gammagl.layers.conv.GCNConv

class GCNConv(in_channels, out_channels, norm='both', add_bias=True)

The graph convolutional operator from the “Semi-supervised Classification with Graph Convolutional Networks” paper

\[\mathbf{X}^{\prime} = \mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} \mathbf{X} \mathbf{\Theta},\]

where \(\mathbf{\hat{A}} = \mathbf{A} + \mathbf{I}\) denotes the adjacency matrix with inserted self-loops and \(\hat{D}_{ii} = \sum_{j=0} \hat{A}_{ij}\) its diagonal degree matrix. The adjacency matrix can include other values than 1 representing edge weights via the optional edge_weight tensor.

Its node-wise formulation is given by:

\[\mathbf{x}^{\prime}_i = \mathbf{\Theta} \sum_{j \in \mathcal{N}(v) \cup \{ i \}} \frac{e_{j,i}}{\sqrt{\hat{d}_j \hat{d}_i}} \mathbf{x}_j\]

with \(\hat{d}_i = 1 + \sum_{j \in \mathcal{N}(i)} e_{j,i}\), where \(e_{j,i}\) denotes the edge weight from source node j to target node i (default: 1.0)

Parameters:

• in_channels (int) – Size of each input sample.

• out_channels (int) – Size of each output sample.

• norm (str, optional) –

  How to apply the normalizer. Can be one of the following values:

  • right, to divide the aggregated messages by each node’s in-degrees, which is equivalent to averaging the received messages.

  • none, where no normalization is applied.

  • both (default), where the messages are scaled with \(1/c_{ji}\) above, equivalent to symmetric normalization.

  • left, to divide the messages sent out from each node by its out-degrees, equivalent to random walk normalization.

• add_bias (bool, optional) – If set to False, the layer will not learn an additive bias. (default: True)

forward(x, edge_index, edge_weight=None, num_nodes=None)