from typing import Callable, Optional, Tuple, Union
import torch
from torch import Tensor
from torch_geometric.nn.pool.connect import FilterEdges
from torch_geometric.nn.pool.select import SelectTopK
from torch_geometric.typing import OptTensor
[docs]class TopKPooling(torch.nn.Module):
r""":math:`\mathrm{top}_k` pooling operator from the `"Graph U-Nets"
<https://arxiv.org/abs/1905.05178>`_, `"Towards Sparse
Hierarchical Graph Classifiers" <https://arxiv.org/abs/1811.01287>`_
and `"Understanding Attention and Generalization in Graph Neural
Networks" <https://arxiv.org/abs/1905.02850>`_ papers.
If :obj:`min_score` :math:`\tilde{\alpha}` is :obj:`None`, computes:
.. math::
\mathbf{y} &= \sigma \left( \frac{\mathbf{X}\mathbf{p}}{\|
\mathbf{p} \|} \right)
\mathbf{i} &= \mathrm{top}_k(\mathbf{y})
\mathbf{X}^{\prime} &= (\mathbf{X} \odot
\mathrm{tanh}(\mathbf{y}))_{\mathbf{i}}
\mathbf{A}^{\prime} &= \mathbf{A}_{\mathbf{i},\mathbf{i}}
If :obj:`min_score` :math:`\tilde{\alpha}` is a value in :obj:`[0, 1]`,
computes:
.. math::
\mathbf{y} &= \mathrm{softmax}(\mathbf{X}\mathbf{p})
\mathbf{i} &= \mathbf{y}_i > \tilde{\alpha}
\mathbf{X}^{\prime} &= (\mathbf{X} \odot \mathbf{y})_{\mathbf{i}}
\mathbf{A}^{\prime} &= \mathbf{A}_{\mathbf{i},\mathbf{i}},
where nodes are dropped based on a learnable projection score
:math:`\mathbf{p}`.
Args:
in_channels (int): Size of each input sample.
ratio (float or int): The graph pooling ratio, which is used to compute
:math:`k = \lceil \mathrm{ratio} \cdot N \rceil`, or the value
of :math:`k` itself, depending on whether the type of :obj:`ratio`
is :obj:`float` or :obj:`int`.
This value is ignored if :obj:`min_score` is not :obj:`None`.
(default: :obj:`0.5`)
min_score (float, optional): Minimal node score :math:`\tilde{\alpha}`
which is used to compute indices of pooled nodes
:math:`\mathbf{i} = \mathbf{y}_i > \tilde{\alpha}`.
When this value is not :obj:`None`, the :obj:`ratio` argument is
ignored. (default: :obj:`None`)
multiplier (float, optional): Coefficient by which features gets
multiplied after pooling. This can be useful for large graphs and
when :obj:`min_score` is used. (default: :obj:`1`)
nonlinearity (str or callable, optional): The non-linearity
:math:`\sigma`. (default: :obj:`"tanh"`)
"""
def __init__(
self,
in_channels: int,
ratio: Union[int, float] = 0.5,
min_score: Optional[float] = None,
multiplier: float = 1.,
nonlinearity: Union[str, Callable] = 'tanh',
):
super().__init__()
self.in_channels = in_channels
self.ratio = ratio
self.min_score = min_score
self.multiplier = multiplier
self.select = SelectTopK(in_channels, ratio, min_score, nonlinearity)
self.connect = FilterEdges()
self.reset_parameters()
[docs] def reset_parameters(self):
r"""Resets all learnable parameters of the module."""
self.select.reset_parameters()
[docs] def forward(
self,
x: Tensor,
edge_index: Tensor,
edge_attr: Optional[Tensor] = None,
batch: Optional[Tensor] = None,
attn: Optional[Tensor] = None,
) -> Tuple[Tensor, Tensor, OptTensor, OptTensor, Tensor, Tensor]:
r"""Forward pass.
Args:
x (torch.Tensor): The node feature matrix.
edge_index (torch.Tensor): The edge indices.
edge_attr (torch.Tensor, optional): The edge features.
(default: :obj:`None`)
batch (torch.Tensor, optional): The batch vector
:math:`\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N`, which assigns
each node to a specific example. (default: :obj:`None`)
attn (torch.Tensor, optional): Optional node-level matrix to use
for computing attention scores instead of using the node
feature matrix :obj:`x`. (default: :obj:`None`)
"""
if batch is None:
batch = edge_index.new_zeros(x.size(0))
attn = x if attn is None else attn
select_out = self.select(attn, batch)
perm = select_out.node_index
score = select_out.weight
assert score is not None
x = x[perm] * score.view(-1, 1)
x = self.multiplier * x if self.multiplier != 1 else x
connect_out = self.connect(select_out, edge_index, edge_attr, batch)
return (x, connect_out.edge_index, connect_out.edge_attr,
connect_out.batch, perm, score)
def __repr__(self) -> str:
if self.min_score is None:
ratio = f'ratio={self.ratio}'
else:
ratio = f'min_score={self.min_score}'
return (f'{self.__class__.__name__}({self.in_channels}, {ratio}, '
f'multiplier={self.multiplier})')