comment: 13 pages. Published in the Volume: "Algorithms, Probability, Networks
and Games, Springer-Verlag, 2015". (The updated version corrects small
typos/errors
On the limiting behavior of parameter-dependent network centrality measures
We consider a broad class of walk-based, parameterized node centrality
measures for network analysis. These measures are expressed in terms of
functions of the adjacency matrix and generalize various well-known centrality
indices, including Katz and subgraph centrality. We show that the parameter can
be "tuned" to interpolate between degree and eigenvector centrality, which
appear as limiting cases. Our analysis helps explain certain correlations often
observed between the rankings obtained using different centrality measures, and
provides some guidance for the tuning of parameters. We also highlight the
roles played by the spectral gap of the adjacency matrix and by the number of
triangles in the network. Our analysis covers both undirected and directed
networks, including weighted ones. A brief discussion of PageRank is also
given.Comment: First 22 pages are the paper, pages 22-38 are the supplementary
material
Factorizing the Stochastic Galerkin System
Recent work has explored solver strategies for the linear system of equations
arising from a spectral Galerkin approximation of the solution of PDEs with
parameterized (or stochastic) inputs. We consider the related problem of a
matrix equation whose matrix and right hand side depend on a set of parameters
(e.g. a PDE with stochastic inputs semidiscretized in space) and examine the
linear system arising from a similar Galerkin approximation of the solution. We
derive a useful factorization of this system of equations, which yields bounds
on the eigenvalues, clues to preconditioning, and a flexible implementation
method for a wide array of problems. We complement this analysis with (i) a
numerical study of preconditioners on a standard elliptic PDE test problem and
(ii) a fluids application using existing CFD codes; the MATLAB codes used in
the numerical studies are available online.Comment: 13 pages, 4 figures, 2 table
Leadership groups on Social Network Sites based on Personalized PageRank
n this paper we present a new framework to identify leaders in a Social Network Site using the Personalized PageRank vector. The methodology is based on the concept of Leadership group recently introduced by one of the authors. We show how to analyze the structure of the Leadership group as a function of a single parameter. Zachary¿s network and a Facebook university network are used to illustrate the applicability of the model.We thank an unknown referee who made some suggestive comments that improved the readability of the paper. This work is supported by Spanish DGI grant MTM2010-18674.Pedroche Sánchez, F.; Moreno, F.; González, A.; Valencia, A. (2013). Leadership groups on Social Network Sites based on Personalized PageRank. Mathematical and Computer Modelling. 57(7-8):1891-1896. https://doi.org/10.1016/j.mcm.2011.12.026S18911896577-
Ranking algorithms on directed configuration networks
This paper studies the distribution of a family of rankings, which includes
Google's PageRank, on a directed configuration model. In particular, it is
shown that the distribution of the rank of a randomly chosen node in the graph
converges in distribution to a finite random variable that can
be written as a linear combination of i.i.d. copies of the endogenous solution
to a stochastic fixed point equation of the form where is a
real-valued vector with , , and the are i.i.d. copies of ,
independent of . Moreover, we
provide precise asymptotics for the limit , which when the
in-degree distribution in the directed configuration model has a power law
imply a power law distribution for with the same exponent
An Oracle Method to Predict NFL Games
Multiple models are discussed for ranking teams in a league and introduce a new model called the Oracle method. This is a Markovian method that can be customized to incorporate multiple team traits into its ranking. Using a foresight prediction of NFL game outcomes for the 2002–2013 seasons, it is shown that the Oracle method correctly picked 64.1% of the games under consideration, which is higher than any of the methods compared, including ESPN Power Rankings, Massey, Colley, and PageRank
Multi-Step Low-Rank Decomposition of Large PageRank Matrices
The PageRank model, initially proposed by Google for search engine rankings, provides a useful network centrality measure to identify the most important nodes within large graphs arising in several applications. However, its computation is often very difficult due to the huge sizes of the networks and the unfavourable spectral properties of the associated matrices. We present a novel multi-step low-rank factorization that can be used to reduce the huge memory cost demanded for realistic PageRank calculations. Finally, we present some directions of future research