Graph Convolutional Networks

For these models, the goal is then to learn a function of signals/features on a graph \(\mathcal{G}=(\mathcal{V}, \mathcal{E})\) which takes as input:

and produces a node-level output \(Z\) (an \(N\times F\) feature matrix, where \(F\) is the number of output features per node). Let’s take a look at how our simple GCN model (see previous section or Kipf & Welling, ICLR 2017) works on a well-known graph dataset: Zachary’s karate club network (see Figure above). Now, even before training the weights, we simply insert the adjacency matrix of the graph and \(X = I\) (i.e. the identity matrix, as we don’t have any node features) into the model.

Source: tkipf.github.io