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

"""MXNet modules for graph convolutions(GCN)"""
# pylint: disable= no-member, arguments-differ, invalid-name
import math

import mxnet as mx
from mxnet import gluon

from .... import function as fn
from ....base import DGLError
from ....utils import expand_as_pair

[docs]class GraphConv(gluon.Block):
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_{ij}}h_j^{(l)}W^{(l)})

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

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 mxnet as mx
>>> from mxnet import gluon
>>> import numpy as np
>>> 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 = mx.nd.ones((6, 10))
>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True)
>>> conv.initialize(ctx=mx.cpu(0))
>>> res = conv(g, feat)
>>> print(res)
[[1.0209361  0.22472616]
[1.1240715  0.24742813]
[1.0209361  0.22472616]
[1.2924911  0.28450024]
[1.3568745  0.29867214]
[0.7948386  0.17495811]]
<NDArray 6x2 @cpu(0)>

>>> # 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)
[[1.0209361  0.22472616]
[1.1240715  0.24742813]
[1.0209361  0.22472616]
[1.2924911  0.28450024]
[1.3568745  0.29867214]
[0.  0.]]
<NDArray 6x2 @cpu(0)>

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_fea = mx.nd.random.randn(2, 5)
>>> v_fea = mx.nd.random.randn(4, 5)
>>> conv = GraphConv(5, 2, norm='both', weight=True, bias=True)
>>> conv.initialize(ctx=mx.cpu(0))
>>> res = conv(g, (u_fea, v_fea))
>>> res
[[ 0.26967263  0.308129  ]
[ 0.05143356 -0.11355402]
[ 0.22705637  0.1375853 ]
[ 0.26967263  0.308129  ]]
<NDArray 4x2 @cpu(0)>
"""
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

with self.name_scope():
if weight:
self.weight = self.params.get('weight', shape=(in_feats, out_feats),
init=mx.init.Xavier(magnitude=math.sqrt(2.0)))
else:
self.weight = None

if bias:
self.bias = self.params.get('bias', shape=(out_feats,),
init=mx.init.Zero())
else:
self.bias = None

self._activation = activation

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):
r"""

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

Parameters
----------
graph : DGLGraph
The graph.
feat : mxnet.NDArray or pair of mxnet.NDArray
If a single 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 tensors are given, the pair must contain two tensors of shape
:math:(N_{in}, D_{in_{src}}) and :math:(N_{out}, D_{in_{dst}}).

Note that in the special case of graph convolutional networks, if a pair of
tensors is given, the latter element will not participate in computation.
weight : torch.Tensor, optional
Optional external weight tensor.

Returns
-------
mxnet.NDArray
The output feature

Raises
------
DGLError
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.

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().min() == 0:
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.')

feat_src, feat_dst = expand_as_pair(feat, graph)
if self._norm in ['both', 'left']:
degs = graph.out_degrees().as_in_context(feat_dst.context).astype('float32')
degs = mx.nd.clip(degs, a_min=1, a_max=float("inf"))
if self._norm == 'both':
norm = mx.nd.power(degs, -0.5)
else:
norm = 1.0 / degs
shp = norm.shape + (1,) * (feat_src.ndim - 1)
norm = norm.reshape(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.data(feat_src.context)

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

if self._norm in ['both', 'right']:
degs = graph.in_degrees().as_in_context(feat_dst.context).astype('float32')
degs = mx.nd.clip(degs, a_min=1, a_max=float("inf"))
if self._norm == 'both':
norm = mx.nd.power(degs, -0.5)
else:
norm = 1.0 / degs
shp = norm.shape + (1,) * (feat_dst.ndim - 1)
norm = norm.reshape(shp)
rst = rst * norm

if self.bias is not None:
rst = rst + self.bias.data(rst.context)

if self._activation is not None:
rst = self._activation(rst)

return rst

def __repr__(self):
summary = 'GraphConv('
summary += 'in={:d}, out={:d}, normalization={}, activation={}'.format(
self._in_feats, self._out_feats,
self._norm, self._activation)
summary += ')'
return summary