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Showing content from https://pytorch-geometric.readthedocs.io/en/latest/generated/torch_geometric.nn.conv.ChebConv.html below:

torch_geometric.nn.conv.ChebConv — pytorch_geometric documentation

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 a torch.Tensor of size [num_graphs] in a mini-batch scenario and a scalar/zero-dimensional tensor when operating on single graphs. You can pre-compute lambda_max via the torch_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 \((|\mathcal{V}|, F_{out})\)

forward(x: Tensor, edge_index: Tensor, edge_weight: Optional[Tensor] = None, batch: Optional[Tensor] = None, lambda_max: Optional[Tensor] = None) → Tensor[source]

Runs the forward pass of the module.

Return type:

Tensor

reset_parameters()[source]

Resets all learnable parameters of the module.

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