Academic Journal
A Sparse Power Method With Extrapolation for the Higher‐Order Pagerank Problem.
| Title: | A Sparse Power Method With Extrapolation for the Higher‐Order Pagerank Problem. |
|---|---|
| Authors: | Zhou, Sheng‐Wei, Wu, Gang |
| Source: | Numerical Linear Algebra with Applications; Oct2025, Vol. 32 Issue 5, p1-24, 24p |
| Subject Terms: | Extrapolation, Algorithms, Engineering simulations, Electronic data processing, Mathematical analysis, Iterative methods (Mathematics), Data analytics, Markov processes |
| Abstract: | Higher‐order Markov chain plays an important role in high‐dimensional data analysis and modeling multi‐relational problems. As an application, higher‐order PageRank is a generalization to Google's PageRank. For this problem, the challenge is how to solve higher‐order PageRank both rapidly and accurately. Extrapolation methods are effectively accelerating techniques for large‐scale scientific computations. As far as we know, there are no extrapolation accelerated methods for higher‐order PageRank problem. One reason is that the stationary distribution of the higher‐order PageRank problem is a large‐scale and dense dataset, and existing extrapolation methods cannot apply to this problem directly. Sparse higher‐order PageRank generated by the sparse power method is a good alternative to higher‐order PageRank, in which the dense higher‐order PageRank is approximated by using a combination of a sparse component and a rank‐one component. In this work, we propose a sparse power method with extrapolation. The idea is to run the extrapolation method on the rank‐one component and get the weighting coefficients first, and then apply the coefficients to both the sparse component and the rank‐one component simultaneously. However, the difficulty is to show why this works theoretically. To settle this problem, we demonstrate the rationality of our strategy, and prove that the proposed method can converge faster than the original sparse power method. Extensive numerical experiments on both real‐world and synthetic database illustrate the efficiency of the proposed method, and show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR] |
| Copyright of Numerical Linear Algebra with Applications is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Complementary Index |
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| Header | DbId: edb DbLabel: Complementary Index An: 188962670 RelevancyScore: 1023 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1023.09039306641 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Sparse Power Method With Extrapolation for the Higher‐Order Pagerank Problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhou%2C+Sheng‐Wei%22">Zhou, Sheng‐Wei</searchLink><br /><searchLink fieldCode="AR" term="%22Wu%2C+Gang%22">Wu, Gang</searchLink> – Name: TitleSource Label: Source Group: Src Data: Numerical Linear Algebra with Applications; Oct2025, Vol. 32 Issue 5, p1-24, 24p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Extrapolation%22">Extrapolation</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+simulations%22">Engineering simulations</searchLink><br /><searchLink fieldCode="DE" term="%22Electronic+data+processing%22">Electronic data processing</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Data+analytics%22">Data analytics</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Higher‐order Markov chain plays an important role in high‐dimensional data analysis and modeling multi‐relational problems. As an application, higher‐order PageRank is a generalization to Google's PageRank. For this problem, the challenge is how to solve higher‐order PageRank both rapidly and accurately. Extrapolation methods are effectively accelerating techniques for large‐scale scientific computations. As far as we know, there are no extrapolation accelerated methods for higher‐order PageRank problem. One reason is that the stationary distribution of the higher‐order PageRank problem is a large‐scale and dense dataset, and existing extrapolation methods cannot apply to this problem directly. Sparse higher‐order PageRank generated by the sparse power method is a good alternative to higher‐order PageRank, in which the dense higher‐order PageRank is approximated by using a combination of a sparse component and a rank‐one component. In this work, we propose a sparse power method with extrapolation. The idea is to run the extrapolation method on the rank‐one component and get the weighting coefficients first, and then apply the coefficients to both the sparse component and the rank‐one component simultaneously. However, the difficulty is to show why this works theoretically. To settle this problem, we demonstrate the rationality of our strategy, and prove that the proposed method can converge faster than the original sparse power method. Extensive numerical experiments on both real‐world and synthetic database illustrate the efficiency of the proposed method, and show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Numerical Linear Algebra with Applications is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/nla.70042 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 1 Subjects: – SubjectFull: Extrapolation Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Engineering simulations Type: general – SubjectFull: Electronic data processing Type: general – SubjectFull: Mathematical analysis Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Data analytics Type: general – SubjectFull: Markov processes Type: general Titles: – TitleFull: A Sparse Power Method With Extrapolation for the Higher‐Order Pagerank Problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhou, Sheng‐Wei – PersonEntity: Name: NameFull: Wu, Gang IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 10705325 Numbering: – Type: volume Value: 32 – Type: issue Value: 5 Titles: – TitleFull: Numerical Linear Algebra with Applications Type: main |
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