Graph Convolutional Networks

Types of graph tasks: graph and node classification

We discussed a bit about the input representation. But what about the target (output)? The most basic tasks in graph neural networks are:

• Graph classification: We have a lot of graphs and we would like to find a single label for each individual graph (similar to image classification). This task is casted as a standard supervised problem. In graphs, you will see the term inductive learning for this task.

• Node classification: Usually, in this type of task, we have a huge graph (>5000 nodes) and we try to find a label for the nodes (similar to image segmentation). Importantly, we have very few labeled nodes to train the model (for instance <5%). The aim is to predict the missing labels for all the other nodes in the graph. That is why this task is formulated as a semi-supervised learning task or transductive learning equivalently. It is called semi-supervised because even though the nodes do not have labels, we feed the graph (with all the nodes) in the neural network and formulate a supervised loss term for the labeled nodes only.

Next, you will be provided with some minimal theory on how graph data is processed

How are graph convolutions layer formed

Principle: Convolution in the vertex domain is equivalent to multiplication in the graph spectral domain.

The most straightforward implementation of a graph neural network would be something like this:

$$Y = (A X) W$$

Where $W$ is a trainable parameter and $Y$ ...