torch_geometric.nn.conv.GCNConv
- class GCNConv(in_channels: int, out_channels: int, improved: bool = False, cached: bool = False, add_self_loops: bool = True, normalize: bool = True, bias: bool = True, **kwargs)[source]
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 optionaledge_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 nodei
(default:1.0
)- Parameters
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 toTrue
in transductive learning scenarios. (default:False
)add_self_loops (bool, optional) – If set to
False
, will not add self-loops to the input graph. (default:True
)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
.
- Shapes:
input: node features \((|\mathcal{V}|, F_{in})\), edge indices \((2, |\mathcal{E}|)\), edge weights \((|\mathcal{E}|)\) (optional)
output: node features \((|\mathcal{V}|, F_{out})\)