Extrapolation methods for fixed-point multilinear PageRank computations
Extrapolation methods for fixed-point multilinear PageRank computations
Nonnegative tensors arise very naturally in many applications that involve large and complex data flows. Due to the relatively small requirement in terms of memory storage and number of operations per step, the (shifted) higher order power method is one of the most commonly used technique for the computation of positive Z-eigenvectors of this type of tensors. However, unlike the matrix case, the method may fail to converge even for irreducible tensors. Moreover, when it converges, its convergence rate can be very slow. These two drawbacks often make the computation of the eigenvectors demanding or unfeasible for large problems. In this work, we consider a particular class of nonnegative tensors associated with the multilinear PageRank modification of higher order Markov chains. Based on the simplified topological ε-algorithm in its restarted form, we introduce an extrapolation-based acceleration of power method type algorithms, namely, the shifted fixed-point method and the inner-outer method. The accelerated methods show remarkably better performance, with faster convergence rates and reduced overall computational time. Extensive numerical experiments on synthetic and real-world datasets demonstrate the advantages of the introduced extrapolation techniques.
acceleration of convergence, extrapolation methods, fixed-point, graphs, higher order Markov chains, higher order power method, multilinear PageRank, spacey random surfer, tensor
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Redivo-Zaglia, Michela
42d8ec72-4ce1-4339-8a47-d6901217788c
Tudisco, Francesco
3c9b5744-c949-402e-ad23-b9f053c62e37
3 January 2020
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Redivo-Zaglia, Michela
42d8ec72-4ce1-4339-8a47-d6901217788c
Tudisco, Francesco
3c9b5744-c949-402e-ad23-b9f053c62e37
Cipolla, Stefano, Redivo-Zaglia, Michela and Tudisco, Francesco
(2020)
Extrapolation methods for fixed-point multilinear PageRank computations.
Numerical Linear Algebra with Applications, 27 (2), [e2280].
(doi:10.1002/nla.2280).
Abstract
Nonnegative tensors arise very naturally in many applications that involve large and complex data flows. Due to the relatively small requirement in terms of memory storage and number of operations per step, the (shifted) higher order power method is one of the most commonly used technique for the computation of positive Z-eigenvectors of this type of tensors. However, unlike the matrix case, the method may fail to converge even for irreducible tensors. Moreover, when it converges, its convergence rate can be very slow. These two drawbacks often make the computation of the eigenvectors demanding or unfeasible for large problems. In this work, we consider a particular class of nonnegative tensors associated with the multilinear PageRank modification of higher order Markov chains. Based on the simplified topological ε-algorithm in its restarted form, we introduce an extrapolation-based acceleration of power method type algorithms, namely, the shifted fixed-point method and the inner-outer method. The accelerated methods show remarkably better performance, with faster convergence rates and reduced overall computational time. Extensive numerical experiments on synthetic and real-world datasets demonstrate the advantages of the introduced extrapolation techniques.
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Numerical Linear Algebra App - 2020 - Cipolla - Extrapolation methods for fixed%E2%80%90point multilinear PageRank computations
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Accepted/In Press date: 4 December 2019
e-pub ahead of print date: 3 January 2020
Published date: 3 January 2020
Additional Information:
Funding Information: the work of S.C. and M.R.‐Z. was partially funded by University of Padua, Project no. DOR1903575/19 and by the INdAM Research group GNCS. The work of F.T. was funded by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska‐Curie Individual Fellowship “MAGNET” no. 744014. This work does not have any conflicts of interest.
Keywords:
acceleration of convergence, extrapolation methods, fixed-point, graphs, higher order Markov chains, higher order power method, multilinear PageRank, spacey random surfer, tensor
Identifiers
Local EPrints ID: 485536
URI: http://eprints.soton.ac.uk/id/eprint/485536
ISSN: 1070-5325
PURE UUID: 1c2c79e1-55ea-4fff-a268-517ccac70381
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Date deposited: 08 Dec 2023 17:42
Last modified: 18 Mar 2024 04:17
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Author:
Stefano Cipolla
Author:
Michela Redivo-Zaglia
Author:
Francesco Tudisco
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