GCN Convolutional Layer (Kipf & Welling 2016)

Implements the basic GCN layer from Kipf & Welling (2016): $$H^{(k)} = \sigma(\tilde{A} H^{(k-1)} W + b)$$

Usage

layer_gcn(in_features, out_features, bias = TRUE, normalize = TRUE)

Arguments

in_features

Integer. Number of input features per node

out_features

Integer. Number of output features per node

bias

Logical. Add learnable bias. Default: TRUE

normalize

Logical. Whether to add self-loops and compute symmetric normalization on-the-fly. Default: TRUE

Value

Tensor n_nodes x out_features. Transformed node features

Details

Where \(\tilde{A} = \tilde{D}^{-1/2}(A + I)\tilde{D}^{-1/2}\) is the symmetrically normalized adjacency matrix with self-loops, and \(\tilde{D}\) is the degree matrix of \(A + I\).

This is the standard GCN layer that uses:

• Single weight matrix \(W\)

• Symmetric normalization with self-loops

• Optional on-the-fly normalization

When normalize = TRUE (default), the layer computes \(\tilde{A}\) on-the-fly from the input adjacency matrix by adding self-loops and applying symmetric normalization. When normalize = FALSE, you must pass in a pre-normalized adjacency matrix.

Parameters:

• \(W\): in_features x out_features learnable weight matrix

• \(b\): out_features learnable bias term (optional)

Forward pass

layer(x, adj)

• x: Tensor n_nodes x in_features. Node feature matrix.

• adj: Sparse COO tensor n_nodes x n_nodes. Adjacency matrix defining graph structure. Can be binary (0/1) or weighted.

References

Kipf, T. N., & Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907. doi:10.48550/arXiv.1609.02907

Examples

if (FALSE) { # torch::torch_is_installed()
adj <- adj_from_edgelist(from = c(1, 2, 3, 4), to = c(2, 3, 4, 1))
x <- torch::torch_randn(4, 8)

layer <- layer_gcn(8, 4)
layer(x, adj)

# Normalize once up front and reuse across layers
adj_norm <- gcn_normalize(add_graph_self_loops(adj))
layer <- layer_gcn(8, 4, normalize = FALSE)
layer(x, adj_norm)
}