AI 中文总结
该研究针对网络隐空间模型引入节点乘性效应，通过模拟实验与优化推理方案验证，提升了模型生成灵活性，更准确复现真实网络拓扑性质。
AI 中文摘要
隐空间模型将网络节点表示为几何空间中的点，连接概率由潜在位置间在固定度量（通常为欧氏、球面或双曲度量）下的距离决定。我们引入节点乘性效应对经典模型进行推广，该效应由潜在度量的局部变形所驱动，此修改近似于度量张量的共形变形，同时保留了逻辑预测器与模型的几何可解释性，从而在不改变全局参考几何的情况下捕捉额外的结构异质性。我们通过模拟实验研究所提模型的生成行为，并基于带参数正则化的分层贝叶斯公式开发了基于优化的推理方案。对8个真实网络的应用表明，所提方法提升了经典隐空间模型的生成灵活性，能更准确地复现真实网络中观测到的多种拓扑性质。
英文摘要
Latent space models represent network nodes as points in a geometric space, with connection probabilities determined by distances between latent positions under a fixed metric, typically Euclidean, spherical, or hyperbolic. We generalize the classical formulation by introducing nodal multiplicative effects motivated by a local deformation of the latent metric. This modification approximates a conformal deformation of the metric tensor while preserving the logistic predictor and the geometric interpretability of the model, thereby capturing additional structural heterogeneity without altering the global reference geometry. We study the generative behavior of the proposed model through simulation experiments and develop an optimization-based inference scheme derived from a hierarchical Bayesian formulation with parameter regularization. Applications to eight real networks show that the proposed approach increases the generative flexibility of classical latent space models and more accurately reproduces several topological properties observed in real networks.
Comments41 pages, 3 tables, 14 figures
