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)