def forward(self, X, transposed=False):
#X = torch.Tensor(X)
if self.rank_tucker == -1:
result = torch.addmm(self.bias, X, self.order1_tens)
else:
result = torch.addmm(self.bias, X,
tucker_to_tensor(self.order1_tens))
if self.order >= 2:
if self.rank_tucker == -1:
acc = tl.tenalg.mode_dot(self.order2_tens, X, 0)
else:
acc = tl.tenalg.mode_dot(tucker_to_tensor(self.order2_tens), X,
0)
acc = tl.tenalg.mode_dot(acc, X, 1)
result += torch.einsum('iik->ik', acc)
if self.order == 3:
if self.rank_tucker == -1:
acc = tl.tenalg.mode_dot(self.order3_tens, X, 0)
else:
acc = tl.tenalg.mode_dot(tucker_to_tensor(self.order3_tens), X,
0)
acc = tl.tenalg.mode_dot(acc, X, 1)
acc = tl.tenalg.mode_dot(acc, X, 2)
result += torch.einsum('iiik->ik', acc)
return tl.reshape(result, (X.shape[0], self.output_dim))
def impute(tensor_with_nan, laplacians, ranks, alpha, regular, tol, interval):
fill_value = np.nanmean(tensor_with_nan)
tensor = tensor_with_nan.copy()
for index, e in np.ndenumerate(tensor):
if np.isnan(e):
tensor[index] = fill_value
factors = None
while True:
for index, tr in np.ndenumerate(tensor_with_nan):
if not np.isnan(tr):
tensor[index] = tr
core, factors = tucker(tensor, ranks, laplacians, n_iter_max=interval, alpha=alpha, tol=None, regular=regular, factors=factors)
tensor_tmp = tucker_to_tensor((core, factors))
variation = np.sum(np.power(tensor_tmp - tensor, 2)) / np.sum(np.power(tensor, 2))
print(variation)
if variation < tol:
break
tensor = tensor_tmp
return tensor
def reconstruct(self):
"""
Reconstructs the decomposed TensorDecomp object.
Assigns the reconstructed tensor to self.recons attribute.
Parameters
----------
self : object of class TensorDecomp type.
Returns
-------
None
"""
if self.decomp_type == 'svd':
self.recons = self.decomposed[0] @ (
np.diag(self.decomposed[1]) @ self.decomposed[2])
elif self.decomp_type == 'NMF':
self.recons = self.nmf_obj.inverse_transform(self.decomposed[0])
elif self.decomp_type == 'tucker':
from tensorly import tucker_tensor as tt
self.recons = tt.tucker_to_tensor(self.decomposed)
elif self.decomp_type == 'parafac':
from tensorly import cp_tensor as ct
self.recons = ct.cp_to_tensor(self.decomposed)
elif self.decomp_type == 'matrix_product_state':
from tensorly import tt_tensor as tt
self.recons = tt.tt_to_tensor(self.decomposed)
elif self.decomp_type == 'clarkson_woodruff_transform':
self.recons = self.decomposed
def recover(self):
"""
Recover the original shape.
"""
core = self.core_layer.weight.data
out_factor = self.out_channel_layer.weight.data.squeeze()
in_factor = self.in_channel_layer.weight.data.squeeze()
in_factor = torch.transpose(in_factor, 1, 0)
return tucker.tucker_to_tensor(core, [out_factor, in_factor])
def em(self, max_iter=10, tol=1.e-7, init=False):
if init: self._initialize_parameters()
# initialize the expectations of V(m)
Ev, Evv, = _compute_context_expectation(self.L, self.M, self.N, self.S,
self.U, self.xi, self.sgmV,
self._lambda)
# start EM algorithm
for iter in range(max_iter):
print('================')
print(' iter', iter + 1)
print('================')
try:
(Ev, Evv, Ez, self.U, self.B, self.z0, self.psi0, self.sgm0,
self.sgmO, self.sgmR, self.sgmV,
self.xi) = _em(self.X, self.W, self.T, self.S, self.L, self.M,
self.N, self._lambda, Ev, Evv, self.U, self.B,
self.z0, self.psi0, self.sgm0, self.sgmO,
self.sgmR, self.sgmV, self.xi)
except KeyboardInterrupt:
self.z = Ez
print(self.z[:3])
self.save_params()
break
self.llh.append(self.compute_log_likelihood())
# if abs(llh[-1] - llh[-2]) < tol:
# print("converged!!")
# break
print("log-likelihood=", self.llh[-1])
self.z0_log.append(self.z0)
self.sgm0_log.append(self.sgm0)
self.sgmO_log.append(self.sgmO)
self.sgmR_log.append(self.sgmR)
self.sgmV_log.append(deepcopy(self.sgmV))
self.xi_log.append(deepcopy(self.xi))
# EZ = Ez.reshape((self.T, *self.L))
# print(EZ.shape, self.U[0].shape)
self.z = Ez
self.recon_ = recon_ = np.array([
tucker_to_tensor(Ez[t].reshape(*self.L), self.U)
for t in range(self.T)
])
print(self.recon_.shape)
self.recon_ = np.moveaxis(recon_, -1, 1)
def representive_connMatrix_tucker(conn_seg):
""" extract one representive connectivity matrix from a series of connective matrices for each time segment
based on Tucker decomposition
@ parameter conn_seg: a series of connective matrics for a time segment (n_chns * n_chns * n_times)
return conn_repre: one representive connective matrix for this time segment
"""
rank = [15, 15, 3]
core, factors = tucker(conn_seg, ranks=rank)
recon_conn_seg = tucker_to_tensor(core,
factors) # recon_conn_seg: 64*64*60
conn_repre = np.mean(
recon_conn_seg, axis=2
) # conn_repre: n_chns * n_chns, connective matrix summary for each segment
return conn_repre
def recover(self):
"""
Recover original tensor from decomposed tensor
@return: 4D weight tensor with original layer's shape
"""
# get core
core = self.core_layer.weight.data
# get factor
out_factor = self.out_channel_layer.weight.data.squeeze()
in_factor = self.in_channel_layer.weight.data.squeeze()
in_factor = torch.transpose(in_factor, 1, 0)
# recover
recovered = tucker_to_tensor(core, [out_factor, in_factor])
return recovered
matU = kronecker(U, reverse=True)
predict = z @ matU.T
print(predict.shape)
print(unfold(X, -1).shape)
for i in range(unfold(X, -1).shape[1]):
plt.plot(unfold(X, -1)[:, i])
plt.plot(predict[:, i])
plt.show()
exit()
# print(Z.shape)
# Z = np.moveaxis(Z, 1,2)
# print(Z.shape)
Xn = []
for t in range(T):
Xn.append(tucker_to_tensor(Z[t], U))
Xn = np.array(Xn)
Xn = np.moveaxis(Xn, 0, -1)
# mode = 0
# for i in range(X.shape[0]):
# for j in range(X.shape[1]):
# plt.plot(X[i, j, mode, :].T)
# plt.plot(Xn[i, j, mode, :].T)
# plt.show()
# exit()
for i in range(X.shape[0]):
for j in range(X.shape[1]):
plt.plot(X[i, j, :].T)
plt.plot(Xn[i, j, :].T)
plt.show()
for i in range(self.T):
# run sta update
X = self.t[:,:,:,i]
for j in range(3):
self.ita(self.Ulist, self.Dlist, j, X, min(i+1, 200),forget=f)
# reconstruct and find error
temp = tl.tenalg.multi_mode_dot(X, [i.T for i in self.Ulist])
that = tl.tenalg.multi_mode_dot(temp, [i for i in self.Ulist])
emat = that - X
self.reconerror.append(np.linalg.norm(emat) ** 2)
self.error.append(self.reconerror[-1] / np.linalg.norm(X) ** 2)
if print_error:
print(self.reconerror[-1])
self.meanerr = np.mean(self.error)
#%%
m, T, r = 10, 100, 3
sigma = 0.1
np.random.seed(5)
Tensor = np.random.normal(size = (m,m,m))
core, factors = tucker(Tensor, rank = [3, 3, 3])
Tensor = tucker_to_tensor(core, factors)
Tensor = np.outer(Tensor, np.ones(T)).reshape((m,m,m,T))
Tensor += np.random.normal(scale = sigma, size = (m,m,m, T))
Tensor[:,:,:,0] += np.random.normal(scale = 10*sigma, size = (m,m,m,))
model = ita3d(Tensor,3,3,3)
model.fit()
