Source code for dgl.nn.pytorch.conv.densechebconv

"""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 paper `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 Number of input features. out_feats: int Number of output features. k : int Chebyshev filter size. bias : bool, optional If True, adds a learnable bias to the output. Default: ``True``. See also -------- 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() 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