# Gromov-Wasserstein Discrepancy with Local Differential Privacy for Distributed Structural Graphs

arXiv: https://arxiv.org/abs/2202.00808 · HTML: https://mlsanity.com/paper/2202.00808/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 65 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [FedML: A Research Library and Benchmark for Federated Machine Learning](https://mlsanity.com/paper/2007.13518/) (2020)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Practical Secure Aggregation for Federated Learning on User-Held Data](https://mlsanity.com/paper/1611.04482/) (2016)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets](https://mlsanity.com/paper/1811.03761/) (2018)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Gromov-Wasserstein Alignment of Word Embedding Spaces](https://mlsanity.com/paper/1809.00013/) (2018)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Byzantine-Resilient Secure Federated Learning](https://mlsanity.com/paper/2007.11115/) (2020)
- [Accelerating Federated Learning via Momentum Gradient Descent](https://mlsanity.com/paper/1910.03197/) (2019)
- [Locally Private Graph Neural Networks](https://mlsanity.com/paper/2006.05535/) (2020)
- [GraphFL: A Federated Learning Framework for Semi-Supervised Node Classification on Graphs](https://mlsanity.com/paper/2012.04187/) (2020)
- [Information Obfuscation of Graph Neural Networks](https://mlsanity.com/paper/2009.13504/) (2020)
- [FL-AGCNS: Federated Learning Framework for Automatic Graph Convolutional Network Search](https://mlsanity.com/paper/2104.04141/) (2021)
- [Privacy-Utility Tradeoffs in Routing Cryptocurrency over Payment Channel Networks](https://mlsanity.com/paper/1909.02717/) (2019)

## Built on by (most cited first, 6 of 6)

- [Degree-Preserving Randomized Response for Graph Neural Networks under Local Differential Privacy](https://mlsanity.com/paper/2202.10209/) (2022)
- [Decentralized Graph Neural Network for Privacy-Preserving Recommendation](https://mlsanity.com/paper/2308.08072/) (2023)
- [Privacy-Preserving Graph Embedding based on Local Differential Privacy](https://mlsanity.com/paper/2310.11060/) (2023)
- [Wasserstein Differential Privacy](https://mlsanity.com/paper/2401.12436/) (2024)
- [Mitigating the Performance Sacrifice in DP-Satisfied Federated Settings through Graph Contrastive Learning](https://mlsanity.com/paper/2207.11836/) (2022)
- [Optimal Transport for Kernel Gaussian Mixture Models](https://mlsanity.com/paper/2310.18586/) (2023)

## Abstract (arXiv)

Learning the similarity between structured data, especially the graphs, is one of the essential problems. Besides the approach like graph kernels, Gromov-Wasserstein (GW) distance recently draws big attention due to its flexibility to capture both topological and feature characteristics, as well as handling the permutation invariance. However, structured data are widely distributed for different data mining and machine learning applications. With privacy concerns, accessing the decentralized data is limited to either individual clients or different silos. To tackle these issues, we propose a privacy-preserving framework to analyze the GW discrepancy of node embedding learned locally from graph neural networks in a federated flavor, and then explicitly place local differential privacy (LDP) based on Multi-bit Encoder to protect sensitive information. Our experiments show that, with strong privacy protections guaranteed by the varepsilon-LDP algorithm, the proposed framework not only preserves privacy in graph learning but also presents a noised structural metric under GW distance, resulting in comparable and even better performance in classification and clustering tasks. Moreover, we reason the rationale behind the LDP-based GW distance analytically and empirically.