r""" Get representative node for each partition given by :math:`\mathbf{part} \in R^{n}` of a graph with structure matrix :math:`\mathbf{C} \in R^{n \times n}`. Selection is either done randomly or using 'pagerank' algorithm from networkx. Parameters ---------- C : array-lik
(C, part, rep_method="pagerank", random_state=0, nx=None)
| 382 | |
| 383 | |
| 384 | def get_graph_representants(C, part, rep_method="pagerank", random_state=0, nx=None): |
| 385 | r""" |
| 386 | Get representative node for each partition given by :math:`\mathbf{part} \in R^{n}` |
| 387 | of a graph with structure matrix :math:`\mathbf{C} \in R^{n \times n}`. |
| 388 | Selection is either done randomly or using 'pagerank' algorithm from networkx. |
| 389 | |
| 390 | Parameters |
| 391 | ---------- |
| 392 | C : array-like, shape (n, n) |
| 393 | structure matrix. |
| 394 | part : array-like, shape (n,) |
| 395 | Array of partition assignment for each node. |
| 396 | rep_method : str, optional. Default is 'pagerank'. |
| 397 | Selection method for representant in each partition. Can be either 'random' |
| 398 | i.e random sampling within each partition, or 'pagerank' to select a |
| 399 | node with maximal pagerank. |
| 400 | random_state: int, optional |
| 401 | Random seed for the partitioning algorithm |
| 402 | nx : backend, optional |
| 403 | POT backend |
| 404 | |
| 405 | Returns |
| 406 | ------- |
| 407 | rep_indices : list, shape (npart,) |
| 408 | indices for representative node of each partition sorted |
| 409 | according to partition identifiers. |
| 410 | |
| 411 | References |
| 412 | ---------- |
| 413 | .. [68] Chowdhury, S., Miller, D., & Needham, T. (2021). |
| 414 | Quantized gromov-wasserstein. ECML PKDD 2021. Springer International Publishing. |
| 415 | |
| 416 | """ |
| 417 | if nx is None: |
| 418 | nx = get_backend(C, part) |
| 419 | |
| 420 | rep_indices = [] |
| 421 | part_ids = nx.unique(part) |
| 422 | n_part_ids = part_ids.shape[0] |
| 423 | if n_part_ids == C.shape[0]: |
| 424 | rep_indices = nx.arange(n_part_ids) |
| 425 | |
| 426 | elif rep_method == "random": |
| 427 | random.seed(random_state) |
| 428 | for id_, part_id in enumerate(part_ids): |
| 429 | indices = nx.where(part == part_id)[0] |
| 430 | rep_indices.append(random.choice(indices)) |
| 431 | |
| 432 | elif rep_method == "pagerank": |
| 433 | C0, part0 = C, part |
| 434 | C = nx.to_numpy(C0) |
| 435 | part = nx.to_numpy(part0) |
| 436 | part_ids = np.unique(part) |
| 437 | |
| 438 | for id_ in part_ids: |
| 439 | indices = np.where(part == id_)[0] |
| 440 | C_id = C[indices, :][:, indices] |
| 441 | graph = from_numpy_array(C_id) |
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