Source code for torch_geometric.transforms.laplacian_lambda_max

from typing import Optional

from scipy.sparse.linalg import eigs, eigsh

from import Data
from import functional_transform
from torch_geometric.transforms import BaseTransform
from torch_geometric.utils import get_laplacian, to_scipy_sparse_matrix

[docs]@functional_transform('laplacian_lambda_max') class LaplacianLambdaMax(BaseTransform): r"""Computes the highest eigenvalue of the graph Laplacian given by :meth:`torch_geometric.utils.get_laplacian` (functional name: :obj:`laplacian_lambda_max`). Args: normalization (str, optional): The normalization scheme for the graph Laplacian (default: :obj:`None`): 1. :obj:`None`: No normalization :math:`\mathbf{L} = \mathbf{D} - \mathbf{A}` 2. :obj:`"sym"`: Symmetric normalization :math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}` 3. :obj:`"rw"`: Random-walk normalization :math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}` is_undirected (bool, optional): If set to :obj:`True`, this transform expects undirected graphs as input, and can hence speed up the computation of the largest eigenvalue. (default: :obj:`False`) """ def __init__( self, normalization: Optional[str] = None, is_undirected: bool = False, ): assert normalization in [None, 'sym', 'rw'], 'Invalid normalization' self.normalization = normalization self.is_undirected = is_undirected def forward(self, data: Data) -> Data: assert data.edge_index is not None num_nodes = data.num_nodes edge_weight = data.edge_attr if edge_weight is not None and edge_weight.numel() != data.num_edges: edge_weight = None edge_index, edge_weight = get_laplacian( data.edge_index, edge_weight, self.normalization, num_nodes=num_nodes, ) L = to_scipy_sparse_matrix(edge_index, edge_weight, num_nodes) eig_fn = eigs if self.is_undirected and self.normalization != 'rw': eig_fn = eigsh lambda_max = eig_fn(L, k=1, which='LM', return_eigenvectors=False) data.lambda_max = float(lambda_max.real) return data def __repr__(self) -> str: return f'{self.__class__.__name__}(normalization={self.normalization})'