Bases: MessagePassing
The graph convolutional operator from the “Semi-supervised Classification with Graph Convolutional Networks” paper.
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:
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 \((|\mathcal{V}|, F_{out})\)