wehub-resource-sync
325 lines
12 KiB
Python
325 lines
12 KiB
Python
"""MXNet modules for graph convolutions(GCN)"""
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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 gluon
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from .... import function as fn
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from ....base import DGLError
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from ....utils import expand_as_pair
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class GraphConv(gluon.Block):
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r"""Graph convolutional layer from `Semi-Supervised Classification with Graph Convolutional
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Networks <https://arxiv.org/abs/1609.02907>`__
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Mathematically it is defined as follows:
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.. math::
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h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{1}{c_{ij}}h_j^{(l)}W^{(l)})
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where :math:`\mathcal{N}(i)` is the set of neighbors of node :math:`i`,
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:math:`c_{ij}` is the product of the square root of node degrees
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(i.e., :math:`c_{ij} = \sqrt{|\mathcal{N}(i)|}\sqrt{|\mathcal{N}(j)|}`),
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and :math:`\sigma` is an activation function.
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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. Can be one of the following values:
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* ``right``, to divide the aggregated messages by each node's in-degrees,
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which is equivalent to averaging the received messages.
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* ``none``, where no normalization is applied.
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* ``both`` (default), where the messages are scaled with :math:`1/c_{ji}` above, equivalent
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to symmetric normalization.
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* ``left``, to divide the messages sent out from each node by its out-degrees,
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equivalent to random walk normalization.
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weight : bool, optional
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If True, apply a linear layer. Otherwise, aggregating the messages
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without a weight matrix.
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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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allow_zero_in_degree : bool, optional
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If there are 0-in-degree nodes in the graph, output for those nodes will be invalid
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since no message will be passed to those nodes. This is harmful for some applications
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causing silent performance regression. This module will raise a DGLError if it detects
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0-in-degree nodes in input graph. By setting ``True``, it will suppress the check
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and let the users handle it by themselves. Default: ``False``.
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Attributes
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----------
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weight : torch.Tensor
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The learnable weight tensor.
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bias : torch.Tensor
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The learnable bias tensor.
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Note
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----
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Zero in-degree nodes will lead to invalid output value. This is because no message
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will be passed to those nodes, the aggregation function will be appied on empty input.
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A common practice to avoid this is to add a self-loop for each node in the graph if
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it is homogeneous, which can be achieved by:
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>>> g = ... # a DGLGraph
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>>> g = dgl.add_self_loop(g)
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Calling ``add_self_loop`` will not work for some graphs, for example, heterogeneous graph
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since the edge type can not be decided for self_loop edges. Set ``allow_zero_in_degree``
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to ``True`` for those cases to unblock the code and handle zero-in-degree nodes manually.
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A common practise to handle this is to filter out the nodes with zero-in-degree when use
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after conv.
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Examples
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--------
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>>> import dgl
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>>> import mxnet as mx
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>>> from mxnet import gluon
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>>> import numpy as np
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>>> from dgl.nn import GraphConv
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>>> # Case 1: Homogeneous graph
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>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
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>>> g = dgl.add_self_loop(g)
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>>> feat = mx.nd.ones((6, 10))
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>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True)
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>>> conv.initialize(ctx=mx.cpu(0))
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>>> res = conv(g, feat)
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>>> print(res)
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[[1.0209361 0.22472616]
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[1.1240715 0.24742813]
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[1.0209361 0.22472616]
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[1.2924911 0.28450024]
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[1.3568745 0.29867214]
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[0.7948386 0.17495811]]
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<NDArray 6x2 @cpu(0)>
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>>> # allow_zero_in_degree example
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>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
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>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True, allow_zero_in_degree=True)
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>>> res = conv(g, feat)
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>>> print(res)
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[[1.0209361 0.22472616]
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[1.1240715 0.24742813]
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[1.0209361 0.22472616]
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[1.2924911 0.28450024]
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[1.3568745 0.29867214]
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[0. 0.]]
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<NDArray 6x2 @cpu(0)>
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>>> # Case 2: Unidirectional bipartite graph
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>>> u = [0, 1, 0, 0, 1]
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>>> v = [0, 1, 2, 3, 2]
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>>> g = dgl.heterograph({('_N', '_E', '_N'):(u, v)})
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>>> u_fea = mx.nd.random.randn(2, 5)
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>>> v_fea = mx.nd.random.randn(4, 5)
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>>> conv = GraphConv(5, 2, norm='both', weight=True, bias=True)
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>>> conv.initialize(ctx=mx.cpu(0))
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>>> res = conv(g, (u_fea, v_fea))
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>>> res
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[[ 0.26967263 0.308129 ]
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[ 0.05143356 -0.11355402]
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[ 0.22705637 0.1375853 ]
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[ 0.26967263 0.308129 ]]
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<NDArray 4x2 @cpu(0)>
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"""
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def __init__(
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self,
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in_feats,
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out_feats,
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norm="both",
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weight=True,
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bias=True,
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activation=None,
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allow_zero_in_degree=False,
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):
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super(GraphConv, self).__init__()
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if norm not in ("none", "both", "right", "left"):
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raise DGLError(
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'Invalid norm value. Must be either "none", "both", "right" or "left".'
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' But got "{}".'.format(norm)
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)
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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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self._allow_zero_in_degree = allow_zero_in_degree
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with self.name_scope():
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if weight:
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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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else:
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self.weight = None
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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 set_allow_zero_in_degree(self, set_value):
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r"""
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Description
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-----------
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Set allow_zero_in_degree flag.
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Parameters
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----------
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set_value : bool
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The value to be set to the flag.
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"""
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self._allow_zero_in_degree = set_value
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def forward(self, graph, feat, weight=None):
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r"""
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Description
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-----------
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Compute graph convolution.
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Parameters
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----------
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graph : DGLGraph
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The graph.
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feat : mxnet.NDArray or pair of mxnet.NDArray
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If a single tensor is given, it represents the input feature of shape
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:math:`(N, D_{in})`
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where :math:`D_{in}` is size of input feature, :math:`N` is the number of nodes.
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If a pair of tensors are given, the pair must contain two tensors of shape
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:math:`(N_{in}, D_{in_{src}})` and :math:`(N_{out}, D_{in_{dst}})`.
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Note that in the special case of graph convolutional networks, if a pair of
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tensors is given, the latter element will not participate in computation.
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weight : torch.Tensor, optional
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Optional external weight tensor.
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Returns
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-------
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mxnet.NDArray
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The output feature
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Raises
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------
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DGLError
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If there are 0-in-degree nodes in the input graph, it will raise DGLError
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since no message will be passed to those nodes. This will cause invalid output.
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The error can be ignored by setting ``allow_zero_in_degree`` parameter to ``True``.
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Note
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----
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* Input shape: :math:`(N, *, \text{in_feats})` where * means any number of additional
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dimensions, :math:`N` is the number of nodes.
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* Output shape: :math:`(N, *, \text{out_feats})` where all but the last dimension are
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the same shape as the input.
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* Weight shape: :math:`(\text{in_feats}, \text{out_feats})`.
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"""
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with graph.local_scope():
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if not self._allow_zero_in_degree:
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if graph.in_degrees().min() == 0:
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raise DGLError(
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"There are 0-in-degree nodes in the graph, "
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"output for those nodes will be invalid. "
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"This is harmful for some applications, "
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"causing silent performance regression. "
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"Adding self-loop on the input graph by "
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"calling `g = dgl.add_self_loop(g)` will resolve "
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"the issue. Setting ``allow_zero_in_degree`` "
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"to be `True` when constructing this module will "
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"suppress the check and let the code run."
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)
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feat_src, feat_dst = expand_as_pair(feat, graph)
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if self._norm in ["both", "left"]:
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degs = (
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graph.out_degrees()
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.as_in_context(feat_dst.context)
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.astype("float32")
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)
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degs = mx.nd.clip(degs, a_min=1, a_max=float("inf"))
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if self._norm == "both":
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norm = mx.nd.power(degs, -0.5)
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else:
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norm = 1.0 / degs
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shp = norm.shape + (1,) * (feat_src.ndim - 1)
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norm = norm.reshape(shp)
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feat_src = feat_src * norm
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if weight is not None:
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if self.weight is not None:
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raise DGLError(
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"External weight is provided while at the same time the"
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" module has defined its own weight parameter. Please"
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" create the module with flag weight=False."
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)
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else:
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weight = self.weight.data(feat_src.context)
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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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if weight is not None:
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feat_src = mx.nd.dot(feat_src, weight)
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graph.srcdata["h"] = feat_src
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graph.update_all(
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fn.copy_u(u="h", out="m"), fn.sum(msg="m", out="h")
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)
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rst = graph.dstdata.pop("h")
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else:
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# aggregate first then mult W
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graph.srcdata["h"] = feat_src
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graph.update_all(
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fn.copy_u(u="h", out="m"), fn.sum(msg="m", out="h")
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)
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rst = graph.dstdata.pop("h")
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if weight is not None:
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rst = mx.nd.dot(rst, weight)
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if self._norm in ["both", "right"]:
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degs = (
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graph.in_degrees()
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.as_in_context(feat_dst.context)
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.astype("float32")
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)
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degs = mx.nd.clip(degs, a_min=1, a_max=float("inf"))
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if self._norm == "both":
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norm = mx.nd.power(degs, -0.5)
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else:
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norm = 1.0 / degs
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shp = norm.shape + (1,) * (feat_dst.ndim - 1)
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norm = norm.reshape(shp)
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rst = rst * norm
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if self.bias is not None:
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rst = rst + self.bias.data(rst.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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def __repr__(self):
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summary = "GraphConv("
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summary += "in={:d}, out={:d}, normalization={}, activation={}".format(
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self._in_feats, self._out_feats, self._norm, self._activation
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)
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summary += ")"
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return summary
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