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A family of gradient methods using Householder transformation with application to hypergraph partitioning

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Abstract

In this paper, we propose a constraint preserving algorithm for the smallest Z-eigenpair of the compact Laplacian tensor of an even-uniform hypergraph, where Householder transform is employed and a family of modified conjugate directions with sufficient descent is determined. Besides, we prove that there exists a positive step size in the new constraint preserving update scheme such that the Wolfe conditions hold. Based on these properties, we prove the convergence of the new algorithm. Furthermore, we apply our algorithm to the hypergraph partitioning and image segmentation, and numerical results are reported to illustrate the efficiency of the proposed algorithm.

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Acknowledgements

The authors would like to thank Dr. Yannan Chen for his insightful discussions on hypergraph partitioning and image segmentation.

Funding

This paper was supported by Suqian Sci & Tech Program (Grant No. Z2020135 and K202112), the National Natural Science Foundation of China (Grant No. 11901118, 12001281 and 62073087), the Anhui Provincial Natural Science Foundation (Grant No. 2208085QA07), and the Youth Foundation of Anhui University of Technology (Grant No. QZ202114) and was sponsored by Qing Lan Project.

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Authors and Affiliations

  1. School of Sciences and Arts, Suqian University, Suqian, 223800, China

    Xin Zhang

  2. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510006, China

    Jingya Chang

  3. School of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing, 210038, China

    Zhili Ge

  4. Department of Data Science, Anhui University of Technology, Maanshan, 243002, China

    Zhou Sheng

  5. Anhui Provincial Joint Key Laboratory of Disciplines for Industrial Big Data Analysis and Intelligent Decision, Maanshan, 243032, China

    Zhou Sheng

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  1. Xin Zhang
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  4. Zhou Sheng
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Contributions

The first author prepared the mathematica programs of the presented algorithms, all authors wrote the main manuscript text and prepared the tables and figures, and all authors reviewed the manuscript.

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Correspondence to Zhou Sheng.

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Zhang, X., Chang, J., Ge, Z. et al. A family of gradient methods using Householder transformation with application to hypergraph partitioning. Numer Algor 95, 897–927 (2024). https://doi.org/10.1007/s11075-023-01593-y

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