from torch import Tensor
from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.conv.gcn_conv import gcn_norm
from torch_geometric.typing import Adj, OptTensor, SparseTensor
from torch_geometric.utils import spmm
[docs]class LGConv(MessagePassing):
r"""The Light Graph Convolution (LGC) operator from the `"LightGCN:
Simplifying and Powering Graph Convolution Network for Recommendation"
<https://arxiv.org/abs/2002.02126>`_ paper
.. math::
\mathbf{x}^{\prime}_i = \sum_{j \in \mathcal{N}(i)}
\frac{e_{j,i}}{\sqrt{\deg(i)\deg(j)}} \mathbf{x}_j
Args:
normalize (bool, optional): If set to :obj:`False`, output features
will not be normalized via symmetric normalization.
(default: :obj:`True`)
**kwargs (optional): Additional arguments of
:class:`torch_geometric.nn.conv.MessagePassing`.
Shapes:
- **input:**
node features :math:`(|\mathcal{V}|, F)`,
edge indices :math:`(2, |\mathcal{E}|)`,
edge weights :math:`(|\mathcal{E}|)` *(optional)*
- **output:** node features :math:`(|\mathcal{V}|, F)`
"""
def __init__(self, normalize: bool = True, **kwargs):
kwargs.setdefault('aggr', 'add')
super().__init__(**kwargs)
self.normalize = normalize
[docs] def forward(self, x: Tensor, edge_index: Adj,
edge_weight: OptTensor = None) -> Tensor:
if self.normalize and isinstance(edge_index, Tensor):
out = gcn_norm(edge_index, edge_weight, x.size(self.node_dim),
add_self_loops=False, flow=self.flow, dtype=x.dtype)
edge_index, edge_weight = out
elif self.normalize and isinstance(edge_index, SparseTensor):
edge_index = gcn_norm(edge_index, None, x.size(self.node_dim),
add_self_loops=False, flow=self.flow,
dtype=x.dtype)
# propagate_type: (x: Tensor, edge_weight: OptTensor)
return self.propagate(edge_index, x=x, edge_weight=edge_weight,
size=None)
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: SparseTensor, x: Tensor) -> Tensor:
return spmm(adj_t, x, reduce=self.aggr)