from typing import List, Optional
import torch
from torch import Tensor
from torch.nn import Parameter
from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.conv.gcn_conv import gcn_norm
from torch_geometric.nn.dense.linear import Linear
from torch_geometric.nn.inits import zeros
from torch_geometric.typing import Adj, OptTensor, SparseTensor
from torch_geometric.utils import spmm
[docs]class MixHopConv(MessagePassing):
r"""The Mix-Hop graph convolutional operator from the
`"MixHop: Higher-Order Graph Convolutional Architecturesvia Sparsified
Neighborhood Mixing" <https://arxiv.org/abs/1905.00067>`_ paper.
.. math::
\mathbf{X}^{\prime}={\Bigg\Vert}_{p\in P}
{\left( \mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}}
\mathbf{\hat{D}}^{-1/2} \right)}^p \mathbf{X} \mathbf{\Theta},
where :math:`\mathbf{\hat{A}} = \mathbf{A} + \mathbf{I}` denotes the
adjacency matrix with inserted self-loops and
:math:`\hat{D}_{ii} = \sum_{j=0} \hat{A}_{ij}` its diagonal degree matrix.
Args:
in_channels (int): Size of each input sample, or :obj:`-1` to derive
the size from the first input(s) to the forward method.
out_channels (int): Size of each output sample.
powers (List[int], optional): The powers of the adjacency matrix to
use. (default: :obj:`[0, 1, 2]`)
add_self_loops (bool, optional): If set to :obj:`False`, will not add
self-loops to the input graph. (default: :obj:`True`)
bias (bool, optional): If set to :obj:`False`, the layer will not learn
an additive bias. (default: :obj:`True`)
**kwargs (optional): Additional arguments of
:class:`torch_geometric.nn.conv.MessagePassing`.
Shapes:
- **input:**
node features :math:`(|\mathcal{V}|, F_{in})`,
edge indices :math:`(2, |\mathcal{E}|)`,
edge weights :math:`(|\mathcal{E}|)` *(optional)*
- **output:**
node features :math:`(|\mathcal{V}|, |P| \cdot F_{out})`
"""
def __init__(
self,
in_channels: int,
out_channels: int,
powers: Optional[List[int]] = None,
add_self_loops: bool = True,
bias: bool = True,
**kwargs,
):
kwargs.setdefault('aggr', 'add')
super().__init__(**kwargs)
if powers is None:
powers = [0, 1, 2]
self.in_channels = in_channels
self.out_channels = out_channels
self.powers = powers
self.add_self_loops = add_self_loops
self.lins = torch.nn.ModuleList([
Linear(in_channels, out_channels, bias=False)
if p in powers else torch.nn.Identity()
for p in range(max(powers) + 1)
])
if bias:
self.bias = Parameter(torch.empty(len(powers) * out_channels))
else:
self.register_parameter('bias', None)
self.reset_parameters()
[docs] def reset_parameters(self):
for lin in self.lins:
if hasattr(lin, 'reset_parameters'):
lin.reset_parameters()
zeros(self.bias)
[docs] def forward(self, x: Tensor, edge_index: Adj,
edge_weight: OptTensor = None) -> Tensor:
if isinstance(edge_index, Tensor):
edge_index, edge_weight = gcn_norm( # yapf: disable
edge_index, edge_weight, x.size(self.node_dim), False,
self.add_self_loops, self.flow, x.dtype)
elif isinstance(edge_index, SparseTensor):
edge_index = gcn_norm( # yapf: disable
edge_index, edge_weight, x.size(self.node_dim), False,
self.add_self_loops, self.flow, x.dtype)
outs = [self.lins[0](x)]
for lin in self.lins[1:]:
# propagate_type: (x: Tensor, edge_weight: OptTensor)
x = self.propagate(edge_index, x=x, edge_weight=edge_weight)
outs.append(lin.forward(x))
out = torch.cat([outs[p] for p in self.powers], dim=-1)
if self.bias is not None:
out = out + self.bias
return out
def message(self, x_j: Tensor, edge_weight: OptTensor) -> Tensor:
return x_j if edge_weight is None else edge_weight.view(-1, 1) * x_j
def message_and_aggregate(self, adj_t: Adj, x: Tensor) -> Tensor:
return spmm(adj_t, x, reduce=self.aggr)
def __repr__(self) -> str:
return (f'{self.__class__.__name__}({self.in_channels}, '
f'{self.out_channels}, powers={self.powers})')