"""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 check_eq_shape, expand_as_pair class SAGEConv(nn.Block): r"""GraphSAGE layer from `Inductive Representation Learning on Large Graphs `__ .. 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 `__. 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])) >>> 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 ]] >>> # Case 2: Unidirectional bipartite graph >>> u = [0, 1, 0, 0, 1] >>> v = [0, 1, 2, 3, 2] >>> g = dgl.heterograph({('_N', '_E', '_N'):(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 ]] """ def __init__( self, in_feats, out_feats, aggregator_type="mean", feat_drop=0.0, 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 {}. " "But got {!r} instead.".format( valid_aggre_types, aggregator_type ) ) 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, ) 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.num_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