Deep Graph Matching Consensus

Package Reference

• dgmc.models
• dgmc.utils

class dgmc.DGMC(psi_1, psi_2, num_steps, k=- 1, detach=False)

The Deep Graph Matching Consensus module which first matches nodes locally via a graph neural network \(\Psi_{\theta_1}\), and then updates correspondence scores iteratively by reaching for neighborhood consensus via a second graph neural network \(\Psi_{\theta_2}\).

Note

See the PyTorch Geometric introductory tutorial for a detailed overview of the used GNN modules and the respective data format.

Parameters

• psi_1 (torch.nn.Module) – The first GNN \(\Psi_{\theta_1}\) which takes in node features x, edge connectivity edge_index, and optional edge features edge_attr and computes node embeddings.

• psi_2 (torch.nn.Module) – The second GNN \(\Psi_{\theta_2}\) which takes in node features x, edge connectivity edge_index, and optional edge features edge_attr and validates for neighborhood consensus. psi_2 needs to hold the attributes in_channels and out_channels which indicates the dimensionality of randomly drawn node indicator functions and the output dimensionality of psi_2, respectively.

• num_steps (int) – Number of consensus iterations.

• k (int, optional) – Sparsity parameter. If set to -1, will not sparsify initial correspondence rankings. (default: -1)

• detach (bool, optional) – If set to True, will detach the computation of \(\Psi_{\theta_1}\) from the current computation graph. (default: False)

acc(S, y, reduction='mean')

Computes the accuracy of correspondence predictions.

Parameters

• S (Tensor) – Sparse or dense correspondence matrix of shape [batch_size * num_nodes, num_nodes].

• y (LongTensor) – Ground-truth matchings of shape [2, num_ground_truths].

• reduction (string, optional) – Specifies the reduction to apply to the output: 'mean'|'sum'. (default: 'mean')

forward(x_s, edge_index_s, edge_attr_s, batch_s, x_t, edge_index_t, edge_attr_t, batch_t, y=None)

Parameters

• x_s (Tensor) – Source graph node features of shape [batch_size * num_nodes, C_in].

• edge_index_s (LongTensor) – Source graph edge connectivity of shape [2, num_edges].

• edge_attr_s (Tensor) – Source graph edge features of shape [num_edges, D]. Set to None if the GNNs are not taking edge features into account.

• batch_s (LongTensor) – Source graph batch vector of shape [batch_size * num_nodes] indicating node to graph assignment. Set to None if operating on single graphs.

• x_t (Tensor) – Target graph node features of shape [batch_size * num_nodes, C_in].

• edge_index_t (LongTensor) – Target graph edge connectivity of shape [2, num_edges].

• edge_attr_t (Tensor) – Target graph edge features of shape [num_edges, D]. Set to None if the GNNs are not taking edge features into account.

• batch_s – Target graph batch vector of shape [batch_size * num_nodes] indicating node to graph assignment. Set to None if operating on single graphs.

• y (LongTensor, optional) – Ground-truth matchings of shape [2, num_ground_truths] to include ground-truth values when training against sparse correspondences. Ground-truths are only used in case the model is in training mode. (default: None)

Returns

Initial and refined correspondence matrices (S_0, S_L) of shapes [batch_size * num_nodes, num_nodes]. The correspondence matrix are either given as dense or sparse matrices.

hits_at_k(k, S, y, reduction='mean')

Computes the hits@k of correspondence predictions.

Parameters

• k (int) – The \(\mathrm{top}_k\) predictions to consider.

• S (Tensor) – Sparse or dense correspondence matrix of shape [batch_size * num_nodes, num_nodes].

• y (LongTensor) – Ground-truth matchings of shape [2, num_ground_truths].

• reduction (string, optional) – Specifies the reduction to apply to the output: 'mean'|'sum'. (default: 'mean')

loss(S, y, reduction='mean')

Computes the negative log-likelihood loss on the correspondence matrix.

Parameters

• S (Tensor) – Sparse or dense correspondence matrix of shape [batch_size * num_nodes, num_nodes].

• y (LongTensor) – Ground-truth matchings of shape [2, num_ground_truths].

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none'|'mean'|'sum'. (default: 'mean')