wehub-resource-sync
2017 lines
66 KiB
Python
2017 lines
66 KiB
Python
##
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# Copyright 2019-2021 Contributors
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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#
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"""Modules for transform"""
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# pylint: disable= no-member, arguments-differ, invalid-name, missing-function-docstring
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from scipy.linalg import expm
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from .. import backend as F, convert, function as fn, utils
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from ..base import dgl_warning, DGLError
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from . import functional
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try:
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import torch
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from torch.distributions import Bernoulli
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except ImportError:
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pass
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__all__ = [
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"BaseTransform",
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"RowFeatNormalizer",
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"FeatMask",
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"RandomWalkPE",
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"LaplacianPE",
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"LapPE",
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"AddSelfLoop",
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"RemoveSelfLoop",
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"AddReverse",
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"ToSimple",
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"LineGraph",
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"KHopGraph",
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"AddMetaPaths",
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"Compose",
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"GCNNorm",
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"PPR",
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"HeatKernel",
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"GDC",
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"NodeShuffle",
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"DropNode",
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"DropEdge",
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"AddEdge",
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"SIGNDiffusion",
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"ToLevi",
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"SVDPE",
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]
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def update_graph_structure(g, data_dict, copy_edata=True):
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r"""Update the structure of a graph.
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Parameters
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----------
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g : DGLGraph
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The graph to update.
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data_dict : graph data
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The dictionary data for constructing a heterogeneous graph.
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copy_edata : bool
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If True, it will copy the edge features to the updated graph.
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Returns
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-------
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DGLGraph
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The updated graph.
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"""
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device = g.device
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idtype = g.idtype
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num_nodes_dict = dict()
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for ntype in g.ntypes:
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num_nodes_dict[ntype] = g.num_nodes(ntype)
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new_g = convert.heterograph(
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data_dict, num_nodes_dict=num_nodes_dict, idtype=idtype, device=device
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)
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# Copy features
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for ntype in g.ntypes:
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for key, feat in g.nodes[ntype].data.items():
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new_g.nodes[ntype].data[key] = feat
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if copy_edata:
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for c_etype in g.canonical_etypes:
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for key, feat in g.edges[c_etype].data.items():
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new_g.edges[c_etype].data[key] = feat
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return new_g
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class BaseTransform:
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r"""An abstract class for writing transforms."""
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def __call__(self, g):
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raise NotImplementedError
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def __repr__(self):
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return self.__class__.__name__ + "()"
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class RowFeatNormalizer(BaseTransform):
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r"""
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Row-normalizes the features given in ``node_feat_names`` and ``edge_feat_names``.
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The row normalization formular is:
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.. math::
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x = \frac{x}{\sum_i x_i}
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where :math:`x` denotes a row of the feature tensor.
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Parameters
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----------
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subtract_min: bool
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If True, the minimum value of whole feature tensor will be subtracted before normalization.
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Default: False.
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Subtraction will make all values non-negative. If all values are negative, after
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normalisation, the sum of each row of the feature tensor will be 1.
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node_feat_names : list[str], optional
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The names of the node feature tensors to be row-normalized. Default: `None`, which will
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not normalize any node feature tensor.
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edge_feat_names : list[str], optional
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The names of the edge feature tensors to be row-normalized. Default: `None`, which will
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not normalize any edge feature tensor.
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Example
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-------
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The following example uses PyTorch backend.
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>>> import dgl
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>>> import torch
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>>> from dgl import RowFeatNormalizer
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Case1: Row normalize features of a homogeneous graph.
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>>> transform = RowFeatNormalizer(subtract_min=True,
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... node_feat_names=['h'], edge_feat_names=['w'])
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>>> g = dgl.rand_graph(5, 20)
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>>> g.ndata['h'] = torch.randn((g.num_nodes(), 5))
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>>> g.edata['w'] = torch.randn((g.num_edges(), 5))
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>>> g = transform(g)
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>>> print(g.ndata['h'].sum(1))
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tensor([1., 1., 1., 1., 1.])
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>>> print(g.edata['w'].sum(1))
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tensor([1., 1., 1., 1., 1., 1., 1., 1., 1.,
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1., 1., 1., 1., 1., 1., 1., 1., 1.,
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1., 1.])
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Case2: Row normalize features of a heterogeneous graph.
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>>> g = dgl.heterograph({
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... ('user', 'follows', 'user'): (torch.tensor([1, 2]), torch.tensor([3, 4])),
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... ('player', 'plays', 'game'): (torch.tensor([2, 2]), torch.tensor([1, 1]))
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... })
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>>> g.ndata['h'] = {'game': torch.randn(2, 5), 'player': torch.randn(3, 5)}
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>>> g.edata['w'] = {
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... ('user', 'follows', 'user'): torch.randn(2, 5),
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... ('player', 'plays', 'game'): torch.randn(2, 5)
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... }
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>>> g = transform(g)
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>>> print(g.ndata['h']['game'].sum(1), g.ndata['h']['player'].sum(1))
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tensor([1., 1.]) tensor([1., 1., 1.])
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>>> print(g.edata['w'][('user', 'follows', 'user')].sum(1),
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... g.edata['w'][('player', 'plays', 'game')].sum(1))
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tensor([1., 1.]) tensor([1., 1.])
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"""
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def __init__(
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self, subtract_min=False, node_feat_names=None, edge_feat_names=None
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):
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self.node_feat_names = (
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[] if node_feat_names is None else node_feat_names
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)
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self.edge_feat_names = (
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[] if edge_feat_names is None else edge_feat_names
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)
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self.subtract_min = subtract_min
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def row_normalize(self, feat):
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r"""
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Description
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-----------
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Row-normalize the given feature.
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Parameters
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----------
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feat : Tensor
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The feature to be normalized.
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Returns
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-------
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Tensor
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The normalized feature.
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"""
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if self.subtract_min:
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feat = feat - feat.min()
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feat.div_(feat.sum(dim=-1, keepdim=True).clamp_(min=1.0))
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return feat
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def __call__(self, g):
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for node_feat_name in self.node_feat_names:
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if isinstance(g.ndata[node_feat_name], torch.Tensor):
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g.ndata[node_feat_name] = self.row_normalize(
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g.ndata[node_feat_name]
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)
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else:
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for ntype in g.ndata[node_feat_name].keys():
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g.nodes[ntype].data[node_feat_name] = self.row_normalize(
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g.nodes[ntype].data[node_feat_name]
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)
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for edge_feat_name in self.edge_feat_names:
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if isinstance(g.edata[edge_feat_name], torch.Tensor):
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g.edata[edge_feat_name] = self.row_normalize(
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g.edata[edge_feat_name]
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)
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else:
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for etype in g.edata[edge_feat_name].keys():
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g.edges[etype].data[edge_feat_name] = self.row_normalize(
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g.edges[etype].data[edge_feat_name]
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)
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return g
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class FeatMask(BaseTransform):
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r"""Randomly mask columns of the node and edge feature tensors, as described in `Graph
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Contrastive Learning with Augmentations <https://arxiv.org/abs/2010.13902>`__.
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Parameters
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----------
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p : float, optional
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Probability of masking a column of a feature tensor. Default: `0.5`.
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node_feat_names : list[str], optional
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The names of the node feature tensors to be masked. Default: `None`, which will
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not mask any node feature tensor.
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edge_feat_names : list[str], optional
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The names of the edge features to be masked. Default: `None`, which will not mask
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any edge feature tensor.
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Example
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-------
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The following example uses PyTorch backend.
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>>> import dgl
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>>> import torch
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>>> from dgl import FeatMask
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Case1 : Mask node and edge feature tensors of a homogeneous graph.
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>>> transform = FeatMask(node_feat_names=['h'], edge_feat_names=['w'])
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>>> g = dgl.rand_graph(5, 10)
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>>> g.ndata['h'] = torch.ones((g.num_nodes(), 10))
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>>> g.edata['w'] = torch.ones((g.num_edges(), 10))
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>>> g = transform(g)
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>>> print(g.ndata['h'])
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tensor([[0., 0., 1., 1., 0., 0., 1., 1., 1., 0.],
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[0., 0., 1., 1., 0., 0., 1., 1., 1., 0.],
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[0., 0., 1., 1., 0., 0., 1., 1., 1., 0.],
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[0., 0., 1., 1., 0., 0., 1., 1., 1., 0.],
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[0., 0., 1., 1., 0., 0., 1., 1., 1., 0.]])
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>>> print(g.edata['w'])
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tensor([[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.],
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[1., 1., 0., 1., 0., 1., 0., 0., 0., 1.]])
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Case2 : Mask node and edge feature tensors of a heterogeneous graph.
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>>> g = dgl.heterograph({
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... ('user', 'follows', 'user'): (torch.tensor([1, 2]), torch.tensor([3, 4])),
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... ('player', 'plays', 'game'): (torch.tensor([2, 2]), torch.tensor([1, 1]))
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... })
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>>> g.ndata['h'] = {'game': torch.ones(2, 5), 'player': torch.ones(3, 5)}
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>>> g.edata['w'] = {('user', 'follows', 'user'): torch.ones(2, 5)}
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>>> print(g.ndata['h']['game'])
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tensor([[1., 1., 1., 1., 1.],
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[1., 1., 1., 1., 1.]])
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>>> print(g.edata['w'][('user', 'follows', 'user')])
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tensor([[1., 1., 1., 1., 1.],
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[1., 1., 1., 1., 1.]])
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>>> g = transform(g)
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>>> print(g.ndata['h']['game'])
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tensor([[1., 1., 0., 1., 0.],
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[1., 1., 0., 1., 0.]])
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>>> print(g.edata['w'][('user', 'follows', 'user')])
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tensor([[0., 1., 0., 1., 0.],
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[0., 1., 0., 1., 0.]])
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"""
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def __init__(self, p=0.5, node_feat_names=None, edge_feat_names=None):
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self.p = p
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self.node_feat_names = (
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[] if node_feat_names is None else node_feat_names
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)
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self.edge_feat_names = (
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[] if edge_feat_names is None else edge_feat_names
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)
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self.dist = Bernoulli(p)
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def __call__(self, g):
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# Fast path
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if self.p == 0:
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return g
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for node_feat_name in self.node_feat_names:
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if isinstance(g.ndata[node_feat_name], torch.Tensor):
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feat_mask = self.dist.sample(
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torch.Size(
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[
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g.ndata[node_feat_name].shape[-1],
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]
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)
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)
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g.ndata[node_feat_name][:, feat_mask.bool().to(g.device)] = 0
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else:
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for ntype in g.ndata[node_feat_name].keys():
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mask_shape = g.ndata[node_feat_name][ntype].shape[-1]
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feat_mask = self.dist.sample(
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torch.Size(
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[
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mask_shape,
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]
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)
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)
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g.ndata[node_feat_name][ntype][
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:, feat_mask.bool().to(g.device)
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] = 0
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for edge_feat_name in self.edge_feat_names:
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if isinstance(g.edata[edge_feat_name], torch.Tensor):
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feat_mask = self.dist.sample(
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torch.Size(
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[
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g.edata[edge_feat_name].shape[-1],
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]
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)
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)
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g.edata[edge_feat_name][:, feat_mask.bool().to(g.device)] = 0
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else:
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for etype in g.edata[edge_feat_name].keys():
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mask_shape = g.edata[edge_feat_name][etype].shape[-1]
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feat_mask = self.dist.sample(
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torch.Size(
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[
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mask_shape,
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]
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)
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)
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g.edata[edge_feat_name][etype][
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:, feat_mask.bool().to(g.device)
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] = 0
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return g
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class RandomWalkPE(BaseTransform):
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r"""Random Walk Positional Encoding, as introduced in
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`Graph Neural Networks with Learnable Structural and Positional Representations
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<https://arxiv.org/abs/2110.07875>`__
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This module only works for homogeneous graphs.
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Parameters
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----------
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k : int
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Number of random walk steps. The paper found the best value to be 16 and 20
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for two experiments.
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feat_name : str, optional
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Name to store the computed positional encodings in ndata.
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eweight_name : str, optional
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Name to retrieve the edge weights. Default: None, not using the edge weights.
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Example
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-------
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>>> import dgl
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>>> from dgl import RandomWalkPE
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>>> transform = RandomWalkPE(k=2)
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>>> g = dgl.graph(([0, 1, 1], [1, 1, 0]))
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>>> g = transform(g)
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>>> print(g.ndata['PE'])
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tensor([[0.0000, 0.5000],
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[0.5000, 0.7500]])
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"""
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def __init__(self, k, feat_name="PE", eweight_name=None):
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self.k = k
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self.feat_name = feat_name
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self.eweight_name = eweight_name
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def __call__(self, g):
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PE = functional.random_walk_pe(
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g, k=self.k, eweight_name=self.eweight_name
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)
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g.ndata[self.feat_name] = F.copy_to(PE, g.device)
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return g
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class LapPE(BaseTransform):
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r"""Laplacian Positional Encoding, as introduced in
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`Benchmarking Graph Neural Networks
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<https://arxiv.org/abs/2003.00982>`__
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This module only works for homogeneous bidirected graphs.
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Parameters
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----------
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k : int
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Number of smallest non-trivial eigenvectors to use for positional encoding.
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feat_name : str, optional
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Name to store the computed positional encodings in ndata.
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eigval_name : str, optional
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If None, store laplacian eigenvectors only. Otherwise, it's the name to
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store corresponding laplacian eigenvalues in ndata. Default: None.
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padding : bool, optional
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If False, raise an exception when k>=n.
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Otherwise, add zero paddings in the end of eigenvectors and 'nan'
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paddings in the end of eigenvalues when k>=n. Default: False.
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n is the number of nodes in the given graph.
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Example
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||
-------
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>>> import dgl
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>>> from dgl import LapPE
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>>> transform1 = LapPE(k=3)
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>>> transform2 = LapPE(k=5, padding=True)
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>>> transform3 = LapPE(k=5, feat_name='eigvec', eigval_name='eigval', padding=True)
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>>> g = dgl.graph(([0,1,2,3,4,2,3,1,4,0], [2,3,1,4,0,0,1,2,3,4]))
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>>> g1 = transform1(g)
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>>> print(g1.ndata['PE'])
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tensor([[ 0.6325, 0.1039, 0.3489],
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[-0.5117, 0.2826, 0.6095],
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[ 0.1954, 0.6254, -0.5923],
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[-0.5117, -0.4508, -0.3938],
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[ 0.1954, -0.5612, 0.0278]])
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>>> g2 = transform2(g)
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>>> print(g2.ndata['PE'])
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tensor([[-0.6325, -0.1039, 0.3489, -0.2530, 0.0000],
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[ 0.5117, -0.2826, 0.6095, 0.4731, 0.0000],
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[-0.1954, -0.6254, -0.5923, -0.1361, 0.0000],
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[ 0.5117, 0.4508, -0.3938, -0.6295, 0.0000],
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[-0.1954, 0.5612, 0.0278, 0.5454, 0.0000]])
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>>> g3 = transform3(g)
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>>> print(g3.ndata['eigval'])
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tensor([[0.6910, 0.6910, 1.8090, 1.8090, nan],
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[0.6910, 0.6910, 1.8090, 1.8090, nan],
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[0.6910, 0.6910, 1.8090, 1.8090, nan],
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[0.6910, 0.6910, 1.8090, 1.8090, nan],
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[0.6910, 0.6910, 1.8090, 1.8090, nan]])
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>>> print(g3.ndata['eigvec'])
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tensor([[ 0.6325, -0.1039, 0.3489, 0.2530, 0.0000],
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[-0.5117, -0.2826, 0.6095, -0.4731, 0.0000],
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[ 0.1954, -0.6254, -0.5923, 0.1361, 0.0000],
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[-0.5117, 0.4508, -0.3938, 0.6295, 0.0000],
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[ 0.1954, 0.5612, 0.0278, -0.5454, 0.0000]])
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"""
|
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|
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def __init__(self, k, feat_name="PE", eigval_name=None, padding=False):
|
||
self.k = k
|
||
self.feat_name = feat_name
|
||
self.eigval_name = eigval_name
|
||
self.padding = padding
|
||
|
||
def __call__(self, g):
|
||
if self.eigval_name:
|
||
PE, eigval = functional.lap_pe(
|
||
g, k=self.k, padding=self.padding, return_eigval=True
|
||
)
|
||
eigval = F.repeat(F.reshape(eigval, [1, -1]), g.num_nodes(), dim=0)
|
||
g.ndata[self.eigval_name] = F.copy_to(eigval, g.device)
|
||
else:
|
||
PE = functional.lap_pe(g, k=self.k, padding=self.padding)
|
||
g.ndata[self.feat_name] = F.copy_to(PE, g.device)
|
||
|
||
return g
|
||
|
||
|
||
class LaplacianPE(LapPE):
|
||
r"""Alias of `LapPE`."""
|
||
|
||
def __init__(self, k, feat_name="PE", eigval_name=None, padding=False):
|
||
super().__init__(k, feat_name, eigval_name, padding)
|
||
dgl_warning("LaplacianPE will be deprecated. Use LapPE please.")
|
||
|
||
|
||
class AddSelfLoop(BaseTransform):
|
||
r"""Add self-loops for each node in the graph and return a new graph.
|
||
|
||
For heterogeneous graphs, self-loops are added only for edge types with same
|
||
source and destination node types.
|
||
|
||
Parameters
|
||
----------
|
||
allow_duplicate : bool, optional
|
||
If False, it will first remove self-loops to prevent duplicate self-loops.
|
||
new_etypes : bool, optional
|
||
If True, it will add an edge type 'self' per node type, which holds self-loops.
|
||
edge_feat_names : list[str], optional
|
||
The names of the self-loop features to apply `fill_data`. If None, it
|
||
will apply `fill_data` to all self-loop features. Default: None.
|
||
fill_data : int, float or str, optional
|
||
The value to fill the self-loop features. Default: 1.
|
||
|
||
* If ``fill_data`` is ``int`` or ``float``, self-loop features will be directly given by
|
||
``fill_data``.
|
||
* if ``fill_data`` is ``str``, self-loop features will be generated by aggregating the
|
||
features of the incoming edges of the corresponding nodes. The supported aggregation are:
|
||
``'mean'``, ``'sum'``, ``'max'``, ``'min'``.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> from dgl import AddSelfLoop
|
||
|
||
Case1: Add self-loops for a homogeneous graph
|
||
|
||
>>> transform = AddSelfLoop(fill_data='sum')
|
||
>>> g = dgl.graph(([0, 0, 2], [2, 1, 0]))
|
||
>>> g.edata['he'] = torch.arange(3).float().reshape(-1, 1)
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges())
|
||
(tensor([0, 0, 2, 0, 1, 2]), tensor([2, 1, 0, 0, 1, 2]))
|
||
>>> print(new_g.edata('he'))
|
||
tensor([[0.],
|
||
[1.],
|
||
[2.],
|
||
[2.],
|
||
[1.],
|
||
[0.]])
|
||
|
||
Case2: Add self-loops for a heterogeneous graph
|
||
|
||
>>> transform = AddSelfLoop(fill_data='sum')
|
||
>>> g = dgl.heterograph({
|
||
... ('user', 'follows', 'user'): (torch.tensor([1, 2]),
|
||
... torch.tensor([0, 1])),
|
||
... ('user', 'plays', 'game'): (torch.tensor([0, 1]),
|
||
... torch.tensor([0, 1]))})
|
||
>>> g.edata['feat'] = {('user', 'follows', 'user'): torch.randn(2, 5),
|
||
... ('user', 'plays', 'game'): torch.randn(2, 5)}
|
||
>>> g.edata['feat1'] = {('user', 'follows', 'user'): torch.randn(2, 15),
|
||
... ('user', 'plays', 'game'): torch.randn(2, 15)}
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges(etype='plays'))
|
||
(tensor([0, 1]), tensor([0, 1]))
|
||
>>> print(new_g.edges(etype='follows'))
|
||
(tensor([1, 2, 0, 1, 2]), tensor([0, 1, 0, 1, 2]))
|
||
>>> print(new_g.edata['feat'][('user', 'follows', 'user')].shape)
|
||
torch.Size([5, 5])
|
||
|
||
Case3: Add self-etypes for a heterogeneous graph
|
||
|
||
>>> transform = AddSelfLoop(new_etypes=True)
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges(etype='follows'))
|
||
(tensor([1, 2, 0, 1, 2]), tensor([0, 1, 0, 1, 2]))
|
||
>>> print(new_g.edges(etype=('game', 'self', 'game')))
|
||
(tensor([0, 1]), tensor([0, 1]))
|
||
"""
|
||
|
||
def __init__(
|
||
self,
|
||
allow_duplicate=False,
|
||
new_etypes=False,
|
||
edge_feat_names=None,
|
||
fill_data=1.0,
|
||
):
|
||
self.allow_duplicate = allow_duplicate
|
||
self.new_etypes = new_etypes
|
||
self.edge_feat_names = edge_feat_names
|
||
self.fill_data = fill_data
|
||
|
||
def transform_etype(self, c_etype, g):
|
||
r"""
|
||
|
||
Description
|
||
-----------
|
||
Transform the graph corresponding to a canonical edge type.
|
||
|
||
Parameters
|
||
----------
|
||
c_etype : tuple of str
|
||
A canonical edge type.
|
||
g : DGLGraph
|
||
The graph.
|
||
|
||
Returns
|
||
-------
|
||
DGLGraph
|
||
The transformed graph.
|
||
"""
|
||
utype, _, vtype = c_etype
|
||
if utype != vtype:
|
||
return g
|
||
|
||
if not self.allow_duplicate:
|
||
g = functional.remove_self_loop(g, etype=c_etype)
|
||
return functional.add_self_loop(
|
||
g,
|
||
edge_feat_names=self.edge_feat_names,
|
||
fill_data=self.fill_data,
|
||
etype=c_etype,
|
||
)
|
||
|
||
def __call__(self, g):
|
||
for c_etype in g.canonical_etypes:
|
||
g = self.transform_etype(c_etype, g)
|
||
|
||
if self.new_etypes:
|
||
device = g.device
|
||
idtype = g.idtype
|
||
data_dict = dict()
|
||
|
||
# Add self etypes
|
||
for ntype in g.ntypes:
|
||
nids = F.arange(0, g.num_nodes(ntype), idtype, device)
|
||
data_dict[(ntype, "self", ntype)] = (nids, nids)
|
||
|
||
# Copy edges
|
||
for c_etype in g.canonical_etypes:
|
||
data_dict[c_etype] = g.edges(etype=c_etype)
|
||
|
||
g = update_graph_structure(g, data_dict)
|
||
|
||
return g
|
||
|
||
|
||
class RemoveSelfLoop(BaseTransform):
|
||
r"""Remove self-loops for each node in the graph and return a new graph.
|
||
|
||
For heterogeneous graphs, this operation only applies to edge types with same
|
||
source and destination node types.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> from dgl import RemoveSelfLoop
|
||
|
||
Case1: Remove self-loops for a homogeneous graph
|
||
|
||
>>> transform = RemoveSelfLoop()
|
||
>>> g = dgl.graph(([1, 1], [1, 2]))
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges())
|
||
(tensor([1]), tensor([2]))
|
||
|
||
Case2: Remove self-loops for a heterogeneous graph
|
||
|
||
>>> g = dgl.heterograph({
|
||
... ('user', 'plays', 'game'): ([0, 1], [1, 1]),
|
||
... ('user', 'follows', 'user'): ([1, 2], [2, 2])
|
||
... })
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges(etype='plays'))
|
||
(tensor([0, 1]), tensor([1, 1]))
|
||
>>> print(new_g.edges(etype='follows'))
|
||
(tensor([1]), tensor([2]))
|
||
"""
|
||
|
||
def transform_etype(self, c_etype, g):
|
||
r"""Transform the graph corresponding to a canonical edge type.
|
||
|
||
Parameters
|
||
----------
|
||
c_etype : tuple of str
|
||
A canonical edge type.
|
||
g : DGLGraph
|
||
The graph.
|
||
|
||
Returns
|
||
-------
|
||
DGLGraph
|
||
The transformed graph.
|
||
"""
|
||
utype, _, vtype = c_etype
|
||
if utype == vtype:
|
||
g = functional.remove_self_loop(g, etype=c_etype)
|
||
return g
|
||
|
||
def __call__(self, g):
|
||
for c_etype in g.canonical_etypes:
|
||
g = self.transform_etype(c_etype, g)
|
||
return g
|
||
|
||
|
||
class AddReverse(BaseTransform):
|
||
r"""Add a reverse edge :math:`(i,j)` for each edge :math:`(j,i)` in the input graph and
|
||
return a new graph.
|
||
|
||
For a heterogeneous graph, it adds a "reverse" edge type for each edge type
|
||
to hold the reverse edges. For example, for a canonical edge type ('A', 'r', 'B'),
|
||
it adds a canonical edge type ('B', 'rev_r', 'A').
|
||
|
||
Parameters
|
||
----------
|
||
copy_edata : bool, optional
|
||
If True, the features of the reverse edges will be identical to the original ones.
|
||
sym_new_etype : bool, optional
|
||
If False, it will not add a reverse edge type if the source and destination node type
|
||
in a canonical edge type are identical. Instead, it will directly add edges to the
|
||
original edge type.
|
||
|
||
Example
|
||
-------
|
||
|
||
The following example uses PyTorch backend.
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import AddReverse
|
||
|
||
Case1: Add reverse edges for a homogeneous graph
|
||
|
||
>>> transform = AddReverse()
|
||
>>> g = dgl.graph(([0], [1]))
|
||
>>> g.edata['w'] = torch.ones(1, 2)
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges())
|
||
(tensor([0, 1]), tensor([1, 0]))
|
||
>>> print(new_g.edata['w'])
|
||
tensor([[1., 1.],
|
||
[0., 0.]])
|
||
|
||
Case2: Add reverse edges for a homogeneous graph and copy edata
|
||
|
||
>>> transform = AddReverse(copy_edata=True)
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edata['w'])
|
||
tensor([[1., 1.],
|
||
[1., 1.]])
|
||
|
||
Case3: Add reverse edges for a heterogeneous graph
|
||
|
||
>>> g = dgl.heterograph({
|
||
... ('user', 'plays', 'game'): ([0, 1], [1, 1]),
|
||
... ('user', 'follows', 'user'): ([1, 2], [2, 2])
|
||
... })
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.canonical_etypes)
|
||
[('game', 'rev_plays', 'user'), ('user', 'follows', 'user'), ('user', 'plays', 'game')]
|
||
>>> print(new_g.edges(etype='rev_plays'))
|
||
(tensor([1, 1]), tensor([0, 1]))
|
||
>>> print(new_g.edges(etype='follows'))
|
||
(tensor([1, 2, 2, 2]), tensor([2, 2, 1, 2]))
|
||
"""
|
||
|
||
def __init__(self, copy_edata=False, sym_new_etype=False):
|
||
self.copy_edata = copy_edata
|
||
self.sym_new_etype = sym_new_etype
|
||
|
||
def transform_symmetric_etype(self, c_etype, g, data_dict):
|
||
r"""Transform the graph corresponding to a symmetric canonical edge type.
|
||
|
||
Parameters
|
||
----------
|
||
c_etype : tuple of str
|
||
A canonical edge type.
|
||
g : DGLGraph
|
||
The graph.
|
||
data_dict : dict
|
||
The edge data to update.
|
||
"""
|
||
if self.sym_new_etype:
|
||
self.transform_asymmetric_etype(c_etype, g, data_dict)
|
||
else:
|
||
src, dst = g.edges(etype=c_etype)
|
||
src, dst = F.cat([src, dst], dim=0), F.cat([dst, src], dim=0)
|
||
data_dict[c_etype] = (src, dst)
|
||
|
||
def transform_asymmetric_etype(self, c_etype, g, data_dict):
|
||
r"""Transform the graph corresponding to an asymmetric canonical edge type.
|
||
|
||
Parameters
|
||
----------
|
||
c_etype : tuple of str
|
||
A canonical edge type.
|
||
g : DGLGraph
|
||
The graph.
|
||
data_dict : dict
|
||
The edge data to update.
|
||
"""
|
||
utype, etype, vtype = c_etype
|
||
src, dst = g.edges(etype=c_etype)
|
||
data_dict.update(
|
||
{
|
||
c_etype: (src, dst),
|
||
(vtype, "rev_{}".format(etype), utype): (dst, src),
|
||
}
|
||
)
|
||
|
||
def transform_etype(self, c_etype, g, data_dict):
|
||
r"""Transform the graph corresponding to a canonical edge type.
|
||
|
||
Parameters
|
||
----------
|
||
c_etype : tuple of str
|
||
A canonical edge type.
|
||
g : DGLGraph
|
||
The graph.
|
||
data_dict : dict
|
||
The edge data to update.
|
||
"""
|
||
utype, _, vtype = c_etype
|
||
if utype == vtype:
|
||
self.transform_symmetric_etype(c_etype, g, data_dict)
|
||
else:
|
||
self.transform_asymmetric_etype(c_etype, g, data_dict)
|
||
|
||
def __call__(self, g):
|
||
data_dict = dict()
|
||
for c_etype in g.canonical_etypes:
|
||
self.transform_etype(c_etype, g, data_dict)
|
||
new_g = update_graph_structure(g, data_dict, copy_edata=False)
|
||
|
||
# Copy and expand edata
|
||
for c_etype in g.canonical_etypes:
|
||
utype, etype, vtype = c_etype
|
||
if utype != vtype or self.sym_new_etype:
|
||
rev_c_etype = (vtype, "rev_{}".format(etype), utype)
|
||
for key, feat in g.edges[c_etype].data.items():
|
||
new_g.edges[c_etype].data[key] = feat
|
||
if self.copy_edata:
|
||
new_g.edges[rev_c_etype].data[key] = feat
|
||
else:
|
||
for key, feat in g.edges[c_etype].data.items():
|
||
new_feat = (
|
||
feat
|
||
if self.copy_edata
|
||
else F.zeros(
|
||
F.shape(feat), F.dtype(feat), F.context(feat)
|
||
)
|
||
)
|
||
new_g.edges[c_etype].data[key] = F.cat(
|
||
[feat, new_feat], dim=0
|
||
)
|
||
|
||
return new_g
|
||
|
||
|
||
class ToSimple(BaseTransform):
|
||
r"""Convert a graph to a simple graph without parallel edges and return a new graph.
|
||
|
||
Parameters
|
||
----------
|
||
return_counts : str, optional
|
||
The edge feature name to hold the edge count in the original graph.
|
||
aggregator : str, optional
|
||
The way to coalesce features of duplicate edges.
|
||
|
||
* ``'arbitrary'``: select arbitrarily from one of the duplicate edges
|
||
* ``'sum'``: take the sum over the duplicate edges
|
||
* ``'mean'``: take the mean over the duplicate edges
|
||
|
||
Example
|
||
-------
|
||
|
||
The following example uses PyTorch backend.
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import ToSimple
|
||
|
||
Case1: Convert a homogeneous graph to a simple graph
|
||
|
||
>>> transform = ToSimple()
|
||
>>> g = dgl.graph(([0, 1, 1], [1, 2, 2]))
|
||
>>> g.edata['w'] = torch.tensor([[0.1], [0.2], [0.3]])
|
||
>>> sg = transform(g)
|
||
>>> print(sg.edges())
|
||
(tensor([0, 1]), tensor([1, 2]))
|
||
>>> print(sg.edata['count'])
|
||
tensor([1, 2])
|
||
>>> print(sg.edata['w'])
|
||
tensor([[0.1000], [0.2000]])
|
||
|
||
Case2: Convert a heterogeneous graph to a simple graph
|
||
|
||
>>> g = dgl.heterograph({
|
||
... ('user', 'follows', 'user'): ([0, 1, 1], [1, 2, 2]),
|
||
... ('user', 'plays', 'game'): ([0, 1, 0], [1, 1, 1])
|
||
... })
|
||
>>> sg = transform(g)
|
||
>>> print(sg.edges(etype='follows'))
|
||
(tensor([0, 1]), tensor([1, 2]))
|
||
>>> print(sg.edges(etype='plays'))
|
||
(tensor([0, 1]), tensor([1, 1]))
|
||
"""
|
||
|
||
def __init__(self, return_counts="count", aggregator="arbitrary"):
|
||
self.return_counts = return_counts
|
||
self.aggregator = aggregator
|
||
|
||
def __call__(self, g):
|
||
return functional.to_simple(
|
||
g,
|
||
return_counts=self.return_counts,
|
||
copy_edata=True,
|
||
aggregator=self.aggregator,
|
||
)
|
||
|
||
|
||
class LineGraph(BaseTransform):
|
||
r"""Return the line graph of the input graph.
|
||
|
||
The line graph :math:`L(G)` of a given graph :math:`G` is a graph where
|
||
the nodes in :math:`L(G)` correspond to the edges in :math:`G`. For a pair
|
||
of edges :math:`(u, v)` and :math:`(v, w)` in :math:`G`, there will be an
|
||
edge from the node corresponding to :math:`(u, v)` to the node corresponding to
|
||
:math:`(v, w)` in :math:`L(G)`.
|
||
|
||
This module only works for homogeneous graphs.
|
||
|
||
Parameters
|
||
----------
|
||
backtracking : bool, optional
|
||
If False, there will be an edge from the line graph node corresponding to
|
||
:math:`(u, v)` to the line graph node corresponding to :math:`(v, u)`.
|
||
|
||
Example
|
||
-------
|
||
|
||
The following example uses PyTorch backend.
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import LineGraph
|
||
|
||
Case1: Backtracking is True
|
||
|
||
>>> transform = LineGraph()
|
||
>>> g = dgl.graph(([0, 1, 1], [1, 0, 2]))
|
||
>>> g.ndata['h'] = torch.tensor([[0.], [1.], [2.]])
|
||
>>> g.edata['w'] = torch.tensor([[0.], [0.1], [0.2]])
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g)
|
||
Graph(num_nodes=3, num_edges=3,
|
||
ndata_schemes={'w': Scheme(shape=(1,), dtype=torch.float32)}
|
||
edata_schemes={})
|
||
>>> print(new_g.edges())
|
||
(tensor([0, 0, 1]), tensor([1, 2, 0]))
|
||
|
||
Case2: Backtracking is False
|
||
|
||
>>> transform = LineGraph(backtracking=False)
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges())
|
||
(tensor([0]), tensor([2]))
|
||
"""
|
||
|
||
def __init__(self, backtracking=True):
|
||
self.backtracking = backtracking
|
||
|
||
def __call__(self, g):
|
||
return functional.line_graph(
|
||
g, backtracking=self.backtracking, shared=True
|
||
)
|
||
|
||
|
||
class KHopGraph(BaseTransform):
|
||
r"""Return the graph whose edges connect the :math:`k`-hop neighbors of the original graph.
|
||
|
||
This module only works for homogeneous graphs.
|
||
|
||
Parameters
|
||
----------
|
||
k : int
|
||
The number of hops.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> from dgl import KHopGraph
|
||
|
||
>>> transform = KHopGraph(2)
|
||
>>> g = dgl.graph(([0, 1], [1, 2]))
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges())
|
||
(tensor([0]), tensor([2]))
|
||
"""
|
||
|
||
def __init__(self, k):
|
||
self.k = k
|
||
|
||
def __call__(self, g):
|
||
return functional.khop_graph(g, self.k)
|
||
|
||
|
||
class AddMetaPaths(BaseTransform):
|
||
r"""Add new edges to an input graph based on given metapaths, as described in
|
||
`Heterogeneous Graph Attention Network <https://arxiv.org/abs/1903.07293>`__.
|
||
|
||
Formally, a metapath is a path of the form
|
||
|
||
.. math::
|
||
|
||
\mathcal{V}_1 \xrightarrow{R_1} \mathcal{V}_2 \xrightarrow{R_2} \ldots
|
||
\xrightarrow{R_{\ell-1}} \mathcal{V}_{\ell}
|
||
|
||
in which :math:`\mathcal{V}_i` represents a node type and :math:`\xrightarrow{R_j}`
|
||
represents a relation type connecting its two adjacent node types. The adjacency matrix
|
||
corresponding to the metapath is obtained by sequential multiplication of adjacency matrices
|
||
along the metapath.
|
||
|
||
Parameters
|
||
----------
|
||
metapaths : dict[str, list]
|
||
The metapaths to add, mapping a metapath name to a metapath. For example,
|
||
:attr:`{'co-author': [('person', 'author', 'paper'), ('paper', 'authored by', 'person')]}`
|
||
keep_orig_edges : bool, optional
|
||
If True, it will keep the edges of the original graph. Otherwise, it will drop them.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> from dgl import AddMetaPaths
|
||
|
||
>>> transform = AddMetaPaths({
|
||
... 'accepted': [('person', 'author', 'paper'), ('paper', 'accepted', 'venue')],
|
||
... 'rejected': [('person', 'author', 'paper'), ('paper', 'rejected', 'venue')]
|
||
... })
|
||
>>> g = dgl.heterograph({
|
||
... ('person', 'author', 'paper'): ([0, 0, 1], [1, 2, 2]),
|
||
... ('paper', 'accepted', 'venue'): ([1], [0]),
|
||
... ('paper', 'rejected', 'venue'): ([2], [1])
|
||
... })
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges(etype=('person', 'accepted', 'venue')))
|
||
(tensor([0]), tensor([0]))
|
||
>>> print(new_g.edges(etype=('person', 'rejected', 'venue')))
|
||
(tensor([0, 1]), tensor([1, 1]))
|
||
"""
|
||
|
||
def __init__(self, metapaths, keep_orig_edges=True):
|
||
self.metapaths = metapaths
|
||
self.keep_orig_edges = keep_orig_edges
|
||
|
||
def __call__(self, g):
|
||
data_dict = dict()
|
||
|
||
for meta_etype, metapath in self.metapaths.items():
|
||
meta_g = functional.metapath_reachable_graph(g, metapath)
|
||
u_type = metapath[0][0]
|
||
v_type = metapath[-1][-1]
|
||
data_dict[(u_type, meta_etype, v_type)] = meta_g.edges()
|
||
|
||
if self.keep_orig_edges:
|
||
for c_etype in g.canonical_etypes:
|
||
data_dict[c_etype] = g.edges(etype=c_etype)
|
||
new_g = update_graph_structure(g, data_dict, copy_edata=True)
|
||
else:
|
||
new_g = update_graph_structure(g, data_dict, copy_edata=False)
|
||
|
||
return new_g
|
||
|
||
|
||
class Compose(BaseTransform):
|
||
r"""Create a transform composed of multiple transforms in sequence.
|
||
|
||
Parameters
|
||
----------
|
||
transforms : list of Callable
|
||
A list of transform objects to apply in order. A transform object should inherit
|
||
:class:`~dgl.BaseTransform` and implement :func:`~dgl.BaseTransform.__call__`.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> from dgl import transforms as T
|
||
|
||
>>> g = dgl.graph(([0, 0], [1, 1]))
|
||
>>> transform = T.Compose([T.ToSimple(), T.AddReverse()])
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edges())
|
||
(tensor([0, 1]), tensor([1, 0]))
|
||
"""
|
||
|
||
def __init__(self, transforms):
|
||
self.transforms = transforms
|
||
|
||
def __call__(self, g):
|
||
for transform in self.transforms:
|
||
g = transform(g)
|
||
return g
|
||
|
||
def __repr__(self):
|
||
args = [" " + str(transform) for transform in self.transforms]
|
||
return self.__class__.__name__ + "([\n" + ",\n".join(args) + "\n])"
|
||
|
||
|
||
class GCNNorm(BaseTransform):
|
||
r"""Apply symmetric adjacency normalization to an input graph and save the result edge
|
||
weights, as described in `Semi-Supervised Classification with Graph Convolutional Networks
|
||
<https://arxiv.org/abs/1609.02907>`__.
|
||
|
||
For a heterogeneous graph, this only applies to symmetric canonical edge types, whose source
|
||
and destination node types are identical.
|
||
|
||
Parameters
|
||
----------
|
||
eweight_name : str, optional
|
||
:attr:`edata` name to retrieve and store edge weights. The edge weights are optional.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import GCNNorm
|
||
>>> transform = GCNNorm()
|
||
>>> g = dgl.graph(([0, 1, 2], [0, 0, 1]))
|
||
|
||
Case1: Transform an unweighted graph
|
||
|
||
>>> g = transform(g)
|
||
>>> print(g.edata['w'])
|
||
tensor([0.5000, 0.7071, 0.0000])
|
||
|
||
Case2: Transform a weighted graph
|
||
|
||
>>> g.edata['w'] = torch.tensor([0.1, 0.2, 0.3])
|
||
>>> g = transform(g)
|
||
>>> print(g.edata['w'])
|
||
tensor([0.3333, 0.6667, 0.0000])
|
||
"""
|
||
|
||
def __init__(self, eweight_name="w"):
|
||
self.eweight_name = eweight_name
|
||
|
||
def calc_etype(self, c_etype, g):
|
||
r"""
|
||
|
||
Description
|
||
-----------
|
||
Get edge weights for an edge type.
|
||
"""
|
||
ntype = c_etype[0]
|
||
with g.local_scope():
|
||
if self.eweight_name in g.edges[c_etype].data:
|
||
g.update_all(
|
||
fn.copy_e(self.eweight_name, "m"),
|
||
fn.sum("m", "deg"),
|
||
etype=c_etype,
|
||
)
|
||
deg_inv_sqrt = 1.0 / F.sqrt(g.nodes[ntype].data["deg"])
|
||
g.nodes[ntype].data["w"] = F.replace_inf_with_zero(deg_inv_sqrt)
|
||
g.apply_edges(
|
||
lambda edge: {
|
||
"w": edge.src["w"]
|
||
* edge.data[self.eweight_name]
|
||
* edge.dst["w"]
|
||
},
|
||
etype=c_etype,
|
||
)
|
||
else:
|
||
deg = g.in_degrees(etype=c_etype)
|
||
deg_inv_sqrt = 1.0 / F.sqrt(F.astype(deg, F.float32))
|
||
g.nodes[ntype].data["w"] = F.replace_inf_with_zero(deg_inv_sqrt)
|
||
g.apply_edges(
|
||
lambda edges: {"w": edges.src["w"] * edges.dst["w"]},
|
||
etype=c_etype,
|
||
)
|
||
return g.edges[c_etype].data["w"]
|
||
|
||
def __call__(self, g):
|
||
result = dict()
|
||
for c_etype in g.canonical_etypes:
|
||
utype, _, vtype = c_etype
|
||
if utype == vtype:
|
||
result[c_etype] = self.calc_etype(c_etype, g)
|
||
|
||
for c_etype, eweight in result.items():
|
||
g.edges[c_etype].data[self.eweight_name] = eweight
|
||
return g
|
||
|
||
|
||
class PPR(BaseTransform):
|
||
r"""Apply personalized PageRank (PPR) to an input graph for diffusion, as introduced in
|
||
`The pagerank citation ranking: Bringing order to the web
|
||
<http://ilpubs.stanford.edu:8090/422/>`__.
|
||
|
||
A sparsification will be applied to the weighted adjacency matrix after diffusion.
|
||
Specifically, edges whose weight is below a threshold will be dropped.
|
||
|
||
This module only works for homogeneous graphs.
|
||
|
||
Parameters
|
||
----------
|
||
alpha : float, optional
|
||
Restart probability, which commonly lies in :math:`[0.05, 0.2]`.
|
||
eweight_name : str, optional
|
||
:attr:`edata` name to retrieve and store edge weights. If it does
|
||
not exist in an input graph, this module initializes a weight of 1
|
||
for all edges. The edge weights should be a tensor of shape :math:`(E)`,
|
||
where E is the number of edges.
|
||
eps : float, optional
|
||
The threshold to preserve edges in sparsification after diffusion. Edges of a
|
||
weight smaller than eps will be dropped.
|
||
avg_degree : int, optional
|
||
The desired average node degree of the result graph. This is the other way to
|
||
control the sparsity of the result graph and will only be effective if
|
||
:attr:`eps` is not given.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import PPR
|
||
|
||
>>> transform = PPR(avg_degree=2)
|
||
>>> g = dgl.graph(([0, 1, 2, 3, 4], [2, 3, 4, 5, 3]))
|
||
>>> g.edata['w'] = torch.tensor([0.1, 0.2, 0.3, 0.4, 0.5])
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edata['w'])
|
||
tensor([0.1500, 0.1500, 0.1500, 0.0255, 0.0163, 0.1500, 0.0638, 0.0383, 0.1500,
|
||
0.0510, 0.0217, 0.1500])
|
||
"""
|
||
|
||
def __init__(self, alpha=0.15, eweight_name="w", eps=None, avg_degree=5):
|
||
self.alpha = alpha
|
||
self.eweight_name = eweight_name
|
||
self.eps = eps
|
||
self.avg_degree = avg_degree
|
||
|
||
def get_eps(self, num_nodes, mat):
|
||
r"""Get the threshold for graph sparsification."""
|
||
if self.eps is None:
|
||
# Infer from self.avg_degree
|
||
if self.avg_degree > num_nodes:
|
||
return float("-inf")
|
||
sorted_weights = torch.sort(mat.flatten(), descending=True).values
|
||
return sorted_weights[self.avg_degree * num_nodes - 1]
|
||
else:
|
||
return self.eps
|
||
|
||
def __call__(self, g):
|
||
# Step1: PPR diffusion
|
||
# (α - 1) A
|
||
device = g.device
|
||
eweight = (self.alpha - 1) * g.edata.get(
|
||
self.eweight_name, F.ones((g.num_edges(),), F.float32, device)
|
||
)
|
||
num_nodes = g.num_nodes()
|
||
mat = F.zeros((num_nodes, num_nodes), F.float32, device)
|
||
src, dst = g.edges()
|
||
src, dst = F.astype(src, F.int64), F.astype(dst, F.int64)
|
||
mat[dst, src] = eweight
|
||
# I_n + (α - 1) A
|
||
nids = F.astype(g.nodes(), F.int64)
|
||
mat[nids, nids] = mat[nids, nids] + 1
|
||
# α (I_n + (α - 1) A)^-1
|
||
diff_mat = self.alpha * F.inverse(mat)
|
||
|
||
# Step2: sparsification
|
||
num_nodes = g.num_nodes()
|
||
eps = self.get_eps(num_nodes, diff_mat)
|
||
dst, src = (diff_mat >= eps).nonzero(as_tuple=False).t()
|
||
data_dict = {g.canonical_etypes[0]: (src, dst)}
|
||
new_g = update_graph_structure(g, data_dict, copy_edata=False)
|
||
new_g.edata[self.eweight_name] = diff_mat[dst, src]
|
||
|
||
return new_g
|
||
|
||
|
||
def is_bidirected(g):
|
||
"""Return whether the graph is a bidirected graph.
|
||
|
||
A graph is bidirected if for any edge :math:`(u, v)` in :math:`G` with weight :math:`w`,
|
||
there exists an edge :math:`(v, u)` in :math:`G` with the same weight.
|
||
"""
|
||
src, dst = g.edges()
|
||
num_nodes = g.num_nodes()
|
||
|
||
# Sort first by src then dst
|
||
idx_src_dst = src * num_nodes + dst
|
||
perm_src_dst = F.argsort(idx_src_dst, dim=0, descending=False)
|
||
src1, dst1 = src[perm_src_dst], dst[perm_src_dst]
|
||
|
||
# Sort first by dst then src
|
||
idx_dst_src = dst * num_nodes + src
|
||
perm_dst_src = F.argsort(idx_dst_src, dim=0, descending=False)
|
||
src2, dst2 = src[perm_dst_src], dst[perm_dst_src]
|
||
|
||
return F.allclose(src1, dst2) and F.allclose(src2, dst1)
|
||
|
||
|
||
# pylint: disable=C0103
|
||
class HeatKernel(BaseTransform):
|
||
r"""Apply heat kernel to an input graph for diffusion, as introduced in
|
||
`Diffusion kernels on graphs and other discrete structures
|
||
<https://www.ml.cmu.edu/research/dap-papers/kondor-diffusion-kernels.pdf>`__.
|
||
|
||
A sparsification will be applied to the weighted adjacency matrix after diffusion.
|
||
Specifically, edges whose weight is below a threshold will be dropped.
|
||
|
||
This module only works for homogeneous graphs.
|
||
|
||
Parameters
|
||
----------
|
||
t : float, optional
|
||
Diffusion time, which commonly lies in :math:`[2, 10]`.
|
||
eweight_name : str, optional
|
||
:attr:`edata` name to retrieve and store edge weights. If it does
|
||
not exist in an input graph, this module initializes a weight of 1
|
||
for all edges. The edge weights should be a tensor of shape :math:`(E)`,
|
||
where E is the number of edges.
|
||
eps : float, optional
|
||
The threshold to preserve edges in sparsification after diffusion. Edges of a
|
||
weight smaller than eps will be dropped.
|
||
avg_degree : int, optional
|
||
The desired average node degree of the result graph. This is the other way to
|
||
control the sparsity of the result graph and will only be effective if
|
||
:attr:`eps` is not given.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import HeatKernel
|
||
|
||
>>> transform = HeatKernel(avg_degree=2)
|
||
>>> g = dgl.graph(([0, 1, 2, 3, 4], [2, 3, 4, 5, 3]))
|
||
>>> g.edata['w'] = torch.tensor([0.1, 0.2, 0.3, 0.4, 0.5])
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edata['w'])
|
||
tensor([0.1353, 0.1353, 0.1353, 0.0541, 0.0406, 0.1353, 0.1353, 0.0812, 0.1353,
|
||
0.1083, 0.0541, 0.1353])
|
||
"""
|
||
|
||
def __init__(self, t=2.0, eweight_name="w", eps=None, avg_degree=5):
|
||
self.t = t
|
||
self.eweight_name = eweight_name
|
||
self.eps = eps
|
||
self.avg_degree = avg_degree
|
||
|
||
def get_eps(self, num_nodes, mat):
|
||
r"""Get the threshold for graph sparsification."""
|
||
if self.eps is None:
|
||
# Infer from self.avg_degree
|
||
if self.avg_degree > num_nodes:
|
||
return float("-inf")
|
||
sorted_weights = torch.sort(mat.flatten(), descending=True).values
|
||
return sorted_weights[self.avg_degree * num_nodes - 1]
|
||
else:
|
||
return self.eps
|
||
|
||
def __call__(self, g):
|
||
# Step1: heat kernel diffusion
|
||
# t A
|
||
device = g.device
|
||
eweight = self.t * g.edata.get(
|
||
self.eweight_name, F.ones((g.num_edges(),), F.float32, device)
|
||
)
|
||
num_nodes = g.num_nodes()
|
||
mat = F.zeros((num_nodes, num_nodes), F.float32, device)
|
||
src, dst = g.edges()
|
||
src, dst = F.astype(src, F.int64), F.astype(dst, F.int64)
|
||
mat[dst, src] = eweight
|
||
# t (A - I_n)
|
||
nids = F.astype(g.nodes(), F.int64)
|
||
mat[nids, nids] = mat[nids, nids] - self.t
|
||
|
||
if is_bidirected(g):
|
||
e, V = torch.linalg.eigh(mat, UPLO="U")
|
||
diff_mat = V @ torch.diag(e.exp()) @ V.t()
|
||
else:
|
||
diff_mat_np = expm(mat.cpu().numpy())
|
||
diff_mat = torch.Tensor(diff_mat_np).to(device)
|
||
|
||
# Step2: sparsification
|
||
num_nodes = g.num_nodes()
|
||
eps = self.get_eps(num_nodes, diff_mat)
|
||
dst, src = (diff_mat >= eps).nonzero(as_tuple=False).t()
|
||
data_dict = {g.canonical_etypes[0]: (src, dst)}
|
||
new_g = update_graph_structure(g, data_dict, copy_edata=False)
|
||
new_g.edata[self.eweight_name] = diff_mat[dst, src]
|
||
|
||
return new_g
|
||
|
||
|
||
class GDC(BaseTransform):
|
||
r"""Apply graph diffusion convolution (GDC) to an input graph, as introduced in
|
||
`Diffusion Improves Graph Learning <https://www.in.tum.de/daml/gdc/>`__.
|
||
|
||
A sparsification will be applied to the weighted adjacency matrix after diffusion.
|
||
Specifically, edges whose weight is below a threshold will be dropped.
|
||
|
||
This module only works for homogeneous graphs.
|
||
|
||
Parameters
|
||
----------
|
||
coefs : list[float], optional
|
||
List of coefficients. :math:`\theta_k` for each power of the adjacency matrix.
|
||
eweight_name : str, optional
|
||
:attr:`edata` name to retrieve and store edge weights. If it does
|
||
not exist in an input graph, this module initializes a weight of 1
|
||
for all edges. The edge weights should be a tensor of shape :math:`(E)`,
|
||
where E is the number of edges.
|
||
eps : float, optional
|
||
The threshold to preserve edges in sparsification after diffusion. Edges of a
|
||
weight smaller than eps will be dropped.
|
||
avg_degree : int, optional
|
||
The desired average node degree of the result graph. This is the other way to
|
||
control the sparsity of the result graph and will only be effective if
|
||
:attr:`eps` is not given.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import GDC
|
||
|
||
>>> transform = GDC([0.3, 0.2, 0.1], avg_degree=2)
|
||
>>> g = dgl.graph(([0, 1, 2, 3, 4], [2, 3, 4, 5, 3]))
|
||
>>> g.edata['w'] = torch.tensor([0.1, 0.2, 0.3, 0.4, 0.5])
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.edata['w'])
|
||
tensor([0.3000, 0.3000, 0.0200, 0.3000, 0.0400, 0.3000, 0.1000, 0.0600, 0.3000,
|
||
0.0800, 0.0200, 0.3000])
|
||
"""
|
||
|
||
def __init__(self, coefs, eweight_name="w", eps=None, avg_degree=5):
|
||
self.coefs = coefs
|
||
self.eweight_name = eweight_name
|
||
self.eps = eps
|
||
self.avg_degree = avg_degree
|
||
|
||
def get_eps(self, num_nodes, mat):
|
||
r"""Get the threshold for graph sparsification."""
|
||
if self.eps is None:
|
||
# Infer from self.avg_degree
|
||
if self.avg_degree > num_nodes:
|
||
return float("-inf")
|
||
sorted_weights = torch.sort(mat.flatten(), descending=True).values
|
||
return sorted_weights[self.avg_degree * num_nodes - 1]
|
||
else:
|
||
return self.eps
|
||
|
||
def __call__(self, g):
|
||
# Step1: diffusion
|
||
# A
|
||
device = g.device
|
||
eweight = g.edata.get(
|
||
self.eweight_name, F.ones((g.num_edges(),), F.float32, device)
|
||
)
|
||
num_nodes = g.num_nodes()
|
||
adj = F.zeros((num_nodes, num_nodes), F.float32, device)
|
||
src, dst = g.edges()
|
||
src, dst = F.astype(src, F.int64), F.astype(dst, F.int64)
|
||
adj[dst, src] = eweight
|
||
|
||
# theta_0 I_n
|
||
mat = torch.eye(num_nodes, device=device)
|
||
diff_mat = self.coefs[0] * mat
|
||
# add theta_k A^k
|
||
for coef in self.coefs[1:]:
|
||
mat = mat @ adj
|
||
diff_mat += coef * mat
|
||
|
||
# Step2: sparsification
|
||
num_nodes = g.num_nodes()
|
||
eps = self.get_eps(num_nodes, diff_mat)
|
||
dst, src = (diff_mat >= eps).nonzero(as_tuple=False).t()
|
||
data_dict = {g.canonical_etypes[0]: (src, dst)}
|
||
new_g = update_graph_structure(g, data_dict, copy_edata=False)
|
||
new_g.edata[self.eweight_name] = diff_mat[dst, src]
|
||
|
||
return new_g
|
||
|
||
|
||
class NodeShuffle(BaseTransform):
|
||
r"""Randomly shuffle the nodes.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import NodeShuffle
|
||
|
||
>>> transform = NodeShuffle()
|
||
>>> g = dgl.graph(([0, 1], [1, 2]))
|
||
>>> g.ndata['h1'] = torch.tensor([[1., 2.], [3., 4.], [5., 6.]])
|
||
>>> g.ndata['h2'] = torch.tensor([[7., 8.], [9., 10.], [11., 12.]])
|
||
>>> g = transform(g)
|
||
>>> print(g.ndata['h1'])
|
||
tensor([[5., 6.],
|
||
[3., 4.],
|
||
[1., 2.]])
|
||
>>> print(g.ndata['h2'])
|
||
tensor([[11., 12.],
|
||
[ 9., 10.],
|
||
[ 7., 8.]])
|
||
"""
|
||
|
||
def __call__(self, g):
|
||
g = g.clone()
|
||
for ntype in g.ntypes:
|
||
nids = F.astype(g.nodes(ntype), F.int64)
|
||
perm = F.rand_shuffle(nids)
|
||
for key, feat in g.nodes[ntype].data.items():
|
||
g.nodes[ntype].data[key] = feat[perm]
|
||
return g
|
||
|
||
|
||
# pylint: disable=C0103
|
||
class DropNode(BaseTransform):
|
||
r"""Randomly drop nodes, as described in
|
||
`Graph Contrastive Learning with Augmentations <https://arxiv.org/abs/2010.13902>`__.
|
||
|
||
Parameters
|
||
----------
|
||
p : float, optional
|
||
Probability of a node to be dropped.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import DropNode
|
||
|
||
>>> transform = DropNode()
|
||
>>> g = dgl.rand_graph(5, 20)
|
||
>>> g.ndata['h'] = torch.arange(g.num_nodes())
|
||
>>> g.edata['h'] = torch.arange(g.num_edges())
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g)
|
||
Graph(num_nodes=3, num_edges=7,
|
||
ndata_schemes={'h': Scheme(shape=(), dtype=torch.int64)}
|
||
edata_schemes={'h': Scheme(shape=(), dtype=torch.int64)})
|
||
>>> print(new_g.ndata['h'])
|
||
tensor([0, 1, 2])
|
||
>>> print(new_g.edata['h'])
|
||
tensor([0, 6, 14, 5, 17, 3, 11])
|
||
"""
|
||
|
||
def __init__(self, p=0.5):
|
||
self.p = p
|
||
self.dist = Bernoulli(p)
|
||
|
||
def __call__(self, g):
|
||
g = g.clone()
|
||
|
||
# Fast path
|
||
if self.p == 0:
|
||
return g
|
||
|
||
for ntype in g.ntypes:
|
||
samples = self.dist.sample(torch.Size([g.num_nodes(ntype)]))
|
||
nids_to_remove = g.nodes(ntype)[samples.bool().to(g.device)]
|
||
g.remove_nodes(nids_to_remove, ntype=ntype)
|
||
return g
|
||
|
||
|
||
# pylint: disable=C0103
|
||
class DropEdge(BaseTransform):
|
||
r"""Randomly drop edges, as described in
|
||
`DropEdge: Towards Deep Graph Convolutional Networks on Node Classification
|
||
<https://arxiv.org/abs/1907.10903>`__ and `Graph Contrastive Learning with Augmentations
|
||
<https://arxiv.org/abs/2010.13902>`__.
|
||
|
||
Parameters
|
||
----------
|
||
p : float, optional
|
||
Probability of an edge to be dropped.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import DropEdge
|
||
|
||
>>> transform = DropEdge()
|
||
>>> g = dgl.rand_graph(5, 20)
|
||
>>> g.edata['h'] = torch.arange(g.num_edges())
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g)
|
||
Graph(num_nodes=5, num_edges=12,
|
||
ndata_schemes={}
|
||
edata_schemes={'h': Scheme(shape=(), dtype=torch.int64)})
|
||
>>> print(new_g.edata['h'])
|
||
tensor([0, 1, 3, 7, 8, 10, 11, 12, 13, 15, 18, 19])
|
||
"""
|
||
|
||
def __init__(self, p=0.5):
|
||
self.p = p
|
||
self.dist = Bernoulli(p)
|
||
|
||
def __call__(self, g):
|
||
g = g.clone()
|
||
|
||
# Fast path
|
||
if self.p == 0:
|
||
return g
|
||
|
||
for c_etype in g.canonical_etypes:
|
||
samples = self.dist.sample(torch.Size([g.num_edges(c_etype)]))
|
||
eids_to_remove = g.edges(form="eid", etype=c_etype)[
|
||
samples.bool().to(g.device)
|
||
]
|
||
g.remove_edges(eids_to_remove, etype=c_etype)
|
||
return g
|
||
|
||
|
||
class AddEdge(BaseTransform):
|
||
r"""Randomly add edges, as described in `Graph Contrastive Learning with Augmentations
|
||
<https://arxiv.org/abs/2010.13902>`__.
|
||
|
||
Parameters
|
||
----------
|
||
ratio : float, optional
|
||
Number of edges to add divided by the number of existing edges.
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> from dgl import AddEdge
|
||
|
||
>>> transform = AddEdge()
|
||
>>> g = dgl.rand_graph(5, 20)
|
||
>>> new_g = transform(g)
|
||
>>> print(new_g.num_edges())
|
||
24
|
||
"""
|
||
|
||
def __init__(self, ratio=0.2):
|
||
self.ratio = ratio
|
||
|
||
def __call__(self, g):
|
||
# Fast path
|
||
if self.ratio == 0.0:
|
||
return g
|
||
|
||
device = g.device
|
||
idtype = g.idtype
|
||
g = g.clone()
|
||
for c_etype in g.canonical_etypes:
|
||
utype, _, vtype = c_etype
|
||
num_edges_to_add = int(g.num_edges(c_etype) * self.ratio)
|
||
src = F.randint(
|
||
[num_edges_to_add],
|
||
idtype,
|
||
device,
|
||
low=0,
|
||
high=g.num_nodes(utype),
|
||
)
|
||
dst = F.randint(
|
||
[num_edges_to_add],
|
||
idtype,
|
||
device,
|
||
low=0,
|
||
high=g.num_nodes(vtype),
|
||
)
|
||
g.add_edges(src, dst, etype=c_etype)
|
||
return g
|
||
|
||
|
||
class SIGNDiffusion(BaseTransform):
|
||
r"""The diffusion operator from `SIGN: Scalable Inception Graph Neural Networks
|
||
<https://arxiv.org/abs/2004.11198>`__
|
||
|
||
It performs node feature diffusion with :math:`TX, \cdots, T^{k}X`, where :math:`T`
|
||
is a diffusion matrix and :math:`X` is the input node features.
|
||
|
||
Specifically, this module provides four options for :math:`T`.
|
||
|
||
**raw**: raw adjacency matrix :math:`A`
|
||
|
||
**rw**: random walk (row-normalized) adjacency matrix :math:`D^{-1}A`, where
|
||
:math:`D` is the degree matrix.
|
||
|
||
**gcn**: symmetrically normalized adjacency matrix used by
|
||
`GCN <https://arxiv.org/abs/1609.02907>`__, :math:`D^{-1/2}AD^{-1/2}`
|
||
|
||
**ppr**: approximate personalized PageRank used by
|
||
`APPNP <https://arxiv.org/abs/1810.05997>`__
|
||
|
||
.. math::
|
||
H^{0} &= X
|
||
|
||
H^{l+1} &= (1-\alpha)\left(D^{-1/2}AD^{-1/2} H^{l}\right) + \alpha X
|
||
|
||
This module only works for homogeneous graphs.
|
||
|
||
Parameters
|
||
----------
|
||
k : int
|
||
The maximum number of times for node feature diffusion.
|
||
in_feat_name : str, optional
|
||
:attr:`g.ndata[{in_feat_name}]` should store the input node features. Default: 'feat'
|
||
out_feat_name : str, optional
|
||
:attr:`g.ndata[{out_feat_name}_i]` will store the result of diffusing
|
||
input node features for i times. Default: 'out_feat'
|
||
eweight_name : str, optional
|
||
Name to retrieve edge weights from :attr:`g.edata`. Default: None,
|
||
treating the graph as unweighted.
|
||
diffuse_op : str, optional
|
||
The diffusion operator to use, which can be 'raw', 'rw', 'gcn', or 'ppr'.
|
||
Default: 'raw'
|
||
alpha : float, optional
|
||
Restart probability if :attr:`diffuse_op` is :attr:`'ppr'`,
|
||
which commonly lies in :math:`[0.05, 0.2]`. Default: 0.2
|
||
|
||
Example
|
||
-------
|
||
|
||
>>> import dgl
|
||
>>> import torch
|
||
>>> from dgl import SIGNDiffusion
|
||
|
||
>>> transform = SIGNDiffusion(k=2, eweight_name='w')
|
||
>>> num_nodes = 5
|
||
>>> num_edges = 20
|
||
>>> g = dgl.rand_graph(num_nodes, num_edges)
|
||
>>> g.ndata['feat'] = torch.randn(num_nodes, 10)
|
||
>>> g.edata['w'] = torch.randn(num_edges)
|
||
>>> transform(g)
|
||
Graph(num_nodes=5, num_edges=20,
|
||
ndata_schemes={'feat': Scheme(shape=(10,), dtype=torch.float32),
|
||
'out_feat_1': Scheme(shape=(10,), dtype=torch.float32),
|
||
'out_feat_2': Scheme(shape=(10,), dtype=torch.float32)}
|
||
edata_schemes={'w': Scheme(shape=(), dtype=torch.float32)})
|
||
"""
|
||
|
||
def __init__(
|
||
self,
|
||
k,
|
||
in_feat_name="feat",
|
||
out_feat_name="out_feat",
|
||
eweight_name=None,
|
||
diffuse_op="raw",
|
||
alpha=0.2,
|
||
):
|
||
self.k = k
|
||
self.in_feat_name = in_feat_name
|
||
self.out_feat_name = out_feat_name
|
||
self.eweight_name = eweight_name
|
||
self.diffuse_op = diffuse_op
|
||
self.alpha = alpha
|
||
|
||
if diffuse_op == "raw":
|
||
self.diffuse = self.raw
|
||
elif diffuse_op == "rw":
|
||
self.diffuse = self.rw
|
||
elif diffuse_op == "gcn":
|
||
self.diffuse = self.gcn
|
||
elif diffuse_op == "ppr":
|
||
self.diffuse = self.ppr
|
||
else:
|
||
raise DGLError(
|
||
"Expect diffuse_op to be from ['raw', 'rw', 'gcn', 'ppr'], \
|
||
got {}".format(
|
||
diffuse_op
|
||
)
|
||
)
|
||
|
||
def __call__(self, g):
|
||
feat_list = self.diffuse(g)
|
||
|
||
for i in range(1, self.k + 1):
|
||
g.ndata[self.out_feat_name + "_" + str(i)] = feat_list[i - 1]
|
||
return g
|
||
|
||
def raw(self, g):
|
||
use_eweight = False
|
||
if (self.eweight_name is not None) and self.eweight_name in g.edata:
|
||
use_eweight = True
|
||
|
||
feat_list = []
|
||
with g.local_scope():
|
||
if use_eweight:
|
||
message_func = fn.u_mul_e(
|
||
self.in_feat_name, self.eweight_name, "m"
|
||
)
|
||
else:
|
||
message_func = fn.copy_u(self.in_feat_name, "m")
|
||
for _ in range(self.k):
|
||
g.update_all(message_func, fn.sum("m", self.in_feat_name))
|
||
feat_list.append(g.ndata[self.in_feat_name])
|
||
return feat_list
|
||
|
||
def rw(self, g):
|
||
use_eweight = False
|
||
if (self.eweight_name is not None) and self.eweight_name in g.edata:
|
||
use_eweight = True
|
||
|
||
feat_list = []
|
||
with g.local_scope():
|
||
g.ndata["h"] = g.ndata[self.in_feat_name]
|
||
if use_eweight:
|
||
message_func = fn.u_mul_e("h", self.eweight_name, "m")
|
||
reduce_func = fn.sum("m", "h")
|
||
# Compute the diagonal entries of D from the weighted A
|
||
g.update_all(
|
||
fn.copy_e(self.eweight_name, "m"), fn.sum("m", "z")
|
||
)
|
||
else:
|
||
message_func = fn.copy_u("h", "m")
|
||
reduce_func = fn.mean("m", "h")
|
||
|
||
for _ in range(self.k):
|
||
g.update_all(message_func, reduce_func)
|
||
if use_eweight:
|
||
g.ndata["h"] = g.ndata["h"] / F.reshape(
|
||
g.ndata["z"], (g.num_nodes(), 1)
|
||
)
|
||
feat_list.append(g.ndata["h"])
|
||
return feat_list
|
||
|
||
def gcn(self, g):
|
||
feat_list = []
|
||
with g.local_scope():
|
||
if self.eweight_name is None:
|
||
eweight_name = "w"
|
||
if eweight_name in g.edata:
|
||
g.edata.pop(eweight_name)
|
||
else:
|
||
eweight_name = self.eweight_name
|
||
|
||
transform = GCNNorm(eweight_name=eweight_name)
|
||
transform(g)
|
||
|
||
for _ in range(self.k):
|
||
g.update_all(
|
||
fn.u_mul_e(self.in_feat_name, eweight_name, "m"),
|
||
fn.sum("m", self.in_feat_name),
|
||
)
|
||
feat_list.append(g.ndata[self.in_feat_name])
|
||
return feat_list
|
||
|
||
def ppr(self, g):
|
||
feat_list = []
|
||
with g.local_scope():
|
||
if self.eweight_name is None:
|
||
eweight_name = "w"
|
||
if eweight_name in g.edata:
|
||
g.edata.pop(eweight_name)
|
||
else:
|
||
eweight_name = self.eweight_name
|
||
transform = GCNNorm(eweight_name=eweight_name)
|
||
transform(g)
|
||
|
||
in_feat = g.ndata[self.in_feat_name]
|
||
for _ in range(self.k):
|
||
g.update_all(
|
||
fn.u_mul_e(self.in_feat_name, eweight_name, "m"),
|
||
fn.sum("m", self.in_feat_name),
|
||
)
|
||
g.ndata[self.in_feat_name] = (1 - self.alpha) * g.ndata[
|
||
self.in_feat_name
|
||
] + self.alpha * in_feat
|
||
feat_list.append(g.ndata[self.in_feat_name])
|
||
return feat_list
|
||
|
||
|
||
class ToLevi(BaseTransform):
|
||
r"""This function transforms the original graph to its heterogeneous Levi graph,
|
||
by converting edges to intermediate nodes, only support homogeneous directed graph.
|
||
|
||
Example
|
||
-------
|
||
>>> import dgl
|
||
>>> import torch as th
|
||
>>> from dgl import ToLevi
|
||
|
||
>>> transform = ToLevi()
|
||
>>> g = dgl.graph(([0, 1, 2, 3], [1, 2, 3, 0]))
|
||
>>> g.ndata['h'] = th.randn((g.num_nodes(), 2))
|
||
>>> g.edata['w'] = th.randn((g.num_edges(), 2))
|
||
>>> lg = transform(g)
|
||
>>> lg
|
||
Grpah(num_nodes={'edge': 4, 'node': 4},
|
||
num_edges={('edge', 'e2n', 'node'): 4,
|
||
('node', 'n2e', 'edge'): 4},
|
||
metagraph=[('edge', 'node', 'e2n'),
|
||
('node', 'edge', 'n2e')])
|
||
>>> lg.nodes('node')
|
||
tensor([0, 1, 2, 3])
|
||
>>> lg.nodes('edge')
|
||
tensor([0, 1, 2, 3])
|
||
>>> lg.nodes['node'].data['h'].shape
|
||
torch.Size([4, 2])
|
||
>>> lg.nodes['edge'].data['w'].shape
|
||
torch.Size([4, 2])
|
||
"""
|
||
|
||
def __init__(self):
|
||
pass
|
||
|
||
def __call__(self, g):
|
||
r"""
|
||
Parameters
|
||
----------
|
||
g : DGLGraph
|
||
The input graph, should be a homogeneous directed graph.
|
||
|
||
Returns
|
||
-------
|
||
DGLGraph
|
||
The Levi graph of input, will be a heterogeneous graph, where nodes of
|
||
ntypes ``'node'`` and ``'edge'`` have corresponding IDs of nodes and edges
|
||
in the original graph. Edge features of the input graph are copied to
|
||
corresponding new nodes of ntype ``'edge'``.
|
||
"""
|
||
device = g.device
|
||
idtype = g.idtype
|
||
|
||
edge_list = g.edges()
|
||
n2e = edge_list[0], F.arange(0, g.num_edges(), idtype, device)
|
||
e2n = F.arange(0, g.num_edges(), idtype, device), edge_list[1]
|
||
graph_data = {
|
||
("node", "n2e", "edge"): n2e,
|
||
("edge", "e2n", "node"): e2n,
|
||
}
|
||
levi_g = convert.heterograph(graph_data, idtype=idtype, device=device)
|
||
|
||
# Copy ndata and edata
|
||
# Since the node types in dgl.heterograph are in alphabetical order
|
||
# ('edge' < 'node'), edge_frames should be in front of node_frames.
|
||
node_frames = utils.extract_node_subframes(g, nodes_or_device=device)
|
||
edge_frames = utils.extract_edge_subframes(g, edges_or_device=device)
|
||
utils.set_new_frames(levi_g, node_frames=edge_frames + node_frames)
|
||
|
||
return levi_g
|
||
|
||
|
||
class SVDPE(BaseTransform):
|
||
r"""SVD-based Positional Encoding, as introduced in
|
||
`Global Self-Attention as a Replacement for Graph Convolution
|
||
<https://arxiv.org/pdf/2108.03348.pdf>`__
|
||
|
||
This function computes the largest :math:`k` singular values and
|
||
corresponding left and right singular vectors to form positional encodings,
|
||
which could be stored in ndata.
|
||
|
||
Parameters
|
||
----------
|
||
k : int
|
||
Number of largest singular values and corresponding singular vectors
|
||
used for positional encoding.
|
||
feat_name : str, optional
|
||
Name to store the computed positional encodings in ndata.
|
||
Default : ``svd_pe``
|
||
padding : bool, optional
|
||
If False, raise an error when :math:`k > N`,
|
||
where :math:`N` is the number of nodes in :attr:`g`.
|
||
If True, add zero paddings in the end of encodings when :math:`k > N`.
|
||
Default : False.
|
||
random_flip : bool, optional
|
||
If True, randomly flip the signs of encoding vectors.
|
||
Proposed to be activated during training for better generalization.
|
||
Default : True.
|
||
|
||
Example
|
||
-------
|
||
>>> import dgl
|
||
>>> from dgl import SVDPE
|
||
|
||
>>> transform = SVDPE(k=2, feat_name="svd_pe")
|
||
>>> g = dgl.graph(([0,1,2,3,4,2,3,1,4,0], [2,3,1,4,0,0,1,2,3,4]))
|
||
>>> g_ = transform(g)
|
||
>>> print(g_.ndata['svd_pe'])
|
||
tensor([[-6.3246e-01, -1.1373e-07, -6.3246e-01, 0.0000e+00],
|
||
[-6.3246e-01, 7.6512e-01, -6.3246e-01, -7.6512e-01],
|
||
[ 6.3246e-01, 4.7287e-01, 6.3246e-01, -4.7287e-01],
|
||
[-6.3246e-01, -7.6512e-01, -6.3246e-01, 7.6512e-01],
|
||
[ 6.3246e-01, -4.7287e-01, 6.3246e-01, 4.7287e-01]])
|
||
"""
|
||
|
||
def __init__(self, k, feat_name="svd_pe", padding=False, random_flip=True):
|
||
self.k = k
|
||
self.feat_name = feat_name
|
||
self.padding = padding
|
||
self.random_flip = random_flip
|
||
|
||
def __call__(self, g):
|
||
encoding = functional.svd_pe(
|
||
g, k=self.k, padding=self.padding, random_flip=self.random_flip
|
||
)
|
||
g.ndata[self.feat_name] = F.copy_to(encoding, g.device)
|
||
|
||
return g
|