def none_negative_svd(matrix, threshold=1.0):
# mode 1
shape1 = matrix.shape
matrix_mode_one = unfold(matrix, 1)
u, s, v = np.linalg.svd(matrix_mode_one, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_one.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
print "is all close: ", np.allclose(matrix_mode_one,
u.dot(singular_matrix).dot(v))
result_u, sigma, param_matrix = matrix_sn_nn(u)
print "result: ", result_u
print "sigma: ", sigma
print "param_matrix: ", param_matrix
remain_matrix = inv(param_matrix).dot(
inv(sigma)).dot(singular_matrix).dot(v)
shape2 = (result_u.shape[1], shape1[1])
tensor2 = fold(remain_matrix, 1, shape2)
print "tensor2: ", tensor2
# mode 2
matrix_mode_two = unfold(tensor2, 2)
u, s, v = np.linalg.svd(matrix_mode_two, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_two.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
result_v, sigma, param_matrix = matrix_sn_nn(u)
remain_matrix = inv(param_matrix).dot(
inv(sigma)).dot(singular_matrix).dot(v)
shape3 = (result_u.shape[1], result_v.shape[1])
r = fold(remain_matrix, 2, shape3)
print "u: ", result_u
print "v: ", result_v
print "r: ", r
return result_u, result_v, r
def none_negative_svd(matrix, threshold=1.0):
# mode 1
shape1 = matrix.shape
matrix_mode_one = unfold(matrix, 1)
u, s, v = np.linalg.svd(matrix_mode_one, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_one.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
print "is all close: ", np.allclose(matrix_mode_one, u.dot(singular_matrix).dot(v))
result_u, sigma, param_matrix = matrix_sn_nn(u)
print "result: ", result_u
print "sigma: ", sigma
print "param_matrix: ", param_matrix
remain_matrix = inv(param_matrix).dot(inv(sigma)).dot(singular_matrix).dot(v)
shape2 = (result_u.shape[1], shape1[1])
tensor2 = fold(remain_matrix, 1, shape2)
print "tensor2: ", tensor2
# mode 2
matrix_mode_two = unfold(tensor2, 2)
u, s, v = np.linalg.svd(matrix_mode_two, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_two.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
result_v, sigma, param_matrix = matrix_sn_nn(u)
remain_matrix = inv(param_matrix).dot(inv(sigma)).dot(singular_matrix).dot(v)
shape3 = (result_u.shape[1], result_v.shape[1])
r = fold(remain_matrix, 2, shape3)
print "u: ", result_u
print "v: ", result_v
print "r: ", r
return result_u, result_v, r
def none_negative_svd2(matrix, threshold=1.0):
# mode 1
shape1 = matrix.shape
matrix_mode_one = unfold(matrix, 1)
u, s, v = np.linalg.svd(matrix_mode_one, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_one.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
print "is all close: ", np.allclose(matrix_mode_one, u.dot(singular_matrix).dot(v))
result_u, sigma, param_matrix = matrix_sn_nn(u)
result_v, sigma2, param_matrix2 = matrix_sn_nn(v)
print "result: ", result_u
print "sigma: ", sigma
print "param_matrix: ", param_matrix
print "sigma2: ", sigma2
print "param_matrix2: ", param_matrix2
r = inv(param_matrix).dot(inv(sigma)).dot(singular_matrix).dot(inv(sigma2).transpose()).dot(inv(param_matrix2).transpose())
return result_u, result_v, r
def none_negative_svd2(matrix, threshold=1.0):
# mode 1
shape1 = matrix.shape
matrix_mode_one = unfold(matrix, 1)
u, s, v = np.linalg.svd(matrix_mode_one, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_one.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
print "is all close: ", np.allclose(matrix_mode_one,
u.dot(singular_matrix).dot(v))
result_u, sigma, param_matrix = matrix_sn_nn(u)
result_v, sigma2, param_matrix2 = matrix_sn_nn(v)
print "result: ", result_u
print "sigma: ", sigma
print "param_matrix: ", param_matrix
print "sigma2: ", sigma2
print "param_matrix2: ", param_matrix2
r = inv(param_matrix).dot(inv(sigma)).dot(singular_matrix).dot(
inv(sigma2).transpose()).dot(inv(param_matrix2).transpose())
return result_u, result_v, r
def none_negative_hosvd(tensor, threshold=1.0):
# mode 1
shape1 = tensor.shape
matrix_mode_one = unfold(tensor, 1)
u, s, v = np.linalg.svd(matrix_mode_one, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_one.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
print "is all close: ", np.allclose(matrix_mode_one,
u.dot(singular_matrix).dot(v))
result_u, sigma, param_matrix = matrix_sn_nn(u)
print "result: ", result_u
print "sigma: ", sigma
print "param_matrix: ", param_matrix
remain_matrix = inv(param_matrix).dot(
inv(sigma)).dot(singular_matrix).dot(v)
shape2 = (result_u.shape[1], shape1[1], shape1[2])
tensor2 = fold(remain_matrix, 1, shape2)
print "tensor2: ", tensor2
# mode 2
matrix_mode_two = unfold(tensor2, 2)
u, s, v = np.linalg.svd(matrix_mode_two, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_two.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
result_v, sigma, param_matrix = matrix_sn_nn(u)
remain_matrix = inv(param_matrix).dot(
inv(sigma)).dot(singular_matrix).dot(v)
shape3 = (result_u.shape[1], result_v.shape[1], shape1[2])
tensor3 = fold(remain_matrix, 2, shape3)
print "tensor3: ", tensor3
# mode 3
matrix_mode_three = unfold(tensor3, 3)
u, s, v = np.linalg.svd(matrix_mode_three, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_three.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
result_w, sigma, param_matrix = matrix_sn_nn(u)
remain_matrix = inv(param_matrix).dot(
inv(sigma)).dot(singular_matrix).dot(v)
shape4 = (result_u.shape[1], result_v.shape[1], result_w.shape[1])
r = fold(remain_matrix, 3, shape4)
# print "tensor4: ", r
print "u: ", result_u
print "v: ", result_v
print "w: ", result_w
print "r: ", r
# print r.dot(result_u).dot(result_v).dot(result_w)
x = recon(r, result_u, 1)
x = recon(x, result_v, 2)
x = recon(x, result_w, 3)
print "reconstruct tensor: ", x
print "tensor: ", tensor
return x, result_u, result_v, result_w, r
print list(D[0])
print D[1]
print D[2]
s1 = unfold(S, 1)
print "core tensor unfold: ", s1
print "orthogonal: ", s1[1].dot(s1[2])
# print np.array([1, 2]).dot(np.array([2, 3]))
A2 = reconstruct(S, U)
print "reconstruct tensor: ", A2
print frobenius_norm(A - A2)
aaa = matrix_sn_nn(U[1])
print "before:", U[1]
print "after:", aaa
x, result_u, result_v, result_w, r = none_negative_hosvd(A)
n_a = result_u.shape[1]
n_b = result_v.shape[1]
n_c = result_w.shape[1]
print A[2][1][0]
print n_a, n_b, n_c, result_u.shape, result_v.shape, result_w.shape, r.shape, np.array(
result_u)[2][2]
B = np.zeros((3, 3, 3))
for index_i in range(0, 3):
for index_j in range(0, 3):
for index_k in range(0, 3):
def none_negative_hosvd(tensor, threshold=1.0):
# mode 1
shape1 = tensor.shape
matrix_mode_one = unfold(tensor, 1)
u, s, v = np.linalg.svd(matrix_mode_one, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_one.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
print "is all close: ", np.allclose(matrix_mode_one, u.dot(singular_matrix).dot(v))
result_u, sigma, param_matrix = matrix_sn_nn(u)
print "result: ", result_u
print "sigma: ", sigma
print "param_matrix: ", param_matrix
remain_matrix = inv(param_matrix).dot(inv(sigma)).dot(singular_matrix).dot(v)
shape2 = (result_u.shape[1], shape1[1], shape1[2])
tensor2 = fold(remain_matrix, 1, shape2)
print "tensor2: ", tensor2
# mode 2
matrix_mode_two = unfold(tensor2, 2)
u, s, v = np.linalg.svd(matrix_mode_two, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_two.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
result_v, sigma, param_matrix = matrix_sn_nn(u)
remain_matrix = inv(param_matrix).dot(inv(sigma)).dot(singular_matrix).dot(v)
shape3 = (result_u.shape[1], result_v.shape[1], shape1[2])
tensor3 = fold(remain_matrix, 2, shape3)
print "tensor3: ", tensor3
# mode 3
matrix_mode_three = unfold(tensor3, 3)
u, s, v = np.linalg.svd(matrix_mode_three, full_matrices=True)
print u.shape, s.shape, v.shape
singular_matrix = np.zeros(matrix_mode_three.shape)
l = s.shape[0]
singular_matrix[:l, :l] = np.diag(s)
result_w, sigma, param_matrix = matrix_sn_nn(u)
remain_matrix = inv(param_matrix).dot(inv(sigma)).dot(singular_matrix).dot(v)
shape4 = (result_u.shape[1], result_v.shape[1], result_w.shape[1])
r = fold(remain_matrix, 3, shape4)
# print "tensor4: ", r
print "u: ", result_u
print "v: ", result_v
print "w: ", result_w
print "r: ", r
# print r.dot(result_u).dot(result_v).dot(result_w)
x = recon(r, result_u, 1)
x = recon(x, result_v, 2)
x = recon(x, result_w, 3)
print "reconstruct tensor: ", x
print "tensor: ", tensor
return x, result_u, result_v, result_w, r
print list(D[0])
print D[1]
print D[2]
s1 = unfold(S, 1)
print "core tensor unfold: ", s1
print "orthogonal: ", s1[1].dot(s1[2])
# print np.array([1, 2]).dot(np.array([2, 3]))
A2 = reconstruct(S, U)
print "reconstruct tensor: ", A2
print frobenius_norm(A-A2)
aaa = matrix_sn_nn(U[1])
print "before:", U[1]
print "after:", aaa
x, result_u, result_v, result_w, r = none_negative_hosvd(A)
n_a = result_u.shape[1]
n_b = result_v.shape[1]
n_c = result_w.shape[1]
print A[2][1][0]
print n_a, n_b, n_c, result_u.shape, result_v.shape, result_w.shape, r.shape, np.array(result_u)[2][2]
B = np.zeros((3, 3, 3))
for index_i in range(0, 3):
for index_j in range(0, 3):
for index_k in range(0, 3):
for i in range(0, n_a):
