torch_geometric.nn.conv.ChebConv
- class ChebConv(in_channels: int, out_channels: int, K: int, normalization: Optional[str] = 'sym', bias: bool = True, **kwargs)[source]
Bases:
MessagePassing来自“Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering”论文的切比雪夫谱图卷积算子。
\[\mathbf{X}^{\prime} = \sum_{k=1}^{K} \mathbf{Z}^{(k)} \cdot \mathbf{\Theta}^{(k)}\]其中 \(\mathbf{Z}^{(k)}\) 是通过递归计算的
\[ \begin{align}\begin{aligned}\mathbf{Z}^{(1)} &= \mathbf{X}\\\mathbf{Z}^{(2)} &= \mathbf{\hat{L}} \cdot \mathbf{X}\\\mathbf{Z}^{(k)} &= 2 \cdot \mathbf{\hat{L}} \cdot \mathbf{Z}^{(k-1)} - \mathbf{Z}^{(k-2)}\end{aligned}\end{align} \]并且 \(\mathbf{\hat{L}}\) 表示缩放和归一化的拉普拉斯矩阵 \(\frac{2\mathbf{L}}{\lambda_{\max}} - \mathbf{I}\)。
- Parameters:
in_channels (int) – Size of each input sample, or
-1to derive the size from the first input(s) to the forward method.out_channels (int) – Size of each output sample.
K (int) – 切比雪夫滤波器大小 \(K\)。
normalization (str, optional) –
图的拉普拉斯矩阵的归一化方案（默认：
"sym"）：1.
None: 无归一化 \(\mathbf{L} = \mathbf{D} - \mathbf{A}\)2.
"sym": 对称归一化 \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}\)3.
"rw": 随机游走归一化 \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}\)lambda_max应该是一个torch.Tensor，在小批量场景下大小为[num_graphs]，在单个图上操作时为标量/零维张量。 你可以通过torch_geometric.transforms.LaplacianLambdaMax变换预先计算lambda_max。bias (bool, optional) – If set to
False, the layer will not learn an additive bias. (default:True)**kwargs (optional) – Additional arguments of
torch_geometric.nn.conv.MessagePassing.
- Shapes:
输入: 节点特征 \((|\mathcal{V}|, F_{in})\), 边索引 \((2, |\mathcal{E}|)\), 边权重 \((|\mathcal{E}|)\) (可选), 批次向量 \((|\mathcal{V}|)\) (可选), 最大
lambda值 \((|\mathcal{G}|)\) (可选)output: node features \((|\mathcal{V}|, F_{out})\)