# Source code for dgl.nn.pytorch.conv.graphconv

"""Torch modules for graph convolutions(GCN)."""
# pylint: disable= no-member, arguments-differ, invalid-name
import torch as th
from torch import nn
from torch.nn import init

from .... import function as fn
from ....base import DGLError
from ....utils import expand_as_pair
from ....transforms import reverse
from ....convert import block_to_graph
from ....heterograph import DGLBlock

[docs]class EdgeWeightNorm(nn.Module):
r"""This module normalizes positive scalar edge weights on a graph
following the form in GCN <https://arxiv.org/abs/1609.02907>__.

Mathematically, setting norm='both' yields the following normalization term:

.. math::
c_{ji} = (\sqrt{\sum_{k\in\mathcal{N}(j)}e_{jk}}\sqrt{\sum_{k\in\mathcal{N}(i)}e_{ki}})

And, setting norm='right' yields the following normalization term:

.. math::
c_{ji} = (\sum_{k\in\mathcal{N}(i)}e_{ki})

where :math:e_{ji} is the scalar weight on the edge from node :math:j to node :math:i.

The module returns the normalized weight :math:e_{ji} / c_{ji}.

Parameters
----------
norm : str, optional
The normalizer as specified above. Default is 'both'.
eps : float, optional
A small offset value in the denominator. Default is 0.

Examples
--------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import EdgeWeightNorm, GraphConv

>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> edge_weight = th.tensor([0.5, 0.6, 0.4, 0.7, 0.9, 0.1, 1, 1, 1, 1, 1, 1])
>>> norm = EdgeWeightNorm(norm='both')
>>> norm_edge_weight = norm(g, edge_weight)
>>> conv = GraphConv(10, 2, norm='none', weight=True, bias=True)
>>> res = conv(g, feat, edge_weight=norm_edge_weight)
>>> print(res)
tensor([[-1.1849, -0.7525],
[-1.3514, -0.8582],
[-1.2384, -0.7865],
[-1.9949, -1.2669],
[-1.3658, -0.8674],
"""
def __init__(self, norm='both', eps=0.):
super(EdgeWeightNorm, self).__init__()
self._norm = norm
self._eps = eps

[docs]    def forward(self, graph, edge_weight):
r"""

Description
-----------
Compute normalized edge weight for the GCN model.

Parameters
----------
graph : DGLGraph
The graph.
edge_weight : torch.Tensor
Unnormalized scalar weights on the edges.
The shape is expected to be :math:(|E|).

Returns
-------
torch.Tensor
The normalized edge weight.

Raises
------
DGLError
Case 1:
The edge weight is multi-dimensional. Currently this module
only supports a scalar weight on each edge.

Case 2:
The edge weight has non-positive values with norm='both'.
This will trigger square root and division by a non-positive number.
"""
with graph.local_scope():
if isinstance(graph, DGLBlock):
graph = block_to_graph(graph)
if len(edge_weight.shape) > 1:
raise DGLError('Currently the normalization is only defined '
'on scalar edge weight. Please customize the '
if self._norm == 'both' and th.any(edge_weight <= 0).item():
raise DGLError('Non-positive edge weight detected with norm="both". '
'This leads to square root of zero or negative values.')

dev = graph.device
dtype = edge_weight.dtype
graph.srcdata['_src_out_w'] = th.ones(
graph.number_of_src_nodes(), dtype=dtype, device=dev)
graph.dstdata['_dst_in_w'] = th.ones(
graph.number_of_dst_nodes(), dtype=dtype, device=dev)
graph.edata['_edge_w'] = edge_weight

if self._norm == 'both':
reversed_g = reverse(graph)
reversed_g.edata['_edge_w'] = edge_weight
reversed_g.update_all(fn.copy_e('_edge_w', 'm'), fn.sum('m', 'out_weight'))
degs = reversed_g.dstdata['out_weight'] + self._eps
norm = th.pow(degs, -0.5)
graph.srcdata['_src_out_w'] = norm

if self._norm != 'none':
graph.update_all(fn.copy_e('_edge_w', 'm'), fn.sum('m', 'in_weight'))
degs = graph.dstdata['in_weight'] + self._eps
if self._norm == 'both':
norm = th.pow(degs, -0.5)
else:
norm = 1.0 / degs
graph.dstdata['_dst_in_w'] = norm

graph.apply_edges(lambda e: {'_norm_edge_weights': e.src['_src_out_w'] * \
e.dst['_dst_in_w'] * \
e.data['_edge_w']})
return graph.edata['_norm_edge_weights']

# pylint: disable=W0235
[docs]class GraphConv(nn.Module):
r"""Graph convolutional layer from Semi-Supervised Classification with Graph Convolutional
Networks <https://arxiv.org/abs/1609.02907>__

Mathematically it is defined as follows:

.. math::
h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{1}{c_{ji}}h_j^{(l)}W^{(l)})

where :math:\mathcal{N}(i) is the set of neighbors of node :math:i,
:math:c_{ji} is the product of the square root of node degrees
(i.e.,  :math:c_{ji} = \sqrt{|\mathcal{N}(j)|}\sqrt{|\mathcal{N}(i)|}),
and :math:\sigma is an activation function.

If a weight tensor on each edge is provided, the weighted graph convolution is defined as:

.. math::
h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{e_{ji}}{c_{ji}}h_j^{(l)}W^{(l)})

where :math:e_{ji} is the scalar weight on the edge from node :math:j to node :math:i.
This is NOT equivalent to the weighted graph convolutional network formulation in the paper.

To customize the normalization term :math:c_{ji}, one can first set norm='none' for
the model, and send the pre-normalized :math:e_{ji} to the forward computation. We provide
:class:~dgl.nn.pytorch.EdgeWeightNorm to normalize scalar edge weight following the GCN paper.

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.  Can be one of the following values:

* right, to divide the aggregated messages by each node's in-degrees,
which is equivalent to averaging the received messages.

* none, where no normalization is applied.

* both (default), where the messages are scaled with :math:1/c_{ji} above, equivalent
to symmetric normalization.

* left, to divide the messages sent out from each node by its out-degrees,
equivalent to random walk normalization.
weight : bool, optional
If True, apply a linear layer. Otherwise, aggregating the messages
without a weight matrix.
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.
allow_zero_in_degree : bool, optional
If there are 0-in-degree nodes in the graph, output for those nodes will be invalid
since no message will be passed to those nodes. This is harmful for some applications
causing silent performance regression. This module will raise a DGLError if it detects
0-in-degree nodes in input graph. By setting True, it will suppress the check
and let the users handle it by themselves. Default: False.

Attributes
----------
weight : torch.Tensor
The learnable weight tensor.
bias : torch.Tensor
The learnable bias tensor.

Note
----
Zero in-degree nodes will lead to invalid output value. This is because no message
will be passed to those nodes, the aggregation function will be appied on empty input.
A common practice to avoid this is to add a self-loop for each node in the graph if
it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph

Calling add_self_loop will not work for some graphs, for example, heterogeneous graph
since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree
to True for those cases to unblock the code and handle zero-in-degree nodes manually.
A common practise to handle this is to filter out the nodes with zero-in-degree when use
after conv.

Examples
--------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GraphConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True)
>>> res = conv(g, feat)
>>> print(res)
tensor([[ 1.3326, -0.2797],
[ 1.4673, -0.3080],
[ 1.3326, -0.2797],
[ 1.6871, -0.3541],
[ 1.7711, -0.3717],
>>> # allow_zero_in_degree example
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True, allow_zero_in_degree=True)
>>> res = conv(g, feat)
>>> print(res)
tensor([[-0.2473, -0.4631],
[-0.3497, -0.6549],
[-0.3497, -0.6549],
[-0.4221, -0.7905],
[-0.3497, -0.6549],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.heterograph({('_U', '_E', '_V') : (u, v)})
>>> u_fea = th.rand(2, 5)
>>> v_fea = th.rand(4, 5)
>>> conv = GraphConv(5, 2, norm='both', weight=True, bias=True)
>>> res = conv(g, (u_fea, v_fea))
>>> res
tensor([[-0.2994,  0.6106],
[-0.4482,  0.5540],
[-0.5287,  0.8235],
"""
def __init__(self,
in_feats,
out_feats,
norm='both',
weight=True,
bias=True,
activation=None,
allow_zero_in_degree=False):
super(GraphConv, self).__init__()
if norm not in ('none', 'both', 'right', 'left'):
raise DGLError('Invalid norm value. Must be either "none", "both", "right" or "left".'
' But got "{}".'.format(norm))
self._in_feats = in_feats
self._out_feats = out_feats
self._norm = norm
self._allow_zero_in_degree = allow_zero_in_degree

if weight:
self.weight = nn.Parameter(th.Tensor(in_feats, out_feats))
else:
self.register_parameter('weight', None)

if bias:
self.bias = nn.Parameter(th.Tensor(out_feats))
else:
self.register_parameter('bias', None)

self.reset_parameters()

self._activation = activation

[docs]    def reset_parameters(self):
r"""

Description
-----------
Reinitialize learnable parameters.

Note
----
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.

"""
if self.weight is not None:
init.xavier_uniform_(self.weight)
if self.bias is not None:
init.zeros_(self.bias)

def set_allow_zero_in_degree(self, set_value):
r"""

Description
-----------
Set allow_zero_in_degree flag.

Parameters
----------
set_value : bool
The value to be set to the flag.
"""
self._allow_zero_in_degree = set_value

[docs]    def forward(self, graph, feat, weight=None, edge_weight=None):
r"""

Description
-----------
Compute graph convolution.

Parameters
----------
graph : DGLGraph
The graph.
feat : torch.Tensor or pair of torch.Tensor
If a torch.Tensor is given, it represents the input feature of shape
:math:(N, D_{in})
where :math:D_{in} is size of input feature, :math:N is the number of nodes.
If a pair of torch.Tensor is given, which is the case for bipartite graph, the pair
must contain two tensors of shape :math:(N_{in}, D_{in_{src}}) and
:math:(N_{out}, D_{in_{dst}}).
weight : torch.Tensor, optional
Optional external weight tensor.
edge_weight : torch.Tensor, optional
Optional tensor on the edge. If given, the convolution will weight
with regard to the message.

Returns
-------
torch.Tensor
The output feature

Raises
------
DGLError
Case 1:
If there are 0-in-degree nodes in the input graph, it will raise DGLError
since no message will be passed to those nodes. This will cause invalid output.
The error can be ignored by setting allow_zero_in_degree parameter to True.

Case 2:
External weight is provided while at the same time the module
has defined its own weight parameter.

Note
----
* 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.
* Weight shape: :math:(\text{in_feats}, \text{out_feats}).
"""
with graph.local_scope():
if not self._allow_zero_in_degree:
if (graph.in_degrees() == 0).any():
raise DGLError('There are 0-in-degree nodes in the graph, '
'output for those nodes will be invalid. '
'This is harmful for some applications, '
'causing silent performance regression. '
'Adding self-loop on the input graph by '
'calling g = dgl.add_self_loop(g) will resolve '
'the issue. Setting allow_zero_in_degree '
'to be True when constructing this module will '
'suppress the check and let the code run.')
aggregate_fn = fn.copy_u('h', 'm')
if edge_weight is not None:
assert edge_weight.shape == graph.number_of_edges()
graph.edata['_edge_weight'] = edge_weight
aggregate_fn = fn.u_mul_e('h', '_edge_weight', 'm')

# (BarclayII) For RGCN on heterogeneous graphs we need to support GCN on bipartite.
feat_src, feat_dst = expand_as_pair(feat, graph)
if self._norm in ['left', 'both']:
degs = graph.out_degrees().to(feat_src).clamp(min=1)
if self._norm == 'both':
norm = th.pow(degs, -0.5)
else:
norm = 1.0 / degs
shp = norm.shape + (1,) * (feat_src.dim() - 1)
norm = th.reshape(norm, shp)
feat_src = feat_src * norm

if weight is not None:
if self.weight is not None:
raise DGLError('External weight is provided while at the same time the'
' module has defined its own weight parameter. Please'
' create the module with flag weight=False.')
else:
weight = self.weight

if self._in_feats > self._out_feats:
# mult W first to reduce the feature size for aggregation.
if weight is not None:
feat_src = th.matmul(feat_src, weight)
graph.srcdata['h'] = feat_src
graph.update_all(aggregate_fn, fn.sum(msg='m', out='h'))
rst = graph.dstdata['h']
else:
# aggregate first then mult W
graph.srcdata['h'] = feat_src
graph.update_all(aggregate_fn, fn.sum(msg='m', out='h'))
rst = graph.dstdata['h']
if weight is not None:
rst = th.matmul(rst, weight)

if self._norm in ['right', 'both']:
degs = graph.in_degrees().to(feat_dst).clamp(min=1)
if self._norm == 'both':
norm = th.pow(degs, -0.5)
else:
norm = 1.0 / degs
shp = norm.shape + (1,) * (feat_dst.dim() - 1)
norm = th.reshape(norm, shp)
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__)