dgl.nn.mxnet

dgl.nn.mxnet.conv

MXNet modules for graph convolutions.

class dgl.nn.mxnet.conv.GraphConv(in_feats, out_feats, norm=True, bias=True, activation=None)[source]

Bases: mxnet.gluon.block.Block

Apply graph convolution over an input signal.

Graph convolution is introduced in GCN and can be described as below:

\[h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{1}{c_{ij}}h_j^{(l)}W^{(l)})\]

where \(\mathcal{N}(i)\) is the neighbor set of node \(i\). \(c_{ij}\) is equal to the product of the square root of node degrees: \(\sqrt{|\mathcal{N}(i)|}\sqrt{|\mathcal{N}(j)|}\). \(\sigma\) is an activation function.

The model parameters are initialized as in the original implementation where the weight \(W^{(l)}\) is initialized using Glorot uniform initialization and the bias is initialized to be zero.

Notes

Zero in degree nodes could lead to invalid normalizer. A common practice to avoid this is to add a self-loop for each node in the graph, which can be achieved by:

>>> g = ... # some DGLGraph
>>> g.add_edges(g.nodes(), g.nodes())
Parameters:
  • in_feats (int) – Number of input features.
  • out_feats (int) – Number of output features.
  • norm (bool, optional) – If True, the normalizer \(c_{ij}\) is applied. Default: True.
  • bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.
  • activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.
weight

mxnet.gluon.parameter.Parameter – The learnable weight tensor.

bias

mxnet.gluon.parameter.Parameter – The learnable bias tensor.

forward(feat, graph)[source]

Compute graph convolution.

Notes

  • Input shape: \((N, *, \text{in_feats})\) where * means any number of additional dimensions, \(N\) is the number of nodes.
  • Output shape: \((N, *, \text{out_feats})\) where all but the last dimension are the same shape as the input.
Parameters:
  • feat (mxnet.NDArray) – The input feature
  • graph (DGLGraph) – The graph.
Returns:

The output feature
Return type:

mxnet.NDArray