class SSGConv(in_channels: int, out_channels: int, alpha: float, K: int = 1, cached: bool = False, add_self_loops: bool = True, bias: bool = True, **kwargs)[source]

Bases: MessagePassing

The simple spectral graph convolutional operator from the “Simple Spectral Graph Convolution” paper

\[\mathbf{X}^{\prime} = \frac{1}{K} \sum_{k=1}^K\left((1-\alpha) {\left(\mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} \right)}^k \mathbf{X}+\alpha \mathbf{X}\right) \mathbf{\Theta},\]

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. SSGConv is an improved operator of SGConv by introducing the alpha parameter to address the oversmoothing issue.

  • 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.

  • alpha (float) – Teleport probability \(\alpha \in [0, 1]\).

  • K (int, optional) – Number of hops \(K\). (default: 1)

  • cached (bool, optional) – If set to True, the layer will cache the computation of \(\frac{1}{K} \sum_{k=1}^K\left((1-\alpha) {\left(\mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} \right)}^k \mathbf{X}+ \alpha \mathbf{X}\right)\) 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. (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 \((2, |\mathcal{E}|)\), edge weights \((|\mathcal{E}|)\) (optional)

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

forward(x: Tensor, edge_index: Union[Tensor, SparseTensor], edge_weight: Optional[Tensor] = None) Tensor[source]

Runs the forward pass of the module.


Resets all learnable parameters of the module.