import torch
from torch.nn import Parameter
from torch_scatter import scatter_add
from torch_geometric.nn.conv import MessagePassing
from torch_geometric.utils import remove_self_loops
from ..inits import uniform
[docs]class ChebConv(MessagePassing):
r"""The chebyshev spectral graph convolutional operator from the
`"Convolutional Neural Networks on Graphs with Fast Localized Spectral
Filtering" <https://arxiv.org/abs/1606.09375>`_ paper
.. math::
\mathbf{X}^{\prime} = \sum_{k=0}^{K-1} \mathbf{Z}^{(k)} \cdot
\mathbf{\Theta}^{(k)}
where :math:`\mathbf{Z}^{(k)}` is computed recursively by
.. math::
\mathbf{Z}^{(0)} &= \mathbf{X}
\mathbf{Z}^{(1)} &= \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.
Args:
in_channels (int): Size of each input sample.
out_channels (int): Size of each output sample.
K (int): Chebyshev filter size, *i.e.* number of hops :math:`K`.
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, bias=True, **kwargs):
super(ChebConv, self).__init__(aggr='add', **kwargs)
assert K > 0
self.in_channels = in_channels
self.out_channels = out_channels
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):
size = self.in_channels * self.weight.size(0)
uniform(size, self.weight)
uniform(size, self.bias)
[docs] @staticmethod
def norm(edge_index, num_nodes, edge_weight, dtype=None):
edge_index, edge_weight = remove_self_loops(edge_index, edge_weight)
if edge_weight is None:
edge_weight = torch.ones((edge_index.size(1), ),
dtype=dtype,
device=edge_index.device)
row, col = edge_index
deg = scatter_add(edge_weight, row, dim=0, dim_size=num_nodes)
deg_inv_sqrt = deg.pow(-0.5)
deg_inv_sqrt[deg_inv_sqrt == float('inf')] = 0
return edge_index, -deg_inv_sqrt[row] * edge_weight * deg_inv_sqrt[col]
[docs] def forward(self, x, edge_index, edge_weight=None):
""""""
edge_index, norm = self.norm(edge_index, x.size(0), edge_weight,
x.dtype)
Tx_0 = x
out = torch.matmul(Tx_0, self.weight[0])
if self.weight.size(0) > 1:
Tx_1 = self.propagate(edge_index, x=x, norm=norm)
out = out + torch.matmul(Tx_1, self.weight[1])
for k in range(2, self.weight.size(0)):
Tx_2 = 2 * self.propagate(edge_index, x=Tx_1, norm=norm) - 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 = out + self.bias
return out
def message(self, x_j, norm):
return norm.view(-1, 1) * x_j
def __repr__(self):
return '{}({}, {}, K={})'.format(self.__class__.__name__,
self.in_channels, self.out_channels,
self.weight.size(0))