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from typing import Optional
from torch_geometric.data import Data
from torch_geometric.data.datapipes import functional_transform
from torch_geometric.transforms import BaseTransform
from torch_geometric.utils import get_laplacian, to_scipy_sparse_matrix
@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:
from scipy.sparse.linalg import eigs, eigsh
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 = lambda_max.real.item()
return data
def __repr__(self) -> str:
return f'{self.__class__.__name__}(normalization={self.normalization})'
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