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Hypergraph and Uncertain Hypergraph Representation Learning Theory and Methods

Author

Listed:
  • Liyan Zhang

    (College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Jingfeng Guo

    (College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Jiazheng Wang

    (College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Jing Wang

    (College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Shanshan Li

    (College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Chunying Zhang

    (School of Science, North China University of Science and Technology, Tangshan 063210, China)

Abstract

With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize higher order relationships, which have attracted extensive attention from academia and industry in recent years. Firstly, this paper described the development process, the application areas, and the existing review research of hypergraphs; secondly, introduced the theory of hypergraphs briefly; then, compared the learning methods of ordinary graphs and hypergraphs from three aspects: matrix decomposition, random walk, and deep learning; next, introduced the structural optimization of hypergraphs from three perspectives: dynamic hypergraphs, hyperedge weight optimization, and multimodal hypergraph generation; after that, the applicability of three uncertain hypergraph models were analyzed based on three uncertainty theories: probability theory, fuzzy set, and rough set; finally, the future research directions of hypergraphs and uncertain hypergraphs were prospected.

Suggested Citation

  • Liyan Zhang & Jingfeng Guo & Jiazheng Wang & Jing Wang & Shanshan Li & Chunying Zhang, 2022. "Hypergraph and Uncertain Hypergraph Representation Learning Theory and Methods," Mathematics, MDPI, vol. 10(11), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1921-:d:831140
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    References listed on IDEAS

    as
    1. Musavarah Sarwar & Gohar Ali, 2022. "A Theoretical Investigation Based on the Rough Approximations of Hypergraphs," Journal of Mathematics, Hindawi, vol. 2022, pages 1-19, March.
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    Cited by:

    1. Jing Wang & Jing Wang & Jingfeng Guo & Liya Wang & Chunying Zhang & Bin Liu, 2023. "Research Progress of Complex Network Modeling Methods Based on Uncertainty Theory," Mathematics, MDPI, vol. 11(5), pages 1-27, March.
    2. Liya Wang & Yaxun Dai & Renzhuo Wang & Yuwen Sun & Chunying Zhang & Zhiwei Yang & Yuqing Sun, 2022. "SEIARN: Intelligent Early Warning Model of Epidemic Spread Based on LSTM Trajectory Prediction," Mathematics, MDPI, vol. 10(17), pages 1-23, August.
    3. Jingfeng Guo & Chao Zheng & Shanshan Li & Yutong Jia & Bin Liu, 2022. "BiInfGCN: Bilateral Information Augmentation of Graph Convolutional Networks for Recommendation," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    4. Xiao Chen & Tong Hao & Li Han & Meng Leng & Jing Chen & Jingfeng Guo, 2022. "Heterogeneous Network Embedding Based on Random Walks of Type and Inner Constraint," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    5. Fengchun Liu & Sen Zhang & Weining Ma & Jingguo Qu, 2022. "Research on Attack Detection of Cyber Physical Systems Based on Improved Support Vector Machine," Mathematics, MDPI, vol. 10(15), pages 1-14, August.

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