# Poincar'e Differential Privacy for Hierarchy-Aware Graph Embedding

arXiv: https://arxiv.org/abs/2312.12183 · HTML: https://mlsanity.com/paper/2312.12183/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Membership Inference Attack on Graph Neural Networks](https://mlsanity.com/paper/2101.06570/) (2021)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [Locally Private Graph Neural Networks](https://mlsanity.com/paper/2006.05535/) (2020)
- [GAP: Differentially Private Graph Neural Networks with Aggregation Perturbation](https://mlsanity.com/paper/2203.00949/) (2022)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing](https://mlsanity.com/paper/2208.08302/) (2022)
- [Secure Deep Graph Generation with Link Differential Privacy](https://mlsanity.com/paper/2005.00455/) (2020)
- [A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning](https://mlsanity.com/paper/2208.14073/) (2022)
- [Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification](https://mlsanity.com/paper/2304.05059/) (2023)
- [Contrastive Graph Clustering in Curvature Spaces](https://mlsanity.com/paper/2305.03555/) (2023)
- [A Robust and Generalized Framework for Adversarial Graph Embedding](https://mlsanity.com/paper/2105.10651/) (2021)
- [Heterogeneous Graph Neural Network for Privacy-Preserving Recommendation](https://mlsanity.com/paper/2210.00538/) (2022)
- [Cross-Network Social User Embedding with Hybrid Differential Privacy Guarantees](https://mlsanity.com/paper/2209.01539/) (2022)

## Built on by (most cited first, 7 of 7)

- [Dynamic Graph Information Bottleneck](https://mlsanity.com/paper/2402.06716/) (2024)
- [Intellectual Property in Graph-Based Machine Learning as a Service: Attacks and Defenses](https://mlsanity.com/paper/2508.19641/) (2025)
- [An Out-Of-Distribution Membership Inference Attack Approach for Cross-Domain Graph Attacks](https://mlsanity.com/paper/2505.20074/) (2025)
- [Mitigating Message Imbalance in Fraud Detection with Dual-View Graph Representation Learning](https://mlsanity.com/paper/2507.06469/) (2025)
- [Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs](https://mlsanity.com/paper/2506.15464/) (2025)
- [Harnessing LLM for Noise-Robust Cognitive Diagnosis in Web-Based Intelligent Education Systems](https://mlsanity.com/paper/2510.04093/) (2025)
- [H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation](https://mlsanity.com/paper/2608.07340/) (2026)

## Abstract (arXiv)

Hierarchy is an important and commonly observed topological property in real-world graphs that indicate the relationships between supervisors and subordinates or the organizational behavior of human groups. As hierarchy is introduced as a new inductive bias into the Graph Neural Networks (GNNs) in various tasks, it implies latent topological relations for attackers to improve their inference attack performance, leading to serious privacy leakage issues. In addition, existing privacy-preserving frameworks suffer from reduced protection ability in hierarchical propagation due to the deficiency of adaptive upper-bound estimation of the hierarchical perturbation boundary. It is of great urgency to effectively leverage the hierarchical property of data while satisfying privacy guarantees. To solve the problem, we propose the Poincar'e Differential Privacy framework, named PoinDP, to protect the hierarchy-aware graph embedding based on hyperbolic geometry. Specifically, PoinDP first learns the hierarchy weights for each entity based on the Poincar'e model in hyperbolic space. Then, the Personalized Hierarchy-aware Sensitivity is designed to measure the sensitivity of the hierarchical structure and adaptively allocate the privacy protection strength. Besides, the Hyperbolic Gaussian Mechanism (HGM) is proposed to extend the Gaussian mechanism in Euclidean space to hyperbolic space to realize random perturbations that satisfy differential privacy under the hyperbolic space metric. Extensive experiment results on five real-world datasets demonstrate the proposed PoinDP's advantages of effective privacy protection while maintaining good performance on the node classification task.