gammagl.layers.conv.ChebConv

class ChebConv(in_channels: int, out_channels: int, K: int, normalization: list | None = 'sym', **kwargs)

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

• 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"):

  • None: No normalization \(\mathbf{L} = \mathbf{D} - \mathbf{A}\)

  • "sym": Symmetric normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}\)

  • "rw": Random-walk normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}\)

  You need to pass lambda_max to the forward() method of this operator in case the normalization is non-symmetric.

• **kwargs (optional) – Additional arguments of gammagl.layers.conv.MessagePassing.

Shapes:

• input:

  node features \((|\mathcal{V}|, F_{in})\), edge indices \((2, |\mathcal{E}|)\), edge weights \((|\mathcal{E}|)\) (optional), maximum lambda value \((|\mathcal{G}|)\) (optional)

• output:

  node features \((|\mathcal{V}|, F_{out})\)

forward(x, edge_index, num_nodes, edge_weight=None, lambda_max=None, batch=None)

Define the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.