# Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking

arXiv: https://arxiv.org/abs/1707.03815 · HTML: https://mlsanity.com/paper/1707.03815/

## Key facts

- Cited by 335 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2017.

## Built on by (most cited first, 30 of 335)

- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervision](https://mlsanity.com/paper/2204.04879/) (2022)
- [Robustness of Graph Neural Networks at Scale](https://mlsanity.com/paper/2110.14038/) (2021)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [CONTaiNER: Few-Shot Named Entity Recognition via Contrastive Learning](https://mlsanity.com/paper/2109.07589/) (2021)
- [FederatedScope: A Flexible Federated Learning Platform for Heterogeneity](https://mlsanity.com/paper/2204.05011/) (2022)
- [A Survey on Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2304.08130/) (2023)
- [Virtual Node Tuning for Few-shot Node Classification](https://mlsanity.com/paper/2306.06063/) (2023)
- [Structural Re-weighting Improves Graph Domain Adaptation](https://mlsanity.com/paper/2306.03221/) (2023)
- [Task-Adaptive Few-shot Node Classification](https://mlsanity.com/paper/2206.11972/) (2022)
- [GNNDelete: A General Strategy for Unlearning in Graph Neural Networks](https://mlsanity.com/paper/2302.13406/) (2023)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Linkless Link Prediction via Relational Distillation](https://mlsanity.com/paper/2210.05801/) (2022)
- [Fully-inductive Node Classification on Arbitrary Graphs](https://mlsanity.com/paper/2405.20445/) (2024)
- [Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shift](https://mlsanity.com/paper/2201.11349/) (2022)
- [Are Defenses for Graph Neural Networks Robust?](https://mlsanity.com/paper/2301.13694/) (2023)
- [Sequential Recommendation via Stochastic Self-Attention](https://mlsanity.com/paper/2201.06035/) (2022)
- [GraphControl: Adding Conditional Control to Universal Graph Pre-trained Models for Graph Domain Transfer Learning](https://mlsanity.com/paper/2310.07365/) (2023)
- [GREED: A Neural Framework for Learning Graph Distance Functions](https://mlsanity.com/paper/2112.13143/) (2021)
- [Block Modeling-Guided Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.13507/) (2021)
- [MLPInit: Embarrassingly Simple GNN Training Acceleration with MLP Initialization](https://mlsanity.com/paper/2210.00102/) (2022)
- [A Survey of Mix-based Data Augmentation: Taxonomy, Methods, Applications, and Explainability](https://mlsanity.com/paper/2212.10888/) (2022)
- [Inductive Graph Unlearning](https://mlsanity.com/paper/2304.03093/) (2023)
- [Graph Lifelong Learning: A Survey](https://mlsanity.com/paper/2202.10688/) (2022)

## Abstract (arXiv)

Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on large scale (attributed) graphs that show strong performance on tasks such as link prediction and node classification. Unlike most approaches that represent nodes as point vectors in a low-dimensional continuous space, we embed each node as a Gaussian distribution, allowing us to capture uncertainty about the representation. Furthermore, we propose an unsupervised method that handles inductive learning scenarios and is applicable to different types of graphs: plain/attributed, directed/undirected. By leveraging both the network structure and the associated node attributes, we are able to generalize to unseen nodes without additional training. To learn the embeddings we adopt a personalized ranking formulation w.r.t. the node distances that exploits the natural ordering of the nodes imposed by the network structure. Experiments on real world networks demonstrate the high performance of our approach, outperforming state-of-the-art network embedding methods on several different tasks. Additionally, we demonstrate the benefits of modeling uncertainty - by analyzing it we can estimate neighborhood diversity and detect the intrinsic latent dimensionality of a graph.