def time_measurement(n, m, r, approximate_size, v, iteration, seeds, c_mode,
NMF_or_SNMF):
if NMF_or_SNMF == 0:
# NMF------------------------------------
print("\n\n\n------------------ NMF -------------------")
start = time.time()
w = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h = ff.generate_h(r, m, seeds[1], c_mode=c_mode)
for i in range(0, iteration):
w, h = ff.update(v, w, h, c_mode)
t_result = time.time() - start
print("\nNMF time: " + str(t_result))
else:
# Sketching NMF --------------------------
print("\n\n------------- Sketching NMF --------------")
start = time.time()
v_s = ff.uniform_sampling(v, approximate_size, 0, t=True)
w_s = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r, approximate_size, seeds[1], c_mode=c_mode)
for i in range(0, iteration):
w_s, h_s = ff.update(v_s, w_s, h_s, c_mode)
_ = ff.calculate_h(v, w_s, True)
t_result = time.time() - start
print("\nSketching NMF time: " + str(t_result) + "\n")
return t_result
def v_error_eval(n, m, r, approximate_size, v, iteration, seeds, c_mode, nmfqp,
column_sketching):
nmf_error = np.zeros(iteration)
snmf_error = np.zeros(iteration)
w = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h = ff.generate_h(r, m, seeds[1], c_mode=c_mode)
v_s = ff.uniform_sampling(v,
approximate_size,
seeds[0] + 1,
right_product=column_sketching)
print("\n\n\n------------------ NMF -------------------")
if nmfqp:
print("NMF matrix H is calculated by QP.")
for i in range(0, iteration):
w, h = ff.update(v, w, h, c_mode)
h_qp = ff.calculate_h(v, w, print_interim=True)
nmf_error[i] = np.linalg.norm(v - np.dot(w, h_qp))**2
if (i == 0) | (i % 100 == 99):
print(
str(i + 1) + " times update error: " + str(nmf_error[i]))
h = h_qp
else:
for i in range(0, iteration):
w, h = ff.update(v, w, h, c_mode)
nmf_error[i] = np.linalg.norm(v - np.dot(w, h))**2
if (i == 0) | (i % 100 == 99):
print(
str(i + 1) + " times update error: " + str(nmf_error[i]))
print("\n\n------------- Sketching NMF --------------")
if column_sketching:
w_s = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r, approximate_size, seeds[1], c_mode=c_mode)
for i in range(0, iteration):
w_s, h_s = ff.update(v_s, w_s, h_s, c_mode)
h_os = ff.calculate_h(v, w_s, print_interim=True)
snmf_error[i] = np.linalg.norm(v - np.dot(w_s, h_os))**2
if (i == 0) | (i % 100 == 99):
print(
str(i + 1) + " times update error: " + str(snmf_error[i]))
h_s = h_os
else:
w_s = ff.generate_w(approximate_size, r, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r, m, seeds[1], c_mode=c_mode)
for i in range(0, iteration):
w_s, h_s = ff.update(v_s, w_s, h_s, c_mode)
w_os = ff.calculate_h(v, h_s, print_interim=True)
snmf_error[i] = np.linalg.norm(v - np.dot(w_os, h_s))**2
if (i == 0) | (i % 100 == 99):
print(
str(i + 1) + " times update error: " + str(snmf_error[i]))
w_s = w_os
return nmf_error, snmf_error, w, h, w_s, h_s
def get_v_ite(v, n, m, r, approximate_size, seeds, c_mode, CDC, NMFQP=False):
iteration_list = np.zeros([2], dtype="int")
# NMF------------------------------------
print("\n------------------ NMF -------------------")
nmf_error = 1000000
w = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h = ff.generate_h(r, m, seeds[1], c_mode=c_mode)
if NMFQP:
print("NMF matrix H is calculated by QP.")
while nmf_error >= CDC:
w, h = ff.update(v, w, h, c_mode)
h_qp = ff.calculate_h(v, w, True)
nmf_error = np.linalg.norm(v - np.dot(w, h_qp))**2
if (iteration_list[0] == 0) | (iteration_list[0] % 100 == 99):
print(
str(iteration_list[0] + 1) + " times update error: " +
str(nmf_error))
iteration_list[0] += 1
else:
while nmf_error >= CDC:
w, h = ff.update(v, w, h, c_mode)
nmf_error = np.linalg.norm(v - np.dot(w, h))**2
if (iteration_list[0] == 0) | (iteration_list[0] % 100 == 99):
print(
str(iteration_list[0] + 1) + " times update error: " +
str(nmf_error))
iteration_list[0] += 1
# Sketching NMF --------------------------
print("\n------------- Sketching NMF --------------")
snmf_error = 1000000
v_s = ff.uniform_sampling(v, approximate_size, 0, t=True)
w_s = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r, approximate_size, seeds[1], c_mode=c_mode)
while snmf_error >= CDC:
w_s, h_s = ff.update(v_s, w_s, h_s, c_mode)
h_os = ff.calculate_h(v, w_s, True)
snmf_error = np.linalg.norm(v - np.dot(w_s, h_os))**2
if (iteration_list[1] == 0) | (iteration_list[1] % 100 == 99):
print(
str(iteration_list[1] + 1) + " times update error: " +
str(snmf_error))
iteration_list[1] = iteration_list[1] + 1
print(iteration_list)
return iteration_list
def pivoting_qr_q_eval(n,
m,
r,
approximate_size,
v,
iteration,
seeds,
c_mode,
o_w=0):
print("\n\n\n------------------ NMF -------------------")
nmf_error = np.zeros(iteration)
snmf_error = np.zeros(iteration)
w = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h = ff.generate_h(r, m, seeds[1], c_mode=c_mode)
v_s = ff.uniform_sampling(v, approximate_size, 0, t=True)
w_s = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r, approximate_size, seeds[1], c_mode=c_mode)
if np.all(o_w == 0):
for i in range(0, iteration):
w, h = ff.update(v, w, h, r, c_mode)
qr_q, qr_r, p = linalg.qr(w, pivoting=True)
w_s, h_s = ff.update(v_s, w_s, h_s, c_mode)
qr_q_s, qr_r_s, p_s = linalg.qr(w_s, pivoting=True)
frobenius_norm = np.linalg.norm(
np.dot(qr_q_s, qr_r_s) - np.dot(qr_q, qr_r))**2
nmf_error[i] = frobenius_norm
if (i == 0) | (i % 100 == 99):
print(
str(i + 1) + " times update error: " +
str(frobenius_norm))
return nmf_error, snmf_error, w, h, w_s, h_s
else:
original_q, original_r, original_p = linalg.qr(o_w, pivoting=True)
o_w = np.dot(original_q, original_r)
# NMF------------------------------------
print("\n\n\n------------------ NMF -------------------")
for i in range(0, iteration):
nmf_error[i] = calculate(v, o_w, w, h, c_mode, i)
print("\n\n------------- Sketching NMF --------------")
for i in range(0, iteration):
snmf_error[i] = calculate(v_s, o_w, w_s, h_s, c_mode, i)
h_os = ff.calculate_h(v, w_s, True)
return nmf_error, snmf_error, w, h, w_s, h_os
def bcv(v, r, iteration, seed, row_sep_num, column_sep_num, error_print):
n, m = v.shape
n_sep_size = int(n / row_sep_num)
m_sep_size = int(m / column_sep_num)
counter = 1
bic_tmp = 0
seeds = ff.two_seeds(seed)
error = np.zeros(iteration)
if n - n_sep_size < r | m - m_sep_size < r:
print("Error: row or column size of D is bigger than R",
file=sys.stderr)
sys.exit(1)
for r_sep in range(row_sep_num):
for c_sep in range(column_sep_num): # for folded row and column
row_s = n_sep_size * r_sep
column_s = m_sep_size * c_sep
if r_sep != row_sep_num - 1:
row_e = n_sep_size * (r_sep + 1)
else:
row_e = n
if c_sep != column_sep_num - 1:
column_e = m_sep_size * (c_sep + 1)
else:
column_e = m
# set Matrices ABCD ------------------------------------------------------------------------------------
a = v[row_s:row_e, column_s:column_e]
b = np.concatenate(
[v[row_s:row_e, :column_s], v[row_s:row_e, column_e:]], 1)
c = np.concatenate(
[v[:row_s, column_s:column_e], v[row_e:, column_s:column_e]],
0)
d_1 = np.concatenate([v[:row_s, :column_s], v[:row_s, column_e:]],
1)
d_2 = np.concatenate([v[row_e:, :column_s], v[row_e:, column_e:]],
1)
d = np.concatenate([d_1, d_2], 0)
# fit NMF to D --------------------------------------------------------------------------------
w_d = ff.generate_w(d.shape[0], r, seeds[0], c_mode=0)
h_d = ff.generate_h(r, d.shape[1], seeds[1], c_mode=0)
for i in range(iteration):
w_d, h_d = ff.update(d, w_d, h_d, 0)
if error_print & (row_e == n) & (column_e == m):
error[i] = np.linalg.norm(d - np.dot(w_d, h_d))**2
if i % 1000 == 999:
print("BCV NMF ( r={} {} / {}) : {} times update".format(
r, counter, row_sep_num * column_sep_num, i + 1))
# calculate BCV
a_r = np.dot(np.dot(b, np.linalg.pinv(h_d)),
np.dot(np.linalg.pinv(w_d), c))
bic_tmp += np.linalg.norm(a - a_r)**2
counter += 1
return bic_tmp, error
def least_square_w_eval(n,
m,
r,
approximate_size,
v,
iteration,
seeds,
c_mode,
o_w=0):
nmf_error = np.zeros(iteration)
snmf_error = np.zeros(iteration)
w = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h = ff.generate_h(r, m, seeds[1], c_mode=c_mode)
v_s = ff.uniform_sampling(v, approximate_size, seeds[0] + 1, t=True)
w_s = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r, approximate_size, seeds[1], c_mode=c_mode)
if np.all(o_w == 0):
print("\n\n\n------------------ NMF -------------------")
for i in range(0, iteration):
w, h = ff.update(v, w, h, r, c_mode)
w_s, h_s, nmf_error[i] = calculate(v, w, w_s, h_s, c_mode, i)
return nmf_error, snmf_error, w, h, w_s, h_s
else:
print("\n\n\n------------------ NMF -------------------")
for i in range(0, iteration):
w, h, nmf_error[i] = calculate(v, o_w, w, h, c_mode, i)
print("\n\n------------- Sketching NMF --------------")
for i in range(0, iteration):
w_s, h_s, snmf_error[i] = calculate(v_s, o_w, w_s, h_s, c_mode, i)
h_os = ff.calculate_h(v, w_s, print_interim=True)
return nmf_error, snmf_error, w, h, w_s, h_os
def calculate(v, o_w, w, h, c_mode, i):
w, h = ff.update(v, w, h, c_mode)
qr_q, qr_r, p = linalg.qr(w, pivoting=True)
frobenius_norm = np.linalg.norm(o_w - np.dot(qr_q, qr_r))**2
if (i == 0) | (i % 100 == 99):
print(str(i + 1) + " times update error: " + str(frobenius_norm))
return w, h, frobenius_norm
def calculate(v, o_w, w, h, c_mode, i):
w, h = ff.update(v, w, h, c_mode)
d = np.linalg.lstsq(w, o_w)[0]
frobenius_norm = np.linalg.norm(w - np.dot(w, d))**2
if (i == 0) | (i % 100 == 99):
print(str(i + 1) + " times update error: " + str(frobenius_norm))
return w, h, frobenius_norm
def calculate(v, w, h, c_mode, i, qp_opt=False):
w, h = ff.update(v, w, h, c_mode)
if qp_opt:
h_qp = ff.calculate_h(v, w, print_interim=True)
frobenius_norm = np.linalg.norm(v - np.dot(w, h_qp))**2
else:
frobenius_norm = np.linalg.norm(v - np.dot(w, h))**2
if (i == 0) | (i % 100 == 99):
print(str(i + 1) + " times update error: " + str(frobenius_norm))
return w, h, frobenius_norm
def bic(v, r, iteration, seed):
n, m = v.shape
seeds = ff.two_seeds(seed)
w = ff.generate_w(n, r, seeds[0], c_mode=0)
h = ff.generate_h(r, m, seeds[1], c_mode=0)
error = np.zeros(iteration)
for i in range(iteration):
w, h = ff.update(v, w, h, 0)
error[i] = np.linalg.norm(v - np.dot(w, h))**2
if i % 1000 == 999:
print("BIC NMF ( r={} ) : {} times update".format(r, i + 1))
v_reconstructed = np.dot(w, h)
a = (n + m) / (n * m)
d_eu = np.linalg.norm(v - v_reconstructed)**2
return np.log(d_eu) + r * a * np.log(1 / a), error
def error_calculate(r_size, ap_size, v_origin, w_origin, ite, wh_seed, c_mode,
nmfqp, t_flag):
theta_start = 5
seeds = ff.two_seeds(wh_seed)
v_nmf_error = np.zeros(ite)
v_snmf_error = np.zeros(ite)
w_nmf_error = np.zeros(ite)
w_snmf_error = np.zeros(ite)
n_size, m_size = v_origin.shape
w = ff.generate_w(n_size, r_size, seeds[0], c_mode=c_mode)
h = ff.generate_h(r_size, m_size, seeds[1], c_mode=c_mode)
v_s = ff.uniform_sampling(v_origin, ap_size, 0)
# NMF calculate ---------------------------------------------------------------------------------------------------
if c_mode == 2:
theta_w = theta_h = theta_start
if nmfqp:
print("NMF matrix H is calculated by QP.")
for i in range(0, ite):
if c_mode == 2:
w, h, theta_w, theta_h = ff.fgd_update(v_origin, w, h, theta_w,
theta_h)
else:
w, h = ff.update(v_origin, w, h, c_mode)
if nmfqp:
h_result = ff.calculate_h(v_origin, w, print_interim=False)
else:
h_result = h
# v evaluate -------------------
v_nmf_error[i] = np.linalg.norm(v_origin - np.dot(w, h_result))**2
# w evaluate -------------------
if t_flag:
d = np.linalg.lstsq(h.T, w_origin)[0]
w_nmf_error[i] = np.linalg.norm(w_origin - np.dot(h.T, d))**2
else:
d = np.linalg.lstsq(w, w_origin)[0]
w_nmf_error[i] = np.linalg.norm(w_origin - np.dot(w, d))**2
if (i == 0) | (i % 100 == 99):
print("NMF ( r=" + str(r_size) + " k=" + str(ap_size) + " ) : " +
str(i + 1) + " times update")
# else:
# for i in range(0, ite):
# if c_mode != 2:
# w, h = ff.update(v_origin, w, h, c_mode)
# else:
# w, h, theta_w, theta_h = ff.fgd_update(v_origin, w, h, theta_w, theta_h)
#
# # v evaluate -------------------
# v_nmf_error[i] = np.linalg.norm(v_origin - np.dot(w, h)) ** 2
# # w evaluate -------------------
# d = np.linalg.lstsq(w, w_origin)[0]
# w_nmf_error[i] = np.linalg.norm(w_origin - np.dot(w, d)) ** 2
#
# if (i == 0) | (i % 2000 == 1999):
# print("NMF ( r=" + str(r_size) + " k=" + str(ap_size) + " ) : " + str(i + 1) + " times update")
# SNMF calculate --------------------------------------------------------------------------------------------------
if c_mode == 2:
theta_w = theta_h = theta_start
w_s = ff.generate_w(n_size, r_size, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r_size, ap_size, seeds[1], c_mode=c_mode)
for i in range(0, ite):
if c_mode == 2:
w_s, h_s, theta_w, theta_h = ff.fgd_update(v_s, w_s, h_s, theta_w,
theta_h)
else:
w_s, h_s = ff.update(v_s, w_s, h_s, c_mode)
# v evaluate -------------------
os_M = ff.calculate_h(v_origin, w_s, print_interim=False)
v_snmf_error[i] = np.linalg.norm(v_origin - np.dot(w_s, os_M))**2
# w evaluate -------------------
if t_flag:
d_s = np.linalg.lstsq(os_M.T, w_origin)[0]
w_snmf_error[i] = np.linalg.norm(w_origin - np.dot(os_M.T, d_s))**2
else:
d_s = np.linalg.lstsq(w_s, w_origin)[0]
w_snmf_error[i] = np.linalg.norm(w_origin - np.dot(w_s, d_s))**2
if (i == 0) | (i % 100 == 99):
print(
"SketchingNMF ( r={} k={} seed={} ) : {} times update".format(
r_size, ap_size, wh_seed, i + 1))
if t_flag:
return v_nmf_error, v_snmf_error, w_nmf_error, w_snmf_error, h.T, w.T, h_s.T, w_s.T, os_M
else:
return v_nmf_error, v_snmf_error, w_nmf_error, w_snmf_error, w, h, w_s, h_s, os_M
def parallel_v_error_eval(r,
approximate_size,
v,
iteration,
wh_seed,
c_mode,
nmfqp,
t_flag,
snmf_only=False):
theta_start = 5
n, m = v.shape
seeds = ff.two_seeds(wh_seed)
nmf_error = np.zeros(iteration)
snmf_error = np.zeros(iteration)
w = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h = ff.generate_h(r, m, seeds[1], c_mode=c_mode)
v_s = ff.uniform_sampling(v, approximate_size, seeds[0] + 1)
# NMF -------------------------------------------------------------------------------------------------------------
theta_w = theta_h = theta_start
if not snmf_only:
if nmfqp:
print("NMF matrix H is calculated by QP.")
for i in range(0, iteration):
if c_mode != 2:
w, h = ff.update(v, w, h, c_mode)
else:
w, h, theta_w, theta_h = ff.fgd_update(
v, w, h, theta_w, theta_h)
h_qp = ff.calculate_h(v, w, print_interim=False)
nmf_error[i] = np.linalg.norm(v - np.dot(w, h_qp))**2
if (i == 0) | (i % 100 == 99):
print("NMF ( r=" + str(r) + " k=" +
str(approximate_size) + " ) : " + str(i + 1) +
" times update")
h = h_qp
else:
for i in range(0, iteration):
if c_mode != 2:
w, h = ff.update(v, w, h, c_mode)
else:
w, h, theta_w, theta_h = ff.fgd_update(
v, w, h, theta_w, theta_h)
nmf_error[i] = np.linalg.norm(v - np.dot(w, h))**2
if (i == 0) | (i % 2000 == 1999):
print("NMF ( r=" + str(r) + " k=" +
str(approximate_size) + " ) : " + str(i + 1) +
" times update")
# SNMF ------------------------------------------------------------------------------------------------------------
w_s = ff.generate_w(n, r, seeds[0], c_mode=c_mode)
h_s = ff.generate_h(r, approximate_size, seeds[1], c_mode=c_mode)
for i in range(0, iteration):
if c_mode != 2:
w_s, h_s = ff.update(v_s, w_s, h_s, c_mode)
else:
w_s, h_s, theta_w, theta_h = ff.fgd_update(v_s, w_s, h_s, theta_w,
theta_h)
h_os = ff.calculate_h(v, w_s, print_interim=False)
snmf_error[i] = np.linalg.norm(v - np.dot(w_s, h_os))**2
if (i == 0) | (i % 100 == 99):
print(
"SketchingNMF ( r={} k={} seed={} ) : {} times update".format(
r, approximate_size, wh_seed, i + 1))
if t_flag & snmf_only:
return nmf_error, snmf_error, None, None, h_os.T, w_s.T, h_s.T
elif t_flag:
return nmf_error, snmf_error, h.T, w.T, h_os.T, w_s.T, h_s.T
elif snmf_only:
return nmf_error, snmf_error, None, None, w_s, h_os, h_s
else:
return nmf_error, snmf_error, w, h, w_s, h_os, h_s