# Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction

arXiv: https://arxiv.org/abs/2202.09025 · HTML: https://mlsanity.com/paper/2202.09025/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 62 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 30 of 42)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)

## Built on by (most cited first, 28 of 28)

- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modeling](https://mlsanity.com/paper/2304.02806/) (2023)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs](https://mlsanity.com/paper/2308.02117/) (2023)
- [Graph Neural Networks in IoT: A Survey](https://mlsanity.com/paper/2203.15935/) (2022)
- [GraphAlign: Pretraining One Graph Neural Network on Multiple Graphs via Feature Alignment](https://mlsanity.com/paper/2406.02953/) (2024)
- [Deep Efficient Private Neighbor Generation for Subgraph Federated Learning](https://mlsanity.com/paper/2401.04336/) (2024)
- [MUSE: Multi-View Contrastive Learning for Heterophilic Graphs](https://mlsanity.com/paper/2307.16026/) (2023)
- [Decoupled Self-supervised Learning for Non-Homophilous Graphs](https://mlsanity.com/paper/2206.03601/) (2022)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Unsupervised Network Embedding Beyond Homophily](https://mlsanity.com/paper/2203.10866/) (2022)
- [Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidance](https://mlsanity.com/paper/2510.10402/) (2025)
- [A Survey of Few-Shot Learning on Graphs: from Meta-Learning to Pre-Training and Prompt Learning](https://mlsanity.com/paper/2402.01440/) (2024)
- [A Pure Transformer Pretraining Framework on Text-attributed Graphs](https://mlsanity.com/paper/2406.13873/) (2024)
- [AI-accelerated Discovery of Altermagnetic Materials](https://mlsanity.com/paper/2311.04418/) (2023)
- [Empowering Dual-Level Graph Self-Supervised Pretraining with Motif Discovery](https://mlsanity.com/paper/2312.11927/) (2023)
- [Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings](https://mlsanity.com/paper/2409.10452/) (2024)
- [Discrepancy-Aware Graph Mask Auto-Encoder](https://mlsanity.com/paper/2506.19343/) (2025)
- [Contrastive Learning for Non-Local Graphs with Multi-Resolution Structural Views](https://mlsanity.com/paper/2308.10077/) (2023)
- [ROGPL: Robust Open-Set Graph Learning via Region-Based Prototype Learning](https://mlsanity.com/paper/2402.18495/) (2024)
- [Towards Consistency and Complementarity: A Multiview Graph Information Bottleneck Approach](https://mlsanity.com/paper/2210.05676/) (2022)
- [Isomorphic-Consistent Variational Graph Auto-Encoders for Multi-Level Graph Representation Learning](https://mlsanity.com/paper/2312.05519/) (2023)
- [Establishing Deep InfoMax as an effective self-supervised learning methodology in materials informatics](https://mlsanity.com/paper/2407.00671/) (2024)
- [High-Pass Graph Convolutional Network for Enhanced Anomaly Detection: A Novel Approach](https://mlsanity.com/paper/2411.01817/) (2024)
- [Auto-encoding Molecules: Graph-Matching Capabilities Matter](https://mlsanity.com/paper/2503.00426/) (2025)
- [α-Graph: Attention-Infused Normalizing Flow Approach to Tractable Graph Modeling](https://mlsanity.com/paper/2609.07961/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have drawn significant research attention recently, mostly under the setting of semi-supervised learning. When task-agnostic representations are preferred or supervision is simply unavailable, the auto-encoder framework comes in handy with a natural graph reconstruction objective for unsupervised GNN training. However, existing graph auto-encoders are designed to reconstruct the direct links, so GNNs trained in this way are only optimized towards proximity-oriented graph mining tasks, and will fall short when the topological structures matter. In this work, we revisit the graph encoding process of GNNs which essentially learns to encode the neighborhood information of each node into an embedding vector, and propose a novel graph decoder to reconstruct the entire neighborhood information regarding both proximity and structure via Neighborhood Wasserstein Reconstruction (NWR). Specifically, from the GNN embedding of each node, NWR jointly predicts its node degree and neighbor feature distribution, where the distribution prediction adopts an optimal-transport loss based on the Wasserstein distance. Extensive experiments on both synthetic and real-world network datasets show that the unsupervised node representations learned with NWR have much more advantageous in structure-oriented graph mining tasks, while also achieving competitive performance in proximity-oriented ones.