Influence Strength Estimation in Hyperbolic Space for Social Influence Maximization

The Influence Maximization (IM) problem aims to identify a small set of influential users, as seed users, to maximize their influence spread in a social network. Recently, graph representation learning approaches have gained wide attention in the IM field for their ability to encode social influence patterns into user representations, which are then used by various strategies to identify target seed users. While effective, these graph learning-based IM methods face two main limitations. First, they fail to model the influence propagation process explicitly, limiting their ability to capture the essential underlying propagation patterns. Second, they build representations in Euclidean space, which cannot reflect the latent hierarchical structure of social influence distribution. As a result, the learned representations are ineffective in supporting seed user selection. To address these limitations, we propose a novel hyperbolic learning-based IM method, HIM, which leverages hyperbolic representation learning to estimate users' influence strength from social data, particularly historical propagation processes, for solving IM tasks. Unlike previous approaches, HIM comprises two key components. First, Hyperbolic Influence Representation encodes influence spread patterns from both the social network and influence propagation instances into hyperbolic user representations. When learning from these data sources, the geometric properties of hyperbolic space naturally place highly influential users closer to the space origin, enabling practical estimation of influence strength from the distances of learned representations. Second, Adaptive Seed Selection introduces a novel scoring mechanism grounded in estimated influence strength. It leverages the geometric advantages of hyperbolic space to incrementally refine scores using multiple types of hyperbolic distance information, enabling flexible and effective seed user selection. Extensive experiments on five network datasets demonstrate the superior effectiveness and efficiency of our method under various diffusion models with both known and unknown propagation parameters, highlighting its potential for solving IM problems in large-scale, real-world social networks.