How to do Deep Learning on Graphs with Graph Convolutional Networks

Machine learning on graphs is a difficult task due to the highly complex, but also informative graph structure. This post is the second in a series on how to do deep learning on graphs with Graph Convolutional Networks (GCNs), a powerful type of neural network designed to work directly on graphs and leverage their structural information. In my previous post on GCNs, we a saw a simple mathematical framework for expressing propagation in GCNs. In short, given an N F⁰ feature matrix X and a matrix representation of the graph structure, e.g., the N N adjacency matrix A of G, each hidden layer in the GCN can be expressed as Hⁱ f(Hⁱ ¹, A)) where H⁰ X and f is a propagation rule. Each layer Hⁱ corresponds to an N Fⁱ feature matrix where each row is a feature representation of a node. These rules computes the feature representation of a node as an aggregate of the feature representations of its neighbors before it is transformed by applying the weights Wⁱ and activation function σ.