class GeomGCN(*args: Any, **kwargs: Any)

Bases: MessagePassing

The graph convolutional operator from the “GEOM-GCN: GEOMETRIC GRAPH CONVOLUTIONAL NETWORKS” paper

\[\textbf{e}_{(i,r)}^{v,l+1} = \sum_{u \in N_{i}(v)} \delta(\tau(z_v,z_u),r)(deg(v)deg(u))^{\frac{1}{2}} \textbf{h}_u^l, \forall i \in {g,s}, \forall r \in R \]
\[\textbf{h}_v^{l+1}=\sigma(W_l \cdot \mathbin\Vert_{i\in \{g,s\}} \mathbin\Vert_{r \in R} \textbf{e}_{(i,r)}^{v,l+1}) \]

where \(\textbf{e}_{(i,r)}^{v,l+1}\) is a virtual vertex, recieved by summing up representations \(\textbf{h}_u^l\) of nodes on layer l in structural neighbourhoods \(i=s\) and graph neighbourhood \(i=g\) separately for each neighbors with relation \(r\) from the set of relations \(R\). \(z_v\) is an embedding of nodes in latent space, \(deg(v)\) is a degree of node \(v\)

Parameters:

  • in_channels – (int): Size of each input sample.

  • out_channels – (int): Size of each output sample.

  • data – (Graph): Input dataset

  • last_layer – (bool): When true, the virtual vertices are summed, otherwise – concatenated.

  • embeddings – (NDArray): array of node unsupervised embeddings

forward(x: torch.Tensor, edge_index: torch.Tensor) → numpy.typing.NDArray

Modify representations, convolutional layer

Parameters:

  • x – (Tensor): Representations of nodes

  • edge_index – (Tensor): Edges of input graph

Returns:

Hidden representation of nodes on the next layer

message(x_j: torch.Tensor, norm: torch.Tensor) → torch.Tensor

Count message from the neighbour

Parameters:

  • (Tensor) (norm) – Representation of the node neighbour

  • (Tensor) – Normalization term

Returns:

(Tensor): Message from the neighbor

reset_parameters() → None

Reset parameters