- import sys
- import pathlib
- sys.path.insert(0, "../")
-
- import networkx as nx
- import numpy as np
- import time
-
- from pygraph.kernels.deltaKernel import deltakernel
-
- def marginalizedkernel(*args, node_label = 'atom', edge_label = 'bond_type'):
- """Calculate marginalized graph kernels between graphs.
-
- Parameters
- ----------
- Gn : List of NetworkX graph
- List of graphs between which the kernels are calculated.
- /
- G1, G2 : NetworkX graphs
- 2 graphs between which the kernel is calculated.
- p_quit : integer
- the termination probability in the random walks generating step
- itr : integer
- time of iterations to calculate R_inf
- node_label : string
- node attribute used as label. The default node label is atom.
- edge_label : string
- edge attribute used as label. The default edge label is bond_type.
-
- Return
- ------
- Kmatrix/Kernel : Numpy matrix/int
- Kernel matrix, each element of which is the marginalized kernel between 2 praphs. / Marginalized Kernel between 2 graphs.
-
- References
- ----------
- [1] H. Kashima, K. Tsuda, and A. Inokuchi. Marginalized kernels between labeled graphs. In Proceedings of the 20th International Conference on Machine Learning, Washington, DC, United States, 2003.
- """
- if len(args) == 3: # for a list of graphs
- Gn = args[0]
- Kmatrix = np.zeros((len(Gn), len(Gn)))
-
- start_time = time.time()
-
- for i in range(0, len(Gn)):
- for j in range(i, len(Gn)):
- Kmatrix[i][j] = _marginalizedkernel_do(Gn[i], Gn[j], node_label, edge_label, args[1], args[2])
- Kmatrix[j][i] = Kmatrix[i][j]
-
- run_time = time.time() - start_time
- print("\n --- marginalized kernel matrix of size %d built in %s seconds ---" % (len(Gn), run_time))
-
- return Kmatrix, run_time
-
- else: # for only 2 graphs
-
- start_time = time.time()
-
- kernel = _marginalizedkernel_do(args[0], args[1], node_label, edge_label, args[2], args[3])
-
- run_time = time.time() - start_time
- print("\n --- marginalized kernel built in %s seconds ---" % (run_time))
-
- return kernel, run_time
-
-
- def _marginalizedkernel_do(G1, G2, node_label = 'atom', edge_label = 'bond_type', p_quit, itr):
- """Calculate marginalized graph kernels between 2 graphs.
-
- Parameters
- ----------
- G1, G2 : NetworkX graphs
- 2 graphs between which the kernel is calculated.
- node_label : string
- node attribute used as label. The default node label is atom.
- edge_label : string
- edge attribute used as label. The default edge label is bond_type.
- p_quit : integer
- the termination probability in the random walks generating step
- itr : integer
- time of iterations to calculate R_inf
-
- Return
- ------
- Kernel : int
- Marginalized Kernel between 2 graphs.
- """
- # init parameters
- kernel = 0
- num_nodes_G1 = nx.number_of_nodes(G1)
- num_nodes_G2 = nx.number_of_nodes(G2)
- p_init_G1 = 1 / num_nodes_G1 # the initial probability distribution in the random walks generating step (uniform distribution over |G|)
- p_init_G2 = 1 / num_nodes_G2
-
- q = p_quit * p_quit
- r1 = q
-
- # initial R_inf
- R_inf = np.zeros([num_nodes_G1, num_nodes_G2]) # matrix to save all the R_inf for all pairs of nodes
-
- # calculate R_inf with a simple interative method
- for i in range(1, itr):
- R_inf_new = np.zeros([num_nodes_G1, num_nodes_G2])
- R_inf_new.fill(r1)
-
- # calculate R_inf for each pair of nodes
- for node1 in G1.nodes(data = True):
- neighbor_n1 = G1[node1[0]]
- p_trans_n1 = (1 - p_quit) / len(neighbor_n1) # the transition probability distribution in the random walks generating step (uniform distribution over the vertices adjacent to the current vertex)
- for node2 in G2.nodes(data = True):
- neighbor_n2 = G2[node2[0]]
- p_trans_n2 = (1 - p_quit) / len(neighbor_n2)
-
- for neighbor1 in neighbor_n1:
- for neighbor2 in neighbor_n2:
-
- t = p_trans_n1 * p_trans_n2 * \
- deltakernel(G1.node[neighbor1][node_label] == G2.node[neighbor2][node_label]) * \
- deltakernel(neighbor_n1[neighbor1][edge_label] == neighbor_n2[neighbor2][edge_label])
- R_inf_new[node1[0]][node2[0]] += t * R_inf[neighbor1][neighbor2] # ref [1] equation (8)
-
- R_inf[:] = R_inf_new
-
- # add elements of R_inf up and calculate kernel
- for node1 in G1.nodes(data = True):
- for node2 in G2.nodes(data = True):
- s = p_init_G1 * p_init_G2 * deltakernel(node1[1][node_label] == node2[1][node_label])
- kernel += s * R_inf[node1[0]][node2[0]] # ref [1] equation (6)
-
- return kernel
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