/
utils.py
140 lines (130 loc) · 3.51 KB
/
utils.py
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import os
import numpy as np
def dist_map(F):
'''
Obtain the matrix V, V_{ij} = ||f_i - f_j||^2_2
'''
N = F.shape[0]
V = np.zeros((N, N))
squ = np.zeros(N)
for i in range(N):
squ[i] = np.linalg.norm(F[i]) ** 2
V_1 = 2 * F @ F.T
for i in range(N):
for j in range(N):
V[i, j] = squ[i] + squ[j] - V_1[i, j]
return V
def obtain_affinity_graph(data, m = 9):
N = data.shape[0]
e = dist_map(data)
idx = np.zeros((N, m + 1))
for i in range(N):
idx[i] = np.argsort(e[i])[:m + 1]
idx = idx.astype(np.int16)
W = np.zeros((N, N))
eps = 1e-8
for i in range(N):
id = idx[i, 1:m + 1]
d = e[i, id]
W[i, id] = (d[m - 1] - d) / (m * d[m - 1] - np.sum(d) + eps)
return W
def simplex_opt(v):
'''
Column Vector :param v:
:return:
'''
n = v.shape[0]
u = v - v.mean() + 1 / n
if np.min(u) < 0:
f = 1
turn = 0
lambda_b = 0
while (abs(f) > 1e-8):
turn += 1
u_1 = u - lambda_b
p_idx = (u_1 > 0)
q_idx = (u_1 < 0)
f = np.sum(np.maximum(-u_1[q_idx], 0)) - n * lambda_b
g = np.sum(q_idx) - n
lambda_b = lambda_b - f / g
if turn > 100:
print("Diverge!!!!")
break
x = np.maximum(u_1, 0)
else:
x = u
return x
def simplex_opt_1(v, k = 30):
'''
Sparse solution for simplex optimization problem.
return:
x: The desired vector.
'''
N = v.shape[0]
idx = np.argsort(v)[::-1][:k]
t_sum = 0
flag = 0
for i in range(k - 1):
t_sum += v[idx[i]]
t_avg = (t_sum - 1) / (i + 1)
if t_avg >= v[idx[i + 1]]:
flag = 1
break
if not flag:
t_avg = (t_sum + v[idx[k - 1]] - 1) / k
mask = np.zeros(v.shape[0])
mask[idx] = 1
x = np.maximum(v - t_avg, 0)
x = x * mask
return x
def get_data(dataset="MSRC_v1"):
dir = "./data/"
data_v = []
for filename in os.listdir(dir):
if filename.split(".")[0] == dataset:
datas = np.load(dir + filename, allow_pickle=True)
data = datas.item()["X"].squeeze()
label = datas.item()["Y"].squeeze()
for i in range(data.shape[0]) :
data1 = data[i].astype(float) # data[i] : feature * sample
data_v.append(data1.T)
if label.shape[0] < 50:
label = label[0].squeeze()
label = label.astype(np.int)
label -= np.min(label)
k = label.max() + 1
print("Data Gotten")
return data_v, label, k
print("Not Found")
def get_laplacian(W, normalization = 1):
'''
W: Adjacency matrix(num_samples*num_samples)
normalization: whether or not apply normalized method.
output:
L: Laplace Matrix
'''
S = (W + W.T) / 2
d = np.sum(S, axis=0)
D = np.diag(np.abs(d))
L = D - S
if normalization == 1:
D_w = np.diag(np.sqrt(1/(d)))
# D_w[D_w > 100] = 0
L = D_w @ L @ D_w
return L
def calc_eigen(L, k):
'''
L: Laplace Matrix
k: Clustering number
output:
lamb: all_lambda (sorted)
F: Eigenvector
'''
# lamb, V = np.linalg.eig(L) # Unstable!
V, lamb, _ = np.linalg.svd(L)
idx = np.argsort(lamb)[:k]
lamb = np.sort(lamb)
F = V[:, idx]
for i in range(F.shape[1]) :
F[:, i] = F[:, i] / np.sqrt(np.sum(F[:, i] ** 2))
return lamb, F