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- import sys
- import pathlib
- sys.path.insert(0, "../")
-
- import networkx as nx
- import numpy as np
- import time
-
- def marginalizedkernel(*args):
- """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
-
- 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(Gn[i], Gn[j], args[1], args[2])
- Kmatrix[j][i] = Kmatrix[i][j]
-
- print("\n --- marginalized kernel matrix of size %d built in %s seconds ---" % (len(Gn), (time.time() - start_time)))
-
- return Kmatrix
-
- else: # for only 2 graphs
-
- # init parameters
- G1 = args[0]
- G2 = args[1]
- p_quit = args[2] # the termination probability in the random walks generating step
- itr = args[3] # time of iterations to calculate R_inf
-
- 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]['label'] == G2.node[neighbor2]['label']) * \
- deltaKernel(neighbor_n1[neighbor1]['label'] == neighbor_n2[neighbor2]['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]['label'] == node2[1]['label'])
- kernel += s * R_inf[node1[0]][node2[0]] # ref [1] equation (6)
-
- return kernel
-
- def deltaKernel(condition):
- """Return 1 if condition holds, 0 otherwise.
-
- Parameters
- ----------
- condition : Boolean
- A condition, according to which the kernel is set to 1 or 0.
-
- Return
- ------
- Kernel : integer
- Delta Kernel.
-
- 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.
- """
- return (1 if condition else 0)
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