gammagl.layers.conv.PNAConv

class PNAConv(in_channels, out_channels, aggregators, scalers, deg, edge_dim, towers=1, pre_layers=1, post_layers=1, divide_input=False)[source]

The Principal Neighbourhood Aggregation graph convolution operator from the “Principal Neighbourhood Aggregation for Graph Nets” paper

\[\mathbf{x}_i^{\prime} = \gamma_{\mathbf{\Theta}} \left( \mathbf{x}_i, \underset{j \in \mathcal{N}(i)}{\bigoplus} h_{\mathbf{\Theta}} \left( \mathbf{x}_i, \mathbf{x}_j \right) \right)\]

with

\[\begin{split}\bigoplus = \underbrace{\begin{bmatrix} 1 \\ S(\mathbf{D}, \alpha=1) \\ S(\mathbf{D}, \alpha=-1) \end{bmatrix} }_{\text{scalers}} \otimes \underbrace{\begin{bmatrix} \mu \\ \sigma \\ \max \\ \min \end{bmatrix}}_{\text{aggregators}},\end{split}\]

where \(\gamma_{\mathbf{\Theta}}\) and \(h_{\mathbf{\Theta}}\) denote MLPs.

Parameters:

  • 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.

  • aggregators (list[str]) – Set of aggregation function identifiers, namely "sum", "mean", "min", "max", "var" and "std".

  • scalers (list[str]) – Set of scaling function identifiers, namely "identity", "amplification", "attenuation", "linear" and "inverse_linear".

  • deg (tensor) – Histogram of in-degrees of nodes in the training set, used by scalers to normalize.

  • edge_dim (int, optional) – Edge feature dimensionality (in case there are any). (default None)

  • towers (int, optional) – Number of towers (default: 1).

  • pre_layers (int, optional) – Number of transformation layers before aggregation (default: 1).

  • post_layers (int, optional) – Number of transformation layers after aggregation (default: 1).

  • divide_input (bool, optional) – Whether the input features should be split between towers or not (default: False).

  • Shapes –

    • input: node features \((|\mathcal{V}|, F_{in})\), edge indices \((2, |\mathcal{E}|)\), edge features \((|\mathcal{E}|, D)\) (optional)

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

forward(x, edge_index, edge_attr=None)[source]
message(x, edge_index, edge_attr=None)[source]

Function that construct message from source nodes to destination nodes.

Parameters:

  • x (tensor) – input node feature.

  • edge_index (tensor) – edges from src to dst.

  • edge_weight (tensor, optional) – weight of each edge.

Returns:

  • tensor – output message

  • Returns – the message matrix, and the shape is [num_edges, message_dim]

aggregate(inputs, index, num_nodes=None, aggr=None)[source]

Function that aggregates message from edges to destination nodes.

Parameters:

  • msg (tensor) – message construct by message function.

  • edge_index (tensor) – edges from src to dst.

  • num_nodes (int, optional) – number of nodes of the graph.

  • aggr (str, optional) – aggregation type, default = ‘sum’, optional=[‘sum’, ‘mean’, ‘max’].

Returns:

aggregation outcome.

Return type:

tensor