wehub-resource-sync
127 lines
4.6 KiB
Python
127 lines
4.6 KiB
Python
"""MXNet Module for DenseGraphConv"""
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# pylint: disable= no-member, arguments-differ, invalid-name
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import math
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import mxnet as mx
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from mxnet import nd
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from mxnet.gluon import nn
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class DenseGraphConv(nn.Block):
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"""Graph Convolutional layer from `Semi-Supervised Classification with Graph
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Convolutional Networks <https://arxiv.org/abs/1609.02907>`__
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We recommend user to use this module when applying graph convolution on
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dense graphs.
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Parameters
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----------
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in_feats : int
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Input feature size; i.e, the number of dimensions of :math:`h_j^{(l)}`.
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out_feats : int
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Output feature size; i.e., the number of dimensions of :math:`h_i^{(l+1)}`.
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norm : str, optional
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How to apply the normalizer. If is `'right'`, divide the aggregated messages
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by each node's in-degrees, which is equivalent to averaging the received messages.
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If is `'none'`, no normalization is applied. Default is `'both'`,
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where the :math:`c_{ij}` in the paper is applied.
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bias : bool, optional
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If True, adds a learnable bias to the output. Default: ``True``.
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activation : callable activation function/layer or None, optional
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If not None, applies an activation function to the updated node features.
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Default: ``None``.
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Notes
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-----
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Zero in-degree nodes will lead to all-zero output. A common practice
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to avoid this is to add a self-loop for each node in the graph,
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which can be achieved by setting the diagonal of the adjacency matrix to be 1.
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See also
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--------
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`GraphConv <https://docs.dgl.ai/api/python/nn.pytorch.html#graphconv>`__
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"""
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def __init__(
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self, in_feats, out_feats, norm="both", bias=True, activation=None
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):
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super(DenseGraphConv, self).__init__()
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self._in_feats = in_feats
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self._out_feats = out_feats
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self._norm = norm
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with self.name_scope():
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self.weight = self.params.get(
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"weight",
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shape=(in_feats, out_feats),
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init=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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)
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if bias:
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self.bias = self.params.get(
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"bias", shape=(out_feats,), init=mx.init.Zero()
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)
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else:
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self.bias = None
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self._activation = activation
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def forward(self, adj, feat):
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r"""
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Description
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-----------
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Compute (Dense) Graph Convolution layer.
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Parameters
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----------
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adj : mxnet.NDArray
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The adjacency matrix of the graph to apply Graph Convolution on, when
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applied to a unidirectional bipartite graph, ``adj`` should be of shape
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should be of shape :math:`(N_{out}, N_{in})`; when applied to a homo
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graph, ``adj`` should be of shape :math:`(N, N)`. In both cases,
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a row represents a destination node while a column represents a source
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node.
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feat : mxnet.NDArray
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The input feature.
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Returns
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-------
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mxnet.NDArray
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The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
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is size of output feature.
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"""
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adj = adj.astype(feat.dtype).as_in_context(feat.context)
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src_degrees = nd.clip(adj.sum(axis=0), a_min=1, a_max=float("inf"))
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dst_degrees = nd.clip(adj.sum(axis=1), a_min=1, a_max=float("inf"))
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feat_src = feat
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if self._norm == "both":
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norm_src = nd.power(src_degrees, -0.5)
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shp_src = norm_src.shape + (1,) * (feat.ndim - 1)
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norm_src = norm_src.reshape(shp_src).as_in_context(feat.context)
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feat_src = feat_src * norm_src
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if self._in_feats > self._out_feats:
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# mult W first to reduce the feature size for aggregation.
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feat_src = nd.dot(feat_src, self.weight.data(feat_src.context))
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rst = nd.dot(adj, feat_src)
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else:
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# aggregate first then mult W
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rst = nd.dot(adj, feat_src)
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rst = nd.dot(rst, self.weight.data(feat_src.context))
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if self._norm != "none":
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if self._norm == "both":
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norm_dst = nd.power(dst_degrees, -0.5)
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else: # right
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norm_dst = 1.0 / dst_degrees
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shp_dst = norm_dst.shape + (1,) * (feat.ndim - 1)
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norm_dst = norm_dst.reshape(shp_dst).as_in_context(feat.context)
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rst = rst * norm_dst
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if self.bias is not None:
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rst = rst + self.bias.data(feat.context)
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if self._activation is not None:
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rst = self._activation(rst)
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return rst
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