Predicting links with node embeddings

In the previous chapters, we saw how to use GNNs to produce node embeddings. A popular link prediction technique consists of using these embeddings to perform matrix factorization. This section will discuss two GNN architectures for link prediction – the Graph Autoencoder (GAE) and the Variational Graph Autoencoder (VGAE).

Introducing Graph Autoencoders

Both architectures were introduced by Kipf and Welling in 2016 [5] in a three-page paper. They represent the GNN counterparts of two popular neural network architectures – the autoencoder and the variational autoencoder. Prior knowledge about these architectures is helpful but not necessary. For ease of understanding, we will first focus on the GAE.

The GAE is composed of two modules:

• The encoder is a classic two-layer GCN that computes node embeddings as follows:

• The decoder approximates the adjacency matrix, , using matrix factorization...