# Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning

arXiv: https://arxiv.org/abs/1908.02441 · HTML: https://mlsanity.com/paper/1908.02441/

## Key facts

- Cited by 94 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2019.

## Built on by (most cited first, 30 of 94)

- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervision](https://mlsanity.com/paper/2204.04879/) (2022)
- [Deep Graph Clustering via Dual Correlation Reduction](https://mlsanity.com/paper/2112.14772/) (2021)
- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modeling](https://mlsanity.com/paper/2304.02806/) (2023)
- [Graph Prompt Learning: A Comprehensive Survey and Beyond](https://mlsanity.com/paper/2311.16534/) (2023)
- [Simple Contrastive Graph Clustering](https://mlsanity.com/paper/2205.07865/) (2022)
- [Heterogeneous Graph Masked Autoencoders](https://mlsanity.com/paper/2208.09957/) (2022)
- [SkeletonMAE: Graph-based Masked Autoencoder for Skeleton Sequence Pre-training](https://mlsanity.com/paper/2307.08476/) (2023)
- [Attention-driven Graph Clustering Network](https://mlsanity.com/paper/2108.05499/) (2021)
- [A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and Open Resource](https://mlsanity.com/paper/2211.12875/) (2022)
- [SeeGera: Self-supervised Semi-implicit Graph Variational Auto-encoders with Masking](https://mlsanity.com/paper/2301.12458/) (2023)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [GiGaMAE: Generalizable Graph Masked Autoencoder via Collaborative Latent Space Reconstruction](https://mlsanity.com/paper/2308.09663/) (2023)
- [DGCLUSTER: A Neural Framework for Attributed Graph Clustering via Modularity Maximization](https://mlsanity.com/paper/2312.12697/) (2023)
- [Eliciting Structural and Semantic Global Knowledge in Unsupervised Graph Contrastive Learning](https://mlsanity.com/paper/2202.08480/) (2022)
- [MAGIC: Detecting Advanced Persistent Threats via Masked Graph Representation Learning](https://mlsanity.com/paper/2310.09831/) (2023)
- [Self-supervised Contrastive Attributed Graph Clustering](https://mlsanity.com/paper/2110.08264/) (2021)
- [Revisiting Modularity Maximization for Graph Clustering: A Contrastive Learning Perspective](https://mlsanity.com/paper/2406.14288/) (2024)
- [Graph Neural Networks: Methods, Applications, and Opportunities](https://mlsanity.com/paper/2108.10733/) (2021)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Reinforcement Graph Clustering with Unknown Cluster Number](https://mlsanity.com/paper/2308.06827/) (2023)
- [Motif-aware Attribute Masking for Molecular Graph Pre-training](https://mlsanity.com/paper/2309.04589/) (2023)
- [Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoders](https://mlsanity.com/paper/2103.16046/) (2021)
- [Improved Dual Correlation Reduction Network](https://mlsanity.com/paper/2202.12533/) (2022)
- [Learning Graph Augmentations to Learn Graph Representations](https://mlsanity.com/paper/2201.09830/) (2022)
- [Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learning](https://mlsanity.com/paper/2206.12933/) (2022)

## Abstract (arXiv)

We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly designed decoder which builds a completely symmetric autoencoder form. For the reconstruction of node features, the decoder is designed based on Laplacian sharpening as the counterpart of Laplacian smoothing of the encoder, which allows utilizing the graph structure in the whole processes of the proposed autoencoder architecture. In order to prevent the numerical instability of the network caused by the Laplacian sharpening introduction, we further propose a new numerically stable form of the Laplacian sharpening by incorporating the signed graphs. In addition, a new cost function which finds a latent representation and a latent affinity matrix simultaneously is devised to boost the performance of image clustering tasks. The experimental results on clustering, link prediction and visualization tasks strongly support that the proposed model is stable and outperforms various state-of-the-art algorithms.