关于一类潜在空间问题的数值计算

doi:10.12286/jssx.j2022-0945

计算数学 ›› 2023, Vol. 45 ›› Issue (2): 240-250.DOI: 10.12286/jssx.j2022-0945

关于一类潜在空间问题的数值计算

王硕¹, 王承竞¹, 何文伶¹, 唐培培²

1. 西南交通大学数学学院, 成都 611731;
2. 浙大城市学院计算机与计算科学学院, 杭州 310015

收稿日期:2022-05-13 出版日期:2023-05-14 发布日期:2023-05-13
通讯作者: 王承竞, Email:matwc@swjtu.edu.cn

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王硕, 王承竞, 何文伶, 唐培培. 关于一类潜在空间问题的数值计算[J]. 计算数学, 2023, 45(2): 240-250.

Wang Shuo, Wang Chengjing, He Wenling, Tang Peipei. ON THE NUMERICAL COMPUTATION OF A CLASS OF LATENT SPACE PROBLEMS[J]. Mathematica Numerica Sinica, 2023, 45(2): 240-250.

ON THE NUMERICAL COMPUTATION OF A CLASS OF LATENT SPACE PROBLEMS

Wang Shuo¹, Wang Chengjing¹, He Wenling¹, Tang Peipei²

1. School of Mathematics, Southwest Jiaotong University, Chengdu 61173, China;
2. School of Computer and Computing Science, Zhejiang University City College, Hangzhou 310015, China

Received:2022-05-13 Online:2023-05-14 Published:2023-05-13

潜在空间模型是网络数据统计建模和可视化的有效工具. 随着网络规模的不断扩大, 潜在空间模型的计算也面临着巨大挑战. 在本文我们应用对偶半邻近交替方向乘子法(dual semi-proximal Alternating Direction Method of Multipliers, 简称dsADMM)求解大型网络的通用潜在空间模型拟合问题. 并在一些温和的条件下分析了该算法的全局收敛性. 数值试验验证了该算法的有效性.

关键词： 潜在空间模型, 基于增广拉格朗日函数的方法, 交替方向乘子法

Latent space models are effective tools for statistical modeling and visualization of network data. With the increasing of the networks scale, the computation of latent space models faces great challenges. In this paper, we employ the dual semi-proximal alternating direction method of multipliers (dsADMM) to solve the universal latent space model fitting problems for Large Networks. We also analyze the global convergence of the algorithm under some mild conditions. Numerical experiments demonstrate the effectiveness of the algorithm.

Key words: latent space models, augmented Lagrangian function based method, alternating direction method of multipliers

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关于一类潜在空间问题的数值计算

ON THE NUMERICAL COMPUTATION OF A CLASS OF LATENT SPACE PROBLEMS

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