wehub-resource-sync
489 lines
18 KiB
Python
489 lines
18 KiB
Python
"""Torch modules for graph convolutions(GCN)."""
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# pylint: disable= no-member, arguments-differ, invalid-name
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import torch as th
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from torch import nn
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from torch.nn import init
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from .... import function as fn
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from ....base import DGLError
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from ....convert import block_to_graph
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from ....heterograph import DGLBlock
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from ....transforms import reverse
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from ....utils import expand_as_pair
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class EdgeWeightNorm(nn.Module):
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r"""This module normalizes positive scalar edge weights on a graph
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following the form in `GCN <https://arxiv.org/abs/1609.02907>`__.
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Mathematically, setting ``norm='both'`` yields the following normalization term:
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.. math::
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c_{ji} = (\sqrt{\sum_{k\in\mathcal{N}(j)}e_{jk}}\sqrt{\sum_{k\in\mathcal{N}(i)}e_{ki}})
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And, setting ``norm='right'`` yields the following normalization term:
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.. math::
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c_{ji} = (\sum_{k\in\mathcal{N}(i)}e_{ki})
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where :math:`e_{ji}` is the scalar weight on the edge from node :math:`j` to node :math:`i`.
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The module returns the normalized weight :math:`e_{ji} / c_{ji}`.
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Parameters
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----------
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norm : str, optional
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The normalizer as specified above. Default is `'both'`.
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eps : float, optional
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A small offset value in the denominator. Default is 0.
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Examples
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--------
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>>> import dgl
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>>> import numpy as np
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>>> import torch as th
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>>> from dgl.nn import EdgeWeightNorm, GraphConv
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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 = th.ones(6, 10)
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>>> edge_weight = th.tensor([0.5, 0.6, 0.4, 0.7, 0.9, 0.1, 1, 1, 1, 1, 1, 1])
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>>> norm = EdgeWeightNorm(norm='both')
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>>> norm_edge_weight = norm(g, edge_weight)
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>>> conv = GraphConv(10, 2, norm='none', weight=True, bias=True)
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>>> res = conv(g, feat, edge_weight=norm_edge_weight)
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>>> print(res)
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tensor([[-1.1849, -0.7525],
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[-1.3514, -0.8582],
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[-1.2384, -0.7865],
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[-1.9949, -1.2669],
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[-1.3658, -0.8674],
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[-0.8323, -0.5286]], grad_fn=<AddBackward0>)
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"""
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def __init__(self, norm="both", eps=0.0):
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super(EdgeWeightNorm, self).__init__()
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self._norm = norm
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self._eps = eps
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def forward(self, graph, edge_weight):
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r"""
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Description
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-----------
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Compute normalized edge weight for the GCN model.
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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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edge_weight : torch.Tensor
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Unnormalized scalar weights on the edges.
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The shape is expected to be :math:`(|E|)`.
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Returns
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-------
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torch.Tensor
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The normalized edge weight.
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Raises
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------
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DGLError
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Case 1:
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The edge weight is multi-dimensional. Currently this module
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only supports a scalar weight on each edge.
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Case 2:
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The edge weight has non-positive values with ``norm='both'``.
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This will trigger square root and division by a non-positive number.
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"""
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with graph.local_scope():
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if isinstance(graph, DGLBlock):
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graph = block_to_graph(graph)
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if len(edge_weight.shape) > 1:
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raise DGLError(
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"Currently the normalization is only defined "
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"on scalar edge weight. Please customize the "
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"normalization for your high-dimensional weights."
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)
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if self._norm == "both" and th.any(edge_weight <= 0).item():
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raise DGLError(
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'Non-positive edge weight detected with `norm="both"`. '
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"This leads to square root of zero or negative values."
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)
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dev = graph.device
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dtype = edge_weight.dtype
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graph.srcdata["_src_out_w"] = th.ones(
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graph.number_of_src_nodes(), dtype=dtype, device=dev
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)
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graph.dstdata["_dst_in_w"] = th.ones(
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graph.number_of_dst_nodes(), dtype=dtype, device=dev
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)
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graph.edata["_edge_w"] = edge_weight
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if self._norm == "both":
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reversed_g = reverse(graph)
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reversed_g.edata["_edge_w"] = edge_weight
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reversed_g.update_all(
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fn.copy_e("_edge_w", "m"), fn.sum("m", "out_weight")
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)
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degs = reversed_g.dstdata["out_weight"] + self._eps
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norm = th.pow(degs, -0.5)
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graph.srcdata["_src_out_w"] = norm
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if self._norm != "none":
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graph.update_all(
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fn.copy_e("_edge_w", "m"), fn.sum("m", "in_weight")
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)
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degs = graph.dstdata["in_weight"] + self._eps
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if self._norm == "both":
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norm = th.pow(degs, -0.5)
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else:
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norm = 1.0 / degs
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graph.dstdata["_dst_in_w"] = norm
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graph.apply_edges(
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lambda e: {
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"_norm_edge_weights": e.src["_src_out_w"]
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* e.dst["_dst_in_w"]
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* e.data["_edge_w"]
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}
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)
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return graph.edata["_norm_edge_weights"]
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# pylint: disable=W0235
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class GraphConv(nn.Module):
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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_{ji}}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_{ji}` is the product of the square root of node degrees
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(i.e., :math:`c_{ji} = \sqrt{|\mathcal{N}(j)|}\sqrt{|\mathcal{N}(i)|}`),
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and :math:`\sigma` is an activation function.
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If a weight tensor on each edge is provided, the weighted graph convolution is defined as:
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.. math::
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h_i^{(l+1)} = \sigma(b^{(l)} + \sum_{j\in\mathcal{N}(i)}\frac{e_{ji}}{c_{ji}}h_j^{(l)}W^{(l)})
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where :math:`e_{ji}` is the scalar weight on the edge from node :math:`j` to node :math:`i`.
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This is NOT equivalent to the weighted graph convolutional network formulation in the paper.
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To customize the normalization term :math:`c_{ji}`, one can first set ``norm='none'`` for
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the model, and send the pre-normalized :math:`e_{ji}` to the forward computation. We provide
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:class:`~dgl.nn.pytorch.EdgeWeightNorm` to normalize scalar edge weight following the GCN paper.
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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 numpy as np
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>>> import torch as th
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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 = th.ones(6, 10)
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>>> conv = GraphConv(10, 2, norm='both', weight=True, bias=True)
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>>> res = conv(g, feat)
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>>> print(res)
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tensor([[ 1.3326, -0.2797],
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[ 1.4673, -0.3080],
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[ 1.3326, -0.2797],
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[ 1.6871, -0.3541],
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[ 1.7711, -0.3717],
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[ 1.0375, -0.2178]], grad_fn=<AddBackward0>)
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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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tensor([[-0.2473, -0.4631],
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[-0.3497, -0.6549],
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[-0.3497, -0.6549],
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[-0.4221, -0.7905],
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[-0.3497, -0.6549],
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[ 0.0000, 0.0000]], grad_fn=<AddBackward0>)
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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({('_U', '_E', '_V') : (u, v)})
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>>> u_fea = th.rand(2, 5)
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>>> v_fea = th.rand(4, 5)
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>>> conv = GraphConv(5, 2, norm='both', weight=True, bias=True)
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>>> res = conv(g, (u_fea, v_fea))
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>>> res
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tensor([[-0.2994, 0.6106],
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[-0.4482, 0.5540],
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[-0.5287, 0.8235],
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[-0.2994, 0.6106]], grad_fn=<AddBackward0>)
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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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if weight:
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self.weight = nn.Parameter(th.Tensor(in_feats, out_feats))
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else:
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self.register_parameter("weight", None)
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if bias:
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self.bias = nn.Parameter(th.Tensor(out_feats))
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else:
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self.register_parameter("bias", None)
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self.reset_parameters()
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self._activation = activation
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def reset_parameters(self):
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r"""
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Description
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-----------
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Reinitialize learnable parameters.
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Note
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----
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The model parameters are initialized as in the
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`original implementation <https://github.com/tkipf/gcn/blob/master/gcn/layers.py>`__
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where the weight :math:`W^{(l)}` is initialized using Glorot uniform initialization
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and the bias is initialized to be zero.
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"""
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if self.weight is not None:
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init.xavier_uniform_(self.weight)
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if self.bias is not None:
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init.zeros_(self.bias)
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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, edge_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 : torch.Tensor or pair of torch.Tensor
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If a torch.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 torch.Tensor is given, which is the case for bipartite graph, the pair
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must contain two tensors of shape :math:`(N_{in}, D_{in_{src}})` and
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:math:`(N_{out}, D_{in_{dst}})`.
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weight : torch.Tensor, optional
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Optional external weight tensor.
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edge_weight : torch.Tensor, optional
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Optional tensor on the edge. If given, the convolution will weight
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with regard to the message.
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Returns
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-------
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torch.Tensor
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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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Case 1:
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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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Case 2:
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External weight is provided while at the same time the module
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has defined its own weight parameter.
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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() == 0).any():
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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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aggregate_fn = fn.copy_u("h", "m")
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if edge_weight is not None:
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assert edge_weight.shape[0] == graph.num_edges()
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graph.edata["_edge_weight"] = edge_weight
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aggregate_fn = fn.u_mul_e("h", "_edge_weight", "m")
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# (BarclayII) For RGCN on heterogeneous graphs we need to support GCN on bipartite.
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feat_src, feat_dst = expand_as_pair(feat, graph)
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if self._norm in ["left", "both"]:
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degs = graph.out_degrees().to(feat_src).clamp(min=1)
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if self._norm == "both":
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norm = th.pow(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.dim() - 1)
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norm = th.reshape(norm, 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
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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 = th.matmul(feat_src, weight)
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graph.srcdata["h"] = feat_src
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graph.update_all(aggregate_fn, fn.sum(msg="m", out="h"))
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rst = graph.dstdata["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(aggregate_fn, fn.sum(msg="m", out="h"))
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rst = graph.dstdata["h"]
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if weight is not None:
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rst = th.matmul(rst, weight)
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if self._norm in ["right", "both"]:
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degs = graph.in_degrees().to(feat_dst).clamp(min=1)
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if self._norm == "both":
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norm = th.pow(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.dim() - 1)
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norm = th.reshape(norm, 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
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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 extra_repr(self):
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"""Set the extra representation of the module,
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which will come into effect when printing the model.
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"""
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summary = "in={_in_feats}, out={_out_feats}"
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summary += ", normalization={_norm}"
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if "_activation" in self.__dict__:
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summary += ", activation={_activation}"
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return summary.format(**self.__dict__)
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