"""Torch Module for DenseGraphConv"""
# pylint: disable= no-member, arguments-differ, invalid-name
import torch as th
from torch import nn
from torch.nn import init
[docs]class DenseGraphConv(nn.Module):
"""Graph Convolutional layer from `Semi-Supervised Classification with Graph
Convolutional Networks <https://arxiv.org/abs/1609.02907>`__
We recommend user to use this module when applying graph convolution on
dense graphs.
Parameters
----------
in_feats : int
Input feature size; i.e, the number of dimensions of :math:`h_j^{(l)}`.
out_feats : int
Output feature size; i.e., the number of dimensions of :math:`h_i^{(l+1)}`.
norm : str, optional
How to apply the normalizer. If is `'right'`, divide the aggregated messages
by each node's in-degrees, which is equivalent to averaging the received messages.
If is `'none'`, no normalization is applied. Default is `'both'`,
where the :math:`c_{ij}` in the paper is applied.
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``.
Notes
-----
Zero in-degree nodes will lead to all-zero output. A common practice
to avoid this is to add a self-loop for each node in the graph,
which can be achieved by setting the diagonal of the adjacency matrix to be 1.
Example
-------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import DenseGraphConv
>>>
>>> feat = th.ones(6, 10)
>>> adj = th.tensor([[0., 0., 1., 0., 0., 0.],
... [1., 0., 0., 0., 0., 0.],
... [0., 1., 0., 0., 0., 0.],
... [0., 0., 1., 0., 0., 1.],
... [0., 0., 0., 1., 0., 0.],
... [0., 0., 0., 0., 0., 0.]])
>>> conv = DenseGraphConv(10, 2)
>>> res = conv(adj, feat)
>>> res
tensor([[0.2159, 1.9027],
[0.3053, 2.6908],
[0.3053, 2.6908],
[0.3685, 3.2481],
[0.3053, 2.6908],
[0.0000, 0.0000]], grad_fn=<AddBackward0>)
See also
--------
`GraphConv <https://docs.dgl.ai/api/python/nn.pytorch.html#graphconv>`__
"""
def __init__(
self, in_feats, out_feats, norm="both", bias=True, activation=None
):
super(DenseGraphConv, self).__init__()
self._in_feats = in_feats
self._out_feats = out_feats
self._norm = norm
self.weight = nn.Parameter(th.Tensor(in_feats, out_feats))
if bias:
self.bias = nn.Parameter(th.Tensor(out_feats))
else:
self.register_buffer("bias", None)
self.reset_parameters()
self._activation = activation
[docs] def reset_parameters(self):
"""Reinitialize learnable parameters."""
init.xavier_uniform_(self.weight)
if self.bias is not None:
init.zeros_(self.bias)
[docs] def forward(self, adj, feat):
r"""Compute (Dense) Graph Convolution layer.
Parameters
----------
adj : torch.Tensor
The adjacency matrix of the graph to apply Graph Convolution on, when
applied to a unidirectional bipartite graph, ``adj`` should be of shape
should be of shape :math:`(N_{out}, N_{in})`; when applied to a homo
graph, ``adj`` should be of shape :math:`(N, N)`. In both cases,
a row represents a destination node while a column represents a source
node.
feat : torch.Tensor
The input feature.
Returns
-------
torch.Tensor
The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
is size of output feature.
"""
adj = adj.to(feat)
src_degrees = adj.sum(dim=0).clamp(min=1)
dst_degrees = adj.sum(dim=1).clamp(min=1)
feat_src = feat
if self._norm == "both":
norm_src = th.pow(src_degrees, -0.5)
shp = norm_src.shape + (1,) * (feat.dim() - 1)
norm_src = th.reshape(norm_src, shp).to(feat.device)
feat_src = feat_src * norm_src
if self._in_feats > self._out_feats:
# mult W first to reduce the feature size for aggregation.
feat_src = th.matmul(feat_src, self.weight)
rst = adj @ feat_src
else:
# aggregate first then mult W
rst = adj @ feat_src
rst = th.matmul(rst, self.weight)
if self._norm != "none":
if self._norm == "both":
norm_dst = th.pow(dst_degrees, -0.5)
else: # right
norm_dst = 1.0 / dst_degrees
shp = norm_dst.shape + (1,) * (feat.dim() - 1)
norm_dst = th.reshape(norm_dst, shp).to(feat.device)
rst = rst * norm_dst
if self.bias is not None:
rst = rst + self.bias
if self._activation is not None:
rst = self._activation(rst)
return rst