Update pre-image.

preimage/fitDistance.py

@@ -0,0 +1,103 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Oct 16 14:20:06 2019
+
+@author: ljia
+"""
+import numpy as np
+from tqdm import tqdm
+
+import sys
+sys.path.insert(0, "../")
+from pygraph.utils.graphfiles import loadDataset
+from ged import GED, get_nb_edit_operations
+from utils import kernel_distance_matrix
+
+def fit_GED_to_kernel_distance(Gn, gkernel, itr_max):
+    c_vi = 1
+    c_vr = 1
+    c_vs = 1
+    c_ei = 1
+    c_er = 1
+    c_es = 1
+    
+    # compute distances in feature space.
+    dis_k_mat, _, _, _ = kernel_distance_matrix(Gn, gkernel=gkernel)
+    dis_k_vec = []
+    for i in range(len(dis_k_mat)):
+        for j in range(i, len(dis_k_mat)):
+            dis_k_vec.append(dis_k_mat[i, j])
+    dis_k_vec = np.array(dis_k_vec)
+    
+    residual_list = []
+    edit_cost_list = []
+    
+    for itr in range(itr_max):
+        print('iteration', itr)
+        ged_all = []
+        n_vi_all = []
+        n_vr_all = []
+        n_vs_all = []
+        n_ei_all = []
+        n_er_all = []
+        n_es_all = []
+        # compute GEDs and numbers of edit operations.
+        edit_cost_constant = [c_vi, c_vr, c_vs, c_ei, c_er, c_es]
+        edit_cost_list.append(edit_cost_constant)
+        for i in tqdm(range(len(Gn)), desc='computing GEDs', file=sys.stdout):
+#        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                dis, pi_forward, pi_backward = GED(Gn[i], Gn[j], lib='gedlibpy', 
+                    cost='CONSTANT', method='IPFP', 
+                    edit_cost_constant=edit_cost_constant, stabilizer='min', 
+                    repeat=30)
+                ged_all.append(dis)
+                n_vi, n_vr, n_vs, n_ei, n_er, n_es = get_nb_edit_operations(Gn[i], 
+                    Gn[j], pi_forward, pi_backward)
+                n_vi_all.append(n_vi) 
+                n_vr_all.append(n_vr)
+                n_vs_all.append(n_vs) 
+                n_ei_all.append(n_ei) 
+                n_er_all.append(n_er)
+                n_es_all.append(n_es)
+                
+        residual = np.sqrt(np.sum(np.square(np.array(ged_all) - dis_k_vec)))
+        residual_list.append(residual)
+        
+        # "fit" geds to distances in feature space by tuning edit costs using the
+        # Least Squares Method.
+        nb_cost_mat = np.column_stack((np.array(n_vi_all), np.array(n_vr_all),
+                                       np.array(n_vs_all), np.array(n_ei_all),
+                                       np.array(n_er_all), np.array(n_es_all)))
+        edit_costs, residual, _, _ = np.linalg.lstsq(nb_cost_mat, dis_k_vec,
+                                                     rcond=None)
+        for i in range(len(edit_costs)):
+            if edit_costs[i] < 0:
+                if edit_costs[i] > -1e-3:
+                    edit_costs[i] = 0
+#                else:
+#                    raise ValueError('The edit cost is negative.')
+            
+        c_vi = edit_costs[0]
+        c_vr = edit_costs[1]
+        c_vs = edit_costs[2]
+        c_ei = edit_costs[3]
+        c_er = edit_costs[4]
+        c_es = edit_costs[5]
+    
+    return c_vi, c_vr, c_vs, c_ei, c_er, c_es, residual_list, edit_cost_list
+
+
+
+if __name__ == '__main__':
+    from utils import remove_edges
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+    Gn = Gn[0:10]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    itr_max = 10
+    c_vi, c_vr, c_vs, c_ei, c_er, c_es, residual_list, edit_cost_list = \
+        fit_GED_to_kernel_distance(Gn, gkernel, itr_max)

preimage/ged.py

@@ -0,0 +1,197 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Oct 17 18:44:59 2019
+
+@author: ljia
+"""
+import numpy as np
+import networkx as nx
+from tqdm import tqdm
+import sys
+
+from gedlibpy import librariesImport, gedlibpy
+
+def GED(g1, g2, lib='gedlibpy', cost='CHEM_1', method='IPFP', 
+        edit_cost_constant=[], saveGXL='benoit', stabilizer='min', repeat=50):
+    """
+    Compute GED for 2 graphs.
+    """
+    if lib == 'gedlibpy':
+        def convertGraph(G):
+            """Convert a graph to the proper NetworkX format that can be
+            recognized by library gedlibpy.
+            """
+            G_new = nx.Graph()
+            for nd, attrs in G.nodes(data=True):
+                G_new.add_node(str(nd), chem=attrs['atom'])
+            for nd1, nd2, attrs in G.edges(data=True):
+#                G_new.add_edge(str(nd1), str(nd2), valence=attrs['bond_type'])
+                G_new.add_edge(str(nd1), str(nd2))
+                
+            return G_new
+        
+        gedlibpy.restart_env()
+        gedlibpy.add_nx_graph(convertGraph(g1), "")
+        gedlibpy.add_nx_graph(convertGraph(g2), "")
+
+        listID = gedlibpy.get_all_graph_ids()
+        gedlibpy.set_edit_cost(cost, edit_cost_constant=edit_cost_constant)
+        gedlibpy.init()
+        gedlibpy.set_method(method, "")
+        gedlibpy.init_method()
+
+        g = listID[0]
+        h = listID[1]
+        if stabilizer == None:
+            gedlibpy.run_method(g, h)
+            pi_forward = gedlibpy.get_forward_map(g, h)
+            pi_backward = gedlibpy.get_backward_map(g, h)
+            upper = gedlibpy.get_upper_bound(g, h)
+            lower = gedlibpy.get_lower_bound(g, h)        
+        elif stabilizer == 'min':
+            upper = np.inf
+            for itr in range(repeat):                
+                gedlibpy.run_method(g, h)                
+                upper_tmp = gedlibpy.get_upper_bound(g, h)                
+                if upper_tmp < upper:
+                    upper = upper_tmp
+                    pi_forward = gedlibpy.get_forward_map(g, h)
+                    pi_backward = gedlibpy.get_backward_map(g, h)
+                    lower = gedlibpy.get_lower_bound(g, h)
+                if upper == 0:
+                    break
+                    
+        dis = upper
+        
+        # make the map label correct (label remove map as np.inf)
+        nodes1 = [n for n in g1.nodes()]
+        nodes2 = [n for n in g2.nodes()]
+        nb1 = nx.number_of_nodes(g1)
+        nb2 = nx.number_of_nodes(g2)
+        pi_forward = [nodes2[pi] if pi < nb2 else np.inf for pi in pi_forward]
+        pi_backward = [nodes1[pi] if pi < nb1 else np.inf for pi in pi_backward]      
+        
+    return dis, pi_forward, pi_backward
+
+
+def GED_n(Gn, lib='gedlibpy', cost='CHEM_1', method='IPFP', 
+        edit_cost_constant=[], stabilizer='min', repeat=50):
+    """
+    Compute GEDs for a group of graphs.
+    """
+    if lib == 'gedlibpy':
+        def convertGraph(G):
+            """Convert a graph to the proper NetworkX format that can be
+            recognized by library gedlibpy.
+            """
+            G_new = nx.Graph()
+            for nd, attrs in G.nodes(data=True):
+                G_new.add_node(str(nd), chem=attrs['atom'])
+            for nd1, nd2, attrs in G.edges(data=True):
+#                G_new.add_edge(str(nd1), str(nd2), valence=attrs['bond_type'])
+                G_new.add_edge(str(nd1), str(nd2))
+                
+            return G_new
+        
+        gedlibpy.restart_env()
+        gedlibpy.add_nx_graph(convertGraph(g1), "")
+        gedlibpy.add_nx_graph(convertGraph(g2), "")
+
+        listID = gedlibpy.get_all_graph_ids()
+        gedlibpy.set_edit_cost(cost, edit_cost_constant=edit_cost_constant)
+        gedlibpy.init()
+        gedlibpy.set_method(method, "")
+        gedlibpy.init_method()
+
+        g = listID[0]
+        h = listID[1]
+        if stabilizer == None:
+            gedlibpy.run_method(g, h)
+            pi_forward = gedlibpy.get_forward_map(g, h)
+            pi_backward = gedlibpy.get_backward_map(g, h)
+            upper = gedlibpy.get_upper_bound(g, h)
+            lower = gedlibpy.get_lower_bound(g, h)        
+        elif stabilizer == 'min':
+            upper = np.inf
+            for itr in range(repeat):                
+                gedlibpy.run_method(g, h)                
+                upper_tmp = gedlibpy.get_upper_bound(g, h)                
+                if upper_tmp < upper:
+                    upper = upper_tmp
+                    pi_forward = gedlibpy.get_forward_map(g, h)
+                    pi_backward = gedlibpy.get_backward_map(g, h)
+                    lower = gedlibpy.get_lower_bound(g, h)
+                if upper == 0:
+                    break
+                    
+        dis = upper
+        
+        # make the map label correct (label remove map as np.inf)
+        nodes1 = [n for n in g1.nodes()]
+        nodes2 = [n for n in g2.nodes()]
+        nb1 = nx.number_of_nodes(g1)
+        nb2 = nx.number_of_nodes(g2)
+        pi_forward = [nodes2[pi] if pi < nb2 else np.inf for pi in pi_forward]
+        pi_backward = [nodes1[pi] if pi < nb1 else np.inf for pi in pi_backward]      
+        
+    return dis, pi_forward, pi_backward
+
+
+def ged_median(Gn, Gn_median, measure='ged', verbose=False, 
+                    ged_cost='CHEM_1', ged_method='IPFP', saveGXL='benoit'):
+    dis_list = []
+    pi_forward_list = []
+    for idx, G in tqdm(enumerate(Gn), desc='computing median distances', 
+                       file=sys.stdout) if verbose else enumerate(Gn):
+        dis_sum = 0
+        pi_forward_list.append([])
+        for G_p in Gn_median:
+            dis_tmp, pi_tmp_forward, pi_tmp_backward = GED(G, G_p, 
+                cost=ged_cost, method=ged_method, saveGXL=saveGXL)
+            pi_forward_list[idx].append(pi_tmp_forward)
+            dis_sum += dis_tmp
+        dis_list.append(dis_sum)
+    return dis_list, pi_forward_list
+
+
+def get_nb_edit_operations(g1, g2, forward_map, backward_map):
+    """Compute the number of each edit operations.
+    """
+    n_vi = 0
+    n_vr = 0
+    n_vs = 0
+    n_ei = 0
+    n_er = 0
+    n_es = 0
+    
+    nodes1 = [n for n in g1.nodes()]
+    for i, map_i in enumerate(forward_map):
+        if map_i == np.inf:
+            n_vr += 1
+        elif g1.node[nodes1[i]]['atom'] != g2.node[map_i]['atom']:
+            n_vs += 1
+    for map_i in backward_map:
+        if map_i == np.inf:
+            n_vi += 1
+    
+#    idx_nodes1 = range(0, len(node1))
+    
+    edges1 = [e for e in g1.edges()]
+    nb_edges2_cnted = 0
+    for n1, n2 in edges1:
+        idx1 = nodes1.index(n1)
+        idx2 = nodes1.index(n2)
+        # one of the nodes is removed, thus the edge is removed.
+        if forward_map[idx1] == np.inf or forward_map[idx2] == np.inf:
+            n_er += 1
+        # corresponding edge is in g2. Edge label is not considered.
+        elif (forward_map[idx1], forward_map[idx2]) in g2.edges() or \
+            (forward_map[idx2], forward_map[idx1]) in g2.edges():
+                nb_edges2_cnted += 1
+        # corresponding nodes are in g2, however the edge is removed.
+        else:
+            n_er += 1
+    n_ei = nx.number_of_edges(g2) - nb_edges2_cnted
+    
+    return n_vi, n_vr, n_vs, n_ei, n_er, n_es

preimage/iam.py

@@ -12,10 +12,10 @@ import networkx as nx
 from tqdm import tqdm
 
 import sys
-from gedlibpy import librariesImport, gedlibpy
 sys.path.insert(0, "../")
 from pygraph.utils.graphdataset import get_dataset_attributes
 from pygraph.utils.utils import graph_isIdentical, get_node_labels, get_edge_labels
+from ged import GED, ged_median
 
 
 def iam_upgraded(Gn_median, Gn_candidate, c_ei=3, c_er=3, c_es=1, ite_max=50, 
@@ -237,7 +237,7 @@ def iam_upgraded(Gn_median, Gn_candidate, c_ei=3, c_er=3, c_es=1, ite_max=50,
         
 #        # find the best graph generated in this iteration and update pi_p.
         # @todo: should we update all graphs generated or just the best ones?
-        dis_list, pi_forward_list = median_distance(G_new_list, Gn_median, 
+        dis_list, pi_forward_list = ged_median(G_new_list, Gn_median, 
             **params_ged)
         # @todo: should we remove the identical and connectivity check? 
         # Don't know which is faster.
@@ -362,7 +362,7 @@ def iam_upgraded(Gn_median, Gn_candidate, c_ei=3, c_er=3, c_es=1, ite_max=50,
     # phase 1: initilize.
     # compute set-median.
     dis_min = np.inf
-    dis_list, pi_forward_all = median_distance(Gn_candidate, Gn_median,
+    dis_list, pi_forward_all = ged_median(Gn_candidate, Gn_median,
         **params_ged)
     # find all smallest distances.
     if allBestInit: # try all best init graphs.
@@ -426,96 +426,6 @@ def iam_upgraded(Gn_median, Gn_candidate, c_ei=3, c_er=3, c_es=1, ite_max=50,
 
 
 
-
-
-
-
-
-
-
-###############################################################################
-# Useful functions.
-
-def GED(g1, g2, lib='gedlibpy', cost='CHEM_1', method='IPFP', saveGXL='benoit', 
-        stabilizer='min'):
-    """
-    Compute GED.
-    """
-    if lib == 'gedlibpy':
-        def convertGraph(G):
-            """Convert a graph to the proper NetworkX format that can be
-            recognized by library gedlibpy.
-            """
-            G_new = nx.Graph()
-            for nd, attrs in G.nodes(data=True):
-                G_new.add_node(str(nd), chem=attrs['atom'])
-            for nd1, nd2, attrs in G.edges(data=True):
-#                G_new.add_edge(str(nd1), str(nd2), valence=attrs['bond_type'])
-                G_new.add_edge(str(nd1), str(nd2))
-                
-            return G_new
-        
-        gedlibpy.restart_env()
-        gedlibpy.add_nx_graph(convertGraph(g1), "")
-        gedlibpy.add_nx_graph(convertGraph(g2), "")
-
-        listID = gedlibpy.get_all_graph_ids()
-        gedlibpy.set_edit_cost(cost)
-        gedlibpy.init()
-        gedlibpy.set_method(method, "")
-        gedlibpy.init_method()
-
-        g = listID[0]
-        h = listID[1]
-        if stabilizer == None:
-            gedlibpy.run_method(g, h)
-            pi_forward = gedlibpy.get_forward_map(g, h)
-            pi_backward = gedlibpy.get_backward_map(g, h)
-            upper = gedlibpy.get_upper_bound(g, h)
-            lower = gedlibpy.get_lower_bound(g, h)        
-        elif stabilizer == 'min':
-            upper = np.inf
-            for itr in range(50):                
-                gedlibpy.run_method(g, h)                
-                upper_tmp = gedlibpy.get_upper_bound(g, h)                
-                if upper_tmp < upper:
-                    upper = upper_tmp
-                    pi_forward = gedlibpy.get_forward_map(g, h)
-                    pi_backward = gedlibpy.get_backward_map(g, h)
-                    lower = gedlibpy.get_lower_bound(g, h)
-                if upper == 0:
-                    break
-                    
-        dis = upper
-        
-        # make the map label correct (label remove map as np.inf)
-        nodes1 = [n for n in g1.nodes()]
-        nodes2 = [n for n in g2.nodes()]
-        nb1 = nx.number_of_nodes(g1)
-        nb2 = nx.number_of_nodes(g2)
-        pi_forward = [nodes2[pi] if pi < nb2 else np.inf for pi in pi_forward]
-        pi_backward = [nodes1[pi] if pi < nb1 else np.inf for pi in pi_backward]      
-        
-    return dis, pi_forward, pi_backward
-
-
-def median_distance(Gn, Gn_median, measure='ged', verbose=False, 
-                    ged_cost='CHEM_1', ged_method='IPFP', saveGXL='benoit'):
-    dis_list = []
-    pi_forward_list = []
-    for idx, G in tqdm(enumerate(Gn), desc='computing median distances', 
-                       file=sys.stdout) if verbose else enumerate(Gn):
-        dis_sum = 0
-        pi_forward_list.append([])
-        for G_p in Gn_median:
-            dis_tmp, pi_tmp_forward, pi_tmp_backward = GED(G, G_p, 
-                cost=ged_cost, method=ged_method, saveGXL=saveGXL)
-            pi_forward_list[idx].append(pi_tmp_forward)
-            dis_sum += dis_tmp
-        dis_list.append(dis_sum)
-    return dis_list, pi_forward_list
-
-
 ###############################################################################
 # Old implementations.
     

preimage/preimage_iam.py

@@ -13,20 +13,13 @@ and the iterative alternate minimizations (IAM) in reference [2].
 """
 import sys
 import numpy as np
-import multiprocessing
 from tqdm import tqdm
 import networkx as nx
 import matplotlib.pyplot as plt
 import random
 
 from iam import iam_upgraded
-sys.path.insert(0, "../")
-from pygraph.kernels.marginalizedKernel import marginalizedkernel
-from pygraph.kernels.untilHPathKernel import untilhpathkernel
-from pygraph.kernels.spKernel import spkernel
-import functools
-from pygraph.utils.kernels import deltakernel, gaussiankernel, kernelproduct
-from pygraph.kernels.structuralspKernel import structuralspkernel
+from utils import dis_gstar, compute_kernel
 
 
 def preimage_iam(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max, 
@@ -72,13 +65,13 @@ def preimage_iam(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max,
 #        print(g.nodes(data=True))
 #        print(g.edges(data=True))
     Gk = [Gn_init[ig].copy() for ig in sort_idx[0:k]] # the k nearest neighbors
-    for gi in Gk:
-        nx.draw(gi, labels=nx.get_node_attributes(gi, 'atom'), with_labels=True)
-#        nx.draw_networkx(gi)
-        plt.show()
-#        draw_Letter_graph(g)
-        print(gi.nodes(data=True))
-        print(gi.edges(data=True))
+#    for gi in Gk:
+#        nx.draw(gi, labels=nx.get_node_attributes(gi, 'atom'), with_labels=True)
+##        nx.draw_networkx(gi)
+#        plt.show()
+##        draw_Letter_graph(g)
+#        print(gi.nodes(data=True))
+#        print(gi.edges(data=True))
     
 #    i = 1
     r = 0
@@ -173,7 +166,7 @@ def preimage_iam(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max,
         print('\nthe k shortest distances are', dis_k)
         print('the shortest distances for previous iterations are', dis_of_each_itr)
         
-    print('\nthe graph is updated', nb_updated, 'times.')
+    print('\n\nthe graph is updated', nb_updated, 'times.')
     print('\nthe k nearest neighbors are updated', nb_updated_k, 'times.')
     print('distances in kernel space:', dis_of_each_itr, '\n')
     
@@ -227,13 +220,13 @@ def preimage_iam_random_mix(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max
 #        print(g.nodes(data=True))
 #        print(g.edges(data=True))
     Gk = [Gn_init[ig].copy() for ig in sort_idx[0:k]] # the k nearest neighbors
-    for gi in Gk:
-        nx.draw(gi, labels=nx.get_node_attributes(gi, 'atom'), with_labels=True)
-#        nx.draw_networkx(gi)
-        plt.show()
-#        draw_Letter_graph(g)
-        print(gi.nodes(data=True))
-        print(gi.edges(data=True))
+#    for gi in Gk:
+#        nx.draw(gi, labels=nx.get_node_attributes(gi, 'atom'), with_labels=True)
+##        nx.draw_networkx(gi)
+#        plt.show()
+##        draw_Letter_graph(g)
+#        print(gi.nodes(data=True))
+#        print(gi.edges(data=True))
     
     r = 0
     itr_total = 0
@@ -394,7 +387,8 @@ def preimage_iam_random_mix(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max
                             
                     # compute distance between \psi and the new generated graph.
                     knew = compute_kernel([ghat_new] + Gn_median, gkernel, verbose=False)
-                    dhat_new = dis_gstar(0, [1, 2], alpha, knew, withterm3=False)
+                    dhat_new = dis_gstar(0, range(1, len(Gn_median) + 1), 
+                                         alpha, knew, withterm3=False)
                     # @todo: the new distance is smaller or also equal?
                     if dhat_new < dis_k[-1] and np.abs(dhat_new - dis_k[-1]) >= epsilon:
                         # check if the new distance is the same as one in D_k.
@@ -448,7 +442,7 @@ def preimage_iam_random_mix(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max
         print('\nthe k shortest distances are', dis_k)
         print('the shortest distances for previous iterations are', dis_of_each_itr)
         
-    print('\nthe graph is updated by IAM', nb_updated_iam, 'times, and by random generation',
+    print('\n\nthe graph is updated by IAM', nb_updated_iam, 'times, and by random generation',
           nb_updated_random, 'times.')
     print('\nthe k nearest neighbors are updated by IAM', nb_updated_k_iam, 
           'times, and by random generation', nb_updated_k_random, 'times.')
@@ -458,60 +452,6 @@ def preimage_iam_random_mix(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max
             nb_updated_iam, nb_updated_random, nb_updated_k_iam, nb_updated_k_random
 
 
-###############################################################################
-# useful functions.
-
-def dis_gstar(idx_g, idx_gi, alpha, Kmatrix, term3=0, withterm3=True):
-    term1 = Kmatrix[idx_g, idx_g]
-    term2 = 0
-    for i, a in enumerate(alpha):
-        term2 += a * Kmatrix[idx_g, idx_gi[i]]
-    term2 *= 2
-    if withterm3 == False:
-        for i1, a1 in enumerate(alpha):
-            for i2, a2 in enumerate(alpha):
-                term3 += a1 * a2 * Kmatrix[idx_gi[i1], idx_gi[i2]]
-    return np.sqrt(term1 - term2 + term3)
-
-
-def compute_kernel(Gn, graph_kernel, verbose):
-    if graph_kernel == 'marginalizedkernel':
-        Kmatrix, _ = marginalizedkernel(Gn, node_label='atom', edge_label=None,
-                                  p_quit=0.03, n_iteration=10, remove_totters=False,
-                                  n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-    elif graph_kernel == 'untilhpathkernel':
-        Kmatrix, _ = untilhpathkernel(Gn, node_label='atom', edge_label=None,
-                                  depth=10, k_func='MinMax', compute_method='trie',
-                                  n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-    elif graph_kernel == 'spkernel':
-        mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
-        Kmatrix, _, _ = spkernel(Gn, node_label='atom', node_kernels=
-                              {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel},
-                              n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-    elif graph_kernel == 'structuralspkernel':
-        mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
-        Kmatrix, _ = structuralspkernel(Gn, node_label='atom', node_kernels=
-                              {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel},
-                              n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-        
-    # normalization
-    Kmatrix_diag = Kmatrix.diagonal().copy()
-    for i in range(len(Kmatrix)):
-        for j in range(i, len(Kmatrix)):
-            Kmatrix[i][j] /= np.sqrt(Kmatrix_diag[i] * Kmatrix_diag[j])
-            Kmatrix[j][i] = Kmatrix[i][j]
-    return Kmatrix
-            
-
-def gram2distances(Kmatrix):
-    dmatrix = np.zeros((len(Kmatrix), len(Kmatrix)))
-    for i1 in range(len(Kmatrix)):
-        for i2 in range(len(Kmatrix)):
-            dmatrix[i1, i2] = Kmatrix[i1, i1] + Kmatrix[i2, i2] - 2 * Kmatrix[i1, i2]
-    dmatrix = np.sqrt(dmatrix)
-    return dmatrix
-
-
 ###############################################################################
 # Old implementations.
     

preimage/preimage_random.py

@@ -10,51 +10,14 @@ pre-image
 import sys
 import numpy as np
 import random
-import multiprocessing
 from tqdm import tqdm
 import networkx as nx
 import matplotlib.pyplot as plt
 
 
 sys.path.insert(0, "../")
-from pygraph.utils.graphfiles import loadDataset
-from pygraph.kernels.marginalizedKernel import marginalizedkernel
-from pygraph.kernels.untilHPathKernel import untilhpathkernel
-from pygraph.kernels.spKernel import spkernel
-import functools
-from pygraph.utils.kernels import deltakernel, gaussiankernel, kernelproduct
-from pygraph.kernels.structuralspKernel import structuralspkernel
 
-from gk_iam import dis_gstar
-
-
-def compute_kernel(Gn, graph_kernel, verbose):
-    if graph_kernel == 'marginalizedkernel':
-        Kmatrix, _ = marginalizedkernel(Gn, node_label='atom', edge_label=None,
-                                  p_quit=0.03, n_iteration=10, remove_totters=False,
-                                  n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-    elif graph_kernel == 'untilhpathkernel':
-        Kmatrix, _ = untilhpathkernel(Gn, node_label='atom', edge_label=None,
-                                  depth=10, k_func='MinMax', compute_method='trie',
-                                  n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-    elif graph_kernel == 'spkernel':
-        mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
-        Kmatrix, _, _ = spkernel(Gn, node_label='atom', node_kernels=
-                              {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel},
-                              n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-    elif graph_kernel == 'structuralspkernel':
-        mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
-        Kmatrix, _ = structuralspkernel(Gn, node_label='atom', node_kernels=
-                              {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel},
-                              n_jobs=multiprocessing.cpu_count(), verbose=verbose)
-        
-    # normalization
-    Kmatrix_diag = Kmatrix.diagonal().copy()
-    for i in range(len(Kmatrix)):
-        for j in range(i, len(Kmatrix)):
-            Kmatrix[i][j] /= np.sqrt(Kmatrix_diag[i] * Kmatrix_diag[j])
-            Kmatrix[j][i] = Kmatrix[i][j]
-    return Kmatrix
+from utils import compute_kernel, dis_gstar
 
 
 def preimage_random(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max, l, gkernel):
@@ -105,6 +68,7 @@ def preimage_random(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max, l, gke
     r = 0
 #    sod_list = [dhat]
 #    found = False
+    dis_of_each_itr = [dhat]
     nb_updated = 0
     g_best = []
     while r < r_max:
@@ -162,7 +126,8 @@ def preimage_random(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max, l, gke
 #                               p_quit=lmbda, n_iteration=20, remove_totters=False,
 #                               n_jobs=multiprocessing.cpu_count(), verbose=False)
                 knew = compute_kernel([gtemp] + Gn_median, gkernel, verbose=False)
-                dnew = dis_gstar(0, [1, 2], alpha, knew, withterm3=False)
+                dnew = dis_gstar(0, range(1, len(Gn_median) + 1), alpha, knew, 
+                                 withterm3=False)
                 if dnew <= dhat: # @todo: the new distance is smaller or also equal?
                     if dnew < dhat:
                         print('\nI am smaller!')
@@ -184,13 +149,19 @@ def preimage_random(Gn_init, Gn_median, alpha, idx_gi, Kmatrix, k, r_max, l, gke
             dihat_list = [dhat]
         else:
             r += 1
+            
+        dis_of_each_itr.append(dhat)
+        print('the shortest distances for previous iterations are', dis_of_each_itr)
 #    dis_best.append(dhat)
-    g_best = (g0hat_list[0] if len(gihat_list) == 0 else gihat_list[0])  
+    g_best = (g0hat_list[0] if len(gihat_list) == 0 else gihat_list[0])
+    print('distances in kernel space:', dis_of_each_itr, '\n')
+    
     return dhat, g_best, nb_updated
 #    return 0, 0, 0
 
 
 if __name__ == '__main__':
+    from pygraph.utils.graphfiles import loadDataset
     
 #    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
 #          'extra_params': {}}  # node/edge symb

preimage/test.py

@@ -80,5 +80,6 @@ def testNxGrapĥ():
     print("Forward map : " , gedlibpy.get_forward_map(g, h), ", Backward map : ", gedlibpy.get_backward_map(g, h))
     print ("Upper Bound = " + str(gedlibpy.get_upper_bound(g, h)) + ", Lower Bound = " + str(gedlibpy.get_lower_bound(g, h)) + ", Runtime = " + str(gedlibpy.get_runtime(g, h)))
 
+#test()
 init() 
 #testNxGrapĥ()

preimage/test_iam.py

@@ -0,0 +1,167 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Sep  5 15:59:00 2019
+
+@author: ljia
+"""
+
+import numpy as np
+import networkx as nx
+import matplotlib.pyplot as plt
+import time
+import random
+#from tqdm import tqdm
+
+#import os
+import sys
+sys.path.insert(0, "../")
+from pygraph.utils.graphfiles import loadDataset
+from iam import iam_upgraded
+from utils import remove_edges, compute_kernel, get_same_item_indices
+from ged import ged_median
+
+###############################################################################
+# tests on different numbers of median-sets.
+
+def test_iam_median_nb():
+    
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:50]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    
+#    lmbda = 0.03 # termination probalility
+#    r_max = 10 # iteration limit for pre-image.
+#    alpha_range = np.linspace(0.5, 0.5, 1)
+#    k = 5 # k nearest neighbors
+#    epsilon = 1e-6
+#    InitIAMWithAllDk = True
+    # parameters for GED function
+    ged_cost='CHEM_1'
+    ged_method='IPFP'
+    saveGXL='gedlib'
+    # parameters for IAM function
+    c_ei=1
+    c_er=1
+    c_es=1
+    ite_max_iam = 50
+    epsilon_iam = 0.001
+    removeNodes = False
+    connected_iam = False
+    
+    # number of graphs; we what to compute the median of these graphs. 
+    nb_median_range = [2, 3, 4, 5, 10, 20, 30, 40, 50, 100]
+    
+    # find out all the graphs classified to positive group 1.
+    idx_dict = get_same_item_indices(y_all)
+    Gn = [Gn[i] for i in idx_dict[1]]
+    
+#    # compute Gram matrix.
+#    time0 = time.time()
+#    km = compute_kernel(Gn, gkernel, True)
+#    time_km = time.time() - time0    
+#    # write Gram matrix to file.
+#    np.savez('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm', gm=km, gmtime=time_km)
+        
+    
+    time_list = []
+    dis_ks_min_list = []
+    sod_gs_list = []
+    sod_gs_min_list = []
+    nb_updated_list = []
+    nb_updated_k_list = []
+    g_best = []
+    for nb_median in nb_median_range:
+        print('\n-------------------------------------------------------')
+        print('number of median graphs =', nb_median)
+        random.seed(1)
+        idx_rdm = random.sample(range(len(Gn)), nb_median)
+        print('graphs chosen:', idx_rdm)
+        Gn_median = [Gn[idx].copy() for idx in idx_rdm]
+        Gn_candidate = [g.copy() for g in Gn_median]
+        
+#        for g in Gn_median:
+#            nx.draw(g, labels=nx.get_node_attributes(g, 'atom'), with_labels=True)
+##            plt.savefig("results/preimage_mix/mutag.png", format="PNG")
+#            plt.show()
+#            plt.clf()                         
+                    
+        ###################################################################
+        gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm.npz')
+        km_tmp = gmfile['gm']
+        time_km = gmfile['gmtime']
+        # modify mixed gram matrix.
+        km = np.zeros((len(Gn) + nb_median, len(Gn) + nb_median))
+        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                km[i, j] = km_tmp[i, j]
+                km[j, i] = km[i, j]
+        for i in range(len(Gn)):
+            for j, idx in enumerate(idx_rdm):
+                km[i, len(Gn) + j] = km[i, idx]
+                km[len(Gn) + j, i] = km[i, idx]
+        for i, idx1 in enumerate(idx_rdm):
+            for j, idx2 in enumerate(idx_rdm):
+                km[len(Gn) + i, len(Gn) + j] = km[idx1, idx2]
+                
+        ###################################################################
+        alpha_range = [1 / nb_median] * nb_median
+        time0 = time.time()
+        ghat_new_list, dis_min = iam_upgraded(Gn_median, Gn_candidate, 
+            c_ei=c_ei, c_er=c_er, c_es=c_es, ite_max=ite_max_iam, 
+            epsilon=epsilon_iam, removeNodes=removeNodes, 
+            connected=connected_iam, 
+            params_ged={'ged_cost': ged_cost, 'ged_method': ged_method, 
+                        'saveGXL': saveGXL})
+            
+        time_total = time.time() - time0
+        print('\ntime: ', time_total)
+        time_list.append(time_total)
+        print('\nsmallest distance in kernel space: ', dhat) 
+        dis_ks_min_list.append(dhat)
+        g_best.append(ghat_list)
+        print('\nnumber of updates of the best graph: ', nb_updated)
+        nb_updated_list.append(nb_updated)
+        print('\nnumber of updates of k nearest graphs: ', nb_updated_k)
+        nb_updated_k_list.append(nb_updated_k)
+        
+        # show the best graph and save it to file.
+        print('the shortest distance is', dhat)
+        print('one of the possible corresponding pre-images is')
+        nx.draw(ghat_list[0], labels=nx.get_node_attributes(ghat_list[0], 'atom'), 
+                with_labels=True)
+        plt.show()
+        plt.savefig('results/preimage_iam/mutag_median_nb' + str(nb_median) + 
+                    '.png', format="PNG")
+        plt.clf()
+#        print(ghat_list[0].nodes(data=True))
+#        print(ghat_list[0].edges(data=True))
+    
+        # compute the corresponding sod in graph space.
+        sod_tmp, _ = ged_median([ghat_list[0]], Gn_median, ged_cost=ged_cost, 
+                                     ged_method=ged_method, saveGXL=saveGXL)
+        sod_gs_list.append(sod_tmp)
+        sod_gs_min_list.append(np.min(sod_tmp))
+        print('\nsmallest sod in graph space: ', np.min(sod_tmp))
+        
+    print('\nsods in graph space: ', sod_gs_list)
+    print('\nsmallest sod in graph space for each set of median graphs: ', sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each set of median graphs: ', 
+          dis_ks_min_list) 
+    print('\nnumber of updates of the best graph for each set of median graphs by IAM: ', 
+          nb_updated_list)
+    print('\nnumber of updates of k nearest graphs for each set of median graphs by IAM: ', 
+          nb_updated_k_list)
+    print('\ntimes:', time_list)
+    
+    
+###############################################################################
+
+    
+if __name__ == '__main__':
+###############################################################################
+# tests on different numbers of median-sets.
+    test_iam_median_nb()

preimage/run_gk_iam.py → preimage/test_others.py

@@ -15,6 +15,9 @@ import sys
 sys.path.insert(0, "../")
 from pygraph.utils.graphfiles import loadDataset
 from median import draw_Letter_graph
+from ged import GED, ged_median
+from utils import get_same_item_indices, compute_kernel, gram2distances, \
+    dis_gstar, remove_edges
 
 
 # --------------------------- These are tests --------------------------------#
@@ -47,7 +50,6 @@ def test_who_is_the_closest_in_kernel_space(Gn):
 
 
 def test_who_is_the_closest_in_GED_space(Gn):
-    from iam import GED
     idx_gi = [0, 6]
     g1 = Gn[idx_gi[0]]
     g2 = Gn[idx_gi[1]]
@@ -142,7 +144,7 @@ def test_new_IAM_allGraph_deleteNodes(Gn):
     
     
 def test_the_simple_two(Gn, gkernel):
-    from gk_iam import gk_iam_nearest_multi, compute_kernel
+    from gk_iam import gk_iam_nearest_multi
     lmbda = 0.03 # termination probalility
     r_max = 10 # recursions
     l = 500
@@ -199,7 +201,7 @@ def test_the_simple_two(Gn, gkernel):
             
     
 def test_remove_bests(Gn, gkernel):
-    from gk_iam import gk_iam_nearest_multi, compute_kernel
+    from gk_iam import gk_iam_nearest_multi
     lmbda = 0.03 # termination probalility
     r_max = 10 # recursions
     l = 500
@@ -249,8 +251,7 @@ def test_remove_bests(Gn, gkernel):
 # Tests on dataset Letter-H.
             
 def test_gkiam_letter_h():
-    from gk_iam import gk_iam_nearest_multi, compute_kernel
-    from iam import median_distance
+    from gk_iam import gk_iam_nearest_multi
     ds = {'name': 'Letter-high', 'dataset': '../datasets/Letter-high/Letter-high_A.txt',
           'extra_params': {}} # node nsymb
 #    ds = {'name': 'Letter-med', 'dataset': '../datasets/Letter-med/Letter-med_A.txt',
@@ -305,7 +306,7 @@ def test_gkiam_letter_h():
                 print(g.edges(data=True))
                 
         # compute the corresponding sod in graph space. (alpha range not considered.)
-        sod_tmp, _ = median_distance(g_best[0], Gn_let, ged_cost='LETTER', 
+        sod_tmp, _ = ged_median(g_best[0], Gn_let, ged_cost='LETTER', 
                                      ged_method='IPFP', saveGXL='gedlib-letter')
         sod_gs_list.append(sod_tmp)
         sod_gs_min_list.append(np.min(sod_tmp))
@@ -318,19 +319,6 @@ def test_gkiam_letter_h():
     print('\nsmallest sod in kernel space for each letter: ', sod_ks_min_list) 
     print('\nnumber of updates for each letter: ', nb_updated_list)             
     print('\ntimes:', time_list)
-                
-                
-def get_same_item_indices(ls):
-    """Get the indices of the same items in a list. Return a dict keyed by items.
-    """
-    idx_dict = {}
-    for idx, item in enumerate(ls):
-        if item in idx_dict:
-            idx_dict[item].append(idx)
-        else:
-            idx_dict[item] = [idx]
-    return idx_dict
-
 
 #def compute_letter_median_by_average(Gn):
 #    return g_median
@@ -338,7 +326,6 @@ def get_same_item_indices(ls):
 
 def test_iam_letter_h():
     from iam import test_iam_moreGraphsAsInit_tryAllPossibleBestGraphs_deleteNodesInIterations
-    from gk_iam import dis_gstar, compute_kernel
     ds = {'name': 'Letter-high', 'dataset': '../datasets/Letter-high/Letter-high_A.txt',
           'extra_params': {}} # node nsymb
 #    ds = {'name': 'Letter-med', 'dataset': '../datasets/Letter-med/Letter-med_A.txt',
@@ -402,7 +389,7 @@ def test_iam_letter_h():
     
     
 def test_random_preimage_letter_h():
-    from preimage_random import preimage_random, compute_kernel
+    from preimage_random import preimage_random
     ds = {'name': 'Letter-high', 'dataset': '../datasets/Letter-high/Letter-high_A.txt',
           'extra_params': {}} # node nsymb
 #    ds = {'name': 'Letter-med', 'dataset': '../datasets/Letter-med/Letter-med_A.txt',
@@ -463,7 +450,7 @@ def test_random_preimage_letter_h():
                 print(g.edges(data=True))
                 
         # compute the corresponding sod in graph space. (alpha range not considered.)
-        sod_tmp, _ = median_distance(g_best[0], Gn_let)
+        sod_tmp, _ = ged_median(g_best[0], Gn_let)
         sod_list.append(sod_tmp)
         sod_min_list.append(np.min(sod_tmp))
         
@@ -479,8 +466,7 @@ def test_random_preimage_letter_h():
     
     
 def test_gkiam_mutag():
-    from gk_iam import gk_iam_nearest_multi, compute_kernel
-    from iam import median_distance
+    from gk_iam import gk_iam_nearest_multi
     ds = {'name': 'Letter-high', 'dataset': '../datasets/Letter-high/Letter-high_A.txt',
           'extra_params': {}} # node nsymb
 #    ds = {'name': 'Letter-med', 'dataset': '../datasets/Letter-med/Letter-med_A.txt',
@@ -535,7 +521,7 @@ def test_gkiam_mutag():
                 print(g.edges(data=True))
                 
         # compute the corresponding sod in graph space. (alpha range not considered.)
-        sod_tmp, _ = median_distance(g_best[0], Gn_let)
+        sod_tmp, _ = ged_median(g_best[0], Gn_let)
         sod_gs_list.append(sod_tmp)
         sod_gs_min_list.append(np.min(sod_tmp))
         sod_ks_min_list.append(sod_ks)
@@ -553,9 +539,7 @@ def test_gkiam_mutag():
 # Re-test.
     
 def retest_the_simple_two():
-    from gk_iam import gk_iam_nearest_multi, compute_kernel
-    from iam import median_distance
-    from test_random_mutag import remove_edges
+    from gk_iam import gk_iam_nearest_multi
     
     # The two simple graphs.
 #    g1 = nx.Graph(name='haha')
@@ -653,7 +637,7 @@ def retest_the_simple_two():
             
     # compute the corresponding sod in graph space.
     for idx, item in enumerate(alpha_range):
-        sod_tmp, _ = median_distance(g_best[0], [g1, g2], ged_cost=ged_cost, 
+        sod_tmp, _ = ged_median(g_best[0], [g1, g2], ged_cost=ged_cost, 
                                      ged_method=ged_method, saveGXL=saveGXL)
         sod_gs_list.append(sod_tmp)
         sod_gs_min_list.append(np.min(sod_tmp))

preimage/test_random_mutag.py → preimage/test_preimage_iam.py

@@ -10,20 +10,23 @@ import numpy as np
 import networkx as nx
 import matplotlib.pyplot as plt
 import time
-from tqdm import tqdm
+import random
+#from tqdm import tqdm
 
-import os
+#import os
 import sys
 sys.path.insert(0, "../")
 from pygraph.utils.graphfiles import loadDataset
+from utils import remove_edges, compute_kernel, get_same_item_indices
+from ged import ged_median
+
+from preimage_iam import preimage_iam 
+
 
 ###############################################################################
-# test on the combination of the two randomly chosen graphs. (the same as in the
-# random pre-image paper.)
+# tests on different values on grid of median-sets and k.
 
-def test_preimage_mix_2combination_all_pairs():
-    from preimage_iam import preimage_iam_random_mix, compute_kernel
-    from iam import median_distance
+def test_preimage_iam_grid_k_median_nb():       
     ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
           'extra_params': {}}  # node/edge symb
     Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
@@ -32,13 +35,11 @@ def test_preimage_mix_2combination_all_pairs():
     gkernel = 'marginalizedkernel'
     
     lmbda = 0.03 # termination probalility
-    r_max = 10 # iteration limit for pre-image.
-    l_max = 500 # update limit for random generation
-    alpha_range = np.linspace(0.5, 0.5, 1)
-    k = 5 # k nearest neighbors
+    r_max = 5 # iteration limit for pre-image.
+#    alpha_range = np.linspace(0.5, 0.5, 1)
+#    k = 5 # k nearest neighbors
     epsilon = 1e-6
     InitIAMWithAllDk = True
-    InitRandomWithAllDk = True
     # parameters for GED function
     ged_cost='CHEM_1'
     ged_method='IPFP'
@@ -52,153 +53,280 @@ def test_preimage_mix_2combination_all_pairs():
     removeNodes = True
     connected_iam = False
     
-    nb_update_mat_iam = np.full((len(Gn), len(Gn)), np.inf)
-    nb_update_mat_random = np.full((len(Gn), len(Gn)), np.inf)
-    # test on each pair of graphs.
-#    for idx1 in range(len(Gn) - 1, -1, -1):
-#        for idx2 in range(idx1, -1, -1):
-    for idx1 in range(187, 188):
-        for idx2 in range(167, 168):
-            g1 = Gn[idx1].copy()
-            g2 = Gn[idx2].copy()
-        #    Gn[10] = []
-        #    Gn[10] = []
+    # number of graphs; we what to compute the median of these graphs. 
+    nb_median_range = [2, 3, 4, 5, 10, 20, 30, 40, 50, 100]
+    # number of nearest neighbors.
+    k_range = [5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100]
+    
+    # find out all the graphs classified to positive group 1.
+    idx_dict = get_same_item_indices(y_all)
+    Gn = [Gn[i] for i in idx_dict[1]]
+    
+#    # compute Gram matrix.
+#    time0 = time.time()
+#    km = compute_kernel(Gn, gkernel, True)
+#    time_km = time.time() - time0    
+#    # write Gram matrix to file.
+#    np.savez('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm', gm=km, gmtime=time_km)
+        
+    
+    time_list = []
+    dis_ks_min_list = []
+    sod_gs_list = []
+    sod_gs_min_list = []
+    nb_updated_list = []
+    nb_updated_k_list = []
+    g_best = []
+    for idx_nb, nb_median in enumerate(nb_median_range):
+        print('\n-------------------------------------------------------')
+        print('number of median graphs =', nb_median)
+        random.seed(1)
+        idx_rdm = random.sample(range(len(Gn)), nb_median)
+        print('graphs chosen:', idx_rdm)
+        Gn_median = [Gn[idx].copy() for idx in idx_rdm]
+        
+#        for g in Gn_median:
+#            nx.draw(g, labels=nx.get_node_attributes(g, 'atom'), with_labels=True)
+##            plt.savefig("results/preimage_mix/mutag.png", format="PNG")
+#            plt.show()
+#            plt.clf()                         
+                    
+        ###################################################################
+        gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm.npz')
+        km_tmp = gmfile['gm']
+        time_km = gmfile['gmtime']
+        # modify mixed gram matrix.
+        km = np.zeros((len(Gn) + nb_median, len(Gn) + nb_median))
+        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                km[i, j] = km_tmp[i, j]
+                km[j, i] = km[i, j]
+        for i in range(len(Gn)):
+            for j, idx in enumerate(idx_rdm):
+                km[i, len(Gn) + j] = km[i, idx]
+                km[len(Gn) + j, i] = km[i, idx]
+        for i, idx1 in enumerate(idx_rdm):
+            for j, idx2 in enumerate(idx_rdm):
+                km[len(Gn) + i, len(Gn) + j] = km[idx1, idx2]
+                
+        ###################################################################
+        alpha_range = [1 / nb_median] * nb_median
+        
+        time_list.append([])
+        dis_ks_min_list.append([])
+        sod_gs_list.append([])
+        sod_gs_min_list.append([])
+        nb_updated_list.append([])
+        nb_updated_k_list.append([])
+        g_best.append([])   
+        
+        for k in k_range:
+            print('\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n')
+            print('k =', k)
+            time0 = time.time()
+            dhat, ghat_list, dis_of_each_itr, nb_updated, nb_updated_k = \
+                preimage_iam(Gn, Gn_median,
+                alpha_range, range(len(Gn), len(Gn) + nb_median), km, k, r_max, 
+                gkernel, epsilon=epsilon, InitIAMWithAllDk=InitIAMWithAllDk,
+                params_iam={'c_ei': c_ei, 'c_er': c_er, 'c_es': c_es, 
+                            'ite_max': ite_max_iam, 'epsilon': epsilon_iam,
+                            'removeNodes': removeNodes, 'connected': connected_iam},
+                params_ged={'ged_cost': ged_cost, 'ged_method': ged_method, 
+                            'saveGXL': saveGXL})
+                
+            time_total = time.time() - time0 + time_km
+            print('time: ', time_total)
+            time_list[idx_nb].append(time_total)
+            print('\nsmallest distance in kernel space: ', dhat) 
+            dis_ks_min_list[idx_nb].append(dhat)
+            g_best[idx_nb].append(ghat_list)
+            print('\nnumber of updates of the best graph by IAM: ', nb_updated)
+            nb_updated_list[idx_nb].append(nb_updated)
+            print('\nnumber of updates of k nearest graphs by IAM: ', nb_updated_k)
+            nb_updated_k_list[idx_nb].append(nb_updated_k)
             
-            nx.draw(g1, labels=nx.get_node_attributes(g1, 'atom'), with_labels=True)
-            plt.savefig("results/preimage_mix/mutag187.png", format="PNG")
-            plt.show()
-            plt.clf()
-            nx.draw(g2, labels=nx.get_node_attributes(g2, 'atom'), with_labels=True)
-            plt.savefig("results/preimage_mix/mutag167.png", format="PNG")
-            plt.show()
+            # show the best graph and save it to file.
+            print('the shortest distance is', dhat)
+            print('one of the possible corresponding pre-images is')
+            nx.draw(ghat_list[0], labels=nx.get_node_attributes(ghat_list[0], 'atom'), 
+                    with_labels=True)
+            plt.savefig('results/preimage_iam/mutag_median_nb' + str(nb_median) + 
+                        '_k' + str(k) + '.png', format="PNG")
+    #        plt.show()
             plt.clf()
+    #        print(ghat_list[0].nodes(data=True))
+    #        print(ghat_list[0].edges(data=True))
+        
+            # compute the corresponding sod in graph space.
+            sod_tmp, _ = ged_median([ghat_list[0]], Gn_median, ged_cost=ged_cost, 
+                                         ged_method=ged_method, saveGXL=saveGXL)
+            sod_gs_list[idx_nb].append(sod_tmp)
+            sod_gs_min_list[idx_nb].append(np.min(sod_tmp))
+            print('\nsmallest sod in graph space: ', np.min(sod_tmp))
+        
+    print('\nsods in graph space: ', sod_gs_list)
+    print('\nsmallest sod in graph space for each set of median graphs and k: ', 
+          sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each set of median graphs and k: ', 
+          dis_ks_min_list) 
+    print('\nnumber of updates of the best graph for each set of median graphs and k by IAM: ', 
+          nb_updated_list)
+    print('\nnumber of updates of k nearest graphs for each set of median graphs and k by IAM: ', 
+          nb_updated_k_list)
+    print('\ntimes:', time_list)
+    
+    
+    
+    
 
-            ###################################################################            
-#            Gn_mix = [g.copy() for g in Gn]
-#            Gn_mix.append(g1.copy())
-#            Gn_mix.append(g2.copy())
-#            
-#            # compute
-#            time0 = time.time()
-#            km = compute_kernel(Gn_mix, gkernel, True)
-#            time_km = time.time() - time0
-#            
-#            # write Gram matrix to file and read it.
-#            np.savez('results/gram_matrix_uhpath_itr7_pq0.8.gm', gm=km, gmtime=time_km)
-            
-            ###################################################################
-            gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03.gm.npz')
-            km = gmfile['gm']
-            time_km = gmfile['gmtime']
-            # modify mixed gram matrix.
-            for i in range(len(Gn)):
-                km[i, len(Gn)] = km[i, idx1]
-                km[i, len(Gn) + 1] = km[i, idx2]
-                km[len(Gn), i] = km[i, idx1]
-                km[len(Gn) + 1, i] = km[i, idx2]
-            km[len(Gn), len(Gn)] = km[idx1, idx1]
-            km[len(Gn), len(Gn) + 1] = km[idx1, idx2]
-            km[len(Gn) + 1, len(Gn)] = km[idx2, idx1]
-            km[len(Gn) + 1, len(Gn) + 1] = km[idx2, idx2]
-            
-            ###################################################################
-#            # use only the two graphs in median set as candidates.
-#            Gn = [g1.copy(), g2.copy()]
-#            Gn_mix = Gn + [g1.copy(), g2.copy()]
-#            # compute         
-#            time0 = time.time()
-#            km = compute_kernel(Gn_mix, gkernel, True)
-#            time_km = time.time() - time0
+
+###############################################################################
+# tests on different numbers of median-sets.
+
+def test_preimage_iam_median_nb():
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:50]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
     
-            
-            time_list = []
-            dis_ks_min_list = []
-            sod_gs_list = []
-            sod_gs_min_list = []
-            nb_updated_list_iam = []
-            nb_updated_list_random = []
-            nb_updated_k_list_iam = []
-            nb_updated_k_list_random = []
-            g_best = []
-            # for each alpha
-            for alpha in alpha_range:
-                print('\n-------------------------------------------------------\n')
-                print('alpha =', alpha)
-                time0 = time.time()
-                dhat, ghat_list, dis_of_each_itr, nb_updated_iam, nb_updated_random, \
-                    nb_updated_k_iam, nb_updated_k_random = \
-                    preimage_iam_random_mix(Gn, [g1, g2],
-                    [alpha, 1 - alpha], range(len(Gn), len(Gn) + 2), km, k, r_max, 
-                    l_max, gkernel, epsilon=epsilon, InitIAMWithAllDk=InitIAMWithAllDk, 
-                    InitRandomWithAllDk=InitRandomWithAllDk,
-                    params_iam={'c_ei': c_ei, 'c_er': c_er, 'c_es': c_es, 
-                                'ite_max': ite_max_iam, 'epsilon': epsilon_iam,
-                                'removeNodes': removeNodes, 'connected': connected_iam},
-                    params_ged={'ged_cost': ged_cost, 'ged_method': ged_method, 
-                                'saveGXL': saveGXL})
-                time_total = time.time() - time0 + time_km
-                print('time: ', time_total)
-                time_list.append(time_total)
-                dis_ks_min_list.append(dhat)
-                g_best.append(ghat_list)
-                nb_updated_list_iam.append(nb_updated_iam)       
-                nb_updated_list_random.append(nb_updated_random)
-                nb_updated_k_list_iam.append(nb_updated_k_iam)       
-                nb_updated_k_list_random.append(nb_updated_k_random) 
-                
-            # show best graphs and save them to file.
-            for idx, item in enumerate(alpha_range):
-                print('when alpha is', item, 'the shortest distance is', dis_ks_min_list[idx])
-                print('one of the possible corresponding pre-images is')
-                nx.draw(g_best[idx][0], labels=nx.get_node_attributes(g_best[idx][0], 'atom'), 
-                        with_labels=True)
-                plt.savefig('results/preimage_mix/mutag' + str(idx1) + '_' + str(idx2) 
-                            + '_alpha' + str(item) + '.png', format="PNG")
-#                plt.show()
-                plt.clf()
-#                print(g_best[idx][0].nodes(data=True))
-#                print(g_best[idx][0].edges(data=True))
-                
-        #        for g in g_best[idx]:
-        #            draw_Letter_graph(g, savepath='results/gk_iam/')
-        ##            nx.draw_networkx(g)
-        ##            plt.show()
-        #            print(g.nodes(data=True))
-        #            print(g.edges(data=True))
+    lmbda = 0.03 # termination probalility
+    r_max = 10 # iteration limit for pre-image.
+#    alpha_range = np.linspace(0.5, 0.5, 1)
+    k = 5 # k nearest neighbors
+    epsilon = 1e-6
+    InitIAMWithAllDk = True
+    # parameters for GED function
+    ged_cost='CHEM_1'
+    ged_method='IPFP'
+    saveGXL='gedlib'
+    # parameters for IAM function
+    c_ei=1
+    c_er=1
+    c_es=1
+    ite_max_iam = 50
+    epsilon_iam = 0.001
+    removeNodes = True
+    connected_iam = False
+    
+    # number of graphs; we what to compute the median of these graphs. 
+    nb_median_range = [2, 3, 4, 5, 10, 20, 30, 40, 50, 100]
+    
+    # find out all the graphs classified to positive group 1.
+    idx_dict = get_same_item_indices(y_all)
+    Gn = [Gn[i] for i in idx_dict[1]]
+    
+#    # compute Gram matrix.
+#    time0 = time.time()
+#    km = compute_kernel(Gn, gkernel, True)
+#    time_km = time.time() - time0    
+#    # write Gram matrix to file.
+#    np.savez('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm', gm=km, gmtime=time_km)
+        
+    
+    time_list = []
+    dis_ks_min_list = []
+    sod_gs_list = []
+    sod_gs_min_list = []
+    nb_updated_list = []
+    nb_updated_k_list = []
+    g_best = []
+    for nb_median in nb_median_range:
+        print('\n-------------------------------------------------------')
+        print('number of median graphs =', nb_median)
+        random.seed(1)
+        idx_rdm = random.sample(range(len(Gn)), nb_median)
+        print('graphs chosen:', idx_rdm)
+        Gn_median = [Gn[idx].copy() for idx in idx_rdm]
+        
+#        for g in Gn_median:
+#            nx.draw(g, labels=nx.get_node_attributes(g, 'atom'), with_labels=True)
+##            plt.savefig("results/preimage_mix/mutag.png", format="PNG")
+#            plt.show()
+#            plt.clf()                         
                     
-            # compute the corresponding sod in graph space.
-            for idx, item in enumerate(alpha_range):
-                sod_tmp, _ = median_distance(g_best[0], [g1, g2], ged_cost=ged_cost, 
-                                             ged_method=ged_method, saveGXL=saveGXL)
-                sod_gs_list.append(sod_tmp)
-                sod_gs_min_list.append(np.min(sod_tmp))
+        ###################################################################
+        gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm.npz')
+        km_tmp = gmfile['gm']
+        time_km = gmfile['gmtime']
+        # modify mixed gram matrix.
+        km = np.zeros((len(Gn) + nb_median, len(Gn) + nb_median))
+        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                km[i, j] = km_tmp[i, j]
+                km[j, i] = km[i, j]
+        for i in range(len(Gn)):
+            for j, idx in enumerate(idx_rdm):
+                km[i, len(Gn) + j] = km[i, idx]
+                km[len(Gn) + j, i] = km[i, idx]
+        for i, idx1 in enumerate(idx_rdm):
+            for j, idx2 in enumerate(idx_rdm):
+                km[len(Gn) + i, len(Gn) + j] = km[idx1, idx2]
                 
-            print('\nsods in graph space: ', sod_gs_list)
-            print('\nsmallest sod in graph space for each alpha: ', sod_gs_min_list)  
-            print('\nsmallest distance in kernel space for each alpha: ', dis_ks_min_list) 
-            print('\nnumber of updates of the best graph for each alpha by IAM: ', nb_updated_list_iam)
-            print('\nnumber of updates of the best graph for each alpha by random generation: ', 
-                  nb_updated_list_random)
-            print('\nnumber of updates of k nearest graphs for each alpha by IAM: ', 
-                  nb_updated_k_list_iam)
-            print('\nnumber of updates of k nearest graphs for each alpha by random generation: ', 
-                  nb_updated_k_list_random)
-            print('\ntimes:', time_list)
-            nb_update_mat_iam[idx1, idx2] = nb_updated_list_iam[0]
-            nb_update_mat_random[idx1, idx2] = nb_updated_list_random[0]
+        ###################################################################
+        alpha_range = [1 / nb_median] * nb_median
+        time0 = time.time()
+        dhat, ghat_list, dis_of_each_itr, nb_updated, nb_updated_k = \
+            preimage_iam(Gn, Gn_median,
+            alpha_range, range(len(Gn), len(Gn) + nb_median), km, k, r_max, 
+            gkernel, epsilon=epsilon, InitIAMWithAllDk=InitIAMWithAllDk,
+            params_iam={'c_ei': c_ei, 'c_er': c_er, 'c_es': c_es, 
+                        'ite_max': ite_max_iam, 'epsilon': epsilon_iam,
+                        'removeNodes': removeNodes, 'connected': connected_iam},
+            params_ged={'ged_cost': ged_cost, 'ged_method': ged_method, 
+                        'saveGXL': saveGXL})
             
-            str_fw = 'graphs %d and %d: %d times by IAM, %d times by random generation.\n' \
-                % (idx1, idx2, nb_updated_list_iam[0], nb_updated_list_random[0])
-            with open('results/preimage_mix/nb_updates.txt', 'r+') as file:
-                content = file.read()
-                file.seek(0, 0)
-                file.write(str_fw + content)
-                
-                
+        time_total = time.time() - time0 + time_km
+        print('\ntime: ', time_total)
+        time_list.append(time_total)
+        print('\nsmallest distance in kernel space: ', dhat) 
+        dis_ks_min_list.append(dhat)
+        g_best.append(ghat_list)
+        print('\nnumber of updates of the best graph: ', nb_updated)
+        nb_updated_list.append(nb_updated)
+        print('\nnumber of updates of k nearest graphs: ', nb_updated_k)
+        nb_updated_k_list.append(nb_updated_k)
+        
+        # show the best graph and save it to file.
+        print('the shortest distance is', dhat)
+        print('one of the possible corresponding pre-images is')
+        nx.draw(ghat_list[0], labels=nx.get_node_attributes(ghat_list[0], 'atom'), 
+                with_labels=True)
+#        plt.show()
+        plt.savefig('results/preimage_iam/mutag_median_nb' + str(nb_median) + 
+                    '.png', format="PNG")
+        plt.clf()
+#        print(ghat_list[0].nodes(data=True))
+#        print(ghat_list[0].edges(data=True))
+    
+        # compute the corresponding sod in graph space.
+        sod_tmp, _ = ged_median([ghat_list[0]], Gn_median, ged_cost=ged_cost, 
+                                     ged_method=ged_method, saveGXL=saveGXL)
+        sod_gs_list.append(sod_tmp)
+        sod_gs_min_list.append(np.min(sod_tmp))
+        print('\nsmallest sod in graph space: ', np.min(sod_tmp))
+        
+    print('\nsods in graph space: ', sod_gs_list)
+    print('\nsmallest sod in graph space for each set of median graphs: ', sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each set of median graphs: ', 
+          dis_ks_min_list) 
+    print('\nnumber of updates of the best graph for each set of median graphs by IAM: ', 
+          nb_updated_list)
+    print('\nnumber of updates of k nearest graphs for each set of median graphs by IAM: ', 
+          nb_updated_k_list)
+    print('\ntimes:', time_list)
+    
+    
+    
+    
+    
+
+###############################################################################
+# test on the combination of the two randomly chosen graphs. (the same as in the
+# random pre-image paper.)
 
 def test_gkiam_2combination_all_pairs():
-    from preimage_iam import preimage_iam, compute_kernel
-    from iam import median_distance
     ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
           'extra_params': {}}  # node/edge symb
     Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
@@ -334,7 +462,7 @@ def test_gkiam_2combination_all_pairs():
                     
             # compute the corresponding sod in graph space.
             for idx, item in enumerate(alpha_range):
-                sod_tmp, _ = median_distance(g_best[0], [g1, g2], ged_cost=ged_cost, 
+                sod_tmp, _ = ged_median([g_best[0]], [g1, g2], ged_cost=ged_cost, 
                                              ged_method=ged_method, saveGXL=saveGXL)
                 sod_gs_list.append(sod_tmp)
                 sod_gs_min_list.append(np.min(sod_tmp))
@@ -358,8 +486,7 @@ def test_gkiam_2combination_all_pairs():
     
 
 def test_gkiam_2combination():
-    from gk_iam import gk_iam_nearest_multi, compute_kernel
-    from iam import median_distance
+    from gk_iam import gk_iam_nearest_multi
     ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
           'extra_params': {}}  # node/edge symb
     Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
@@ -451,7 +578,7 @@ def test_gkiam_2combination():
             
     # compute the corresponding sod in graph space.
     for idx, item in enumerate(alpha_range):
-        sod_tmp, _ = median_distance(g_best[0], [g1, g2], ged_cost=ged_cost, 
+        sod_tmp, _ = ged_median([g_best[0]], [g1, g2], ged_cost=ged_cost, 
                                      ged_method=ged_method, saveGXL=saveGXL)
         sod_gs_list.append(sod_tmp)
         sod_gs_min_list.append(np.min(sod_tmp))
@@ -463,148 +590,6 @@ def test_gkiam_2combination():
     print('\ntimes:', time_list)
     
     
-    
-    
-def test_random_preimage_2combination():
-#    from gk_iam import compute_kernel
-    from preimage_random import preimage_random
-    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
-          'extra_params': {}}  # node/edge symb
-    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
-#    Gn = Gn[0:12]
-    remove_edges(Gn)
-    gkernel = 'marginalizedkernel'
-    
-#    dis_mat, dis_max, dis_min, dis_mean = kernel_distance_matrix(Gn, gkernel=gkernel)
-#    print(dis_max, dis_min, dis_mean)
-    
-    lmbda = 0.03 # termination probalility
-    r_max = 10 # iteration limit for pre-image.
-    l = 500
-    alpha_range = np.linspace(0, 1, 11)
-    k = 5 # k nearest neighbors
-    
-    # randomly select two molecules
-    np.random.seed(1)
-    idx_gi = [187, 167] # np.random.randint(0, len(Gn), 2)
-    g1 = Gn[idx_gi[0]].copy()
-    g2 = Gn[idx_gi[1]].copy()
-    
-#    nx.draw(g1, labels=nx.get_node_attributes(g1, 'atom'), with_labels=True)
-#    plt.savefig("results/random_preimage/mutag10.png", format="PNG")
-#    plt.show()
-#    nx.draw(g2, labels=nx.get_node_attributes(g2, 'atom'), with_labels=True)
-#    plt.savefig("results/random_preimage/mutag11.png", format="PNG")
-#    plt.show()    
-    
-    ######################################################################
-#    Gn_mix = [g.copy() for g in Gn]
-#    Gn_mix.append(g1.copy())
-#    Gn_mix.append(g2.copy())
-#    
-##    g_tmp = iam([g1, g2])
-##    nx.draw_networkx(g_tmp)
-##    plt.show()
-#    
-#    # compute 
-#    time0 = time.time()
-#    km = compute_kernel(Gn_mix, gkernel, True)
-#    time_km = time.time() - time0
-    
-    ###################################################################
-    idx1 = idx_gi[0]
-    idx2 = idx_gi[1]
-    gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03.gm.npz')
-    km = gmfile['gm']
-    time_km = gmfile['gmtime']
-    # modify mixed gram matrix.
-    for i in range(len(Gn)):
-        km[i, len(Gn)] = km[i, idx1]
-        km[i, len(Gn) + 1] = km[i, idx2]
-        km[len(Gn), i] = km[i, idx1]
-        km[len(Gn) + 1, i] = km[i, idx2]
-    km[len(Gn), len(Gn)] = km[idx1, idx1]
-    km[len(Gn), len(Gn) + 1] = km[idx1, idx2]
-    km[len(Gn) + 1, len(Gn)] = km[idx2, idx1]
-    km[len(Gn) + 1, len(Gn) + 1] = km[idx2, idx2]
-            
-    ###################################################################
-
-    time_list = []
-    nb_updated_list = []
-    g_best = []
-    dis_ks_min_list = []
-    # for each alpha
-    for alpha in alpha_range:
-        print('\n-------------------------------------------------------\n')
-        print('alpha =', alpha)
-        time0 = time.time()
-        dhat, ghat, nb_updated = preimage_random(Gn, [g1, g2], [alpha, 1 - alpha], 
-                                          range(len(Gn), len(Gn) + 2), km,
-                                          k, r_max, l, gkernel)
-        time_total = time.time() - time0 + time_km
-        print('time: ', time_total)
-        time_list.append(time_total)
-        dis_ks_min_list.append(dhat)
-        g_best.append(ghat)
-        nb_updated_list.append(nb_updated)
-        
-    # show best graphs and save them to file.
-    for idx, item in enumerate(alpha_range):
-        print('when alpha is', item, 'the shortest distance is', dis_ks_min_list[idx])
-        print('one of the possible corresponding pre-images is')
-        nx.draw(g_best[idx], labels=nx.get_node_attributes(g_best[idx], 'atom'), 
-                with_labels=True)
-        plt.savefig('results/random_preimage/mutag_alpha' + str(item) + '.png', format="PNG")
-        plt.show()
-        plt.clf()
-        print(g_best[idx].nodes(data=True))
-        print(g_best[idx].edges(data=True))
-            
-#        # compute the corresponding sod in graph space. (alpha range not considered.)
-#        sod_tmp, _ = median_distance(g_best[0], Gn_let)
-#        sod_gs_list.append(sod_tmp)
-#        sod_gs_min_list.append(np.min(sod_tmp))
-#        sod_ks_min_list.append(sod_ks)
-#        nb_updated_list.append(nb_updated)
-                      
-#    print('\nsmallest sod in graph space for each alpha: ', sod_gs_min_list)  
-    print('\nsmallest distance in kernel space for each alpha: ', dis_ks_min_list) 
-    print('\nnumber of updates for each alpha: ', nb_updated_list)             
-    print('\ntimes:', time_list)
-    
-    
-
-    
-###############################################################################
-# help functions
-
-def remove_edges(Gn):
-    for G in Gn:
-        for _, _, attrs in G.edges(data=True):
-            attrs.clear()
-            
-            
-def kernel_distance_matrix(Gn, Kmatrix=None, gkernel=None):
-    from gk_iam import compute_kernel
-    dis_mat = np.empty((len(Gn), len(Gn)))
-    if Kmatrix == None:
-        Kmatrix = compute_kernel(Gn, gkernel, True)
-    for i in range(len(Gn)):
-        for j in range(i, len(Gn)):
-            dis = Kmatrix[i, i] + Kmatrix[j, j] - 2 * Kmatrix[i, j]
-            if dis < 0:
-                if dis > -1e-10:
-                    dis = 0
-                else:
-                    raise ValueError('The distance is negative.')
-            dis_mat[i, j] = np.sqrt(dis)
-            dis_mat[j, i] = dis_mat[i, j]
-    dis_max = np.max(np.max(dis_mat))
-    dis_min = np.min(np.min(dis_mat[dis_mat != 0]))
-    dis_mean = np.mean(np.mean(dis_mat))
-    return dis_mat, dis_max, dis_min, dis_mean
-    
 ###############################################################################
 
     
@@ -612,7 +597,13 @@ if __name__ == '__main__':
 ###############################################################################
 # test on the combination of the two randomly chosen graphs. (the same as in the
 # random pre-image paper.)
-#    test_random_preimage_2combination()
 #    test_gkiam_2combination()
 #    test_gkiam_2combination_all_pairs()
-    test_preimage_mix_2combination_all_pairs()
+    
+###############################################################################
+# tests on different numbers of median-sets.
+    test_preimage_iam_median_nb()
+    
+###############################################################################
+# tests on different values on grid of median-sets and k.
+#    test_preimage_iam_grid_k_median_nb()

preimage/test_preimage_mix.py

@@ -0,0 +1,542 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Sep  5 15:59:00 2019
+
+@author: ljia
+"""
+
+import numpy as np
+import networkx as nx
+import matplotlib.pyplot as plt
+import time
+import random
+#from tqdm import tqdm
+
+#import os
+import sys
+sys.path.insert(0, "../")
+from pygraph.utils.graphfiles import loadDataset
+from ged import ged_median
+from utils import compute_kernel, get_same_item_indices, remove_edges
+from preimage_iam import preimage_iam_random_mix
+
+###############################################################################
+# tests on different values on grid of median-sets and k.
+
+def test_preimage_mix_grid_k_median_nb():
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:50]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    
+    lmbda = 0.03 # termination probalility
+    r_max = 5 # iteration limit for pre-image.
+    l_max = 500 # update limit for random generation
+#    alpha_range = np.linspace(0.5, 0.5, 1)
+#    k = 5 # k nearest neighbors
+    epsilon = 1e-6
+    InitIAMWithAllDk = True
+    InitRandomWithAllDk = True
+    # parameters for GED function
+    ged_cost='CHEM_1'
+    ged_method='IPFP'
+    saveGXL='gedlib'
+    # parameters for IAM function
+    c_ei=1
+    c_er=1
+    c_es=1
+    ite_max_iam = 50
+    epsilon_iam = 0.001
+    removeNodes = True
+    connected_iam = False
+    
+    # number of graphs; we what to compute the median of these graphs. 
+    nb_median_range = [2, 3, 4, 5, 10, 20, 30, 40, 50, 100]
+    # number of nearest neighbors.
+    k_range = [5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100]
+    
+    # find out all the graphs classified to positive group 1.
+    idx_dict = get_same_item_indices(y_all)
+    Gn = [Gn[i] for i in idx_dict[1]]
+    
+#    # compute Gram matrix.
+#    time0 = time.time()
+#    km = compute_kernel(Gn, gkernel, True)
+#    time_km = time.time() - time0    
+#    # write Gram matrix to file.
+#    np.savez('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm', gm=km, gmtime=time_km)
+        
+    
+    time_list = []
+    dis_ks_min_list = []
+    sod_gs_list = []
+    sod_gs_min_list = []
+    nb_updated_list_iam = []
+    nb_updated_list_random = []
+    nb_updated_k_list_iam = []
+    nb_updated_k_list_random = []
+    g_best = []
+    for idx_nb, nb_median in enumerate(nb_median_range):
+        print('\n-------------------------------------------------------')
+        print('number of median graphs =', nb_median)
+        random.seed(1)
+        idx_rdm = random.sample(range(len(Gn)), nb_median)
+        print('graphs chosen:', idx_rdm)
+        Gn_median = [Gn[idx].copy() for idx in idx_rdm]
+        
+#        for g in Gn_median:
+#            nx.draw(g, labels=nx.get_node_attributes(g, 'atom'), with_labels=True)
+##            plt.savefig("results/preimage_mix/mutag.png", format="PNG")
+#            plt.show()
+#            plt.clf()                         
+                    
+        ###################################################################
+        gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm.npz')
+        km_tmp = gmfile['gm']
+        time_km = gmfile['gmtime']
+        # modify mixed gram matrix.
+        km = np.zeros((len(Gn) + nb_median, len(Gn) + nb_median))
+        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                km[i, j] = km_tmp[i, j]
+                km[j, i] = km[i, j]
+        for i in range(len(Gn)):
+            for j, idx in enumerate(idx_rdm):
+                km[i, len(Gn) + j] = km[i, idx]
+                km[len(Gn) + j, i] = km[i, idx]
+        for i, idx1 in enumerate(idx_rdm):
+            for j, idx2 in enumerate(idx_rdm):
+                km[len(Gn) + i, len(Gn) + j] = km[idx1, idx2]
+                
+        ###################################################################
+        alpha_range = [1 / nb_median] * nb_median
+        
+        time_list.append([])
+        dis_ks_min_list.append([])
+        sod_gs_list.append([])
+        sod_gs_min_list.append([])
+        nb_updated_list_iam.append([])
+        nb_updated_list_random.append([])
+        nb_updated_k_list_iam.append([])
+        nb_updated_k_list_random.append([])
+        g_best.append([])   
+        
+        for k in k_range:
+            print('\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n')
+            print('k =', k)
+            time0 = time.time()
+            dhat, ghat_list, dis_of_each_itr, nb_updated_iam, nb_updated_random, \
+                nb_updated_k_iam, nb_updated_k_random = \
+                preimage_iam_random_mix(Gn, Gn_median,
+                alpha_range, range(len(Gn), len(Gn) + nb_median), km, k, r_max, 
+                l_max, gkernel, epsilon=epsilon, InitIAMWithAllDk=InitIAMWithAllDk, 
+                InitRandomWithAllDk=InitRandomWithAllDk,
+                params_iam={'c_ei': c_ei, 'c_er': c_er, 'c_es': c_es, 
+                            'ite_max': ite_max_iam, 'epsilon': epsilon_iam,
+                            'removeNodes': removeNodes, 'connected': connected_iam},
+                params_ged={'ged_cost': ged_cost, 'ged_method': ged_method, 
+                            'saveGXL': saveGXL})
+                
+            time_total = time.time() - time0 + time_km
+            print('time: ', time_total)
+            time_list[idx_nb].append(time_total)
+            print('\nsmallest distance in kernel space: ', dhat) 
+            dis_ks_min_list[idx_nb].append(dhat)
+            g_best[idx_nb].append(ghat_list)
+            print('\nnumber of updates of the best graph by IAM: ', nb_updated_iam)
+            nb_updated_list_iam[idx_nb].append(nb_updated_iam)
+            print('\nnumber of updates of the best graph by random generation: ', 
+                  nb_updated_random)
+            nb_updated_list_random[idx_nb].append(nb_updated_random)
+            print('\nnumber of updates of k nearest graphs by IAM: ', nb_updated_k_iam)
+            nb_updated_k_list_iam[idx_nb].append(nb_updated_k_iam)
+            print('\nnumber of updates of k nearest graphs by random generation: ', 
+                  nb_updated_k_random)
+            nb_updated_k_list_random[idx_nb].append(nb_updated_k_random) 
+            
+            # show the best graph and save it to file.
+            print('the shortest distance is', dhat)
+            print('one of the possible corresponding pre-images is')
+            nx.draw(ghat_list[0], labels=nx.get_node_attributes(ghat_list[0], 'atom'), 
+                    with_labels=True)
+            plt.savefig('results/preimage_mix/mutag_median_nb' + str(nb_median) + 
+                        '_k' + str(k) + '.png', format="PNG")
+    #        plt.show()
+            plt.clf()
+    #        print(ghat_list[0].nodes(data=True))
+    #        print(ghat_list[0].edges(data=True))
+        
+            # compute the corresponding sod in graph space.
+            sod_tmp, _ = ged_median([ghat_list[0]], Gn_median, ged_cost=ged_cost, 
+                                         ged_method=ged_method, saveGXL=saveGXL)
+            sod_gs_list[idx_nb].append(sod_tmp)
+            sod_gs_min_list[idx_nb].append(np.min(sod_tmp))
+            print('\nsmallest sod in graph space: ', np.min(sod_tmp))
+        
+    print('\nsods in graph space: ', sod_gs_list)
+    print('\nsmallest sod in graph space for each set of median graphs and k: ', 
+          sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each set of median graphs and k: ', 
+          dis_ks_min_list) 
+    print('\nnumber of updates of the best graph for each set of median graphs and k by IAM: ', 
+          nb_updated_list_iam)
+    print('\nnumber of updates of the best graph for each set of median graphs and k by random generation: ', 
+          nb_updated_list_random)
+    print('\nnumber of updates of k nearest graphs for each set of median graphs and k by IAM: ', 
+          nb_updated_k_list_iam)
+    print('\nnumber of updates of k nearest graphs for each set of median graphs and k by random generation: ', 
+          nb_updated_k_list_random)
+    print('\ntimes:', time_list)
+    
+    
+
+
+###############################################################################
+# tests on different numbers of median-sets.
+
+def test_preimage_mix_median_nb():
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:50]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    
+    lmbda = 0.03 # termination probalility
+    r_max = 5 # iteration limit for pre-image.
+    l_max = 500 # update limit for random generation
+#    alpha_range = np.linspace(0.5, 0.5, 1)
+    k = 5 # k nearest neighbors
+    epsilon = 1e-6
+    InitIAMWithAllDk = True
+    InitRandomWithAllDk = True
+    # parameters for GED function
+    ged_cost='CHEM_1'
+    ged_method='IPFP'
+    saveGXL='gedlib'
+    # parameters for IAM function
+    c_ei=1
+    c_er=1
+    c_es=1
+    ite_max_iam = 50
+    epsilon_iam = 0.001
+    removeNodes = True
+    connected_iam = False
+    
+    # number of graphs; we what to compute the median of these graphs. 
+    nb_median_range = [2, 3, 4, 5, 10, 20, 30, 40, 50, 100]
+    
+    # find out all the graphs classified to positive group 1.
+    idx_dict = get_same_item_indices(y_all)
+    Gn = [Gn[i] for i in idx_dict[1]]
+    
+#    # compute Gram matrix.
+#    time0 = time.time()
+#    km = compute_kernel(Gn, gkernel, True)
+#    time_km = time.time() - time0    
+#    # write Gram matrix to file.
+#    np.savez('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm', gm=km, gmtime=time_km)
+        
+    
+    time_list = []
+    dis_ks_min_list = []
+    sod_gs_list = []
+    sod_gs_min_list = []
+    nb_updated_list_iam = []
+    nb_updated_list_random = []
+    nb_updated_k_list_iam = []
+    nb_updated_k_list_random = []
+    g_best = []
+    for nb_median in nb_median_range:
+        print('\n-------------------------------------------------------')
+        print('number of median graphs =', nb_median)
+        random.seed(1)
+        idx_rdm = random.sample(range(len(Gn)), nb_median)
+        print('graphs chosen:', idx_rdm)
+        Gn_median = [Gn[idx].copy() for idx in idx_rdm]
+        
+#        for g in Gn_median:
+#            nx.draw(g, labels=nx.get_node_attributes(g, 'atom'), with_labels=True)
+##            plt.savefig("results/preimage_mix/mutag.png", format="PNG")
+#            plt.show()
+#            plt.clf()                         
+                    
+        ###################################################################
+        gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm.npz')
+        km_tmp = gmfile['gm']
+        time_km = gmfile['gmtime']
+        # modify mixed gram matrix.
+        km = np.zeros((len(Gn) + nb_median, len(Gn) + nb_median))
+        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                km[i, j] = km_tmp[i, j]
+                km[j, i] = km[i, j]
+        for i in range(len(Gn)):
+            for j, idx in enumerate(idx_rdm):
+                km[i, len(Gn) + j] = km[i, idx]
+                km[len(Gn) + j, i] = km[i, idx]
+        for i, idx1 in enumerate(idx_rdm):
+            for j, idx2 in enumerate(idx_rdm):
+                km[len(Gn) + i, len(Gn) + j] = km[idx1, idx2]
+                
+        ###################################################################
+        alpha_range = [1 / nb_median] * nb_median
+        time0 = time.time()
+        dhat, ghat_list, dis_of_each_itr, nb_updated_iam, nb_updated_random, \
+            nb_updated_k_iam, nb_updated_k_random = \
+            preimage_iam_random_mix(Gn, Gn_median,
+            alpha_range, range(len(Gn), len(Gn) + nb_median), km, k, r_max, 
+            l_max, gkernel, epsilon=epsilon, InitIAMWithAllDk=InitIAMWithAllDk, 
+            InitRandomWithAllDk=InitRandomWithAllDk,
+            params_iam={'c_ei': c_ei, 'c_er': c_er, 'c_es': c_es, 
+                        'ite_max': ite_max_iam, 'epsilon': epsilon_iam,
+                        'removeNodes': removeNodes, 'connected': connected_iam},
+            params_ged={'ged_cost': ged_cost, 'ged_method': ged_method, 
+                        'saveGXL': saveGXL})
+            
+        time_total = time.time() - time0 + time_km
+        print('time: ', time_total)
+        time_list.append(time_total)
+        print('\nsmallest distance in kernel space: ', dhat) 
+        dis_ks_min_list.append(dhat)
+        g_best.append(ghat_list)
+        print('\nnumber of updates of the best graph by IAM: ', nb_updated_iam)
+        nb_updated_list_iam.append(nb_updated_iam)
+        print('\nnumber of updates of the best graph by random generation: ', 
+              nb_updated_random)
+        nb_updated_list_random.append(nb_updated_random)
+        print('\nnumber of updates of k nearest graphs by IAM: ', nb_updated_k_iam)
+        nb_updated_k_list_iam.append(nb_updated_k_iam)
+        print('\nnumber of updates of k nearest graphs by random generation: ', 
+              nb_updated_k_random)
+        nb_updated_k_list_random.append(nb_updated_k_random) 
+        
+        # show the best graph and save it to file.
+        print('the shortest distance is', dhat)
+        print('one of the possible corresponding pre-images is')
+        nx.draw(ghat_list[0], labels=nx.get_node_attributes(ghat_list[0], 'atom'), 
+                with_labels=True)
+        plt.savefig('results/preimage_mix/mutag_median_nb' + str(nb_median) + 
+                    '.png', format="PNG")
+#        plt.show()
+        plt.clf()
+#        print(ghat_list[0].nodes(data=True))
+#        print(ghat_list[0].edges(data=True))
+    
+        # compute the corresponding sod in graph space.
+        sod_tmp, _ = ged_median([ghat_list[0]], Gn_median, ged_cost=ged_cost, 
+                                     ged_method=ged_method, saveGXL=saveGXL)
+        sod_gs_list.append(sod_tmp)
+        sod_gs_min_list.append(np.min(sod_tmp))
+        print('\nsmallest sod in graph space: ', np.min(sod_tmp))
+        
+    print('\nsods in graph space: ', sod_gs_list)
+    print('\nsmallest sod in graph space for each set of median graphs: ', sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each set of median graphs: ', 
+          dis_ks_min_list) 
+    print('\nnumber of updates of the best graph for each set of median graphs by IAM: ', 
+          nb_updated_list_iam)
+    print('\nnumber of updates of the best graph for each set of median graphs by random generation: ', 
+          nb_updated_list_random)
+    print('\nnumber of updates of k nearest graphs for each set of median graphs by IAM: ', 
+          nb_updated_k_list_iam)
+    print('\nnumber of updates of k nearest graphs for each set of median graphs by random generation: ', 
+          nb_updated_k_list_random)
+    print('\ntimes:', time_list)
+    
+    
+
+###############################################################################
+# test on the combination of the two randomly chosen graphs. (the same as in the
+# random pre-image paper.)
+
+def test_preimage_mix_2combination_all_pairs():
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:50]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    
+    lmbda = 0.03 # termination probalility
+    r_max = 10 # iteration limit for pre-image.
+    l_max = 500 # update limit for random generation
+    alpha_range = np.linspace(0.5, 0.5, 1)
+    k = 5 # k nearest neighbors
+    epsilon = 1e-6
+    InitIAMWithAllDk = True
+    InitRandomWithAllDk = True
+    # parameters for GED function
+    ged_cost='CHEM_1'
+    ged_method='IPFP'
+    saveGXL='gedlib'
+    # parameters for IAM function
+    c_ei=1
+    c_er=1
+    c_es=1
+    ite_max_iam = 50
+    epsilon_iam = 0.001
+    removeNodes = True
+    connected_iam = False
+    
+    nb_update_mat_iam = np.full((len(Gn), len(Gn)), np.inf)
+    nb_update_mat_random = np.full((len(Gn), len(Gn)), np.inf)
+    # test on each pair of graphs.
+#    for idx1 in range(len(Gn) - 1, -1, -1):
+#        for idx2 in range(idx1, -1, -1):
+    for idx1 in range(187, 188):
+        for idx2 in range(167, 168):
+            g1 = Gn[idx1].copy()
+            g2 = Gn[idx2].copy()
+        #    Gn[10] = []
+        #    Gn[10] = []
+            
+            nx.draw(g1, labels=nx.get_node_attributes(g1, 'atom'), with_labels=True)
+            plt.savefig("results/preimage_mix/mutag187.png", format="PNG")
+            plt.show()
+            plt.clf()
+            nx.draw(g2, labels=nx.get_node_attributes(g2, 'atom'), with_labels=True)
+            plt.savefig("results/preimage_mix/mutag167.png", format="PNG")
+            plt.show()
+            plt.clf()
+
+            ###################################################################            
+#            Gn_mix = [g.copy() for g in Gn]
+#            Gn_mix.append(g1.copy())
+#            Gn_mix.append(g2.copy())
+#            
+#            # compute
+#            time0 = time.time()
+#            km = compute_kernel(Gn_mix, gkernel, True)
+#            time_km = time.time() - time0
+#            
+#            # write Gram matrix to file and read it.
+#            np.savez('results/gram_matrix_uhpath_itr7_pq0.8.gm', gm=km, gmtime=time_km)
+            
+            ###################################################################
+            gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03.gm.npz')
+            km = gmfile['gm']
+            time_km = gmfile['gmtime']
+            # modify mixed gram matrix.
+            for i in range(len(Gn)):
+                km[i, len(Gn)] = km[i, idx1]
+                km[i, len(Gn) + 1] = km[i, idx2]
+                km[len(Gn), i] = km[i, idx1]
+                km[len(Gn) + 1, i] = km[i, idx2]
+            km[len(Gn), len(Gn)] = km[idx1, idx1]
+            km[len(Gn), len(Gn) + 1] = km[idx1, idx2]
+            km[len(Gn) + 1, len(Gn)] = km[idx2, idx1]
+            km[len(Gn) + 1, len(Gn) + 1] = km[idx2, idx2]
+            
+            ###################################################################
+#            # use only the two graphs in median set as candidates.
+#            Gn = [g1.copy(), g2.copy()]
+#            Gn_mix = Gn + [g1.copy(), g2.copy()]
+#            # compute         
+#            time0 = time.time()
+#            km = compute_kernel(Gn_mix, gkernel, True)
+#            time_km = time.time() - time0
+    
+            
+            time_list = []
+            dis_ks_min_list = []
+            sod_gs_list = []
+            sod_gs_min_list = []
+            nb_updated_list_iam = []
+            nb_updated_list_random = []
+            nb_updated_k_list_iam = []
+            nb_updated_k_list_random = []
+            g_best = []
+            # for each alpha
+            for alpha in alpha_range:
+                print('\n-------------------------------------------------------\n')
+                print('alpha =', alpha)
+                time0 = time.time()
+                dhat, ghat_list, dis_of_each_itr, nb_updated_iam, nb_updated_random, \
+                    nb_updated_k_iam, nb_updated_k_random = \
+                    preimage_iam_random_mix(Gn, [g1, g2],
+                    [alpha, 1 - alpha], range(len(Gn), len(Gn) + 2), km, k, r_max, 
+                    l_max, gkernel, epsilon=epsilon, InitIAMWithAllDk=InitIAMWithAllDk, 
+                    InitRandomWithAllDk=InitRandomWithAllDk,
+                    params_iam={'c_ei': c_ei, 'c_er': c_er, 'c_es': c_es, 
+                                'ite_max': ite_max_iam, 'epsilon': epsilon_iam,
+                                'removeNodes': removeNodes, 'connected': connected_iam},
+                    params_ged={'ged_cost': ged_cost, 'ged_method': ged_method, 
+                                'saveGXL': saveGXL})
+                time_total = time.time() - time0 + time_km
+                print('time: ', time_total)
+                time_list.append(time_total)
+                dis_ks_min_list.append(dhat)
+                g_best.append(ghat_list)
+                nb_updated_list_iam.append(nb_updated_iam)       
+                nb_updated_list_random.append(nb_updated_random)
+                nb_updated_k_list_iam.append(nb_updated_k_iam)       
+                nb_updated_k_list_random.append(nb_updated_k_random) 
+                
+            # show best graphs and save them to file.
+            for idx, item in enumerate(alpha_range):
+                print('when alpha is', item, 'the shortest distance is', dis_ks_min_list[idx])
+                print('one of the possible corresponding pre-images is')
+                nx.draw(g_best[idx][0], labels=nx.get_node_attributes(g_best[idx][0], 'atom'), 
+                        with_labels=True)
+                plt.savefig('results/preimage_mix/mutag' + str(idx1) + '_' + str(idx2) 
+                            + '_alpha' + str(item) + '.png', format="PNG")
+#                plt.show()
+                plt.clf()
+#                print(g_best[idx][0].nodes(data=True))
+#                print(g_best[idx][0].edges(data=True))
+                
+        #        for g in g_best[idx]:
+        #            draw_Letter_graph(g, savepath='results/gk_iam/')
+        ##            nx.draw_networkx(g)
+        ##            plt.show()
+        #            print(g.nodes(data=True))
+        #            print(g.edges(data=True))
+                    
+            # compute the corresponding sod in graph space.
+            for idx, item in enumerate(alpha_range):
+                sod_tmp, _ = ged_median([g_best[0]], [g1, g2], ged_cost=ged_cost, 
+                                             ged_method=ged_method, saveGXL=saveGXL)
+                sod_gs_list.append(sod_tmp)
+                sod_gs_min_list.append(np.min(sod_tmp))
+                
+            print('\nsods in graph space: ', sod_gs_list)
+            print('\nsmallest sod in graph space for each alpha: ', sod_gs_min_list)  
+            print('\nsmallest distance in kernel space for each alpha: ', dis_ks_min_list) 
+            print('\nnumber of updates of the best graph for each alpha by IAM: ', nb_updated_list_iam)
+            print('\nnumber of updates of the best graph for each alpha by random generation: ', 
+                  nb_updated_list_random)
+            print('\nnumber of updates of k nearest graphs for each alpha by IAM: ', 
+                  nb_updated_k_list_iam)
+            print('\nnumber of updates of k nearest graphs for each alpha by random generation: ', 
+                  nb_updated_k_list_random)
+            print('\ntimes:', time_list)
+            nb_update_mat_iam[idx1, idx2] = nb_updated_list_iam[0]
+            nb_update_mat_random[idx1, idx2] = nb_updated_list_random[0]
+            
+            str_fw = 'graphs %d and %d: %d times by IAM, %d times by random generation.\n' \
+                % (idx1, idx2, nb_updated_list_iam[0], nb_updated_list_random[0])
+            with open('results/preimage_mix/nb_updates.txt', 'r+') as file:
+                content = file.read()
+                file.seek(0, 0)
+                file.write(str_fw + content)
+    
+###############################################################################
+
+    
+if __name__ == '__main__':
+###############################################################################
+# test on the combination of the two randomly chosen graphs. (the same as in the
+# random pre-image paper.)
+#    test_preimage_mix_2combination_all_pairs()
+    
+###############################################################################
+# tests on different numbers of median-sets.
+#    test_preimage_mix_median_nb()
+    
+###############################################################################
+# tests on different values on grid of median-sets and k.
+    test_preimage_mix_grid_k_median_nb()

preimage/test_preimage_random.py

@@ -0,0 +1,402 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Sep  5 15:59:00 2019
+
+@author: ljia
+"""
+
+import numpy as np
+import networkx as nx
+import matplotlib.pyplot as plt
+import time
+import random
+#from tqdm import tqdm
+
+#import os
+import sys
+sys.path.insert(0, "../")
+from pygraph.utils.graphfiles import loadDataset
+
+from preimage_random import preimage_random
+from ged import ged_median
+from utils import compute_kernel, get_same_item_indices, remove_edges
+
+
+###############################################################################
+# tests on different values on grid of median-sets and k.
+
+def test_preimage_random_grid_k_median_nb():    
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:50]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    
+    lmbda = 0.03 # termination probalility
+    r_max = 5 # iteration limit for pre-image.
+    l = 500 # update limit for random generation
+#    alpha_range = np.linspace(0.5, 0.5, 1)
+#    k = 5 # k nearest neighbors
+    # parameters for GED function
+    ged_cost='CHEM_1'
+    ged_method='IPFP'
+    saveGXL='gedlib'
+    
+    # number of graphs; we what to compute the median of these graphs. 
+    nb_median_range = [2, 3, 4, 5, 10, 20, 30, 40, 50, 100]
+    # number of nearest neighbors.
+    k_range = [5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100]
+    
+    # find out all the graphs classified to positive group 1.
+    idx_dict = get_same_item_indices(y_all)
+    Gn = [Gn[i] for i in idx_dict[1]]
+    
+#    # compute Gram matrix.
+#    time0 = time.time()
+#    km = compute_kernel(Gn, gkernel, True)
+#    time_km = time.time() - time0    
+#    # write Gram matrix to file.
+#    np.savez('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm', gm=km, gmtime=time_km)
+        
+    
+    time_list = []
+    dis_ks_min_list = []
+    sod_gs_list = []
+    sod_gs_min_list = []
+    nb_updated_list = []
+    g_best = []
+    for idx_nb, nb_median in enumerate(nb_median_range):
+        print('\n-------------------------------------------------------')
+        print('number of median graphs =', nb_median)
+        random.seed(1)
+        idx_rdm = random.sample(range(len(Gn)), nb_median)
+        print('graphs chosen:', idx_rdm)
+        Gn_median = [Gn[idx].copy() for idx in idx_rdm]
+        
+#        for g in Gn_median:
+#            nx.draw(g, labels=nx.get_node_attributes(g, 'atom'), with_labels=True)
+##            plt.savefig("results/preimage_mix/mutag.png", format="PNG")
+#            plt.show()
+#            plt.clf()                         
+                    
+        ###################################################################
+        gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm.npz')
+        km_tmp = gmfile['gm']
+        time_km = gmfile['gmtime']
+        # modify mixed gram matrix.
+        km = np.zeros((len(Gn) + nb_median, len(Gn) + nb_median))
+        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                km[i, j] = km_tmp[i, j]
+                km[j, i] = km[i, j]
+        for i in range(len(Gn)):
+            for j, idx in enumerate(idx_rdm):
+                km[i, len(Gn) + j] = km[i, idx]
+                km[len(Gn) + j, i] = km[i, idx]
+        for i, idx1 in enumerate(idx_rdm):
+            for j, idx2 in enumerate(idx_rdm):
+                km[len(Gn) + i, len(Gn) + j] = km[idx1, idx2]
+                
+        ###################################################################
+        alpha_range = [1 / nb_median] * nb_median
+        
+        time_list.append([])
+        dis_ks_min_list.append([])
+        sod_gs_list.append([])
+        sod_gs_min_list.append([])
+        nb_updated_list.append([])
+        g_best.append([])   
+        
+        for k in k_range:
+            print('\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n')
+            print('k =', k)
+            time0 = time.time()
+            dhat, ghat, nb_updated = preimage_random(Gn, Gn_median, alpha_range, 
+                range(len(Gn), len(Gn) + nb_median), km, k, r_max, l, gkernel)
+                
+            time_total = time.time() - time0 + time_km
+            print('time: ', time_total)
+            time_list[idx_nb].append(time_total)
+            print('\nsmallest distance in kernel space: ', dhat) 
+            dis_ks_min_list[idx_nb].append(dhat)
+            g_best[idx_nb].append(ghat)
+            print('\nnumber of updates of the best graph: ', nb_updated)
+            nb_updated_list[idx_nb].append(nb_updated)
+            
+            # show the best graph and save it to file.
+            print('the shortest distance is', dhat)
+            print('one of the possible corresponding pre-images is')
+            nx.draw(ghat, labels=nx.get_node_attributes(ghat, 'atom'), 
+                    with_labels=True)
+            plt.savefig('results/preimage_random/mutag_median_nb' + str(nb_median) + 
+                        '_k' + str(k) + '.png', format="PNG")
+    #        plt.show()
+            plt.clf()
+    #        print(ghat_list[0].nodes(data=True))
+    #        print(ghat_list[0].edges(data=True))
+        
+            # compute the corresponding sod in graph space.
+            sod_tmp, _ = ged_median([ghat], Gn_median, ged_cost=ged_cost, 
+                                         ged_method=ged_method, saveGXL=saveGXL)
+            sod_gs_list[idx_nb].append(sod_tmp)
+            sod_gs_min_list[idx_nb].append(np.min(sod_tmp))
+            print('\nsmallest sod in graph space: ', np.min(sod_tmp))
+        
+    print('\nsods in graph space: ', sod_gs_list)
+    print('\nsmallest sod in graph space for each set of median graphs and k: ', 
+          sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each set of median graphs and k: ', 
+          dis_ks_min_list) 
+    print('\nnumber of updates of the best graph for each set of median graphs and k by IAM: ', 
+          nb_updated_list)
+    print('\ntimes:', time_list)
+    
+
+
+
+###############################################################################
+# tests on different numbers of median-sets.
+
+def test_preimage_random_median_nb():
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:50]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    
+    lmbda = 0.03 # termination probalility
+    r_max = 5 # iteration limit for pre-image.
+    l = 500 # update limit for random generation
+#    alpha_range = np.linspace(0.5, 0.5, 1)
+    k = 5 # k nearest neighbors
+    # parameters for GED function
+    ged_cost='CHEM_1'
+    ged_method='IPFP'
+    saveGXL='gedlib'
+    
+    # number of graphs; we what to compute the median of these graphs. 
+    nb_median_range = [2, 3, 4, 5, 10, 20, 30, 40, 50, 100]
+    
+    # find out all the graphs classified to positive group 1.
+    idx_dict = get_same_item_indices(y_all)
+    Gn = [Gn[i] for i in idx_dict[1]]
+    
+#    # compute Gram matrix.
+#    time0 = time.time()
+#    km = compute_kernel(Gn, gkernel, True)
+#    time_km = time.time() - time0    
+#    # write Gram matrix to file.
+#    np.savez('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm', gm=km, gmtime=time_km)
+        
+    
+    time_list = []
+    dis_ks_min_list = []
+    sod_gs_list = []
+    sod_gs_min_list = []
+    nb_updated_list = []
+    g_best = []
+    for nb_median in nb_median_range:
+        print('\n-------------------------------------------------------')
+        print('number of median graphs =', nb_median)
+        random.seed(1)
+        idx_rdm = random.sample(range(len(Gn)), nb_median)
+        print('graphs chosen:', idx_rdm)
+        Gn_median = [Gn[idx].copy() for idx in idx_rdm]
+        
+#        for g in Gn_median:
+#            nx.draw(g, labels=nx.get_node_attributes(g, 'atom'), with_labels=True)
+##            plt.savefig("results/preimage_mix/mutag.png", format="PNG")
+#            plt.show()
+#            plt.clf()                         
+                    
+        ###################################################################
+        gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03_mutag_positive.gm.npz')
+        km_tmp = gmfile['gm']
+        time_km = gmfile['gmtime']
+        # modify mixed gram matrix.
+        km = np.zeros((len(Gn) + nb_median, len(Gn) + nb_median))
+        for i in range(len(Gn)):
+            for j in range(i, len(Gn)):
+                km[i, j] = km_tmp[i, j]
+                km[j, i] = km[i, j]
+        for i in range(len(Gn)):
+            for j, idx in enumerate(idx_rdm):
+                km[i, len(Gn) + j] = km[i, idx]
+                km[len(Gn) + j, i] = km[i, idx]
+        for i, idx1 in enumerate(idx_rdm):
+            for j, idx2 in enumerate(idx_rdm):
+                km[len(Gn) + i, len(Gn) + j] = km[idx1, idx2]
+                
+        ###################################################################
+        alpha_range = [1 / nb_median] * nb_median
+        time0 = time.time()
+        dhat, ghat, nb_updated = preimage_random(Gn, Gn_median, alpha_range, 
+            range(len(Gn), len(Gn) + nb_median), km, k, r_max, l, gkernel)
+            
+        time_total = time.time() - time0 + time_km
+        print('time: ', time_total)
+        time_list.append(time_total)
+        print('\nsmallest distance in kernel space: ', dhat) 
+        dis_ks_min_list.append(dhat)
+        g_best.append(ghat)
+        print('\nnumber of updates of the best graph: ', nb_updated)
+        nb_updated_list.append(nb_updated)
+        
+        # show the best graph and save it to file.
+        print('the shortest distance is', dhat)
+        print('one of the possible corresponding pre-images is')
+        nx.draw(ghat, labels=nx.get_node_attributes(ghat, 'atom'), 
+                with_labels=True)
+        plt.savefig('results/preimage_random/mutag_median_nb' + str(nb_median) + 
+                    '.png', format="PNG")
+#        plt.show()
+        plt.clf()
+#        print(ghat_list[0].nodes(data=True))
+#        print(ghat_list[0].edges(data=True))
+    
+        # compute the corresponding sod in graph space.
+        sod_tmp, _ = ged_median([ghat], Gn_median, ged_cost=ged_cost, 
+                                     ged_method=ged_method, saveGXL=saveGXL)
+        sod_gs_list.append(sod_tmp)
+        sod_gs_min_list.append(np.min(sod_tmp))
+        print('\nsmallest sod in graph space: ', np.min(sod_tmp))
+        
+    print('\nsods in graph space: ', sod_gs_list)
+    print('\nsmallest sod in graph space for each set of median graphs: ', sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each set of median graphs: ', 
+          dis_ks_min_list) 
+    print('\nnumber of updates of the best graph for each set of median graphs: ', 
+          nb_updated_list)
+    print('\ntimes:', time_list)
+    
+    
+
+###############################################################################
+# test on the combination of the two randomly chosen graphs. (the same as in the
+# random pre-image paper.)
+    
+def test_random_preimage_2combination():
+    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG_A.txt',
+          'extra_params': {}}  # node/edge symb
+    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])
+#    Gn = Gn[0:12]
+    remove_edges(Gn)
+    gkernel = 'marginalizedkernel'
+    
+#    dis_mat, dis_max, dis_min, dis_mean = kernel_distance_matrix(Gn, gkernel=gkernel)
+#    print(dis_max, dis_min, dis_mean)
+    
+    lmbda = 0.03 # termination probalility
+    r_max = 10 # iteration limit for pre-image.
+    l = 500
+    alpha_range = np.linspace(0, 1, 11)
+    k = 5 # k nearest neighbors
+    
+    # randomly select two molecules
+    np.random.seed(1)
+    idx_gi = [187, 167] # np.random.randint(0, len(Gn), 2)
+    g1 = Gn[idx_gi[0]].copy()
+    g2 = Gn[idx_gi[1]].copy()
+    
+#    nx.draw(g1, labels=nx.get_node_attributes(g1, 'atom'), with_labels=True)
+#    plt.savefig("results/random_preimage/mutag10.png", format="PNG")
+#    plt.show()
+#    nx.draw(g2, labels=nx.get_node_attributes(g2, 'atom'), with_labels=True)
+#    plt.savefig("results/random_preimage/mutag11.png", format="PNG")
+#    plt.show()    
+    
+    ######################################################################
+#    Gn_mix = [g.copy() for g in Gn]
+#    Gn_mix.append(g1.copy())
+#    Gn_mix.append(g2.copy())
+#    
+##    g_tmp = iam([g1, g2])
+##    nx.draw_networkx(g_tmp)
+##    plt.show()
+#    
+#    # compute 
+#    time0 = time.time()
+#    km = compute_kernel(Gn_mix, gkernel, True)
+#    time_km = time.time() - time0
+    
+    ###################################################################
+    idx1 = idx_gi[0]
+    idx2 = idx_gi[1]
+    gmfile = np.load('results/gram_matrix_marg_itr10_pq0.03.gm.npz')
+    km = gmfile['gm']
+    time_km = gmfile['gmtime']
+    # modify mixed gram matrix.
+    for i in range(len(Gn)):
+        km[i, len(Gn)] = km[i, idx1]
+        km[i, len(Gn) + 1] = km[i, idx2]
+        km[len(Gn), i] = km[i, idx1]
+        km[len(Gn) + 1, i] = km[i, idx2]
+    km[len(Gn), len(Gn)] = km[idx1, idx1]
+    km[len(Gn), len(Gn) + 1] = km[idx1, idx2]
+    km[len(Gn) + 1, len(Gn)] = km[idx2, idx1]
+    km[len(Gn) + 1, len(Gn) + 1] = km[idx2, idx2]
+            
+    ###################################################################
+
+    time_list = []
+    nb_updated_list = []
+    g_best = []
+    dis_ks_min_list = []
+    # for each alpha
+    for alpha in alpha_range:
+        print('\n-------------------------------------------------------\n')
+        print('alpha =', alpha)
+        time0 = time.time()
+        dhat, ghat, nb_updated = preimage_random(Gn, [g1, g2], [alpha, 1 - alpha], 
+                                          range(len(Gn), len(Gn) + 2), km,
+                                          k, r_max, l, gkernel)
+        time_total = time.time() - time0 + time_km
+        print('time: ', time_total)
+        time_list.append(time_total)
+        dis_ks_min_list.append(dhat)
+        g_best.append(ghat)
+        nb_updated_list.append(nb_updated)
+        
+    # show best graphs and save them to file.
+    for idx, item in enumerate(alpha_range):
+        print('when alpha is', item, 'the shortest distance is', dis_ks_min_list[idx])
+        print('one of the possible corresponding pre-images is')
+        nx.draw(g_best[idx], labels=nx.get_node_attributes(g_best[idx], 'atom'), 
+                with_labels=True)
+        plt.show()
+        plt.savefig('results/random_preimage/mutag_alpha' + str(item) + '.png', format="PNG")
+        plt.clf()
+        print(g_best[idx].nodes(data=True))
+        print(g_best[idx].edges(data=True))
+            
+#        # compute the corresponding sod in graph space. (alpha range not considered.)
+#        sod_tmp, _ = median_distance(g_best[0], Gn_let)
+#        sod_gs_list.append(sod_tmp)
+#        sod_gs_min_list.append(np.min(sod_tmp))
+#        sod_ks_min_list.append(sod_ks)
+#        nb_updated_list.append(nb_updated)
+                      
+#    print('\nsmallest sod in graph space for each alpha: ', sod_gs_min_list)  
+    print('\nsmallest distance in kernel space for each alpha: ', dis_ks_min_list) 
+    print('\nnumber of updates for each alpha: ', nb_updated_list)             
+    print('\ntimes:', time_list)
+    
+###############################################################################
+
+    
+if __name__ == '__main__':
+###############################################################################
+# test on the combination of the two randomly chosen graphs. (the same as in the
+# random pre-image paper.)
+#    test_random_preimage_2combination()
+    
+###############################################################################
+# tests all algorithms on different numbers of median-sets.
+    test_preimage_random_median_nb()
+    
+###############################################################################
+# tests all algorithms on different values on grid of median-sets and k.
+#    test_preimage_random_grid_k_median_nb()

preimage/utils.py

@@ -0,0 +1,109 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Oct 17 19:05:07 2019
+
+Useful functions.
+@author: ljia
+"""
+#import networkx as nx
+
+import multiprocessing
+import numpy as np
+
+import sys
+sys.path.insert(0, "../")
+from pygraph.kernels.marginalizedKernel import marginalizedkernel
+from pygraph.kernels.untilHPathKernel import untilhpathkernel
+from pygraph.kernels.spKernel import spkernel
+import functools
+from pygraph.utils.kernels import deltakernel, gaussiankernel, kernelproduct
+from pygraph.kernels.structuralspKernel import structuralspkernel
+
+
+def remove_edges(Gn):
+    for G in Gn:
+        for _, _, attrs in G.edges(data=True):
+            attrs.clear()
+            
+def dis_gstar(idx_g, idx_gi, alpha, Kmatrix, term3=0, withterm3=True):
+    term1 = Kmatrix[idx_g, idx_g]
+    term2 = 0
+    for i, a in enumerate(alpha):
+        term2 += a * Kmatrix[idx_g, idx_gi[i]]
+    term2 *= 2
+    if withterm3 == False:
+        for i1, a1 in enumerate(alpha):
+            for i2, a2 in enumerate(alpha):
+                term3 += a1 * a2 * Kmatrix[idx_gi[i1], idx_gi[i2]]
+    return np.sqrt(term1 - term2 + term3)
+
+
+def compute_kernel(Gn, graph_kernel, verbose):
+    if graph_kernel == 'marginalizedkernel':
+        Kmatrix, _ = marginalizedkernel(Gn, node_label='atom', edge_label=None,
+                                  p_quit=0.03, n_iteration=10, remove_totters=False,
+                                  n_jobs=multiprocessing.cpu_count(), verbose=verbose)
+    elif graph_kernel == 'untilhpathkernel':
+        Kmatrix, _ = untilhpathkernel(Gn, node_label='atom', edge_label=None,
+                                  depth=10, k_func='MinMax', compute_method='trie',
+                                  n_jobs=multiprocessing.cpu_count(), verbose=verbose)
+    elif graph_kernel == 'spkernel':
+        mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+        Kmatrix, _, _ = spkernel(Gn, node_label='atom', node_kernels=
+                              {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel},
+                              n_jobs=multiprocessing.cpu_count(), verbose=verbose)
+    elif graph_kernel == 'structuralspkernel':
+        mixkernel = functools.partial(kernelproduct, deltakernel, gaussiankernel)
+        Kmatrix, _ = structuralspkernel(Gn, node_label='atom', node_kernels=
+                              {'symb': deltakernel, 'nsymb': gaussiankernel, 'mix': mixkernel},
+                              n_jobs=multiprocessing.cpu_count(), verbose=verbose)
+        
+    # normalization
+    Kmatrix_diag = Kmatrix.diagonal().copy()
+    for i in range(len(Kmatrix)):
+        for j in range(i, len(Kmatrix)):
+            Kmatrix[i][j] /= np.sqrt(Kmatrix_diag[i] * Kmatrix_diag[j])
+            Kmatrix[j][i] = Kmatrix[i][j]
+    return Kmatrix
+            
+
+def gram2distances(Kmatrix):
+    dmatrix = np.zeros((len(Kmatrix), len(Kmatrix)))
+    for i1 in range(len(Kmatrix)):
+        for i2 in range(len(Kmatrix)):
+            dmatrix[i1, i2] = Kmatrix[i1, i1] + Kmatrix[i2, i2] - 2 * Kmatrix[i1, i2]
+    dmatrix = np.sqrt(dmatrix)
+    return dmatrix
+
+
+def kernel_distance_matrix(Gn, Kmatrix=None, gkernel=None):
+    dis_mat = np.empty((len(Gn), len(Gn)))
+    if Kmatrix == None:
+        Kmatrix = compute_kernel(Gn, gkernel, True)
+    for i in range(len(Gn)):
+        for j in range(i, len(Gn)):
+            dis = Kmatrix[i, i] + Kmatrix[j, j] - 2 * Kmatrix[i, j]
+            if dis < 0:
+                if dis > -1e-10:
+                    dis = 0
+                else:
+                    raise ValueError('The distance is negative.')
+            dis_mat[i, j] = np.sqrt(dis)
+            dis_mat[j, i] = dis_mat[i, j]
+    dis_max = np.max(np.max(dis_mat))
+    dis_min = np.min(np.min(dis_mat[dis_mat != 0]))
+    dis_mean = np.mean(np.mean(dis_mat))
+    return dis_mat, dis_max, dis_min, dis_mean
+
+
+def get_same_item_indices(ls):
+    """Get the indices of the same items in a list. Return a dict keyed by items.
+    """
+    idx_dict = {}
+    for idx, item in enumerate(ls):
+        if item in idx_dict:
+            idx_dict[item].append(idx)
+        else:
+            idx_dict[item] = [idx]
+    return idx_dict