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main.py
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main.py
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import numpy as np
import scipy as sp
from scipy.sparse import csr_matrix, identity, linalg
from sklearn.cluster import KMeans
import networkx as nx
import random
# Read file and create adjency, degree, identity, inverse degree and square root degree matrices
def read_graph():
with open("./graphs_part_1/ca-CondMat.txt", "r") as lines:
firstrow = True
rows = []
cols = []
for idx, line in enumerate(lines):
line = line.split()
if firstrow:
# graphID = line[1]
vertices_number = int(line[2])
edges_number = int(line[3])
edges = np.empty((edges_number, 2))
k = int(line[4])
firstrow = False
datad = [0] * vertices_number
else:
rows.append(int(line[0]))
rows.append(int(line[1]))
cols.append(int(line[0]))
cols.append(int(line[1]))
datad[int(line[0])] += 1
datad[int(line[1])] += 1
edges[idx-1] = [int(line[0]),int(line[1])]
data = [1] * len(rows)
A = csr_matrix((data, (rows, cols)))
D = csr_matrix((datad, (list(range(vertices_number)), list(range(vertices_number)))))
return A, D, edges, k, vertices_number, edges_number
def ng_norm(A, sqrt_D, I, k):
L = I - sqrt_D * A * sqrt_D
w, v = linalg.eigs(L, k)
w = np.real(w)
v = np.real(v)
lengths = np.linalg.norm(v, axis=1)
v = v / lengths[:, np.newaxis]
U = v[:,:k] # first K eigenvectors (step 3)
Y = v
return Y, U
def shi_norm(A, inverse_D, D):
L_normal = D - A
L = np.matmul(inverse_D, L_normal) # Random walk normalized Laplacian
w, v = np.linalg.eig(L) #, eigvals=(L.shape[0]-k, L.shape[0]-1)) #biggest eig
U = np.real(v[:, :k]) # first K eigenvectors (step 3)
return U
# cluster U into k clusters
def kmeans(Y, k):
output = KMeans(n_clusters=k, n_jobs=-1).fit_predict(Y)
fittrans = KMeans(n_clusters=k,random_state=0).fit_transform(Y)
return output, fittrans
# objective function
def objective(r, k, edges):
community_dict = {}
size_coms = np.zeros((k))
differentcommunity = 0
for idx, i in enumerate(r):
community_dict[idx] = i
size_coms[i] += 1
for edge in edges:
unode, vnode = int(edge[0]), int(edge[1])
ucom, vcom = community_dict[unode], community_dict[vnode]
if ucom != vcom:
differentcommunity += 1
phi = differentcommunity/np.min(size_coms)
return phi
def sizes(output, k):
sizes = []
for ka in range(k):
k_array = []
for idx, node in enumerate(output):
if node == ka:
k_array.append(idx)
sizes.append(len(k_array))
return sizes
def shuffle_communities(output, vertices_number, fittrans, k, sizes, edges):
ITERACTION_COUNT = 5000
min_phi = objective(output, k, edges)
for i in range(ITERACTION_COUNT):
o = output[:]
a,b = random.sample(range(0, len(output) - 1), 2)
tmp = o[a]
o[a] = o[b]
o[b] = tmp
phi = objective(o, k, edges)
if phi < min_phi:
min_phi = phi
output = o[:]
return output, objective(output, k, edges)
def balance_communities(output, vertices_number, fittrans, k, sizes, edges):
min_phi = objective(output, k, edges)
changed = []
for r in range(round(vertices_number / k)):
for i in range(len(sizes)):
# print(r, i)
if sizes[i] > round(vertices_number / k):
next_index = i + 1 if i < (len(sizes) - 1) else 0
prev_index = i - 1 if i > 0 else len(sizes) - 1
min_err = vertices_number
movement = -1
for j in range(len(output)):
if output[j] == i and j not in changed:
for ij in range(k):
if ij != i and fittrans[j][ij] < min_err:
min_err = fittrans[j][ij]
movement = ij
replace = j
if movement != -1:
changed.append(replace)
output[replace] = movement
sizes[i] -= 1
sizes[movement] += 1
phi = objective(output, k, edges)
if phi < min_phi:
min_phi = phi
min_output = output[:]
cost = objective(output, k, edges)
return min_output, cost
def main():
A, D, edges, k, vertices_number, edges_number = read_graph()
I = identity(vertices_number, format='csc')
inverse_D = linalg.inv(D)
sqrt_D = np.sqrt(inverse_D)
Y, U = ng_norm(A, sqrt_D, I, k)
print(Y)
output, fittrans = kmeans(Y, k)
s = sizes(output, k)
print("Basic spectral algorithm")
print(objective(output, k, edges))
output, cost = balance_communities(output, vertices_number, fittrans, k, s, edges)
with open('ca-CondMat-balanced.txt', 'a') as the_file:
for idx, community in enumerate(output):
the_file.write(str(idx)+" "+str(community)+"\n")
print("Balanced result")
print(cost)
main()