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)