ChebConv

class dgl.nn.pytorch.conv.ChebConv(in_feats, out_feats, k, activation=<function relu>, bias=True)

Bases: Module

Chebyshev Spectral Graph Convolution layer from Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

\[ \begin{align}\begin{aligned}h_i^{l+1} &= \sum_{k=0}^{K-1} W^{k, l}z_i^{k, l}\\Z^{0, l} &= H^{l}\\Z^{1, l} &= \tilde{L} \cdot H^{l}\\Z^{k, l} &= 2 \cdot \tilde{L} \cdot Z^{k-1, l} - Z^{k-2, l}\\\tilde{L} &= 2\left(I - \tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2}\right)/\lambda_{max} - I\end{aligned}\end{align} \]

where \(\tilde{A}\) is \(A\) + \(I\), \(W\) is learnable weight.

Parameters:

• in_feats (int) – Dimension of input features; i.e, the number of dimensions of \(h_i^{(l)}\).

• out_feats (int) – Dimension of output features \(h_i^{(l+1)}\).

• k (int) – Chebyshev filter size \(K\).

• activation (function, optional) – Activation function. Default 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 ChebConv
>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = ChebConv(10, 2, 2)
>>> res = conv(g, feat)
>>> res
tensor([[ 0.6163, -0.1809],
        [ 0.6163, -0.1809],
        [ 0.6163, -0.1809],
        [ 0.9698, -1.5053],
        [ 0.3664,  0.7556],
        [-0.2370,  3.0164]], grad_fn=<AddBackward0>)

forward(graph, feat, lambda_max=None)

Compute ChebNet layer.

Parameters:

• graph (DGLGraph) – The graph.

• feat (torch.Tensor) – The input feature of shape \((N, D_{in})\) where \(D_{in}\) is size of input feature, \(N\) is the number of nodes.

• lambda_max (list or tensor or None, optional.) –

  A list(tensor) with length \(B\), stores the largest eigenvalue of the normalized laplacian of each individual graph in graph, where \(B\) is the batch size of the input graph. Default: None.

  If None, this method would set the default value to 2. One can use dgl.laplacian_lambda_max() to compute this value.

Returns:

The output feature of shape \((N, D_{out})\) where \(D_{out}\) is size of output feature.

Return type:

torch.Tensor