Refinement

Refinement routines specific to nonlinear branch-and-price workflows.

asunder.nlbnp.algorithms.refinement.refine_partition_linear_group(A, partition, *, p=1, prob_method='threshold', threshold=0.8, verbose=False, seed=42)

Refine a partition by separating a linear-only group from the remaining nodes.

Parameters:

  • A (ndarray of float, shape (N, N)) – Graph adjacency/weight matrix.

  • partition (ndarray of int, shape (N,) or (N, N)) – Predicted community labels or a 2D partition matrix.

  • p (int) – Order of the norm. Defaults to the L1 norm.

  • prob_method (str) – One of "threshold", "gaussian_mixture", or "DBSCAN".

  • threshold (float) – Value below which a node is reassigned to the linear-only group.

  • verbose (bool) – Controls the verbosity of the output.

Returns:

Refined 2D partition matrix.

Return type:

ndarray of int, shape (N, N)

asunder.nlbnp.algorithms.refinement.refine_partition_with_cp(A, partition, *, unworthy_edges=None, nonlinear_nodes=None, cp_algorithm='SPEC', prob_method='gaussian_mixture', threshold=0.8, verbose=False, seed=42)

Refine a partition by detecting and merging a standalone core community.

Existing periphery community assignments are preserved. All detected core nodes are assigned to one shared community.

Parameters:

  • A (ndarray of float, shape (N, N)) – Graph adjacency/weight matrix.

  • partition (ndarray of int, shape (N,) or (N, N)) – Predicted community labels or a 2D partition matrix.

  • unworthy_edges (list[tuple[int, int]] or None) – Node pairs that must be linked because the edges between them cannot connect nodes in different communities.

  • nonlinear_nodes (list[int] | None) – Nodes that correspond to nonlinear constraints and so, should be merged.

  • cp_algorithm (str) – Core periphery algorithm to be used. Should be one of: "SPEC": Continuous spectral core periphery detection "GA": Continuous genetic search for BE objective "KL": Continuous Kernighan-Lin algorithm

  • prob_method (str) – One of "threshold", "gaussian_mixture", or "DBSCAN".

  • threshold (float) – Value below which a node is reassigned to the linear-only group.

  • verbose (bool) – Controls the verbosity of the output.

  • seed (int | None) – Random seed value.

Returns:

Refined 2D partition matrix.

Return type:

ndarray of int, shape (N, N)