Source code for torch_geometric.nn.conv.cheb_conv

from typing import Optional
from torch_geometric.typing import OptTensor

import torch
from torch.nn import Parameter
from torch_geometric.nn.conv import MessagePassing
from torch_geometric.utils import remove_self_loops, add_self_loops
from torch_geometric.utils import get_laplacian

from ..inits import glorot, zeros

[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. 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}` You need to pass :obj:`lambda_max` to the :meth:`forward` method of this operator in case the normalization is non-symmetric. :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`. """ def __init__(self, in_channels, out_channels, K, normalization='sym', bias=True, **kwargs): kwargs.setdefault('aggr', 'add') super(ChebConv, self).__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.weight = Parameter(torch.Tensor(K, in_channels, out_channels)) if bias: self.bias = Parameter(torch.Tensor(out_channels)) else: self.register_parameter('bias', None) self.reset_parameters()
[docs] def reset_parameters(self): glorot(self.weight) zeros(self.bias)
def __norm__(self, edge_index, num_nodes: Optional[int], edge_weight: OptTensor, normalization: Optional[str], lambda_max, dtype: Optional[int] = None, batch: OptTensor = None): edge_index, edge_weight = remove_self_loops(edge_index, edge_weight) edge_index, edge_weight = get_laplacian(edge_index, edge_weight, normalization, dtype, num_nodes) 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) edge_index, edge_weight = add_self_loops(edge_index, edge_weight, fill_value=-1., num_nodes=num_nodes) assert edge_weight is not None return edge_index, edge_weight
[docs] def forward(self, x, edge_index, edge_weight: OptTensor = None, batch: OptTensor = None, lambda_max: OptTensor = None): """""" if self.normalization != 'sym' and lambda_max is None: raise ValueError('You need to pass `lambda_max` to `forward() in`' 'case the normalization is non-symmetric.') if lambda_max is None: lambda_max = torch.tensor(2.0, dtype=x.dtype, device=x.device) if not isinstance(lambda_max, torch.Tensor): lambda_max = torch.tensor(lambda_max, dtype=x.dtype, device=x.device) assert lambda_max is not None 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 = torch.matmul(Tx_0, self.weight[0]) # propagate_type: (x: Tensor, norm: Tensor) if self.weight.size(0) > 1: Tx_1 = self.propagate(edge_index, x=x, norm=norm, size=None) out = out + torch.matmul(Tx_1, self.weight[1]) for k in range(2, self.weight.size(0)): Tx_2 = self.propagate(edge_index, x=Tx_1, norm=norm, size=None) Tx_2 = 2. * Tx_2 - Tx_0 out = out + torch.matmul(Tx_2, self.weight[k]) Tx_0, Tx_1 = Tx_1, Tx_2 if self.bias is not None: out += self.bias return out
def message(self, x_j, norm): return norm.view(-1, 1) * x_j def __repr__(self): return '{}({}, {}, K={}, normalization={})'.format( self.__class__.__name__, self.in_channels, self.out_channels, self.weight.size(0), self.normalization)