Source code for torch_geometric.nn.conv.cheb_conv

from typing import Optional

import torch
from torch import Tensor
from torch.nn import Parameter

from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.dense.linear import Linear
from torch_geometric.nn.inits import zeros
from torch_geometric.typing import OptTensor
from torch_geometric.utils import get_laplacian

[docs]class ChebConv(MessagePassing): r"""The chebyshev spectral graph convolutional operator from the `"Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering" <>`_ paper. .. math:: \mathbf{X}^{\prime} = \sum_{k=1}^{K} \mathbf{Z}^{(k)} \cdot \mathbf{\Theta}^{(k)} where :math:`\mathbf{Z}^{(k)}` is computed recursively by .. math:: \mathbf{Z}^{(1)} &= \mathbf{X} \mathbf{Z}^{(2)} &= \mathbf{\hat{L}} \cdot \mathbf{X} \mathbf{Z}^{(k)} &= 2 \cdot \mathbf{\hat{L}} \cdot \mathbf{Z}^{(k-1)} - \mathbf{Z}^{(k-2)} and :math:`\mathbf{\hat{L}}` denotes the scaled and normalized Laplacian :math:`\frac{2\mathbf{L}}{\lambda_{\max}} - \mathbf{I}`. 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. K (int): Chebyshev filter size :math:`K`. normalization (str, optional): The normalization scheme for the graph Laplacian (default: :obj:`"sym"`): 1. :obj:`None`: No normalization :math:`\mathbf{L} = \mathbf{D} - \mathbf{A}` 2. :obj:`"sym"`: Symmetric normalization :math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}` 3. :obj:`"rw"`: Random-walk normalization :math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}` :obj:`\lambda_max` should be a :class:`torch.Tensor` of size :obj:`[num_graphs]` in a mini-batch scenario and a scalar/zero-dimensional tensor when operating on single graphs. You can pre-compute :obj:`lambda_max` via the :class:`torch_geometric.transforms.LaplacianLambdaMax` transform. 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)*, batch vector :math:`(|\mathcal{V}|)` *(optional)*, maximum :obj:`lambda` value :math:`(|\mathcal{G}|)` *(optional)* - **output:** node features :math:`(|\mathcal{V}|, F_{out})` """ def __init__( self, in_channels: int, out_channels: int, K: int, normalization: Optional[str] = 'sym', bias: bool = True, **kwargs, ): kwargs.setdefault('aggr', 'add') super().__init__(**kwargs) assert K > 0 assert normalization in [None, 'sym', 'rw'], 'Invalid normalization' self.in_channels = in_channels self.out_channels = out_channels self.normalization = normalization self.lins = torch.nn.ModuleList([ Linear(in_channels, out_channels, bias=False, weight_initializer='glorot') for _ in range(K) ]) if bias: self.bias = Parameter(Tensor(out_channels)) else: self.register_parameter('bias', None) self.reset_parameters()
[docs] def reset_parameters(self): super().reset_parameters() for lin in self.lins: lin.reset_parameters() zeros(self.bias)
def __norm__( self, edge_index: Tensor, num_nodes: Optional[int], edge_weight: OptTensor, normalization: Optional[str], lambda_max: OptTensor = None, dtype: Optional[int] = None, batch: OptTensor = None, ): edge_index, edge_weight = get_laplacian(edge_index, edge_weight, normalization, dtype, num_nodes) assert edge_weight is not None if lambda_max is None: lambda_max = 2.0 * edge_weight.max() elif not isinstance(lambda_max, Tensor): lambda_max = torch.tensor(lambda_max, dtype=dtype, device=edge_index.device) assert lambda_max is not None if batch is not None and lambda_max.numel() > 1: lambda_max = lambda_max[batch[edge_index[0]]] edge_weight = (2.0 * edge_weight) / lambda_max edge_weight.masked_fill_(edge_weight == float('inf'), 0) loop_mask = edge_index[0] == edge_index[1] edge_weight[loop_mask] -= 1 return edge_index, edge_weight
[docs] def forward( self, x: Tensor, edge_index: Tensor, edge_weight: OptTensor = None, batch: OptTensor = None, lambda_max: OptTensor = None, ) -> Tensor: edge_index, norm = self.__norm__( edge_index, x.size(self.node_dim), edge_weight, self.normalization, lambda_max, dtype=x.dtype, batch=batch, ) Tx_0 = x Tx_1 = x # Dummy. out = self.lins[0](Tx_0) # propagate_type: (x: Tensor, norm: Tensor) if len(self.lins) > 1: Tx_1 = self.propagate(edge_index, x=x, norm=norm) out = out + self.lins[1](Tx_1) for lin in self.lins[2:]: Tx_2 = self.propagate(edge_index, x=Tx_1, norm=norm) Tx_2 = 2. * Tx_2 - Tx_0 out = out + lin.forward(Tx_2) Tx_0, Tx_1 = Tx_1, Tx_2 if self.bias is not None: out = out + self.bias return out
def message(self, x_j: Tensor, norm: Tensor) -> Tensor: return norm.view(-1, 1) * x_j def __repr__(self) -> str: return (f'{self.__class__.__name__}({self.in_channels}, ' f'{self.out_channels}, K={len(self.lins)}, ' f'normalization={self.normalization})')