def inverse_transform(self, x):
"""Reconstruct projected data to the original shape and add the estimated mean back
Args:
x (array-like tensor): Data to be reconstructed, shape (n_samples, P_1, P_2, ..., P_N), if
self.return_vector == False, where P_1, P_2, ..., P_N are the reduced dimensions of of corresponding
mode (1, 2, ..., N), respectively. If self.return_vector == True, shape (n_samples, self.n_components)
or shape (n_samples, P_1 * P_2 * ... * P_N).
Returns:
array-like tensor:
Reconstructed tensor in original shape, shape (n_samples, I_1, I_2, ..., I_N)
"""
# reshape x to tensor in shape (n_samples, self.shape_out) if x has been unfolded
if x.ndim <= 2:
if x.ndim == 1:
# reshape x to a 2D matrix (1, n_components) if x in shape (n_components,)
x = x.reshape((1, -1))
n_samples = x.shape[0]
n_features = x.shape[1]
if n_features <= np.prod(self.shape_out):
x_ = np.zeros((n_samples, np.prod(self.shape_out)))
x_[:, self.idx_order[:n_features]] = x[:]
else:
msg = "Feature dimension exceeds the shape upper limit."
logging.error(msg)
raise ValueError(msg)
x = fold(x_, mode=0, shape=((n_samples, ) + self.shape_out))
x_rec = multi_mode_dot(x,
self.proj_mats,
modes=[m for m in range(1, self.n_dims)],
transpose=True)
x_rec = x_rec + self.mean_
return x_rec
def select_top_weight(weights, select_ratio: float = 0.05):
"""Select top weights in magnitude, and the rest of weights will be zeros
Args:
weights (array-like): model weights, can be a vector or a higher order tensor
select_ratio (float, optional): ratio of top weights to be selected. Defaults to 0.05.
Returns:
array-like: top weights in the same shape with the input model weights
"""
if type(weights) != np.ndarray:
weights = np.array(weights)
orig_shape = weights.shape
if len(orig_shape) > 1:
weights = unfold(weights, mode=0)[0]
n_top_weights = int(weights.size * select_ratio)
top_weight_idx = (-1 * abs(weights)).argsort()[:n_top_weights]
top_weights = np.zeros(weights.size)
top_weights[top_weight_idx] = weights[top_weight_idx]
if len(orig_shape) > 1:
top_weights = fold(top_weights, mode=0, shape=orig_shape)
return top_weights
Y_pred_linear = Y_scaler.inverse_transform(Y_pred_linear)
Y_pred_MT = Y_pred_MT + Y_pred_linear
####################################### Evaluation ########################
NPMs_MT = normative_prob_map(Y_test, Y_pred_MT, Y_pred_cov_MT, s_n2_MT)
NPMs_MT[~np.isfinite(NPMs_MT)] = 0
EVD_params = extreme_value_prob_fit(NPMs_MT[:train_num,:], 0.01)
abnormal_probs_MT = extreme_value_prob(EVD_params, NPMs_MT[train_num:,:], 0.01)
auc_all[r,] = roc_auc_score(labels, abnormal_probs_MT)
auc_SCHZ[r] = roc_auc_score(labels[(diagnosis_labels==0) | (diagnosis_labels==1),], abnormal_probs_MT[(diagnosis_labels==0) | (diagnosis_labels==1),])
auc_ADHD[r] = roc_auc_score(labels[(diagnosis_labels==0) | (diagnosis_labels==2),], abnormal_probs_MT[(diagnosis_labels==0) | (diagnosis_labels==2),])
auc_BIPL[r] = roc_auc_score(labels[(diagnosis_labels==0) | (diagnosis_labels==3),], abnormal_probs_MT[(diagnosis_labels==0) | (diagnosis_labels==3),])
print ('Results' + 'AUC = %f' %(auc_all[r,]))
################################## Saving Results #########################
ex_img = nib.load(main_dir + 'derivatives/task/sub-10159/taskswitch.feat/example_func.nii.gz')
NPMs_MT = fold(NPMs_MT, mode=0, shape = [NPMs_MT.shape[0],Y_shape[0],Y_shape[1],Y_shape[2]])
original_image_size[0] = NPMs_MT.shape[0]
temp = np.zeros(original_image_size, dtype=np.float32)
temp[:,x_from:x_to,y_from:y_to,z_from:z_to] = NPMs_MT
image = nib.Nifti1Image(np.transpose(temp, [1,2,3,0]), ex_img.affine, ex_img.header)
nib.save(image, save_path + method + '_' + str(b) + '_' + str(nb) + '_NPMs_' + str(r) + '.nii.gz')
savemat(save_path + method + '_' + str(b) + '_' + str(nb) + '_results.mat',
{'elapsed_time_opt': elapsed_time_opt, 'elapsed_time_est': elapsed_time_est,
'auc_all':auc_all, 'auc_SCHZ':auc_SCHZ, 'auc_ADHD':auc_ADHD, 'auc_BIPL':auc_BIPL,
'hyperparams':hyperparams_opt})
# -*- coding: utf-8 -*-
"""
Basic tensor operations
=======================
Example on how to use :mod:`tensorly.base` to perform basic tensor operations.
"""
import matplotlib.pyplot as plt
from tensorly.base import unfold, fold
import numpy as np
###########################################################################
# A tensor is simply a numpy array
tensor = np.arange(24).reshape((3, 4, 2))
print('* original tensor:\n{}'.format(tensor))
###########################################################################
# Unfolding a tensor is easy
for mode in range(tensor.ndim):
print('* mode-{} unfolding:\n{}'.format(mode, unfold(tensor, mode)))
###########################################################################
# Re-folding the tensor is as easy:
for mode in range(tensor.ndim):
unfolding = unfold(tensor, mode)
folded = fold(unfolding, mode, tensor.shape)
print(np.all(folded == tensor))
def robust_pca(X,
mask=None,
tol=10e-7,
reg_E=1,
reg_J=1,
mu_init=10e-5,
mu_max=10e9,
learning_rate=1.1,
n_iter_max=100,
verbose=1):
"""Robust Tensor PCA via ALM with support for missing values
Decomposes a tensor `X` into the sum of a low-rank component `D`
and a sparse component `E`.
Parameters
----------
X : ndarray
tensor data of shape (n_samples, N1, ..., NS)
mask : ndarray
array of booleans with the same shape as `X`
should be zero where the values are missing and 1 everywhere else
tol : float
convergence value
reg_E : float, optional, default is 1
regularisation on the sparse part `E`
reg_J : float, optional, default is 1
regularisation on the low rank part `D`
mu_init : float, optional, default is 10e-5
initial value for mu
mu_max : float, optional, default is 10e9
maximal value for mu
learning_rate : float, optional, default is 1.1
percentage increase of mu at each iteration
n_iter_max : int, optional, default is 100
maximum number of iteration
verbose : int, default is 1
level of verbosity
Returns
-------
(D, E)
Robust decomposition of `X`
D : `X`-like array
low-rank part
E : `X`-like array
sparse error part
Notes
-----
The problem we solve is, for an input tensor :math:`\\tilde X`:
.. math::
:nowrap:
\\begin{equation*}
\\begin{aligned}
& \\min_{\\{J_i\\}, \\tilde D, \\tilde E}
& & \\sum_{i=1}^N \\text{reg}_J \\|J_i\\|_* + \\text{reg}_E \\|E\\|_1 \\\\
& \\text{subject to}
& & \\tilde X = \\tilde A + \\tilde E \\\\
& & & A_{[i]} = J_i, \\text{ for each } i \\in \\{1, 2, \\cdots, N\\}\\\\
\\end{aligned}
\\end{equation*}
"""
if mask is None:
mask = 1
# Initialise the decompositions
D = T.zeros_like(X, **T.context(X)) # low rank part
E = T.zeros_like(X, **T.context(X)) # sparse part
L_x = T.zeros_like(X, **T.context(
X)) # Lagrangian variables for the (X - D - E - L_x/mu) term
J = [T.zeros_like(X, **T.context(X))
for _ in range(T.ndim(X))] # Low-rank modes of X
L = [T.zeros_like(X, **T.context(X))
for _ in range(T.ndim(X))] # Lagrangian or J
# Norm of the reconstructions at each iteration
rec_X = []
rec_D = []
mu = mu_init
for iteration in range(n_iter_max):
for i in range(T.ndim(X)):
J[i] = fold(
svd_thresholding(
unfold(D, i) + unfold(L[i], i) / mu, reg_J / mu), i,
X.shape)
D = L_x / mu + X - E
for i in range(T.ndim(X)):
D += J[i] - L[i] / mu
D /= (T.ndim(X) + 1)
E = soft_thresholding(X - D + L_x / mu, mask * reg_E / mu)
# Update the lagrangian multipliers
for i in range(T.ndim(X)):
L[i] += mu * (D - J[i])
L_x += mu * (X - D - E)
mu = min(mu * learning_rate, mu_max)
# Evolution of the reconstruction errors
rec_X.append(T.norm(X - D - E, 2))
rec_D.append(max([T.norm(low_rank - D, 2) for low_rank in J]))
# Convergence check
if iteration > 1:
if max(rec_X[-1], rec_D[-1]) <= tol:
if verbose:
print('\nConverged in {} iterations'.format(iteration))
break
else:
print("[INFO] iter:", iteration, " error:",
(max(rec_X[-1], rec_D[-1]).item()))
return D, E