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k_adaptive_rPCA.py
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k_adaptive_rPCA.py
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from utils import *
import scipy
import math
import time
from scipy.sparse import csc_matrix, linalg
import numpy as np
# A: numpy.ndarray, m >= n
# output: U, S, V
def eigSVD(A):
n = A.shape[1]
B = A.T.dot(A)
D, V = np.linalg.eig(B)
S = np.sqrt(D)
S2 = np.diag(1 / S)
U = A.dot(V).dot(S2)
return U, S, V.T
# A: scipy.sparse.csc_matrix, m <= n
# output: U(k * k), S(1 * k), V(n * k)
# A = U * diag(S) * V'
def k_adaptive_rPCA(A, relerr=0.5, b=20, q=11):
m, n = A.shape
if m > n:
logger.info('randSVD error: randSVD needs m <= n!')
return
if q < 2:
logger.info('randSVD_error: q must >= 2!')
return
P = int((q - 1) / 2)
Q = np.zeros((m, 0))
B = np.zeros((0, n))
E = scipy.sparse.linalg.norm(A) ** 2
threshold = relerr ** 2 * E
logger.info('\nrelerr = %.5f' % relerr)
logger.info('E0 = %.5f\nthreshold = %.5f' % (E, threshold))
maxiter = int(math.ceil(min(m, n) / 2.0 / b))
for i in range(maxiter):
logger.info('~~~~~~~~~~~~~~~~~~~~~~~~ i = %d ~~~~~~~~~~~~~~~~~~~~~' % i)
start2 = get_time()
if q % 2 == 0:
Omg = np.random.randn(n, b)
Y = A.dot(Omg) - Q.dot(B.dot(Omg))
Qi = np.linalg.qr(Y)[0]
else:
Qi = np.random.randn(m, b)
for j in range(P):
if j == P - 1:
R = A.T.dot(Qi)
Qi = np.linalg.qr(A.dot(R) - Q.dot(B.dot(R)))[0]
else:
Qi = scipy.linalg.lu(A.dot(A.T.dot(Qi)), permute_l=True)[0]
Qi = np.linalg.qr(Qi - Q.dot(Q.T.dot(Qi)))[0]
Bi = (A.T.dot(Qi)).T # Qi.T.dot(A)
Q = np.concatenate((Q, Qi), axis=1)
B = np.concatenate((B, Bi), axis=0)
E -= np.linalg.norm(Bi) ** 2
if E < threshold:
break
logger.info('E: %s' % E)
logger.info('process_time: ' + str(get_time() - start2))
if not E < threshold:
logger.info('randSVD_sparse wrong!')
return Q, B, Q.shape[1]
E = scipy.sparse.linalg.norm(A) ** 2
k = 0
for k in range(B.shape[0]):
E -= np.linalg.norm(B[k]) ** 2
if E < threshold:
break
k += 1
logger.info('k = %d' % k)
U1, S1, Vt1 = eigSVD(B.T)
U = Q.dot(Vt1.T)
S = S1
Vt = U1.T
return U[:, :k], S[:k], Vt[:k, :]
def randQB_EI(A, relerr=0.5, b=20, P=5):
m, n = A.shape
Q = np.zeros((m, 0))
B = np.zeros((0, n))
k = 0
E = scipy.sparse.linalg.norm(A)**2
threshold = relerr**2 * E
logger.info('E0 = %.5f\nthreshold = %.5f' % (E, threshold))
maxiter = int(math.ceil(min(m, n) / 2.0 / b))
flag = False
tt = True
for i in range(1, maxiter + 1):
logger.info('~~~~~~~~~~~~~~~~~~~~~~~~ i = %d ~~~~~~~~~~~~~~~~~~~~~' % i)
start2 = get_time()
Omg = np.random.randn(n, b)
# b = b * 2
Y = A.dot(Omg) - Q.dot(B.dot(Omg))
Qi = np.linalg.qr(Y)[0]
for j in range(1, P + 1):
Qi = np.linalg.qr(A.T.dot(Qi) - B.T.dot(Q.T.dot(Qi)))[0]
Qi = np.linalg.qr(A.dot(Qi) - Q.dot(B.dot(Qi)))[0]
Qi = np.linalg.qr(Qi - Q.dot(Q.T.dot(Qi)))[0]
Bi = (A.T.dot(Qi)).T - Qi.T.dot(Q).dot(B)
Q = np.concatenate((Q, Qi), axis=1)
B = np.concatenate((B, Bi), axis=0)
temp = E - np.linalg.norm(Bi)**2
if temp < threshold:
for j in range(1, b + 1):
E = E - np.linalg.norm(Bi[j-1, :])**2
if E < threshold:
flag = True
k = (i - 1) * b + j
break
else:
E = temp
logger.info('E = %.5f' % E)
if flag:
break
logger.info('process_time: ' + str(get_time() - start2))
if not flag:
logger.info('randQB_EI wrong!')
k = Q.shape[1]
logger.info('k = %d' % k)
U1, S1, Vt1 = eigSVD(B.T)
U = Q.dot(Vt1.T)
S = S1
Vt = U1.T
return U[:, :k], S[:k], Vt[:k, :]
def get_sparse_matrix(m, n):
# row = np.array([0, 2, 2, 0, 1, 2, 0, 0, 0])
# col = np.array([0, 0, 1, 2, 2, 2, 3, 3, 4])
# data = np.array([1, 2, 3, 4, 5, 6, 7, 9, 11]).astype(np.float64)
# return csc_matrix((data, (row, col)))
return load_movielens_small()
if __name__ == '__main__':
# a = np.array([[1, 0, 4], [0, 0, 5], [2, 3, 6]])
# a = np.random.randn(4, 6)
a = get_sparse_matrix(3, 4)
logger.info('a:\n', a.toarray())
start1 = time.time()
start2 = time.process_time()
u, s, vt = randQB_EI(a)
logger.info('u:')
logger.info(u)
logger.info('s:')
logger.info(s)
logger.info('vt:')
logger.info(vt)
logger.info('u*s*vt:')
b = u.dot(np.diag(s)).dot(vt)
logger.info('error:', np.linalg.norm(a - b) ** 2)
# a = a.toarray().T
# logger.info(a)
# u, s, vt = eigSVD(a)
# logger.info('u:')
# logger.info(u)
# logger.info('s:')
# logger.info(s)
# logger.info('vt:')
# logger.info(vt)
# logger.info('u*s*vt:')
# logger.info(u.dot(np.diag(s)).dot(vt))
# u, s, vt = scipy.sparse.linalg.svds(a, 117)
# logger.info('u:')
# logger.info(u)
# logger.info('s:')
# logger.info(s)
# logger.info('vt:')
# logger.info(vt)
# b = u.dot(np.diag(s)).dot(vt)
# logger.info('error:', np.linalg.norm(a - b) ** 2)
logger.info('\n\ntime:', time.time() - start1)
logger.info('process_time:', time.process_time() - start2)