Diffusion Model Agnostic Social Influence Maximization in Hyperbolic Space
Hongliang Qiao
TL;DR
This work tackles Influence Maximization (IM) when diffusion parameters are unknown and demonstrates that hyperbolic representation learning can effectively capture influence patterns from a network and observed propagation data without relying on explicit diffusion models. The proposed HIM framework comprises two components: Hyperbolic Influence Representation, which embeds users in the Lorentz model $\oldsymbol{\mathbb{L}}^n_{\gamma}$ using rotation operations and the squared Lorentzian distance $d^2_{\mathcal{L}}$, and Adaptive Seed Selection, which ranks seeds by their distance to the origin $\mathbf{o}_{\mathcal{L}}$ with a sliding-window strategy. Empirical results on five real networks under IC and WLT diffusion models show that HIM consistently outperforms baselines, including diffusion-model aware methods, while offering superior scalability to large-scale networks (~millions of nodes). The findings indicate that hyperbolic embeddings naturally capture the hierarchical and heavy-tailed structure of social influence, enabling practical, model-robust seed selection for IM in real-world settings.
Abstract
The Influence Maximization (IM) problem aims to find a small set of influential users to maximize their influence spread in a social network. Traditional methods rely on fixed diffusion models with known parameters, limiting their generalization to real-world scenarios. In contrast, graph representation learning-based methods have gained wide attention for overcoming this limitation by learning user representations to capture influence characteristics. However, existing studies are built on Euclidean space, which fails to effectively capture the latent hierarchical features of social influence distribution. As a result, users' influence spread cannot be effectively measured through the learned representations. To alleviate these limitations, we propose HIM, a novel diffusion model agnostic method that leverages hyperbolic representation learning to estimate users' potential influence spread from social propagation data. HIM consists of two key components. First, a hyperbolic influence representation module encodes influence spread patterns from network structure and historical influence activations into expressive hyperbolic user representations. Hence, the influence magnitude of users can be reflected through the geometric properties of hyperbolic space, where highly influential users tend to cluster near the space origin. Second, a novel adaptive seed selection module is developed to flexibly and effectively select seed users using the positional information of learned user representations. Extensive experiments on five network datasets demonstrate the superior effectiveness and efficiency of our method for the IM problem with unknown diffusion model parameters, highlighting its potential for large-scale real-world social networks.