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

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

[docs]class DenseGraphConv(nn.Block): """ Description ----------- Graph Convolutional Network layer where the graph structure is given by an adjacency matrix. We recommend user to use this module when applying graph convolution on dense graphs. 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. If is `'right'`, divide the aggregated messages by each node's in-degrees, which is equivalent to averaging the received messages. If is `'none'`, no normalization is applied. Default is `'both'`, where the :math:`c_{ij}` in the paper is applied. 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``. Notes ----- Zero in-degree nodes will lead to all-zero output. A common practice to avoid this is to add a self-loop for each node in the graph, which can be achieved by setting the diagonal of the adjacency matrix to be 1. See also -------- `GraphConv <>`__ """ def __init__(self, in_feats, out_feats, norm='both', bias=True, activation=None): super(DenseGraphConv, self).__init__() self._in_feats = in_feats self._out_feats = out_feats self._norm = norm with self.name_scope(): self.weight = self.params.get('weight', shape=(in_feats, out_feats), init=mx.init.Xavier(magnitude=math.sqrt(2.0))) if bias: self.bias = self.params.get('bias', shape=(out_feats,), init=mx.init.Zero()) else: self.bias = None self._activation = activation
[docs] def forward(self, adj, feat): r""" Description ----------- Compute (Dense) Graph Convolution layer. Parameters ---------- adj : mxnet.NDArray The adjacency matrix of the graph to apply Graph 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 The input feature. Returns ------- mxnet.NDArray The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}` is size of output feature. """ adj = adj.astype(feat.dtype).as_in_context(feat.context) src_degrees = nd.clip(adj.sum(axis=0), a_min=1, a_max=float('inf')) dst_degrees = nd.clip(adj.sum(axis=1), a_min=1, a_max=float('inf')) feat_src = feat if self._norm == 'both': norm_src = nd.power(src_degrees, -0.5) shp_src = norm_src.shape + (1,) * (feat.ndim - 1) norm_src = norm_src.reshape(shp_src).as_in_context(feat.context) feat_src = feat_src * norm_src if self._in_feats > self._out_feats: # mult W first to reduce the feature size for aggregation. feat_src =, rst =, feat_src) else: # aggregate first then mult W rst =, feat_src) rst =, if self._norm != 'none': if self._norm == 'both': norm_dst = nd.power(dst_degrees, -0.5) else: # right norm_dst = 1.0 / dst_degrees shp_dst = norm_dst.shape + (1,) * (feat.ndim - 1) norm_dst = norm_dst.reshape(shp_dst).as_in_context(feat.context) rst = rst * norm_dst if self.bias is not None: rst = rst + if self._activation is not None: rst = self._activation(rst) return rst