"""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 ....utils import expand_as_pair, check_eq_shape
[docs]class SAGEConv(nn.Block):
r"""
Description
-----------
GraphSAGE layer from paper `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})
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)}`.
feat_drop : float
Dropout rate on features, default: ``0``.
aggregator_type : str
Aggregator type to use (``mean``, ``gcn``, ``pool``, ``lstm``).
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]))
>>> g = dgl.add_self_loop(g)
>>> 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__()
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