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

"""MXNet modules for graph convolutions(GCN)"""
# pylint: disable= no-member, arguments-differ, invalid-name
import math

import mxnet as mx
from mxnet import gluon

from .... import function as fn
from ....base import DGLError

[docs]class GraphConv(gluon.Block): r"""Apply graph convolution over an input signal. Graph convolution is introduced in `GCN <>`__ and can be described as below: .. math:: h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{1}{c_{ij}}h_j^{(l)}W^{(l)}) where :math:`\mathcal{N}(i)` is the neighbor set of node :math:`i`. :math:`c_{ij}` is equal to the product of the square root of node degrees: :math:`\sqrt{|\mathcal{N}(i)|}\sqrt{|\mathcal{N}(j)|}`. :math:`\sigma` is an activation function. The model parameters are initialized as in the `original implementation <>`__ where the weight :math:`W^{(l)}` is initialized using Glorot uniform initialization and the bias is initialized to be zero. Notes ----- Zero in degree nodes could lead to invalid normalizer. A common practice to avoid this is to add a self-loop for each node in the graph, which can be achieved by: >>> g = ... # some DGLGraph >>> g.add_edges(g.nodes(), g.nodes()) Parameters ---------- in_feats : int Number of input features. out_feats : int Number of output features. 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. weight : bool, optional If True, apply a linear layer. Otherwise, aggregating the messages without a weight matrix. 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``. Attributes ---------- weight : mxnet.gluon.parameter.Parameter The learnable weight tensor. bias : mxnet.gluon.parameter.Parameter The learnable bias tensor. """ def __init__(self, in_feats, out_feats, norm='both', weight=True, bias=True, activation=None): super(GraphConv, self).__init__() if norm not in ('none', 'both', 'right'): raise DGLError('Invalid norm value. Must be either "none", "both" or "right".' ' But got "{}".'.format(norm)) self._in_feats = in_feats self._out_feats = out_feats self._norm = norm with self.name_scope(): if weight: self.weight = self.params.get('weight', shape=(in_feats, out_feats), init=mx.init.Xavier(magnitude=math.sqrt(2.0))) else: self.weight = None 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, graph, feat, weight=None): r"""Compute graph convolution. Notes ----- * Input shape: :math:`(N, *, \text{in_feats})` where * means any number of additional dimensions, :math:`N` is the number of nodes. * Output shape: :math:`(N, *, \text{out_feats})` where all but the last dimension are the same shape as the input. * Weight shape: "math:`(\text{in_feats}, \text{out_feats})`. Parameters ---------- graph : DGLGraph The graph. feat : mxnet.NDArray The input feature. weight : torch.Tensor, optional Optional external weight tensor. Returns ------- mxnet.NDArray The output feature """ graph = graph.local_var() if self._norm == 'both': degs = graph.out_degrees().as_in_context(feat.context).astype('float32') degs = mx.nd.clip(degs, a_min=1, a_max=float("inf")) norm = mx.nd.power(degs, -0.5) shp = norm.shape + (1,) * (feat.ndim - 1) norm = norm.reshape(shp) feat = feat * norm if weight is not None: if self.weight is not None: raise DGLError('External weight is provided while at the same time the' ' module has defined its own weight parameter. Please' ' create the module with flag weight=False.') else: weight = if self._in_feats > self._out_feats: # mult W first to reduce the feature size for aggregation. if weight is not None: feat =, weight) graph.srcdata['h'] = feat graph.update_all(fn.copy_src(src='h', out='m'), fn.sum(msg='m', out='h')) rst = graph.dstdata.pop('h') else: # aggregate first then mult W graph.srcdata['h'] = feat graph.update_all(fn.copy_src(src='h', out='m'), fn.sum(msg='m', out='h')) rst = graph.dstdata.pop('h') if weight is not None: rst =, weight) if self._norm != 'none': degs = graph.in_degrees().as_in_context(feat.context).astype('float32') degs = mx.nd.clip(degs, a_min=1, a_max=float("inf")) if self._norm == 'both': norm = mx.nd.power(degs, -0.5) else: norm = 1.0 / degs shp = norm.shape + (1,) * (feat.ndim - 1) norm = norm.reshape(shp) rst = rst * norm if self.bias is not None: rst = rst + if self._activation is not None: rst = self._activation(rst) return rst
def __repr__(self): summary = 'GraphConv(' summary += 'in={:d}, out={:d}, normalization={}, activation={}'.format( self._in_feats, self._out_feats, self._norm, self._activation) summary += ')' return summary