Permutation-Invariant Variational Autoencoder for Graph-Level Representation Learning

Robin Winter, Frank Noe, Djork-Arne Clevert

Keywords: variational autoencoder, permutation invariance, graph, self-attention, representation learning, graph autoencoder

Abstract:

Recently, there has been great success in applying deep neural networks on graph structured data. Most work, however, focuses on either node- or graph-level supervised learning, such as node, link or graph classification or node-level unsupervised learning (e.g. node clustering). Despite its wide range of possible applications, graph-level unsupervised learning has not received much attention yet. This might be mainly attributed to the high representation complexity of graphs, which can be represented by $n!$ equivalent adjacency matrices, where $n$ is the number of nodes.
In this work we address this issue by proposing a permutation-invariant variational autoencoder for graph structured data. Our proposed model indirectly learns to match the node ordering of input and output graph, without imposing a particular node ordering or performing expensive graph matching. We demonstrate the effectiveness of our proposed model for graph reconstruction, generation and interpolation and evaluate the expressive power of extracted representations for downstream graph-level classification and regression.

Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.

TL;DR: We propose a variational autoencoder that encodes graphs in a fixed-size latent space that is invariant under permutation of the input graph.

Code: https://github.com/jrwnter/pigvae

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/permutation-invariant-variational-autoencoder/code)