torch_geometric.nn.conv.ChebConv
- class ChebConv(in_channels: int, out_channels: int, K: int, normalization: Optional[str] = 'sym', bias: bool = True, **kwargs)[source]
Bases:
MessagePassing
The chebyshev spectral graph convolutional operator from the “Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering” paper.
\[\mathbf{X}^{\prime} = \sum_{k=1}^{K} \mathbf{Z}^{(k)} \cdot \mathbf{\Theta}^{(k)}\]where \(\mathbf{Z}^{(k)}\) is computed recursively by
\[ \begin{align}\begin{aligned}\mathbf{Z}^{(1)} &= \mathbf{X}\\\mathbf{Z}^{(2)} &= \mathbf{\hat{L}} \cdot \mathbf{X}\\\mathbf{Z}^{(k)} &= 2 \cdot \mathbf{\hat{L}} \cdot \mathbf{Z}^{(k-1)} - \mathbf{Z}^{(k-2)}\end{aligned}\end{align} \]and \(\mathbf{\hat{L}}\) denotes the scaled and normalized Laplacian \(\frac{2\mathbf{L}}{\lambda_{\max}} - \mathbf{I}\).
- 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.
K (int) – Chebyshev filter size \(K\).
normalization (str, optional) –
The normalization scheme for the graph Laplacian (default:
"sym"
):1.
None
: No normalization \(\mathbf{L} = \mathbf{D} - \mathbf{A}\)2.
"sym"
: Symmetric normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}\)3.
"rw"
: Random-walk normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}\)lambda_max
should be atorch.Tensor
of size[num_graphs]
in a mini-batch scenario and a scalar/zero-dimensional tensor when operating on single graphs. You can pre-computelambda_max
via thetorch_geometric.transforms.LaplacianLambdaMax
transform.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), batch vector \((|\mathcal{V}|)\) (optional), maximum
lambda
value \((|\mathcal{G}|)\) (optional)output: node features \((|\mathcal{V}|, F_{out})\)