# Influence Strength Estimation in Hyperbolic Space for Social Influence Maximization

arXiv: https://arxiv.org/abs/2502.13571 · HTML: https://mlsanity.com/paper/2502.13571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 72 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Builds on (most cited first, 29 of 29)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification](https://mlsanity.com/paper/2304.05059/) (2023)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization](https://mlsanity.com/paper/2211.03074/) (2022)
- [ToupleGDD: A Fine-Designed Solution of Influence Maximization by Deep Reinforcement Learning](https://mlsanity.com/paper/2210.07500/) (2022)
- [Link Recommendation to Augment Influence Diffusion with Provable Guarantees](https://mlsanity.com/paper/2402.19189/) (2024)
- [Scalable Continuous-time Diffusion Framework for Network Inference and Influence Estimation](https://mlsanity.com/paper/2403.02867/) (2024)
- [Influence Maximization via Graph Neural Bandits](https://mlsanity.com/paper/2406.12835/) (2024)
- [DeepSN: A Sheaf Neural Framework for Influence Maximization](https://mlsanity.com/paper/2412.12416/) (2024)
- [Network Inference from a Mixture of Diffusion Models for Fake News Mitigation](https://mlsanity.com/paper/2008.03450/) (2020)
- [Influence Maximization in Social Networks: A Survey](https://mlsanity.com/paper/2309.04668/) (2023)
- [Promoting Fair Vaccination Strategies Through Influence Maximization: A Case Study on COVID-19 Spread](https://mlsanity.com/paper/2403.05564/) (2024)
- [Scalable Fair Influence Maximization](https://mlsanity.com/paper/2306.06820/) (2023)

## Abstract (arXiv)

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.