pygmtools.utils.compute_affinity_score

pygmtools.utils.compute_affinity_score(X, K, backend=None)[source]

Compute the affinity score of graph matching. It is the objective score of the corresponding Quadratic Assignment Problem.

\[\texttt{vec}(\mathbf{X})^\top \mathbf{K} \texttt{vec}(\mathbf{X})\]

here \(\texttt{vec}\) means column-wise vectorization.

Parameters

  • X – \((b\times n_1 \times n_2)\) the permutation matrix that represents the matching result

  • K – \((b\times n_1n_2 \times n_1n_2)\) the affinity matrix

  • backend – (default: pygmtools.BACKEND variable) the backend for computation.

Returns

\((b)\) the objective score

Note

This function also supports non-batched input if the batch dimension of X, K is ignored.

Pytorch Example
>>> import pygmtools as pygm
>>> import torch
>>> pygm.set_backend('pytorch')

# Generate a graph matching problem
>>> X_gt = torch.zeros(4, 4)
>>> X_gt[torch.arange(0, 4, dtype=torch.int64), torch.randperm(4)] =1
>>> A1 = torch.rand(4, 4)
>>> A2 = torch.mm(torch.mm(X_gt.transpose(0,1), A1), X_gt)
>>> conn1, edge1 = pygm.utils.dense_to_sparse(A1)
>>> conn2, edge2 = pygm.utils.dense_to_sparse(A2)
>>> import functools
>>> gaussian_aff = functools.partial(pygm.utils.gaussian_aff_fn, sigma=1.)
>>> K = pygm.utils.build_aff_mat(None, edge1, conn1, None, edge2, conn2, None, None, None, None, edge_aff_fn=gaussian_aff)

# Compute the objective score of ground truth matching
>>> pygm.utils.compute_affinity_score(X_gt, K)
tensor(16.)