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import numpy as np
import pandas as pd
import networkx
from scipy.sparse import lil_matrix, kron,identity
from scipy.sparse.linalg import lsqr
from sklearn.utils import resample
def norm_mat(adj_mat):
norm = adj_mat.sum(axis=0)
norm[norm == 0] = 1
return adj_mat / norm
def my_kernel(X, Y, lmb):
max_size = int(np.sqrt(X.shape[1]))
RWK = np.zeros([X.shape[0], Y.shape[0]])
step = 10
for i in range(0, X.shape[0]):
for j in range(0, Y.shape[0]):
weighted_sum = 0
am_pg = np.kron(norm_mat(np.reshape(X[i, :], (max_size, max_size))), norm_mat(np.reshape(Y[j, :], (max_size, max_size))))
for k in range(step):
weighted_sum += np.dot(lmb ** k, am_pg ** k)
rwk = weighted_sum.sum()
RWK[i, j] = rwk
return RWK
def random_walk_kernel(X, Y, lmb):
max_size = int(np.sqrt(X.shape[1]))
kernel_matrix = np.zeros([X.shape[0], Y.shape[0]])
step = 10
for i in range(0, X.shape[0]):
g1 = lil_matrix(norm_mat(np.reshape(X[i, :], (max_size, max_size))))
for j in range(0, Y.shape[0]):
g2 = lil_matrix(norm_mat(np.reshape(Y[j, :], (max_size, max_size))))
weighted_sum = 0
am_pg = kron(g1, g2)
for k in range(step):
weighted_sum += (am_pg ** k).dot(lmb ** k)
kernel_matrix[i, j] = weighted_sum.sum()
return kernel_matrix
def random_walk_kernel_1(X, Y, lmb):
max_size = int(np.sqrt(X.shape[1]))
kernel_matrix = np.zeros([X.shape[0], Y.shape[0]])
for i in range(0, X.shape[0]):
g1 = norm_mat(np.reshape(X[i, :], (max_size, max_size)))
for j in range(0, Y.shape[0]):
g2 = norm_mat(np.reshape(Y[j, :], (max_size, max_size)))
w_prod = kron(lil_matrix(g1), lil_matrix(g2))
starting_prob = np.ones(w_prod.shape[0]) / (w_prod.shape[0])
stop_prob = starting_prob
A = identity(w_prod.shape[0]) - (w_prod * lmb)
x = lsqr(A, starting_prob)
kernel_matrix[i, j] = stop_prob.T.dot(x[0])
return kernel_matrix
def compute_kernel_matrix(X, Y, lmb, type):
kernel_matrix = np.zeros([len(X), len(Y)])
for i in range(0, len(X)):
for j in range(0, len(Y)):
if type == "RWK":
kernel_matrix[i, j] = RWK(X[i], Y[j], lmb)
elif type == "RWK_norm":
kernel_matrix[i, j] = RWK_norm(X[i], Y[j], lmb)
elif type == "RWK_1":
kernel_matrix[i, j] = RWK_1(X[i], Y[j], lmb)
elif type == "RWK_1_norm":
kernel_matrix[i, j] = RWK_1_norm(X[i], Y[j], lmb)
return kernel_matrix
def RWK(X, Y, lmb):
step = 10
weighted_sum = 0
g1 = norm_mat(networkx.adjacency_matrix(X))
g2 = norm_mat(networkx.adjacency_matrix(Y))
g_prod = kron(lil_matrix(g1), lil_matrix(g2))
for n in range(step):
weighted_sum += (g_prod ** n).dot(lmb ** n)
k = weighted_sum.sum()
return k
def RWK_norm(X, Y, lmb):
step = 10
weighted_sum = 0
weighted_sum_1 = 0
weighted_sum_2 = 0
g1 = norm_mat(networkx.adjacency_matrix(X))
g2 = norm_mat(networkx.adjacency_matrix(Y))
g_prod = kron(lil_matrix(g1), lil_matrix(g2))
g_prod_1 = kron(lil_matrix(g1), lil_matrix(g1))
g_prod_2 = kron(lil_matrix(g2), lil_matrix(g2))
for n in range(step):
weighted_sum += (g_prod ** n).dot(lmb ** n)
weighted_sum_1 += (g_prod_1 ** n).dot(lmb ** n)
weighted_sum_2 += (g_prod_2 ** n).dot(lmb ** n)
k = weighted_sum.sum()
k_1 = weighted_sum_1.sum()
k_2 = weighted_sum_2.sum()
k_norm = k / np.sqrt(k_1 * k_2)
return k_norm
def RWK_1(X, Y, lmb):
g1 = norm_mat(networkx.adjacency_matrix(X))
g2 = norm_mat(networkx.adjacency_matrix(Y))
g_prod = kron(lil_matrix(g1), lil_matrix(g2))
starting_prob = np.ones(g_prod.shape[0]) / (g_prod.shape[0])
stop_prob = starting_prob
A = identity(g_prod.shape[0]) - (g_prod * lmb)
x = lsqr(A, starting_prob)
k = stop_prob.T.dot(x[0])
return k
def RWK_1_norm(X, Y, lmb):
g1 = norm_mat(networkx.adjacency_matrix(X))
g2 = norm_mat(networkx.adjacency_matrix(Y))
g_prod = kron(lil_matrix(g1), lil_matrix(g2))
g_prod_1 = kron(lil_matrix(g1), lil_matrix(g1))
g_prod_2 = kron(lil_matrix(g2), lil_matrix(g2))
starting_prob = np.ones(g_prod.shape[0]) / (g_prod.shape[0])
starting_prob_1 = np.ones(g_prod_1.shape[0]) / (g_prod_1.shape[0])
starting_prob_2 = np.ones(g_prod_2.shape[0]) / (g_prod_2.shape[0])
stop_prob = starting_prob
stop_prob_1 = starting_prob_1
stop_prob_2 = starting_prob_2
A = identity(g_prod.shape[0]) - (g_prod * lmb)
A_1 = identity(g_prod_1.shape[0]) - (g_prod_1 * lmb)
A_2 = identity(g_prod_2.shape[0]) - (g_prod_2 * lmb)
x = lsqr(A, starting_prob)
x_1 = lsqr(A_1, starting_prob_1)
x_2 = lsqr(A_2, starting_prob_2)
k = stop_prob.T.dot(x[0])
k_1 = stop_prob_1.T.dot(x_1[0])
k_2 = stop_prob_2.T.dot(x_2[0])
k_norm = k / np.sqrt(k_1 * k_2)
return k_norm
def balance_data(G, label, random_state):
graphs = {'CFG': G, 'label': label}
#print(graphs)
df = pd.DataFrame(data=graphs)
if len(df[df.label == -1]) > len(df[df.label == 1]):
df_majority = df[df.label == -1]
df_minority = df[df.label == 1]
else:
df_majority = df[df.label == 1]
df_minority = df[df.label == -1]
df_minority_upsampled = resample(df_minority, replace=True, n_samples=len(df_majority), random_state=random_state)
df_upsampled = pd.concat([df_majority, df_minority_upsampled], ignore_index=True)
data = np.asarray(df['CFG'])
target = np.asarray(df['label'])
return data, target
def rename_nodes(node_label):
n = len(node_label)
print(node_label)
labels = [0] * n
label_lookup = {}
label_counter = 0
for i in range(n):
num_nodes = len(node_label[i])
temp_lables = list(node_label[i])
labels[i] = np.zeros(num_nodes, dtype=np.uint64)
for j in range(num_nodes):
temp_node_str = str(np.copy(temp_lables[j]))
if temp_node_str not in label_lookup:
label_lookup[temp_node_str] = label_counter
labels[i][j] = label_counter
label_counter += 1
else:
labels[i][j] = label_lookup[temp_node_str]
L = label_counter
print('Number of original labels: %d' % L)
return L, labels