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
>>> g = dgl.add_self_loop(g)
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]))
>>> g = dgl.add_self_loop(g)
>>> 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],
[ 1.0375, -0.2178]], grad_fn=<AddBackward0>)
>>> # 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],
[ 0.0000, 0.0000]], grad_fn=<AddBackward0>)
>>> # 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],
[-0.2994, 0.6106]], grad_fn=<AddBackward0>)
"""
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
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.
设置是否允许度为0的标志
Parameters
----------
set_value : bool
The value to be set to the flag.
"""
self._allow_zero_in_degree = set_value
def forward(self, graph, feat, weight=None, edge_weight=None):
r"""
Description
-----------
Compute graph convolution.
图卷积计算
Parameters
----------
graph : DGLGraph
The graph.
feat :
结点的特征，对同质图为（N, D）
N为结点个数， D为输入结点特征的维度
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 :
可选参数，为卷积层提供一个权重，若卷积层已经存在一个权重，那么会抛出一个错误
torch.Tensor, optional
Optional external weight tensor.
edge_weight :
可选参数，边权重
torch.Tensor, optional
Optional tensor on the edge. If given, the convolution will weight
with regard to the message.
Returns
-------
返回输出特征
torch.Tensor
The output feature
Raises
------
DGLError
Case 1: 图中有度为0的结点，可以通过设置allow_zero=True来允许有度为0的结点。
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: 从外部提供权重的同时模块定义了自己的权重
External weight is provided while at the same time the module
has defined its own weight parameter.
Note
----
* 输入形状: (N, *, \text{in_feats})
Input shape: :math:`(N, *, \text{in_feats})` where * means any number of additional
dimensions, :math:`N` is the number of nodes.
* 输出形状: (N, *, \text{out_feats})
Output shape: :math:`(N, *, \text{out_feats})` where all but the last dimension are
the same shape as the input.
* 权重形状: (\text{in_feats}, \text{out_feats})
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[0] == graph.num_edges()
graph.edata["_edge_weight"] = edge_weight
aggregate_fn = fn.u_mul_e("h", "_edge_weight", "m")
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:
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:
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__)
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