"""Torch Module for DenseChebConv"""
# pylint: disable= no-member, arguments-differ, invalid-name
import torch as th
from torch import nn
from torch.nn import init
[docs]class DenseChebConv(nn.Module):
r"""Chebyshev Spectral Graph Convolution layer from `Convolutional
Neural Networks on Graphs with Fast Localized Spectral Filtering
<https://arxiv.org/pdf/1606.09375.pdf>`__
We recommend to use this module when applying ChebConv on dense graphs.
Parameters
----------
in_feats: int
Dimension of input features :math:`h_i^{(l)}`.
out_feats: int
Dimension of output features :math:`h_i^{(l+1)}`.
k : int
Chebyshev filter size.
activation : function, optional
Activation function, default is ReLu.
bias : bool, optional
If True, adds a learnable bias to the output. Default: ``True``.
Example
-------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import DenseChebConv
>>>
>>> feat = th.ones(6, 10)
>>> adj = th.tensor([[0., 0., 1., 0., 0., 0.],
... [1., 0., 0., 0., 0., 0.],
... [0., 1., 0., 0., 0., 0.],
... [0., 0., 1., 0., 0., 1.],
... [0., 0., 0., 1., 0., 0.],
... [0., 0., 0., 0., 0., 0.]])
>>> conv = DenseChebConv(10, 2, 2)
>>> res = conv(adj, feat)
>>> res
tensor([[-3.3516, -2.4797],
[-3.3516, -2.4797],
[-3.3516, -2.4797],
[-4.5192, -3.0835],
[-2.5259, -2.0527],
[-0.5327, -1.0219]], grad_fn=<AddBackward0>)
See also
--------
`ChebConv <https://docs.dgl.ai/api/python/nn.pytorch.html#chebconv>`__
"""
def __init__(self, in_feats, out_feats, k, bias=True):
super(DenseChebConv, self).__init__()
self._in_feats = in_feats
self._out_feats = out_feats
self._k = k
self.W = nn.Parameter(th.Tensor(k, in_feats, out_feats))
if bias:
self.bias = nn.Parameter(th.Tensor(out_feats))
else:
self.register_buffer("bias", None)
self.reset_parameters()
[docs] def reset_parameters(self):
"""Reinitialize learnable parameters."""
if self.bias is not None:
init.zeros_(self.bias)
for i in range(self._k):
init.xavier_normal_(self.W[i], init.calculate_gain("relu"))
[docs] def forward(self, adj, feat, lambda_max=None):
r"""Compute (Dense) Chebyshev Spectral Graph Convolution layer
Parameters
----------
adj : torch.Tensor
The adjacency matrix of the graph to apply Graph Convolution on,
should be of shape :math:`(N, N)`, where a row represents the destination
and a column represents the source.
feat : torch.Tensor
The input feature of shape :math:`(N, D_{in})` where :math:`D_{in}`
is size of input feature, :math:`N` is the number of nodes.
lambda_max : float or None, optional
A float value indicates the largest eigenvalue of given graph.
Default: None.
Returns
-------
torch.Tensor
The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
is size of output feature.
"""
A = adj.to(feat)
num_nodes = A.shape[0]
in_degree = 1 / A.sum(dim=1).clamp(min=1).sqrt()
D_invsqrt = th.diag(in_degree)
I = th.eye(num_nodes).to(A)
L = I - D_invsqrt @ A @ D_invsqrt
if lambda_max is None:
lambda_ = th.eig(L)[0][:, 0]
lambda_max = lambda_.max()
L_hat = 2 * L / lambda_max - I
Z = [th.eye(num_nodes).to(A)]
for i in range(1, self._k):
if i == 1:
Z.append(L_hat)
else:
Z.append(2 * L_hat @ Z[-1] - Z[-2])
Zs = th.stack(Z, 0) # (k, n, n)
Zh = Zs @ feat.unsqueeze(0) @ self.W
Zh = Zh.sum(0)
if self.bias is not None:
Zh = Zh + self.bias
return Zh