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