# Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning

## TL;DR

This paper introduces a symmetric graph convolutional autoencoder with a novel decoder design based on Laplacian sharpening, improving stability and performance in graph representation tasks like clustering and link prediction.

## Contribution

It presents a symmetric autoencoder architecture with a Laplacian sharpening-based decoder and a new cost function for enhanced graph representation learning.

## Key findings

- Outperforms state-of-the-art algorithms in clustering and link prediction.
- Demonstrates stability and effectiveness across multiple graph tasks.
- Introduces a numerically stable Laplacian sharpening method using signed graphs.

## Abstract

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.