"""MXNet Module for DenseGraphSAGE"""
# pylint: disable= no-member, arguments-differ, invalid-name
import math
import mxnet as mx
from mxnet import nd
from mxnet.gluon import nn
from ....utils import check_eq_shape
[docs]class DenseSAGEConv(nn.Block):
"""GraphSAGE layer from `Inductive Representation Learning on Large Graphs
<https://arxiv.org/abs/1706.02216>`__
We recommend to use this module when appying GraphSAGE on dense graphs.
Note that we only support gcn aggregator in DenseSAGEConv.
Parameters
----------
in_feats : int
Input feature size; i.e, the number of dimensions of :math:`h_i^{(l)}`.
out_feats : int
Output feature size; i.e, the number of dimensions of :math:`h_i^{(l+1)}`.
feat_drop : float, optional
Dropout rate on features. Default: 0.
bias : bool
If True, adds a learnable bias to the output. Default: ``True``.
norm : callable activation function/layer or None, optional
If not None, applies normalization to the updated node features.
activation : callable activation function/layer or None, optional
If not None, applies an activation function to the updated node features.
Default: ``None``.
See also
--------
`SAGEConv <https://docs.dgl.ai/api/python/nn.pytorch.html#sageconv>`__
"""
def __init__(self,
in_feats,
out_feats,
feat_drop=0.,
bias=True,
norm=None,
activation=None):
super(DenseSAGEConv, self).__init__()
self._in_feats = in_feats
self._out_feats = out_feats
self._norm = norm
with self.name_scope():
self.feat_drop = nn.Dropout(feat_drop)
self.activation = activation
self.fc = nn.Dense(out_feats, in_units=in_feats, use_bias=bias,
weight_initializer=mx.init.Xavier(magnitude=math.sqrt(2.0)))
[docs] def forward(self, adj, feat):
r"""
Description
-----------
Compute (Dense) Graph SAGE layer.
Parameters
----------
adj : mxnet.NDArray
The adjacency matrix of the graph to apply SAGE 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 : mxnet.NDArray or a pair of mxnet.NDArray
If a mxnet.NDArray is given, 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 mxnet.NDArray is given, the pair must contain two tensors of shape
:math:`(N_{in}, D_{in})` and :math:`(N_{out}, D_{in})`.
Returns
-------
mxnet.NDArray
The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
is size of output feature.
"""
check_eq_shape(feat)
if isinstance(feat, tuple):
feat_src = self.feat_drop(feat[0])
feat_dst = self.feat_drop(feat[1])
else:
feat_src = feat_dst = self.feat_drop(feat)
adj = adj.astype(feat_src.dtype).as_in_context(feat_src.context)
in_degrees = adj.sum(axis=1, keepdims=True)
h_neigh = (nd.dot(adj, feat_src) + feat_dst) / (in_degrees + 1)
rst = self.fc(h_neigh)
# activation
if self.activation is not None:
rst = self.activation(rst)
# normalization
if self._norm is not None:
rst = self._norm(rst)
return rst