Bases: MessagePassing
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:
\[\mathbf{x}^{\prime}_i = \mathbf{\Theta}^{\top} \sum_{j \in \mathcal{N}(i) \cup \{ i \}} \frac{e_{j,i}}{\sqrt{\hat{d}_j \hat{d}_i}} \mathbf{x}_j\]
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)
in_channels (int) – Size of each input sample, or -1 to derive the size from the first input(s) to the forward method.
out_channels (int) – Size of each output sample.
improved (bool, optional) – If set to True, the layer computes \(\mathbf{\hat{A}}\) as \(\mathbf{A} + 2\mathbf{I}\). (default: False)
cached (bool, optional) – If set to True, the layer will cache the computation of \(\mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2}\) on first execution, and will use the cached version for further executions. This parameter should only be set to True in transductive learning scenarios. (default: False)
add_self_loops (bool, optional) – If set to False, will not add self-loops to the input graph. By default, self-loops will be added in case normalize is set to True, and not added otherwise. (default: None)
normalize (bool, optional) – Whether to add self-loops and compute symmetric normalization coefficients on-the-fly. (default: True)
bias (bool, optional) – If set to False, the layer will not learn an additive bias. (default: True)
**kwargs (optional) – Additional arguments of torch_geometric.nn.conv.MessagePassing.
input: node features \((|\mathcal{V}|, F_{in})\), edge indices \((2, |\mathcal{E}|)\) or sparse matrix \((|\mathcal{V}|, |\mathcal{V}|)\), edge weights \((|\mathcal{E}|)\) (optional)
output: node features \((|\mathcal{V}|, F_{out})\)
Runs the forward pass of the module.
Resets all learnable parameters of the module.
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