# Variational Graph Normalized Auto-Encoders

arXiv: https://arxiv.org/abs/2108.08046 · HTML: https://mlsanity.com/paper/2108.08046/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 18 Aug 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Transformers without Tears: Improving the Normalization of Self-Attention](https://mlsanity.com/paper/1910.05895/) (2019)
- [L2-constrained Softmax Loss for Discriminative Face Verification](https://mlsanity.com/paper/1703.09507/) (2017)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Ring loss: Convex Feature Normalization for Face Recognition](https://mlsanity.com/paper/1803.00130/) (2018)
- [Graph InfoClust: Leveraging cluster-level node information for unsupervised graph representation learning](https://mlsanity.com/paper/2009.06946/) (2020)
- [Deep Metric Learning with Spherical Embedding](https://mlsanity.com/paper/2011.02785/) (2020)
- [Measuring Word Significance using Distributed Representations of Words](https://mlsanity.com/paper/1508.02297/) (2015)
- [Improving Lexical Choice in Neural Machine Translation](https://mlsanity.com/paper/1710.01329/) (2017)
- [Simple and Effective Graph Autoencoders with One-Hop Linear Models](https://mlsanity.com/paper/2001.07614/) (2020)
- [Mutual Information Maximization in Graph Neural Networks](https://mlsanity.com/paper/1905.08509/) (2019)
- [How much does a word weigh? Weighting word embeddings for word sense induction](https://mlsanity.com/paper/1805.09209/) (2018)
- [Deep Spherical Quantization for Image Search](https://mlsanity.com/paper/1906.02865/) (2019)

## Built on by (most cited first, 29 of 29)

- [Beyond Text: A Deep Dive into Large Language Models' Ability on Understanding Graph Data](https://mlsanity.com/paper/2310.04944/) (2023)
- [Reliable Node Similarity Matrix Guided Contrastive Graph Clustering](https://mlsanity.com/paper/2408.03765/) (2024)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (2024)
- [Accurate Link Prediction for Edge-Incomplete Graphs via PU Learning](https://mlsanity.com/paper/2405.11911/) (2024)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [Independent Distribution Regularization for Private Graph Embedding](https://mlsanity.com/paper/2308.08360/) (2023)
- [TEDDY: Trimming Edges with Degree-based Discrimination strategY](https://mlsanity.com/paper/2402.01261/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Interpretable Node Representation with Attribute Decoding](https://mlsanity.com/paper/2212.01682/) (2022)
- [Variational Disentangled Graph Auto-Encoders for Link Prediction](https://mlsanity.com/paper/2306.11315/) (2023)
- [Graph Perceiver IO: A General Architecture for Graph Structured Data](https://mlsanity.com/paper/2209.06418/) (2022)
- [Evaluating Link Prediction Explanations for Graph Neural Networks](https://mlsanity.com/paper/2308.01682/) (2023)
- [Norm Augmented Graph AutoEncoders for Link Prediction](https://mlsanity.com/paper/2502.05868/) (2025)
- [Residual Reweighted Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2506.07854/) (2025)
- [Variational Mixture of Graph Neural Experts for Alzheimer's Disease Recognition across Frequency Bands in EEG Brain Networks](https://mlsanity.com/paper/2510.11917/) (2025)
- [NESS: Node Embeddings from Static SubGraphs](https://mlsanity.com/paper/2303.08958/) (2023)
- [A parameterised model for link prediction using node centrality and similarity measure based on graph embedding](https://mlsanity.com/paper/2309.05434/) (2023)
- [Introducing New Node Prediction in Graph Mining: Predicting All Links from Isolated Nodes with Graph Neural Networks](https://mlsanity.com/paper/2401.05468/) (2024)
- [Learning Network Representations with Disentangled Graph Auto-Encoder](https://mlsanity.com/paper/2402.01143/) (2024)
- [PROXI: Challenging the GNNs for Link Prediction](https://mlsanity.com/paper/2410.01802/) (2024)
- [Tri-Learn Graph Fusion Network for Attributed Graph Clustering](https://mlsanity.com/paper/2507.13620/) (2025)
- [CoCon: A Data Set on Combined Contextualized Research Artifact Use](https://mlsanity.com/paper/2303.15193/) (2023)
- [NP2L: Negative Pseudo Partial Labels Extraction for Graph Neural Networks](https://mlsanity.com/paper/2310.01098/) (2023)
- [Performance Prediction of Hub-Based Swarms](https://mlsanity.com/paper/2408.04822/) (2024)
- [SCNode: Spatial and Contextual Coordinates for Graph Representation Learning](https://mlsanity.com/paper/2410.02158/) (2024)
- [Enhancing Future Link Prediction in Quantum Computing Semantic Networks through LLM-Initiated Node Features](https://mlsanity.com/paper/2410.04251/) (2024)
- [Can Self Supervision Rejuvenate Similarity-Based Link Prediction?](https://mlsanity.com/paper/2410.19183/) (2024)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [Enhancing Contrastive Link Prediction With Edge Balancing Augmentation](https://mlsanity.com/paper/2508.14808/) (2025)

## Abstract (arXiv)

Link prediction is one of the key problems for graph-structured data. With the advancement of graph neural networks, graph autoencoders (GAEs) and variational graph autoencoders (VGAEs) have been proposed to learn graph embeddings in an unsupervised way. It has been shown that these methods are effective for link prediction tasks. However, they do not work well in link predictions when a node whose degree is zero (i.g., isolated node) is involved. We have found that GAEs/VGAEs make embeddings of isolated nodes close to zero regardless of their content features. In this paper, we propose a novel Variational Graph Normalized AutoEncoder (VGNAE) that utilize L2-normalization to derive better embeddings for isolated nodes. We show that our VGNAEs outperform the existing state-of-the-art models for link prediction tasks. The code is available at https://github.com/SeongJinAhn/VGNAE.