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"""Torch modules for graph convolutions."""
# pylint: disable= no-member, arguments-differ
import torch as th
from torch import nn
from torch.nn import init
from ... import function as fn
__all__ = ['GraphConv']
class GraphConv(nn.Module):
r"""Apply graph convolution over an input signal.
Graph convolution is introduced in `GCN <https://arxiv.org/abs/1609.02907>`__
and can be described as below:
.. math::
h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{1}{c_{ij}}h_j^{(l)}W^{(l)})
where :math:`\mathcal{N}(i)` is the neighbor set of node :math:`i`. :math:`c_{ij}` is equal
to the product of the square root of node degrees:
:math:`\sqrt{|\mathcal{N}(i)|}\sqrt{|\mathcal{N}(j)|}`. :math:`\sigma` is an activation
function.
The model parameters are initialized as in the
`original implementation <https://github.com/tkipf/gcn/blob/master/gcn/layers.py>`__ where
the weight :math:`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 :math:`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``.
Attributes
----------
weight : torch.Tensor
The learnable weight tensor.
bias : torch.Tensor
The learnable bias tensor.
"""
def __init__(self,
in_feats,
out_feats,
norm=True,
bias=True,
activation=None):
super(GraphConv, 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_parameter('bias', None)
self.reset_parameters()
self._activation = activation
def reset_parameters(self):
"""Reinitialize learnable parameters."""
init.xavier_uniform_(self.weight)
if self.bias is not None:
init.zeros_(self.bias)
def forward(self, feat, graph):
r"""Compute graph convolution.
Notes
-----
* Input shape: :math:`(N, *, \text{in_feats})` where * means any number of additional
dimensions, :math:`N` is the number of nodes.
* Output shape: :math:`(N, *, \text{out_feats})` where all but the last dimension are
the same shape as the input.
Parameters
----------
feat : torch.Tensor
The input feature
graph : DGLGraph
The graph.
Returns
-------
torch.Tensor
The output feature
"""
graph = graph.local_var()
if self._norm:
norm = th.pow(graph.in_degrees().float(), -0.5)
shp = norm.shape + (1,) * (feat.dim() - 1)
norm = th.reshape(norm, shp).to(feat.device)
feat = feat * norm
if self._in_feats > self._out_feats:
# mult W first to reduce the feature size for aggregation.
feat = th.matmul(feat, self.weight)
graph.ndata['h'] = feat
graph.update_all(fn.copy_src(src='h', out='m'),
fn.sum(msg='m', out='h'))
rst = graph.ndata['h']
else:
# aggregate first then mult W
graph.ndata['h'] = feat
graph.update_all(fn.copy_src(src='h', out='m'),
fn.sum(msg='m', out='h'))
rst = graph.ndata['h']
rst = th.matmul(rst, self.weight)
if self._norm:
rst = rst * norm
if self.bias is not None:
rst = rst + self.bias
if self._activation is not None:
rst = self._activation(rst)
return rst
def extra_repr(self):
"""Set the extra representation of the module,
which will come into effect when printing the model.
"""
summary = 'in={_in_feats}, out={_out_feats}'
summary += ', normalization={_norm}'
if '_activation' in self.__dict__:
summary += ', activation={_activation}'
return summary.format(**self.__dict__)
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