gammagl.layers.conv.FAGCNConv

class FAGCNConv(hidden_dim, drop_rate)

The Frequency Adaptive Graph Convolution operator from the “Beyond Low-Frequency Information in Graph Convolutional Networks” paper

\[\mathbf{x}^{\prime}_i= \epsilon \cdot \mathbf{x}^{(0)}_i + \sum_{j \in \mathcal{N}(i)} \frac{\alpha_{i,j}}{\sqrt{d_i d_j}} \mathbf{x}_{j}\]

where \(\mathbf{x}^{(0)}_i\) and \(d_i\) denote the initial feature representation and node degree of node \(i\), respectively. The attention coefficients \(\alpha_{i,j}\) are computed as

\[\mathbf{\alpha}_{i,j} = \textrm{tanh}(\mathbf{a}^{\top}[\mathbf{x}_i, \mathbf{x}_j])\]

based on the trainable parameter vector \(\mathbf{a}\).

Parameters:

• hidden_dim (int) – Hidden dimension of layer

• drop_rate (float) – Dropout rate

message(x, edge_index, edge_weight=None, num_nodes=None)

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]

forward(x, edge_index, edge_weight, num_nodes)

Define the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.