def indrect_graph_matching(costs: Dict,
probs: Dict,
p_t: np.ndarray,
idx2nodes: Dict,
ot_hyperpara: Dict,
weights: Dict = None) -> Tuple[List, List, List]:
"""
Matching two or more graphs indirectly via calculate their Gromov-Wasserstein barycenter.
costs: a dictionary of graphs {key: graph idx,
value: (n_s, n_s) adjacency matrix of source graph}
probs: a dictionary of graphs {key: graph idx,
value: (n_s, 1) the distribution of source nodes}
p_t: (n_t, 1) the distribution of target nodes
idx2nodes: a dictionary of graphs {key: graph idx,
value: a dictionary {key: idx of row in cost,
value: name of node}}
ot_hyperpara: a dictionary of hyperparameters
weights: a dictionary of graph {key: graph idx,
value: the weight of the graph}
Returns:
set_idx: a list of node index paired set
set_name: a list of node name paired set
set_confidence: a list of confidence set of node pairs
"""
cost_t, trans, _ = Gwl.gromov_wasserstein_barycenter(
costs, probs, p_t, ot_hyperpara, weights)
set_idx, set_name, set_confidence = node_set_assignment(
trans, probs, idx2nodes)
return set_idx, set_name, set_confidence
def multi_graph_partition(costs: Dict, probs: Dict, p_t: np.ndarray,
idx2nodes: Dict, ot_hyperpara: Dict,
weights: Dict = None,
predefine_barycenter: bool = False) -> \
Tuple[List[Dict], List[Dict], List[Dict], Dict, np.ndarray]:
"""
Achieve multi-graph partition via calculating Gromov-Wasserstein barycenter
between the target graphs and a proposed one
Args:
costs: a dictionary of graphs {key: graph idx,
value: (n_s, n_s) adjacency matrix of source graph}
probs: a dictionary of graphs {key: graph idx,
value: (n_s, 1) the distribution of source nodes}
p_t: (n_t, 1) the distribution of target nodes
idx2nodes: a dictionary of graphs {key: graph idx,
value: a dictionary {key: idx of row in cost,
value: name of node}}
ot_hyperpara: a dictionary of hyperparameters
weights: a dictionary of graph {key: graph idx,
value: the weight of the graph}
predefine_barycenter: False: learn barycenter, True: use predefined barycenter
Returns:
sub_costs_all: a list of graph dictionary: a dictionary {key: graph idx,
value: sub cost matrices}}
sub_idx2nodes: a list of graph dictionary: a dictionary {key: graph idx,
value: a dictionary mapping indices to nodes' names}}
trans: a dictionary {key: graph idx,
value: an optimal transport between the graph and the barycenter}
cost_t: the reference graph corresponding to partition result
"""
sub_costs_cluster = []
sub_idx2nodes_cluster = []
sub_probs_cluster = []
sub_costs_all = {}
sub_idx2nodes_all = {}
sub_probs_all = {}
if predefine_barycenter is True:
cost_t = csr_matrix(np.diag(p_t[:, 0]))
trans = {}
for n in costs.keys():
sub_costs_all[n], sub_probs_all[n], sub_idx2nodes_all[n], trans[
n] = graph_partition(costs[n], probs[n], p_t, idx2nodes[n],
ot_hyperpara)
else:
cost_t, trans, _ = Gwl.gromov_wasserstein_barycenter(
costs, probs, p_t, ot_hyperpara, weights)
for n in costs.keys():
sub_costs, sub_probs, sub_idx2nodes = node_cluster_assignment(
costs[n], trans[n], probs[n], p_t, idx2nodes[n])
sub_costs_all[n] = sub_costs
sub_idx2nodes_all[n] = sub_idx2nodes
sub_probs_all[n] = sub_probs
for i in range(p_t.shape[0]):
sub_costs = {}
sub_idx2nodes = {}
sub_probs = {}
for n in costs.keys():
if i in sub_costs_all[n].keys():
sub_costs[n] = sub_costs_all[n][i]
sub_idx2nodes[n] = sub_idx2nodes_all[n][i]
sub_probs[n] = sub_probs_all[n][i]
sub_costs_cluster.append(sub_costs)
sub_idx2nodes_cluster.append(sub_idx2nodes)
sub_probs_cluster.append(sub_probs)
return sub_costs_cluster, sub_probs_cluster, sub_idx2nodes_cluster, trans, cost_t