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Multi-Linear Pseudo-PageRank for Hypergraph Partitioning

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Abstract

Motivated by the PageRank model for graph partitioning, we develop an extension of PageRank for partitioning uniform hypergraphs. Starting from adjacency tensors of uniform hypergraphs, we establish the multi-linear pseudo-PageRank (MLPPR) model, which is formulated as a multi-linear system with nonnegative constraints. The coefficient tensor of MLPPR is a kind of Laplacian tensors of uniform hypergraphs, which are almost as sparse as adjacency tensors since no dangling corrections are incorporated. Furthermore, all frontal slices of the coefficient tensor of MLPPR are M-matrices. Theoretically, MLPPR has a solution, which is unique under mild conditions. An error bound of the MLPPR solution is analyzed when the Laplacian tensor is slightly perturbed. Computationally, by exploiting the structural Laplacian tensor, we propose a tensor splitting algorithm, which converges linearly to a solution of MLPPR. Finally, numerical experiments illustrate that MLPPR is effective and efficient for hypergraph partitioning problems.

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Acknowledgements

The authors are grateful to the associate editor and anonymous referees for helping us improve the manuscript.

Funding

This work was funded by the National Natural Science Foundation of China grants 12171168, 12071159, 12326302, 62073087, and U1811464.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Yannan Chen & Wen Li

  2. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510520, China

    Jingya Chang

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  1. Yannan Chen
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  2. Wen Li
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Correspondence to Jingya Chang.

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Chen, Y., Li, W. & Chang, J. Multi-Linear Pseudo-PageRank for Hypergraph Partitioning. J Sci Comput 99, 7 (2024). https://doi.org/10.1007/s10915-024-02460-1

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