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dmlc--dgl
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0.7.x
T
gurdaspuriya 4097fa2173 [Feature] [Example] Graph matching routines with DGLGraphs (#1935) 
* Adding graph matching routines

* Adding graph matching routines

Co-authored-by: Ubuntu <ubuntu@ip-172-31-32-199.us-east-2.compute.internal>
Co-authored-by: Zihao Ye <expye@outlook.com>
2020-08-09 20:52:40 +08:00

804 行
44 KiB
Python
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import dgl
import numpy as np
from heapq import heappush, heappop, heapify, nsmallest
from copy import deepcopy
# We use lapjv implementation (https://github.com/src-d/lapjv) to solve assignment problem, because of its scalability
# Also see https://github.com/berhane/LAP-solvers for benchmarking of LAP solvers
from lapjv import lapjv
EPSILON = 0.0000001;
def validate_cost_functions(G1, G2,
node_substitution_cost=None, edge_substitution_cost=None,
G1_node_deletion_cost=None, G1_edge_deletion_cost=None,
G2_node_insertion_cost=None, G2_edge_insertion_cost=None):
"""Validates cost functions (substitution, insertion, deletion) and initializes them with default=0 for substitution
and default=1 for insertion/deletion
if the provided ones are None.
Parameters : see graph_edit_distance
"""
num_G1_nodes = G1.number_of_nodes()
num_G2_nodes = G2.number_of_nodes()
num_G1_edges = G1.number_of_edges()
num_G2_edges = G2.number_of_edges()
# if any cost matrix is None, initialize it with default costs
if node_substitution_cost is None:
node_substitution_cost = np.zeros((num_G1_nodes, num_G2_nodes), dtype=float)
else:
assert node_substitution_cost.shape == (num_G1_nodes, num_G2_nodes);
if edge_substitution_cost is None:
edge_substitution_cost = np.zeros((num_G1_edges, num_G2_edges), dtype=float)
else:
assert edge_substitution_cost.shape == (num_G1_edges, num_G2_edges);
if G1_node_deletion_cost is None:
G1_node_deletion_cost = np.ones(num_G1_nodes, dtype=float)
else:
assert G1_node_deletion_cost.shape[0] == num_G1_nodes;
if G1_edge_deletion_cost is None:
G1_edge_deletion_cost = np.ones(num_G1_edges, dtype=float)
else:
assert G1_edge_deletion_cost.shape[0] == num_G1_edges;
if G2_node_insertion_cost is None:
G2_node_insertion_cost = np.ones(num_G2_nodes, dtype=float)
else:
assert G2_node_insertion_cost.shape[0] == num_G2_nodes;
if G2_edge_insertion_cost is None:
G2_edge_insertion_cost = np.ones(num_G2_edges, dtype=float)
else:
assert G2_edge_insertion_cost.shape[0] == num_G2_edges;
return node_substitution_cost, edge_substitution_cost, \
G1_node_deletion_cost, G1_edge_deletion_cost, \
G2_node_insertion_cost, G2_edge_insertion_cost;
def construct_cost_functions(G1, G2,
node_substitution_cost, edge_substitution_cost,
G1_node_deletion_cost, G1_edge_deletion_cost,
G2_node_insertion_cost, G2_edge_insertion_cost):
"""Constructs cost matrices for LAP solution
Parameters : see graph_edit_distance
"""
num_G1_nodes = G1.number_of_nodes()
num_G2_nodes = G2.number_of_nodes()
num_G1_edges = G1.number_of_edges()
num_G2_edges = G2.number_of_edges()
# cost matrix of node mappings
cost_upper_bound = node_substitution_cost.sum() + G1_node_deletion_cost.sum() + G2_node_insertion_cost.sum() + 1
C_node = np.zeros((num_G1_nodes + num_G2_nodes, num_G1_nodes + num_G2_nodes), dtype=float)
C_node[0:num_G1_nodes, 0:num_G2_nodes] = node_substitution_cost;
C_node[0:num_G1_nodes, num_G2_nodes:num_G2_nodes + num_G1_nodes] = np.array([G1_node_deletion_cost[i] if i == j \
else cost_upper_bound\
for i in range(num_G1_nodes) \
for j in range(num_G1_nodes)]).reshape(num_G1_nodes, num_G1_nodes);
C_node[num_G1_nodes:num_G1_nodes + num_G2_nodes, 0:num_G2_nodes] = np.array([G2_node_insertion_cost[i] if i == j \
else cost_upper_bound\
for i in range(num_G2_nodes) \
for j in range(num_G2_nodes)]).reshape(num_G2_nodes, num_G2_nodes);
# cost matrix of edge mappings
cost_upper_bound = edge_substitution_cost.sum() + G1_edge_deletion_cost.sum() + G2_edge_insertion_cost.sum() + 1
C_edge = np.zeros((num_G1_edges + num_G2_edges, num_G1_edges + num_G2_edges), dtype=float)
C_edge[0:num_G1_edges, 0:num_G2_edges] = edge_substitution_cost;
C_edge[0:num_G1_edges, num_G2_edges:num_G2_edges + num_G1_edges] = np.array([G1_edge_deletion_cost[i] if i == j \
else cost_upper_bound\
for i in range(num_G1_edges) \
for j in range(num_G1_edges)]).reshape(num_G1_edges, num_G1_edges);
C_edge[num_G1_edges:num_G1_edges + num_G2_edges, 0:num_G2_edges] = np.array([G2_edge_insertion_cost[i] if i == j \
else cost_upper_bound\
for i in range(num_G2_edges) \
for j in range(num_G2_edges)]).reshape(num_G2_edges, num_G2_edges);
return C_node, C_edge;
def get_edges_to_match(G, node_id, matched_nodes):
# Find the edges in G with one end-point as node_id and other in matched_nodes or node_id
incident_edges = np.array([], dtype=int)
index = np.array([], dtype=int)
direction = np.array([], dtype=int)
if G.has_edge_between(node_id, node_id):
self_edge_ids = G.edge_id(node_id, node_id, return_array=True).numpy();
incident_edges = np.concatenate((incident_edges, self_edge_ids));
index = np.concatenate((index, [-1]*len(self_edge_ids)));
direction = np.concatenate((direction, [0]*len(self_edge_ids)));
# Find predecessors
src, _, eid = G.in_edges([node_id], 'all');
eid = eid.numpy();
src = src.numpy();
filtered_indices = [(i,matched_nodes.index(src[i])) for i in range(len(src)) if src[i] in matched_nodes];
matched_index = np.array([_[1] for _ in filtered_indices], dtype=int);
eid_index = np.array([_[0] for _ in filtered_indices], dtype=int);
index = np.concatenate((index, matched_index));
incident_edges = np.concatenate((incident_edges, eid[eid_index]));
direction = np.concatenate((direction, np.array([-1]*len(filtered_indices), dtype=int)));
# Find successors
_, dst, eid = G.out_edges([node_id], 'all');
eid = eid.numpy();
dst = dst.numpy();
filtered_indices = [(i,matched_nodes.index(dst[i])) for i in range(len(dst)) if dst[i] in matched_nodes]
matched_index = np.array([_[1] for _ in filtered_indices], dtype=int);
eid_index = np.array([_[0] for _ in filtered_indices], dtype=int);
index = np.concatenate((index, matched_index));
incident_edges = np.concatenate((incident_edges, eid[eid_index]));
direction = np.concatenate((direction, np.array([1]*len(filtered_indices), dtype=int)));
return incident_edges, index, direction;
def subset_cost_matrix(cost_matrix, row_ids, col_ids, num_rows, num_cols):
# Extract thr subset of cost matrix corresponding to rows/cols in arrays row_ids/col_ids
# Note that the shape of cost_matrix is (num_rows+num_cols) * (num_rows+num_cols)
extended_row_ids = np.concatenate((row_ids, np.array([k + num_rows for k in col_ids])));
extended_col_ids = np.concatenate((col_ids, np.array([k + num_cols for k in row_ids])));
return cost_matrix[extended_row_ids, :][:, extended_col_ids]
class search_tree_node:
def __init__(self, G1, G2, parent_matched_cost, parent_matched_nodes, parent_matched_edges, node_G1, node_G2, \
parent_unprocessed_nodes_G1, parent_unprocessed_nodes_G2, parent_unprocessed_edges_G1, parent_unprocessed_edges_G2, \
cost_matrix_nodes, cost_matrix_edges):
self.matched_cost = parent_matched_cost;
self.future_approximate_cost = 0.0;
self.matched_nodes = deepcopy(parent_matched_nodes);
self.matched_nodes[0].append(node_G1);
self.matched_nodes[1].append(node_G2);
self.matched_edges = deepcopy(parent_matched_edges);
self.unprocessed_nodes_G1 = [_ for _ in parent_unprocessed_nodes_G1 if _ != node_G1];
self.unprocessed_nodes_G2 = [_ for _ in parent_unprocessed_nodes_G2 if _ != node_G2];
# Add the cost of matching nodes at this tree-node to the matched cost
if node_G1 is not None and node_G2 is not None: # Substitute node_G1 with node_G2
self.matched_cost += cost_matrix_nodes[node_G1, node_G2];
elif node_G1 is not None: # Delete node_G1
self.matched_cost += cost_matrix_nodes[node_G1, node_G1+G2.number_of_nodes()];
elif node_G2 is not None: # Insert node_G2
self.matched_cost += cost_matrix_nodes[node_G2+G1.number_of_nodes(), node_G2];
# Add the cost of matching edges at this tree-node to the matched cost
incident_edges_G1 = [];
if node_G1 is not None: # Find the edges with one end-point as node_G1 and other in matched nodes or node_G1
incident_edges_G1, index_G1, direction_G1 = get_edges_to_match(G1, node_G1, parent_matched_nodes[0])
incident_edges_G2 = np.array([]);
if node_G2 is not None: # Find the edges with one end-point as node_G2 and other in matched nodes or node_G2
incident_edges_G2, index_G2, direction_G2 = get_edges_to_match(G2, node_G2, parent_matched_nodes[1])
if len(incident_edges_G1) > 0 and len(incident_edges_G2) > 0: # Consider substituting
matched_edges_cost_matrix = subset_cost_matrix(cost_matrix_edges, incident_edges_G1, incident_edges_G2, G1.number_of_edges(), G2.number_of_edges())
max_sum = matched_edges_cost_matrix.sum();
# take care of impossible assignments by assigning maximum cost
for i in range(len(incident_edges_G1)):
for j in range(len(incident_edges_G2)):
# both edges need to have same direction and the other end nodes are matched
if direction_G1[i] == direction_G2[j] and index_G1[i] == index_G2[j]:
continue;
else:
matched_edges_cost_matrix[i,j] = max_sum;
# Match the edges as per the LAP solution
row_ind, col_ind, _ = lapjv(matched_edges_cost_matrix);
lap_cost = 0.00
for i in range(len(row_ind)):
lap_cost += matched_edges_cost_matrix[i, row_ind[i]];
#Update matched edges
for i in range(len(row_ind)):
if i < len(incident_edges_G1):
self.matched_edges[0].append(incident_edges_G1[i]);
if row_ind[i] < len(incident_edges_G2):
self.matched_edges[1].append(incident_edges_G2[row_ind[i]]);
else:
self.matched_edges[1].append(None);
elif row_ind[i] < len(incident_edges_G2):
self.matched_edges[0].append(None);
self.matched_edges[1].append(incident_edges_G2[row_ind[i]]);
self.matched_cost += lap_cost;
elif len(incident_edges_G1) > 0: #only deletion possible
edge_deletion_cost = 0.0;
for edge in incident_edges_G1:
edge_deletion_cost += cost_matrix_edges[edge, G2.number_of_edges()+edge];
#Update matched edges
for edge in incident_edges_G1:
self.matched_edges[0].append(edge);
self.matched_edges[1].append(None);
#Update matched edges
self.matched_cost += edge_deletion_cost;
elif len(incident_edges_G2) > 0: #only insertion possible
edge_insertion_cost = 0.0;
for edge in incident_edges_G2:
edge_insertion_cost += cost_matrix_edges[G1.number_of_edges()+edge, edge];
#Update matched edges
for edge in incident_edges_G2:
self.matched_edges[0].append(None);
self.matched_edges[1].append(edge);
self.matched_cost += edge_insertion_cost;
# Add the cost of matching of unprocessed nodes to the future approximate cost
if len(self.unprocessed_nodes_G1) > 0 and len(self.unprocessed_nodes_G2) > 0: # Consider substituting
unmatched_nodes_cost_matrix = subset_cost_matrix(cost_matrix_nodes, self.unprocessed_nodes_G1, self.unprocessed_nodes_G2, G1.number_of_nodes(), G2.number_of_nodes())
# Match the edges as per the LAP solution
row_ind, col_ind, _ = lapjv(unmatched_nodes_cost_matrix);
lap_cost = 0.00
for i in range(len(row_ind)):
lap_cost += unmatched_nodes_cost_matrix[i, row_ind[i]];
self.future_approximate_cost += lap_cost;
elif len(self.unprocessed_nodes_G1) > 0: # only deletion possible
node_deletion_cost = 0.0;
for node in self.unprocessed_nodes_G1:
node_deletion_cost += cost_matrix_nodes[node, G2.number_of_nodes()+node];
self.future_approximate_cost += node_deletion_cost;
elif len(self.unprocessed_nodes_G2) > 0: # only insertion possible
node_insertion_cost = 0.0;
for node in self.unprocessed_nodes_G2:
node_insertion_cost += cost_matrix_nodes[G1.number_of_nodes()+node, node];
self.future_approximate_cost += node_insertion_cost;
# Add the cost of LAP matching of unprocessed edges to the future approximate cost
self.unprocessed_edges_G1 = [_ for _ in parent_unprocessed_edges_G1 if _ not in incident_edges_G1];
self.unprocessed_edges_G2 = [_ for _ in parent_unprocessed_edges_G2 if _ not in incident_edges_G2];
if len(self.unprocessed_edges_G1) > 0 and len(self.unprocessed_edges_G2) > 0: # Consider substituting
unmatched_edges_cost_matrix = subset_cost_matrix(cost_matrix_edges, self.unprocessed_edges_G1, self.unprocessed_edges_G2, G1.number_of_edges(), G2.number_of_edges())
# Match the edges as per the LAP solution
row_ind, col_ind, _ = lapjv(unmatched_edges_cost_matrix);
lap_cost = 0.00
for i in range(len(row_ind)):
lap_cost += unmatched_edges_cost_matrix[i, row_ind[i]];
self.future_approximate_cost += lap_cost;
elif len(self.unprocessed_edges_G1) > 0: # only deletion possible
edge_deletion_cost = 0.0;
for edge in self.unprocessed_edges_G1:
edge_deletion_cost += cost_matrix_edges[edge, G2.number_of_edges()+edge];
self.future_approximate_cost += edge_deletion_cost;
elif len(self.unprocessed_edges_G2) > 0: # only insertion possible
edge_insertion_cost = 0.0;
for edge in self.unprocessed_edges_G2:
edge_insertion_cost += cost_matrix_edges[G1.number_of_edges()+edge, edge];
self.future_approximate_cost += edge_insertion_cost;
# For heap insertion order
def __lt__(self, other):
if abs((self.matched_cost+self.future_approximate_cost) - (other.matched_cost+other.future_approximate_cost)
)> EPSILON:
return (self.matched_cost+self.future_approximate_cost) < (other.matched_cost+other.future_approximate_cost);
elif abs(self.matched_cost - other.matched_cost) > EPSILON:
return other.matched_cost < self.matched_cost; #matched cost is closer to reality
else:
return (len(self.unprocessed_nodes_G1)+len(self.unprocessed_nodes_G2)+\
len(self.unprocessed_edges_G1)+len(self.unprocessed_edges_G2)) < \
(len(other.unprocessed_nodes_G1)+len(other.unprocessed_nodes_G2)+\
len(other.unprocessed_edges_G1)+len(other.unprocessed_edges_G2));
def edit_cost_from_node_matching(G1, G2, cost_matrix_nodes, cost_matrix_edges, node_matching):
matched_cost = 0.0;
matched_nodes = ([], [])
matched_edges = ([], [])
# Add the cost of matching nodes
for i in range(G1.number_of_nodes()):
matched_cost += cost_matrix_nodes[i, node_matching[i]]
matched_nodes[0].append(i);
if node_matching[i] < G2.number_of_nodes():
matched_nodes[1].append(node_matching[i]);
else:
matched_nodes[1].append(None);
for i in range(G1.number_of_nodes(), len(node_matching)):
matched_cost += cost_matrix_nodes[i, node_matching[i]]
if node_matching[i] < G2.number_of_nodes():
matched_nodes[0].append(None);
matched_nodes[1].append(node_matching[i]);
for i in range(len(matched_nodes[0])):
# Add the cost of matching edges
incident_edges_G1 = [];
if matched_nodes[0][i] is not None: # Find the edges with one end-point as node_G1 and other in matched nodes or node_G1
incident_edges_G1, index_G1, direction_G1 = get_edges_to_match(G1, matched_nodes[0][i], matched_nodes[0][:i])
incident_edges_G2 = np.array([]);
if matched_nodes[1][i] is not None: # Find the edges with one end-point as node_G2 and other in matched nodes or node_G2
incident_edges_G2, index_G2, direction_G2 = get_edges_to_match(G2, matched_nodes[1][i], matched_nodes[1][:i])
if len(incident_edges_G1) > 0 and len(incident_edges_G2) > 0: # Consider substituting
matched_edges_cost_matrix = subset_cost_matrix(cost_matrix_edges, incident_edges_G1, incident_edges_G2, G1.number_of_edges(), G2.number_of_edges())
max_sum = matched_edges_cost_matrix.sum();
# take care of impossible assignments by assigning maximum cost
for i in range(len(incident_edges_G1)):
for j in range(len(incident_edges_G2)):
# both edges need to have same direction and the other end nodes are matched
if direction_G1[i] == direction_G2[j] and index_G1[i] == index_G2[j]:
continue;
else:
matched_edges_cost_matrix[i,j] = max_sum;
# Match the edges as per the LAP solution
row_ind, col_ind, _ = lapjv(matched_edges_cost_matrix);
lap_cost = 0.00
for i in range(len(row_ind)):
lap_cost += matched_edges_cost_matrix[i, row_ind[i]];
#Update matched edges
for i in range(len(row_ind)):
if i < len(incident_edges_G1):
matched_edges[0].append(incident_edges_G1[i]);
if row_ind[i] < len(incident_edges_G2):
matched_edges[1].append(incident_edges_G2[row_ind[i]]);
else:
matched_edges[1].append(None);
elif row_ind[i] < len(incident_edges_G2):
matched_edges[0].append(None);
matched_edges[1].append(incident_edges_G2[row_ind[i]]);
matched_cost += lap_cost;
elif len(incident_edges_G1) > 0: #only deletion possible
edge_deletion_cost = 0.0;
for edge in incident_edges_G1:
edge_deletion_cost += cost_matrix_edges[edge, G2.number_of_edges()+edge];
#Update matched edges
for edge in incident_edges_G1:
matched_edges[0].append(edge);
matched_edges[1].append(None);
#Update matched edges
matched_cost += edge_deletion_cost;
elif len(incident_edges_G2) > 0: #only insertion possible
edge_insertion_cost = 0.0;
for edge in incident_edges_G2:
edge_insertion_cost += cost_matrix_edges[G1.number_of_edges()+edge, edge];
#Update matched edges
for edge in incident_edges_G2:
matched_edges[0].append(None);
matched_edges[1].append(edge);
matched_cost += edge_insertion_cost;
return (matched_cost, matched_nodes, matched_edges);
def contextual_cost_matrix_construction(G1, G2,
node_substitution_cost, edge_substitution_cost,
G1_node_deletion_cost, G1_edge_deletion_cost,
G2_node_insertion_cost, G2_edge_insertion_cost):
# Calculates approximate GED using linear assignment on the nodes with bipartite algorithm
# cost matrix of node mappings
num_G1_nodes = G1.number_of_nodes()
num_G2_nodes = G2.number_of_nodes()
num_G1_edges = G1.number_of_edges()
num_G2_edges = G2.number_of_edges()
cost_upper_bound = 2*(node_substitution_cost.sum() + G1_node_deletion_cost.sum() + G2_node_insertion_cost.sum() + 1)
cost_matrix = np.zeros((num_G1_nodes + num_G2_nodes, num_G1_nodes + num_G2_nodes), dtype=float)
cost_matrix[0:num_G1_nodes, 0:num_G2_nodes] = node_substitution_cost;
cost_matrix[0:num_G1_nodes, num_G2_nodes:num_G2_nodes + num_G1_nodes] = np.array([G1_node_deletion_cost[i] if i == j \
else cost_upper_bound\
for i in range(num_G1_nodes) \
for j in range(num_G1_nodes)]).reshape(num_G1_nodes, num_G1_nodes);
cost_matrix[num_G1_nodes:num_G1_nodes + num_G2_nodes, 0:num_G2_nodes] = np.array([G2_node_insertion_cost[i] if i == j \
else cost_upper_bound\
for i in range(num_G2_nodes) \
for j in range(num_G2_nodes)]).reshape(num_G2_nodes, num_G2_nodes);
self_edge_list_G1 = [np.array([], dtype=int)]*num_G1_nodes;
self_edge_list_G2 = [np.array([], dtype=int)]*num_G2_nodes;
incoming_edges_G1 = [np.array([], dtype=int)]*num_G1_nodes;
incoming_edges_G2 = [np.array([], dtype=int)]*num_G2_nodes;
outgoing_edges_G1 = [np.array([], dtype=int)]*num_G1_nodes;
outgoing_edges_G2 = [np.array([], dtype=int)]*num_G2_nodes;
for i in range(num_G1_nodes):
if G1.has_edge_between(i, i):
self_edge_list_G1[i] = sorted(G1.edge_id(i, i, return_array=True).numpy());
incoming_edges_G1[i] = G1.in_edges([i], 'eid').numpy();
incoming_edges_G1[i] = np.setdiff1d(incoming_edges_G1[i], self_edge_list_G1[i]);
outgoing_edges_G1[i] = G1.out_edges([i], 'eid').numpy();
outgoing_edges_G1[i] = np.setdiff1d(outgoing_edges_G1[i], self_edge_list_G1[i]);
for i in range(num_G2_nodes):
if G2.has_edge_between(i, i):
self_edge_list_G2[i] = sorted(G2.edge_id(i, i, return_array=True).numpy());
incoming_edges_G2[i] = G2.in_edges([i], 'eid').numpy();
incoming_edges_G2[i] = np.setdiff1d(incoming_edges_G2[i], self_edge_list_G2[i]);
outgoing_edges_G2[i] = G2.out_edges([i], 'eid').numpy();
outgoing_edges_G2[i] = np.setdiff1d(outgoing_edges_G2[i], self_edge_list_G2[i]);
selected_deletion_G1 = [G1_edge_deletion_cost[np.concatenate((self_edge_list_G1[i], incoming_edges_G1[i], outgoing_edges_G1[i]))] for i in range(G1.number_of_nodes())];
selected_insertion_G2 = [G2_edge_insertion_cost[np.concatenate((self_edge_list_G2[i], incoming_edges_G2[i], outgoing_edges_G2[i]))] for i in range(G2.number_of_nodes())];
# Add the cost of edge edition which are dependent of a node (see this as the cost associated with a substructure)
for i in range(num_G1_nodes):
for j in range(num_G2_nodes):
m = len(self_edge_list_G1[i])+len(incoming_edges_G1[i])+len(outgoing_edges_G1[i]);
n = len(self_edge_list_G2[j])+len(incoming_edges_G2[j])+len(outgoing_edges_G2[j]);
matrix_dim = m + n;
if matrix_dim == 0:
continue;
temp_edge_cost_matrix = np.empty((matrix_dim, matrix_dim));
temp_edge_cost_matrix.fill(cost_upper_bound);
temp_edge_cost_matrix[:len(self_edge_list_G1[i]),:len(self_edge_list_G2[j])] = edge_substitution_cost[self_edge_list_G1[i],:][:,self_edge_list_G2[j]];
temp_edge_cost_matrix[len(self_edge_list_G1[i]):len(self_edge_list_G1[i])+len(incoming_edges_G1[i]),len(self_edge_list_G2[j]):len(self_edge_list_G2[j])+len(incoming_edges_G2[j])] = edge_substitution_cost[incoming_edges_G1[i],:][:, incoming_edges_G2[j]];
temp_edge_cost_matrix[len(self_edge_list_G1[i])+len(incoming_edges_G1[i]):m,len(self_edge_list_G2[j])+len(incoming_edges_G2[j]):n] = edge_substitution_cost[outgoing_edges_G1[i],:][:, outgoing_edges_G2[j]];
np.fill_diagonal(temp_edge_cost_matrix[:m, n:], selected_deletion_G1[i]);
np.fill_diagonal(temp_edge_cost_matrix[m:, :n], selected_insertion_G2[j]);
temp_edge_cost_matrix[m:, n:].fill(0);
row_ind, col_ind, _ = lapjv(temp_edge_cost_matrix);
lap_cost = 0.00
for k in range(len(row_ind)):
lap_cost += temp_edge_cost_matrix[k, row_ind[k]];
cost_matrix[i,j] += lap_cost;
for i in range(num_G1_nodes):
cost_matrix[i,num_G2_nodes+i] += selected_deletion_G1[i].sum()
for i in range(num_G2_nodes):
cost_matrix[num_G1_nodes+i,i] += selected_insertion_G2[i].sum()
return cost_matrix;
def hausdorff_matching(G1, G2,
node_substitution_cost, edge_substitution_cost,
G1_node_deletion_cost, G1_edge_deletion_cost,
G2_node_insertion_cost, G2_edge_insertion_cost):
# Calculates approximate GED using hausdorff_matching
# cost matrix of node mappings
num_G1_nodes = G1.number_of_nodes()
num_G2_nodes = G2.number_of_nodes()
num_G1_edges = G1.number_of_edges()
num_G2_edges = G2.number_of_edges()
self_edge_list_G1 = [np.array([], dtype=int)]*num_G1_nodes;
self_edge_list_G2 = [np.array([], dtype=int)]*num_G2_nodes;
incoming_edges_G1 = [np.array([], dtype=int)]*num_G1_nodes;
incoming_edges_G2 = [np.array([], dtype=int)]*num_G2_nodes;
outgoing_edges_G1 = [np.array([], dtype=int)]*num_G1_nodes;
outgoing_edges_G2 = [np.array([], dtype=int)]*num_G2_nodes;
for i in range(num_G1_nodes):
if G1.has_edge_between(i, i):
self_edge_list_G1[i] = sorted(G1.edge_id(i, i, return_array=True).numpy());
incoming_edges_G1[i] = G1.in_edges([i], 'eid').numpy();
incoming_edges_G1[i] = np.setdiff1d(incoming_edges_G1[i], self_edge_list_G1[i]);
outgoing_edges_G1[i] = G1.out_edges([i], 'eid').numpy();
outgoing_edges_G1[i] = np.setdiff1d(outgoing_edges_G1[i], self_edge_list_G1[i]);
for i in range(num_G2_nodes):
if G2.has_edge_between(i, i):
self_edge_list_G2[i] = sorted(G2.edge_id(i, i, return_array=True).numpy());
incoming_edges_G2[i] = G2.in_edges([i], 'eid').numpy();
incoming_edges_G2[i] = np.setdiff1d(incoming_edges_G2[i], self_edge_list_G2[i]);
outgoing_edges_G2[i] = G2.out_edges([i], 'eid').numpy();
outgoing_edges_G2[i] = np.setdiff1d(outgoing_edges_G2[i], self_edge_list_G2[i]);
selected_deletion_self_G1 = [G1_edge_deletion_cost[self_edge_list_G1[i]] for i in range(G1.number_of_nodes())];
selected_insertion_self_G2 = [G2_edge_insertion_cost[self_edge_list_G2[i]] for i in range(G2.number_of_nodes())];
selected_deletion_incoming_G1 = [G1_edge_deletion_cost[incoming_edges_G1[i]] for i in range(G1.number_of_nodes())];
selected_insertion_incoming_G2 = [G2_edge_insertion_cost[incoming_edges_G2[i]] for i in range(G2.number_of_nodes())];
selected_deletion_outgoing_G1 = [G1_edge_deletion_cost[outgoing_edges_G1[i]] for i in range(G1.number_of_nodes())];
selected_insertion_outgoing_G2 = [G2_edge_insertion_cost[outgoing_edges_G2[i]] for i in range(G2.number_of_nodes())];
selected_deletion_G1 = [G1_edge_deletion_cost[np.concatenate((self_edge_list_G1[i], incoming_edges_G1[i], outgoing_edges_G1[i]))] for i in range(G1.number_of_nodes())];
selected_insertion_G2 = [G2_edge_insertion_cost[np.concatenate((self_edge_list_G2[i], incoming_edges_G2[i], outgoing_edges_G2[i]))] for i in range(G2.number_of_nodes())];
cost_G1 = np.array([(G1_node_deletion_cost[i] + selected_deletion_G1[i].sum()/2) for i in range(num_G1_nodes)])
cost_G2 = np.array([(G2_node_insertion_cost[i] + selected_insertion_G2[i].sum()/2) for i in range(num_G2_nodes)])
for i in range(num_G1_nodes):
for j in range(num_G2_nodes):
c1_self = deepcopy(selected_deletion_self_G1[i])
c2_self = deepcopy(selected_insertion_self_G2[j])
c1_incoming = deepcopy(selected_deletion_incoming_G1[i])
c2_incoming = deepcopy(selected_insertion_incoming_G2[j])
c1_outgoing = deepcopy(selected_deletion_outgoing_G1[i])
c2_outgoing = deepcopy(selected_insertion_outgoing_G2[j])
for k,a in enumerate(self_edge_list_G1[i]):
for l,b in enumerate(self_edge_list_G2[j]):
c1_self[k] = min(c1_self[k], edge_substitution_cost[a,b]/2);
c2_self[l] = min(c2_self[l], edge_substitution_cost[a,b]/2);
for k,a in enumerate(incoming_edges_G1[i]):
for l,b in enumerate(incoming_edges_G2[j]):
c1_incoming[k] = min(c1_incoming[k], edge_substitution_cost[a,b]/2);
c2_incoming[l] = min(c2_incoming[l], edge_substitution_cost[a,b]/2);
for k,a in enumerate(outgoing_edges_G1[i]):
for l,b in enumerate(outgoing_edges_G2[j]):
c1_outgoing[k] = min(c1_outgoing[k], edge_substitution_cost[a,b]/2);
c2_outgoing[l] = min(c2_outgoing[l], edge_substitution_cost[a,b]/2);
edge_hausdorff_lower_bound = 0.0;
if len(selected_deletion_G1[i])>len(selected_insertion_G2[j]):
idx = np.argpartition(selected_deletion_G1[i], (len(selected_deletion_G1[i])-len(selected_insertion_G2[j])));
edge_hausdorff_lower_bound = selected_deletion_G1[i][idx[:(len(selected_deletion_G1[i])-len(selected_insertion_G2[j]))]].sum();
elif len(selected_deletion_G1[i])<len(selected_insertion_G2[j]):
idx = np.argpartition(selected_insertion_G2[j], (len(selected_insertion_G2[j])-len(selected_deletion_G1[i])));
edge_hausdorff_lower_bound = selected_insertion_G2[j][idx[:(len(selected_insertion_G2[j])-len(selected_deletion_G1[i]))]].sum();
sc_cost = 0.5*(node_substitution_cost[i,j]+0.5*max(c1_self.sum() + c2_self.sum() + \
c1_incoming.sum() + c2_incoming.sum() + \
c1_outgoing.sum() + c2_outgoing.sum(), \
edge_hausdorff_lower_bound));
if cost_G1[i] > sc_cost:
cost_G1[i] = sc_cost;
if cost_G2[j] > sc_cost:
cost_G2[j] = sc_cost;
graph_hausdorff_lower_bound = 0.0;
if num_G1_nodes > num_G2_nodes:
idx = np.argpartition(G1_node_deletion_cost, (num_G1_nodes - num_G2_nodes));
graph_hausdorff_lower_bound = G1_node_deletion_cost[idx[:(num_G1_nodes - num_G2_nodes)]].sum();
elif num_G1_nodes < num_G2_nodes:
idx = np.argpartition(G2_node_insertion_cost, (num_G2_nodes - num_G1_nodes));
graph_hausdorff_lower_bound = G2_node_insertion_cost[idx[:(num_G2_nodes - num_G1_nodes)]].sum();
graph_hausdorff_cost = max(graph_hausdorff_lower_bound, cost_G1.sum() + cost_G2.sum());
return graph_hausdorff_cost;
def a_star_search(G1, G2, cost_matrix_nodes, cost_matrix_edges, max_beam_size):
# A-star traversal
open_list = [];
# Create first nodes in the A-star search tree, matching node 0 of G1 with all possibilities (each node of G2, and deletion)
matched_cost = 0.0;
matched_nodes = ([], []); # No nodes matched in the beginning
matched_edges = ([], []); # No edges matched in the beginning
unprocessed_nodes_G1 = [i for i in range(G1.number_of_nodes())] # No nodes matched in the beginning
unprocessed_nodes_G2 = [i for i in range(G2.number_of_nodes())] # No nodes matched in the beginning
unprocessed_edges_G1 = [i for i in range(G1.number_of_edges())] # No edges matched in the beginning
unprocessed_edges_G2 = [i for i in range(G2.number_of_edges())] # No edges matched in the beginning
for i in range(len(unprocessed_nodes_G2)):
tree_node = search_tree_node(G1, G2, matched_cost, matched_nodes, matched_edges, unprocessed_nodes_G1[0], unprocessed_nodes_G2[i], \
unprocessed_nodes_G1, unprocessed_nodes_G2, unprocessed_edges_G1, unprocessed_edges_G2, \
cost_matrix_nodes, cost_matrix_edges);
# Insert into open-list, implemented as a heap
heappush(open_list, tree_node)
# Consider node deletion
tree_node = search_tree_node(G1, G2, matched_cost, matched_nodes, matched_edges, unprocessed_nodes_G1[0], None, \
unprocessed_nodes_G1, unprocessed_nodes_G2, unprocessed_edges_G1, unprocessed_edges_G2, \
cost_matrix_nodes, cost_matrix_edges);
# Insert into open-list, implemented as a heap
heappush(open_list, tree_node)
while len(open_list) > 0:
# TODO: Create a node that processes multi node insertion deletion in one search node,
# as opposed in multiple search nodes here
parent_tree_node = heappop(open_list);
matched_cost = parent_tree_node.matched_cost;
matched_nodes = parent_tree_node.matched_nodes;
matched_edges = parent_tree_node.matched_edges;
unprocessed_nodes_G1 = parent_tree_node.unprocessed_nodes_G1;
unprocessed_nodes_G2 = parent_tree_node.unprocessed_nodes_G2;
unprocessed_edges_G1 = parent_tree_node.unprocessed_edges_G1;
unprocessed_edges_G2 = parent_tree_node.unprocessed_edges_G2;
if len(unprocessed_nodes_G1) == 0 and len(unprocessed_nodes_G2) == 0:
return (matched_cost, matched_nodes, matched_edges);
elif len(unprocessed_nodes_G1) > 0:
for i in range(len(unprocessed_nodes_G2)):
tree_node = search_tree_node(G1, G2, matched_cost, matched_nodes, matched_edges, unprocessed_nodes_G1[0], unprocessed_nodes_G2[i], \
unprocessed_nodes_G1, unprocessed_nodes_G2, unprocessed_edges_G1, unprocessed_edges_G2, \
cost_matrix_nodes, cost_matrix_edges);
# Insert into open-list, implemented as a heap
heappush(open_list, tree_node)
# Consider node deletion
tree_node = search_tree_node(G1, G2, matched_cost, matched_nodes, matched_edges, unprocessed_nodes_G1[0], None, \
unprocessed_nodes_G1, unprocessed_nodes_G2, unprocessed_edges_G1, unprocessed_edges_G2, \
cost_matrix_nodes, cost_matrix_edges);
# Insert into open-list, implemented as a heap
heappush(open_list, tree_node)
elif len(unprocessed_nodes_G2) > 0:
for i in range(len(unprocessed_nodes_G2)):
tree_node = search_tree_node(G1, G2, matched_cost, matched_nodes, matched_edges, None, unprocessed_nodes_G2[i], \
unprocessed_nodes_G1, unprocessed_nodes_G2, unprocessed_edges_G1, unprocessed_edges_G2, \
cost_matrix_nodes, cost_matrix_edges);
# Insert into open-list, implemented as a heap
heappush(open_list, tree_node)
# Retain the top-k elements in open-list iff algorithm is beam
if max_beam_size > 0 and len(open_list) > max_beam_size:
open_list = nsmallest(max_beam_size, open_list);
heapify(open_list);
return None;
def get_sorted_mapping(mapping_tuple, len1, len2):
# Get sorted mapping of nodes/edges
result_0 = [None]*len1;
result_1 = [None]*len2;
for i in range(len(mapping_tuple[0])):
if mapping_tuple[0][i] is not None and mapping_tuple[1][i] is not None:
result_0[mapping_tuple[0][i]] = mapping_tuple[1][i];
result_1[mapping_tuple[1][i]] = mapping_tuple[0][i];
return (result_0, result_1);
def graph_edit_distance(G1, G2,
node_substitution_cost=None, edge_substitution_cost=None,
G1_node_deletion_cost=None, G2_node_insertion_cost=None,
G1_edge_deletion_cost=None, G2_edge_insertion_cost=None,
algorithm='bipartite', max_beam_size=100):
"""Returns GED (graph edit distance) between DGLGraphs G1 and G2.
Parameters
----------
G1, G2: DGLGraphs
node_substitution_cost, edge_substitution_cost : 2D numpy arrays
node_substitution_cost[i,j] is the cost of substitution node i of G1 with node j of G2,
similar definition for edge_substitution_cost. If None, default cost of 0 is used.
G1_node_deletion_cost, G1_edge_deletion_cost : 1D numpy arrays
G1_node_deletion_cost[i] is the cost of deletion of node i of G1,
similar definition for G1_edge_deletion_cost. If None, default cost of 1 is used.
G2_node_insertion_cost, G2_edge_insertion_cost : 1D numpy arrays
G2_node_insertion_cost[i] is the cost of insertion of node i of G2,
similar definition for G2_edge_insertion_cost. If None, default cost of 1 is used.
algorithm : string
Algorithm to use to calculate the edit distance.
For now, 4 algorithms are supported
i) astar: Calculates exact GED using A* graph traversal algorithm,
the heuristic used is the one proposed in (Riesen and Bunke, 2009) [1].
ii) beam: Calculates approximate GED using A* graph traversal algorithm,
with a maximum number of nodes in the open list. [2]
iii) bipartite (default): Calculates approximate GED using linear assignment on the nodes,
with jv (Jonker-Volgerand) algorithm. [3]
iv) hausdorff: Approximation of graph edit distance based on Hausdorff matching [4].
max_beam_size : int
Maximum number of nodes in the open list, in case the algorithm is 'beam'.
Returns
-------
A tuple of three objects: (edit_distance, node_mapping, edge_mapping)
edit distance is the calculated edit distance (float)
node_mapping is a tuple of size two, containing the node assignments of the two graphs respectively
eg., node_mapping[0][i] is the node mapping of node i of graph G1 (None means that the node is deleted)
Similar definition for the edge_mapping
For 'hausdorff', node_mapping and edge_mapping are returned as None, as this approximation does not return a unique edit path
Examples
--------
>>> src1 = [0, 1, 2, 3, 4, 5];
>>> dst1 = [1, 2, 3, 4, 5, 6];
>>> src2 = [0, 1, 3, 4, 5];
>>> dst2 = [1, 2, 4, 5, 6];
>>> G1 = dgl.DGLGraph((src1, dst1))
>>> G2 = dgl.DGLGraph((src2, dst2))
>>> distance, node_mapping, edge_mapping = graph_edit_distance(G1, G1, algorithm='astar')
>>> print(distance)
0.0
>>> distance, node_mapping, edge_mapping = graph_edit_distance(G1, G2, algorithm='astar')
>>> print(distance)
1.0
References
----------
[1] Riesen, Kaspar, Stefan Fankhauser, and Horst Bunke.
"Speeding Up Graph Edit Distance Computation with a Bipartite Heuristic."
MLG. 2007.
[2] Neuhaus, Michel, Kaspar Riesen, and Horst Bunke.
"Fast suboptimal algorithms for the computation of graph edit distance."
Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR)
and Structural and Syntactic Pattern Recognition (SSPR). 2006.
[3] Fankhauser, Stefan, Kaspar Riesen, and Horst Bunke.
"Speeding up graph edit distance computation through fast bipartite matching."
International Workshop on Graph-Based Representations in Pattern Recognition. 2011.
[4] Fischer, Andreas, et al. "A hausdorff heuristic for efficient computation of graph edit distance."
Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR)
and Structural and Syntactic Pattern Recognition (SSPR). 2014.
"""
# Handle corner cases
if G1 is None and G2 is None:
return (0.0, ([], []), ([], []));
elif G1 is None:
edit_cost = 0.0;
# Validate
if algorithm != "beam":
max_beam_size = -1;
node_substitution_cost, edge_substitution_cost, \
G1_node_deletion_cost, G1_edge_deletion_cost, \
G2_node_insertion_cost, G2_edge_insertion_cost = validate_cost_functions(G1, G2, \
node_substitution_cost, edge_substitution_cost,
G1_node_deletion_cost, G1_edge_deletion_cost,
G2_node_insertion_cost, G2_edge_insertion_cost);
# cost matrices for LAP solution
cost_matrix_nodes, cost_matrix_edges = construct_cost_functions(G1, G2, \
node_substitution_cost, edge_substitution_cost,
G1_node_deletion_cost, G1_edge_deletion_cost,
G2_node_insertion_cost, G2_edge_insertion_cost);
if algorithm == "astar" or algorithm == "beam":
(matched_cost, matched_nodes, matched_edges) = a_star_search(G1, G2, \
cost_matrix_nodes, cost_matrix_edges, max_beam_size);
return (matched_cost, get_sorted_mapping(matched_nodes, G1.number_of_nodes(), G2.number_of_nodes()), get_sorted_mapping(matched_edges, G1.number_of_edges(), G2.number_of_edges()));
elif algorithm == "hausdorff":
hausdorff_cost = hausdorff_matching(G1, G2, \
node_substitution_cost, edge_substitution_cost,
G1_node_deletion_cost, G1_edge_deletion_cost,
G2_node_insertion_cost, G2_edge_insertion_cost);
return (hausdorff_cost, None, None);
else:
cost_matrix = contextual_cost_matrix_construction(G1, G2, \
node_substitution_cost, edge_substitution_cost,
G1_node_deletion_cost, G1_edge_deletion_cost,
G2_node_insertion_cost, G2_edge_insertion_cost);
# Match the nodes as per the LAP solution
row_ind, col_ind, _ = lapjv(cost_matrix);
(matched_cost, matched_nodes, matched_edges) = edit_cost_from_node_matching(G1, G2, \
cost_matrix_nodes, cost_matrix_edges, row_ind);
return (matched_cost, get_sorted_mapping(matched_nodes, G1.number_of_nodes(), G2.number_of_nodes()), get_sorted_mapping(matched_edges, G1.number_of_edges(), G2.number_of_edges()));
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