class HypergraphConv(in_channels, out_channels, use_attention=False, heads=1, concat=True, negative_slope=0.2, dropout=0, bias=True, **kwargs)[source]

Bases: MessagePassing

The hypergraph convolutional operator from the “Hypergraph Convolution and Hypergraph Attention” paper

\[\mathbf{X}^{\prime} = \mathbf{D}^{-1} \mathbf{H} \mathbf{W} \mathbf{B}^{-1} \mathbf{H}^{\top} \mathbf{X} \mathbf{\Theta}\]

where \(\mathbf{H} \in {\{ 0, 1 \}}^{N \times M}\) is the incidence matrix, \(\mathbf{W} \in \mathbb{R}^M\) is the diagonal hyperedge weight matrix, and \(\mathbf{D}\) and \(\mathbf{B}\) are the corresponding degree matrices.

For example, in the hypergraph scenario \(\mathcal{G} = (\mathcal{V}, \mathcal{E})\) with \(\mathcal{V} = \{ 0, 1, 2, 3 \}\) and \(\mathcal{E} = \{ \{ 0, 1, 2 \}, \{ 1, 2, 3 \} \}\), the hyperedge_index is represented as:

hyperedge_index = torch.tensor([
    [0, 1, 2, 1, 2, 3],
    [0, 0, 0, 1, 1, 1],
  • 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.

  • use_attention (bool, optional) – If set to True, attention will be added to this layer. (default: False)

  • heads (int, optional) – Number of multi-head-attentions. (default: 1)

  • concat (bool, optional) – If set to False, the multi-head attentions are averaged instead of concatenated. (default: True)

  • negative_slope (float, optional) – LeakyReLU angle of the negative slope. (default: 0.2)

  • dropout (float, optional) – Dropout probability of the normalized attention coefficients which exposes each node to a stochastically sampled neighborhood during training. (default: 0)

  • 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 \((|\mathcal{V}|, F_{in})\), hyperedge indices \((|\mathcal{V}|, |\mathcal{E}|)\), hyperedge weights \((|\mathcal{E}|)\) (optional) hyperedge features \((|\mathcal{E}|, D)\) (optional)

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

forward(x: Tensor, hyperedge_index: Tensor, hyperedge_weight: Optional[Tensor] = None, hyperedge_attr: Optional[Tensor] = None) Tensor[source]

Runs the forward pass of the module.

  • x (torch.Tensor) – Node feature matrix \(\mathbf{X} \in \mathbb{R}^{N \times F}\).

  • hyperedge_index (torch.Tensor) – The hyperedge indices, i.e. the sparse incidence matrix \(\mathbf{H} \in {\{ 0, 1 \}}^{N \times M}\) mapping from nodes to edges.

  • hyperedge_weight (torch.Tensor, optional) – Hyperedge weights \(\mathbf{W} \in \mathbb{R}^M\). (default: None)

  • hyperedge_attr (torch.Tensor, optional) – Hyperedge feature matrix in \(\mathbb{R}^{M \times F}\). These features only need to get passed in case use_attention=True. (default: None)


Resets all learnable parameters of the module.