GCNs
GCNs are a specific type of GNN that extend the concept of convolution to graph-structured data. GCNs learn node representations by aggregating information from neighboring nodes, allowing for the capture of both node features and graph structure.
In a GCN, the graph convolution operation at layer 
is defined as follows:
Let’s break this down:
is the matrix of node representations at layer 
, with 
(input node features).
is the adjacency matrix 
with added self-loops, where 
is the identity matrix.
is the diagonal degree matrix of 
, with 
.
is a learnable weight matrix for layer .
is a non-linear activation function, such as the rectified linear unit (ReLU) function or sigmoid function.
The term 
is the symmetrically normalized adjacency matrix, which ensures that the scale of the node representations remains consistent across layers.
Imagine a citation network, where each node stands for a scientific paper and each edge represents...
