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Sampling hypergraphs via joint unbiased random walk

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Abstract

Hypergraphs are instrumental in modeling complex relational systems that encompass a wide spectrum of high-order interactions among components. One prevalent analysis task is the properties estimation of large-scale hypergraphs, which involves selecting a subset of nodes and hyperedges while preserving the characteristics of the entire hypergraph. This paper aims to sample hypergraphs via random walks and is the first to perform unbiased random walks for sampling of nodes and hyperedges simultaneously in large-scale hypergraphs to the best of our knowledge. Initially, we analyze the stationary distributions of nodes and hyperedges for the simple random walk, and show that there is a high bias in both nodes and hyperedges. Subsequently, to eliminate the high bias of the simple random walk, we propose unbiased random walk strategies for nodes and hyperedges, respectively. Finally, a single joint walk schema is developed for sampling nodes and hyperedges simultaneously. To accelerate the convergence process, we employ delayed acceptance and history-aware techniques to assist our algorithm in achieving fast convergence. Extensive experimental results validate our theoretical findings, and the unbiased sampling algorithms for nodes and hyperedges have their complex hypergraph scenarios for which they are applicable. The joint random walk algorithm balanced the sampling applicable to both nodes and hyperedges.

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Data Availability

No datasets were generated or analysed during the current study.

Notes

  1. http://www.cs.cornell.edu/~arb/data

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Funding

National Key Research and Development Program of China under Grant 2020YFB1005900, National Natural Science Foundation of China (NSFC) under Grant 62122042, Shandong University multidisciplinary research and innovation team of young scholars under Grant 2020QNQT017. Young Scientists Fund of the Natural Science Foundation of Shandong Province under Grant 61150005202301.

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, 72 Binhai, Qingdao, 266200, Shandong, People’s Republic of China

    Qi Luo, Zhenzhen Xie, Yu Liu, Dongxiao Yu & Xiuzhen Cheng

  2. Antai College of Economics and Management, Shanghai Jiao Tong University, 535 Fahuazhen, Shanghai, 200052, People’s Republic of China

    Xuemin Lin

  3. Department of Computer Science, City University of Hong Kong, 83 Tat Chee Ave, Hong Kong, People’s Republic of China

    Xiaohua Jia

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  1. Qi Luo
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Contributions

Qi Luo and Zhenzhen Xie wrote the manuscript, Dongxiao Yu and Yu Liu collected the data, and Xiuzhen Cheng, Xiahua Jia and Xuemin Lin analyzed the results. All authors reviewed the results and approved the final version of the manuscript.

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Correspondence to Zhenzhen Xie.

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Luo, Q., Xie, Z., Liu, Y. et al. Sampling hypergraphs via joint unbiased random walk. World Wide Web 27, 15 (2024). https://doi.org/10.1007/s11280-024-01253-8

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