ChebConv¶
-
class
dgl.nn.mxnet.conv.
ChebConv
(in_feats, out_feats, k, bias=True)[source]¶ Bases:
mxnet.gluon.block.Block
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 mxnet as mx >>> from dgl.nn import ChebConv >>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3])) >>> feat = mx.nd.ones((6, 10)) >>> conv = ChebConv(10, 2, 2) >>> conv.initialize(ctx=mx.cpu(0)) >>> res = conv(g, feat) >>> res [[ 0.832592 -0.738757 ] [ 0.832592 -0.738757 ] [ 0.832592 -0.738757 ] [ 0.43377423 -1.0455742 ] [ 1.1145986 -0.5218046 ] [ 1.7954229 0.00196505]] <NDArray 6x2 @cpu(0)>
-
forward
(graph, feat, lambda_max=None)[source]¶ Compute ChebNet layer.
- Parameters
graph (DGLGraph) – The graph.
feat (mxnet.NDArray) – 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
mxnet.NDArray