Source code for dgl.nn.mxnet.conv.sageconv

"""MXNet Module for GraphSAGE layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
import math
import mxnet as mx
from mxnet import nd
from mxnet.gluon import nn

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

[docs]class SAGEConv(nn.Block):
r"""GraphSAGE layer from Inductive Representation Learning on
Large Graphs <https://arxiv.org/pdf/1706.02216.pdf>__

.. math::
h_{\mathcal{N}(i)}^{(l+1)} &= \mathrm{aggregate}
\left(\{h_{j}^{l}, \forall j \in \mathcal{N}(i) \}\right)

h_{i}^{(l+1)} &= \sigma \left(W \cdot \mathrm{concat}
(h_{i}^{l}, h_{\mathcal{N}(i)}^{l+1}) \right)

h_{i}^{(l+1)} &= \mathrm{norm}(h_{i}^{(l+1)})

Parameters
----------
in_feats : int, or pair of ints
Input feature size; i.e, the number of dimensions of :math:h_i^{(l)}.

GATConv can be applied on homogeneous graph and unidirectional
bipartite graph <https://docs.dgl.ai/generated/dgl.bipartite.html?highlight=bipartite>__.
If the layer applies on a unidirectional bipartite graph, in_feats
specifies the input feature size on both the source and destination nodes.  If
a scalar is given, the source and destination node feature size would take the
same value.

If aggregator type is gcn, the feature size of source and destination nodes
are required to be the same.
out_feats : int
Output feature size; i.e, the number of dimensions of :math:h_i^{(l+1)}.
aggregator_type : str
Aggregator type to use (mean, gcn, pool, lstm).
feat_drop : float
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.

Examples
--------
>>> import dgl
>>> import numpy as np
>>> import mxnet as mx
>>> from dgl.nn import SAGEConv
>>>
>>> # 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 = SAGEConv(10, 2, 'pool')
>>> conv.initialize(ctx=mx.cpu(0))
>>> res = conv(g, feat)
>>> res
[[ 0.32144994 -0.8729614 ]
[ 0.32144994 -0.8729614 ]
[ 0.32144994 -0.8729614 ]
[ 0.32144994 -0.8729614 ]
[ 0.32144994 -0.8729614 ]
[ 0.32144994 -0.8729614 ]]
<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, 10)
>>> conv = SAGEConv((5, 10), 2, 'pool')
>>> conv.initialize(ctx=mx.cpu(0))
>>> res = conv(g, (u_fea, v_fea))
>>> res
[[-0.60524774  0.7196473 ]
[ 0.8832787  -0.5928619 ]
[-1.8245722   1.159798  ]
[-1.0509381   2.2239418 ]]
<NDArray 4x2 @cpu(0)>
"""
def __init__(self,
in_feats,
out_feats,
aggregator_type='mean',
feat_drop=0.,
bias=True,
norm=None,
activation=None):
super(SAGEConv, self).__init__()
valid_aggre_types = {'mean', 'gcn', 'pool', 'lstm'}
if aggregator_type not in valid_aggre_types:
raise DGLError(
'Invalid aggregator_type. Must be one of {}. '
)

self._in_src_feats, self._in_dst_feats = expand_as_pair(in_feats)
self._out_feats = out_feats
self._aggre_type = aggregator_type
with self.name_scope():
self.norm = norm
self.feat_drop = nn.Dropout(feat_drop)
self.activation = activation
if aggregator_type == 'pool':
self.fc_pool = nn.Dense(self._in_src_feats, use_bias=bias,
weight_initializer=mx.init.Xavier(magnitude=math.sqrt(2.0)),
in_units=self._in_src_feats)
if aggregator_type == 'lstm':
raise NotImplementedError
if aggregator_type != 'gcn':
self.fc_self = nn.Dense(out_feats, use_bias=bias,
weight_initializer=mx.init.Xavier(magnitude=math.sqrt(2.0)),
in_units=self._in_dst_feats)
self.fc_neigh = nn.Dense(out_feats, use_bias=bias,
weight_initializer=mx.init.Xavier(magnitude=math.sqrt(2.0)),
in_units=self._in_src_feats)

[docs]    def forward(self, graph, feat):
r"""Compute GraphSAGE layer.

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}}).

Returns
-------
mxnet.NDArray
The output feature of shape :math:(N, D_{out}) where :math:D_{out}
is size of output feature.
"""
with graph.local_scope():
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)
if graph.is_block:
feat_dst = feat_src[:graph.number_of_dst_nodes()]

h_self = feat_dst

# Handle the case of graphs without edges
if graph.number_of_edges() == 0:
dst_neigh = mx.nd.zeros((graph.number_of_dst_nodes(), self._in_src_feats))
dst_neigh = dst_neigh.as_in_context(feat_dst.context)
graph.dstdata['neigh'] = dst_neigh

if self._aggre_type == 'mean':
graph.srcdata['h'] = feat_src
graph.update_all(fn.copy_u('h', 'm'), fn.mean('m', 'neigh'))
h_neigh = graph.dstdata['neigh']
elif self._aggre_type == 'gcn':
check_eq_shape(feat)
graph.srcdata['h'] = feat_src
graph.dstdata['h'] = feat_dst   # same as above if homogeneous
graph.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'neigh'))
# divide in degrees
degs = graph.in_degrees().astype(feat_dst.dtype)
degs = degs.as_in_context(feat_dst.context)
h_neigh = (graph.dstdata['neigh'] + graph.dstdata['h']) / (degs.expand_dims(-1) + 1)
elif self._aggre_type == 'pool':
graph.srcdata['h'] = nd.relu(self.fc_pool(feat_src))
graph.update_all(fn.copy_u('h', 'm'), fn.max('m', 'neigh'))
h_neigh = graph.dstdata['neigh']
elif self._aggre_type == 'lstm':
raise NotImplementedError
else:
raise KeyError('Aggregator type {} not recognized.'.format(self._aggre_type))

if self._aggre_type == 'gcn':
rst = self.fc_neigh(h_neigh)
else:
rst = self.fc_self(h_self) + self.fc_neigh(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