code
string | signature
string | docstring
string | loss_without_docstring
float64 | loss_with_docstring
float64 | factor
float64 |
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max_sigma = 2.0 * math.pow(np.nanmax(np.std(R, axis=0)), 2)
return max_sigma | def _get_max_sigma(self, R) | Calculate maximum sigma of scanner RAS coordinates
Parameters
----------
R : 2D array, with shape [n_voxel, n_dim]
The coordinate matrix of fMRI data from one subject
Returns
-------
max_sigma : float
The maximum sigma of scanner coordinates. | 4.91178 | 5.244704 | 0.936522 |
max_sigma = self._get_max_sigma(R)
final_lower = np.zeros(self.K * (self.n_dim + 1))
final_lower[0:self.K * self.n_dim] =\
np.tile(np.nanmin(R, axis=0), self.K)
final_lower[self.K * self.n_dim:] =\
np.repeat(self.lower_ratio * max_sigma, self.K)
final_upper = np.zeros(self.K * (self.n_dim + 1))
final_upper[0:self.K * self.n_dim] =\
np.tile(np.nanmax(R, axis=0), self.K)
final_upper[self.K * self.n_dim:] =\
np.repeat(self.upper_ratio * max_sigma, self.K)
bounds = (final_lower, final_upper)
return bounds | def get_bounds(self, R) | Calculate lower and upper bounds for centers and widths
Parameters
----------
R : 2D array, with shape [n_voxel, n_dim]
The coordinate matrix of fMRI data from one subject
Returns
-------
bounds : 2-tuple of array_like, default: None
The lower and upper bounds on factor's centers and widths. | 1.8959 | 1.842941 | 1.028736 |
centers = self.get_centers(estimate)
widths = self.get_widths(estimate)
recon = X.size
other_err = 0 if template_centers is None else (2 * self.K)
final_err = np.zeros(recon + other_err)
F = self.get_factors(unique_R, inds, centers, widths)
sigma = np.zeros((1,))
sigma[0] = data_sigma
tfa_extension.recon(final_err[0:recon], X, F, W, sigma)
if other_err > 0:
# center error
for k in np.arange(self.K):
diff = (centers[k] - template_centers[k])
cov = from_tri_2_sym(template_centers_mean_cov[k], self.n_dim)
final_err[recon + k] = math.sqrt(
self.sample_scaling *
diff.dot(np.linalg.solve(cov, diff.T)))
# width error
base = recon + self.K
dist = template_widths_mean_var_reci *\
(widths - template_widths) ** 2
final_err[base:] = np.sqrt(self.sample_scaling * dist).ravel()
return final_err | def _residual_multivariate(
self,
estimate,
unique_R,
inds,
X,
W,
template_centers,
template_centers_mean_cov,
template_widths,
template_widths_mean_var_reci,
data_sigma) | Residual function for estimating centers and widths
Parameters
----------
estimate : 1D array
Initial estimation on centers
unique_R : a list of array,
Each element contains unique value in one dimension of
coordinate matrix R.
inds : a list of array,
Each element contains the indices to reconstruct one
dimension of original cooridnate matrix from the unique
array.
X : 2D array, with shape [n_voxel, n_tr]
fMRI data from one subject.
W : 2D array, with shape [K, n_tr]
The weight matrix.
template_centers: 2D array, with shape [K, n_dim]
The template prior on centers
template_centers_mean_cov: 2D array, with shape [K, cov_size]
The template prior on covariance of centers' mean
template_widths: 1D array
The template prior on widths
template_widths_mean_var_reci: 1D array
The reciprocal of template prior on variance of widths' mean
data_sigma: float
The variance of X.
Returns
-------
final_err : 1D array
The residual function for estimating centers. | 4.738464 | 4.440427 | 1.067119 |
# least_squares only accept x in 1D format
init_estimate = np.hstack(
(init_centers.ravel(), init_widths.ravel())) # .copy()
data_sigma = 1.0 / math.sqrt(2.0) * np.std(X)
final_estimate = least_squares(
self._residual_multivariate,
init_estimate,
args=(
unique_R,
inds,
X,
W,
template_centers,
template_widths,
template_centers_mean_cov,
template_widths_mean_var_reci,
data_sigma),
method=self.nlss_method,
loss=self.nlss_loss,
bounds=self.bounds,
verbose=0,
x_scale=self.x_scale,
tr_solver=self.tr_solver)
return final_estimate.x, final_estimate.cost | def _estimate_centers_widths(
self,
unique_R,
inds,
X,
W,
init_centers,
init_widths,
template_centers,
template_widths,
template_centers_mean_cov,
template_widths_mean_var_reci) | Estimate centers and widths
Parameters
----------
unique_R : a list of array,
Each element contains unique value in one dimension of
coordinate matrix R.
inds : a list of array,
Each element contains the indices to reconstruct one
dimension of original cooridnate matrix from the unique
array.
X : 2D array, with shape [n_voxel, n_tr]
fMRI data from one subject.
W : 2D array, with shape [K, n_tr]
The weight matrix.
init_centers : 2D array, with shape [K, n_dim]
The initial values of centers.
init_widths : 1D array
The initial values of widths.
template_centers: 1D array
The template prior on centers
template_widths: 1D array
The template prior on widths
template_centers_mean_cov: 2D array, with shape [K, cov_size]
The template prior on centers' mean
template_widths_mean_var_reci: 1D array
The reciprocal of template prior on variance of widths' mean
Returns
-------
final_estimate.x: 1D array
The newly estimated centers and widths.
final_estimate.cost: float
The cost value. | 3.152459 | 3.183125 | 0.990366 |
if template_prior is None:
template_centers = None
template_widths = None
template_centers_mean_cov = None
template_widths_mean_var_reci = None
else:
template_centers = self.get_centers(template_prior)
template_widths = self.get_widths(template_prior)
template_centers_mean_cov =\
self.get_centers_mean_cov(template_prior)
template_widths_mean_var_reci = 1.0 /\
self.get_widths_mean_var(template_prior)
inner_converged = False
np.random.seed(self.seed)
n = 0
while n < self.miter and not inner_converged:
self._fit_tfa_inner(
data,
R,
template_centers,
template_widths,
template_centers_mean_cov,
template_widths_mean_var_reci)
self._assign_posterior()
inner_converged, _ = self._converged()
if not inner_converged:
self.local_prior = self.local_posterior_
else:
logger.info("TFA converged at %d iteration." % (n))
n += 1
gc.collect()
return self | def _fit_tfa(self, data, R, template_prior=None) | TFA main algorithm
Parameters
----------
data: 2D array, in shape [n_voxel, n_tr]
The fMRI data from one subject.
R : 2D array, in shape [n_voxel, n_dim]
The voxel coordinate matrix of fMRI data
template_prior : 1D array,
The template prior on centers and widths.
Returns
-------
TFA
Returns the instance itself. | 2.773533 | 2.846088 | 0.974507 |
unique_R = []
inds = []
for d in np.arange(self.n_dim):
tmp_unique, tmp_inds = np.unique(R[:, d], return_inverse=True)
unique_R.append(tmp_unique)
inds.append(tmp_inds)
return unique_R, inds | def get_unique_R(self, R) | Get unique vlaues from coordinate matrix
Parameters
----------
R : 2D array
The coordinate matrix of a subject's fMRI data
Return
------
unique_R : a list of array,
Each element contains unique value in one dimension of
coordinate matrix R.
inds : a list of array,
Each element contains the indices to reconstruct one
dimension of original cooridnate matrix from the unique
array. | 2.268545 | 2.079082 | 1.091129 |
nfeature = data.shape[0]
nsample = data.shape[1]
feature_indices =\
np.random.choice(nfeature, self.max_num_voxel, replace=False)
sample_features = np.zeros(nfeature).astype(bool)
sample_features[feature_indices] = True
samples_indices =\
np.random.choice(nsample, self.max_num_tr, replace=False)
curr_data = np.zeros((self.max_num_voxel, self.max_num_tr))\
.astype(float)
curr_data = data[feature_indices]
curr_data = curr_data[:, samples_indices].copy()
curr_R = R[feature_indices].copy()
centers = self.get_centers(self.local_prior)
widths = self.get_widths(self.local_prior)
unique_R, inds = self.get_unique_R(curr_R)
F = self.get_factors(unique_R, inds, centers, widths)
W = self.get_weights(curr_data, F)
self.local_posterior_, self.total_cost = self._estimate_centers_widths(
unique_R, inds, curr_data, W, centers, widths,
template_centers, template_centers_mean_cov,
template_widths, template_widths_mean_var_reci)
return self | def _fit_tfa_inner(
self,
data,
R,
template_centers,
template_widths,
template_centers_mean_cov,
template_widths_mean_var_reci) | Fit TFA model, the inner loop part
Parameters
----------
data: 2D array, in shape [n_voxel, n_tr]
The fMRI data of a subject
R : 2D array, in shape [n_voxel, n_dim]
The voxel coordinate matrix of fMRI data
template_centers: 1D array
The template prior on centers
template_widths: 1D array
The template prior on widths
template_centers_mean_cov: 2D array, with shape [K, cov_size]
The template prior on covariance of centers' mean
template_widths_mean_var_reci: 1D array
The reciprocal of template prior on variance of widths' mean
Returns
-------
TFA
Returns the instance itself. | 2.981094 | 2.880653 | 1.034867 |
if self.verbose:
logger.info('Start to fit TFA ')
if not isinstance(X, np.ndarray):
raise TypeError("Input data should be an array")
if X.ndim != 2:
raise TypeError("Input data should be 2D array")
if not isinstance(R, np.ndarray):
raise TypeError("Input coordinate matrix should be an array")
if R.ndim != 2:
raise TypeError("Input coordinate matrix should be 2D array")
if X.shape[0] != R.shape[0]:
raise TypeError(
"The number of voxels should be the same in X and R!")
if self.weight_method != 'rr' and self.weight_method != 'ols':
raise ValueError(
"only 'rr' and 'ols' are accepted as weight_method!")
# main algorithm
self.n_dim = R.shape[1]
self.cov_vec_size = np.sum(np.arange(self.n_dim) + 1)
self.map_offset = self.get_map_offset()
self.bounds = self.get_bounds(R)
n_voxel = X.shape[0]
n_tr = X.shape[1]
self.sample_scaling = 0.5 * float(
self.max_num_voxel * self.max_num_tr) / float(n_voxel * n_tr)
if template_prior is None:
self.init_prior(R)
else:
self.local_prior = template_prior[0: self.map_offset[2]]
self._fit_tfa(X, R, template_prior)
if template_prior is None:
centers = self.get_centers(self.local_posterior_)
widths = self.get_widths(self.local_posterior_)
unique_R, inds = self.get_unique_R(R)
self.F_ = self.get_factors(unique_R, inds, centers, widths)
self.W_ = self.get_weights(X, self.F_)
return self | def fit(self, X, R, template_prior=None) | Topographical Factor Analysis (TFA)[Manning2014]
Parameters
----------
X : 2D array, in shape [n_voxel, n_sample]
The fMRI data of one subject
R : 2D array, in shape [n_voxel, n_dim]
The voxel coordinate matrix of fMRI data
template_prior : None or 1D array
The template prior as an extra constraint
None when fitting TFA alone | 3.133541 | 2.927403 | 1.070416 |
recon = F.dot(W).ravel()
err = mean_squared_error(
data.ravel(),
recon,
multioutput='uniform_average')
return math.sqrt(err) | def recon_err(data, F, W) | Calcuate reconstruction error
Parameters
----------
data : 2D array
True data to recover.
F : 2D array
HTFA factor matrix.
W : 2D array
HTFA weight matrix.
Returns
-------
float
Returns root mean squared reconstruction error. | 4.492583 | 6.174216 | 0.727636 |
W = htfa.get_weights(data, F)
return recon_err(data, F, W) | def get_train_err(htfa, data, F) | Calcuate training error
Parameters
----------
htfa : HTFA
An instance of HTFA, factor anaysis class in BrainIAK.
data : 2D array
Input data to HTFA.
F : 2D array
HTFA factor matrix.
Returns
-------
float
Returns root mean squared error on training. | 5.959761 | 8.76231 | 0.680159 |
clf = bcast_var[2]
data = l[0][mask, :].T
# print(l[0].shape, mask.shape, data.shape)
skf = model_selection.StratifiedKFold(n_splits=bcast_var[1],
shuffle=False)
accuracy = np.mean(model_selection.cross_val_score(clf, data,
y=bcast_var[0],
cv=skf,
n_jobs=1))
return accuracy | def _sfn(l, mask, myrad, bcast_var) | Score classifier on searchlight data using cross-validation.
The classifier is in `bcast_var[2]`. The labels are in `bast_var[0]`. The
number of cross-validation folds is in `bast_var[1]. | 3.48752 | 2.863548 | 1.217902 |
rank = MPI.COMM_WORLD.Get_rank()
if rank == 0:
logger.info(
'running activity-based voxel selection via Searchlight'
)
self.sl.distribute([self.data], self.mask)
self.sl.broadcast((self.labels, self.num_folds, clf))
if rank == 0:
logger.info(
'data preparation done'
)
# obtain a 3D array with accuracy numbers
result_volume = self.sl.run_searchlight(_sfn)
# get result tuple list from the volume
result_list = result_volume[self.mask]
results = []
if rank == 0:
for idx, value in enumerate(result_list):
if value is None:
value = 0
results.append((idx, value))
# Sort the voxels
results.sort(key=lambda tup: tup[1], reverse=True)
logger.info(
'activity-based voxel selection via Searchlight is done'
)
return result_volume, results | def run(self, clf) | run activity-based voxel selection
Sort the voxels based on the cross-validation accuracy
of their activity vectors within the searchlight
Parameters
----------
clf: classification function
the classifier to be used in cross validation
Returns
-------
result_volume: 3D array of accuracy numbers
contains the voxelwise accuracy numbers obtained via Searchlight
results: list of tuple (voxel_id, accuracy)
the accuracy numbers of all voxels, in accuracy descending order
the length of array equals the number of voxels | 5.902512 | 4.261989 | 1.38492 |
# no shuffling in cv
skf = model_selection.StratifiedKFold(n_splits=num_folds,
shuffle=False)
scores = model_selection.cross_val_score(clf, subject_data,
y=labels,
cv=skf, n_jobs=1)
logger.debug(
'cross validation for voxel %d is done' %
vid
)
return (vid, scores.mean()) | def _cross_validation_for_one_voxel(clf, vid, num_folds, subject_data, labels) | Score classifier on data using cross validation. | 3.141211 | 3.234481 | 0.971164 |
rank = MPI.COMM_WORLD.Get_rank()
if rank == self.master_rank:
results = self._master()
# Sort the voxels
results.sort(key=lambda tup: tup[1], reverse=True)
else:
self._worker(clf)
results = []
return results | def run(self, clf) | Run correlation-based voxel selection in master-worker model.
Sort the voxels based on the cross-validation accuracy
of their correlation vectors
Parameters
----------
clf: classification function
the classifier to be used in cross validation
Returns
-------
results: list of tuple (voxel_id, accuracy)
the accuracy numbers of all voxels, in accuracy descending order
the length of array equals the number of voxels | 5.18786 | 4.250209 | 1.220613 |
logger.info(
'Master at rank %d starts to allocate tasks',
MPI.COMM_WORLD.Get_rank()
)
results = []
comm = MPI.COMM_WORLD
size = comm.Get_size()
sending_voxels = self.voxel_unit if self.voxel_unit < self.num_voxels \
else self.num_voxels
current_task = (0, sending_voxels)
status = MPI.Status()
# using_size is used when the number of tasks
# is smaller than the number of workers
using_size = size
for i in range(0, size):
if i == self.master_rank:
continue
if current_task[1] == 0:
using_size = i
break
logger.debug(
'master starts to send a task to worker %d' %
i
)
comm.send(current_task,
dest=i,
tag=self._WORKTAG)
next_start = current_task[0] + current_task[1]
sending_voxels = self.voxel_unit \
if self.voxel_unit < self.num_voxels - next_start \
else self.num_voxels - next_start
current_task = (next_start, sending_voxels)
while using_size == size:
if current_task[1] == 0:
break
result = comm.recv(source=MPI.ANY_SOURCE,
tag=MPI.ANY_TAG,
status=status)
results += result
comm.send(current_task,
dest=status.Get_source(),
tag=self._WORKTAG)
next_start = current_task[0] + current_task[1]
sending_voxels = self.voxel_unit \
if self.voxel_unit < self.num_voxels - next_start \
else self.num_voxels - next_start
current_task = (next_start, sending_voxels)
for i in range(0, using_size):
if i == self.master_rank:
continue
result = comm.recv(source=MPI.ANY_SOURCE, tag=MPI.ANY_TAG)
results += result
for i in range(0, size):
if i == self.master_rank:
continue
comm.send(None,
dest=i,
tag=self._TERMINATETAG)
return results | def _master(self) | Master node's operation.
Assigning tasks to workers and collecting results from them
Parameters
----------
None
Returns
-------
results: list of tuple (voxel_id, accuracy)
the accuracy numbers of all voxels, in accuracy descending order
the length of array equals the number of voxels | 2.292363 | 2.202826 | 1.040646 |
logger.debug(
'worker %d is running, waiting for tasks from master at rank %d' %
(MPI.COMM_WORLD.Get_rank(), self.master_rank)
)
comm = MPI.COMM_WORLD
status = MPI.Status()
while 1:
task = comm.recv(source=self.master_rank,
tag=MPI.ANY_TAG,
status=status)
if status.Get_tag():
break
comm.send(self._voxel_scoring(task, clf),
dest=self.master_rank) | def _worker(self, clf) | Worker node's operation.
Receiving tasks from the master to process and sending the result back
Parameters
----------
clf: classification function
the classifier to be used in cross validation
Returns
-------
None | 3.664976 | 3.575085 | 1.025144 |
time1 = time.time()
s = task[0]
nEpochs = len(self.raw_data)
logger.debug(
'start to compute the correlation: #epochs: %d, '
'#processed voxels: %d, #total voxels to compute against: %d' %
(nEpochs, task[1], self.num_voxels2)
)
corr = np.zeros((task[1], nEpochs, self.num_voxels2),
np.float32, order='C')
count = 0
for i in range(len(self.raw_data)):
mat = self.raw_data[i]
mat2 = self.raw_data2[i] if self.raw_data2 is not None else mat
no_trans = 'N'
trans = 'T'
blas.compute_self_corr_for_voxel_sel(no_trans, trans,
self.num_voxels2, task[1],
mat.shape[0], 1.0,
mat2, self.num_voxels2,
s, mat, self.num_voxels,
0.0, corr,
self.num_voxels2 * nEpochs,
count)
count += 1
time2 = time.time()
logger.debug(
'correlation computation for %d voxels, takes %.2f s' %
(task[1], (time2 - time1))
)
return corr | def _correlation_computation(self, task) | Use BLAS API to do correlation computation (matrix multiplication).
Parameters
----------
task: tuple (start_voxel_id, num_processed_voxels)
depicting the voxels assigned to compute
Returns
-------
corr: 3D array in shape [num_processed_voxels, num_epochs, num_voxels]
the correlation values of all subjects in all epochs
for the assigned values, in row-major
corr[i, e, s + j] = corr[j, e, s + i] | 3.581337 | 3.20664 | 1.11685 |
time1 = time.time()
(sv, e, av) = corr.shape
for i in range(sv):
start = 0
while start < e:
cur_val = corr[i, start: start + self.epochs_per_subj, :]
cur_val = .5 * np.log((cur_val + 1) / (1 - cur_val))
corr[i, start: start + self.epochs_per_subj, :] = \
zscore(cur_val, axis=0, ddof=0)
start += self.epochs_per_subj
# if zscore fails (standard deviation is zero),
# set all values to be zero
corr = np.nan_to_num(corr)
time2 = time.time()
logger.debug(
'within-subject normalization for %d voxels '
'using numpy zscore function, takes %.2f s' %
(sv, (time2 - time1))
)
return corr | def _correlation_normalization(self, corr) | Do within-subject normalization.
This method uses scipy.zscore to normalize the data,
but is much slower than its C++ counterpart.
It is doing in-place z-score.
Parameters
----------
corr: 3D array in shape [num_processed_voxels, num_epochs, num_voxels]
the correlation values of all subjects in all epochs
for the assigned values, in row-major
Returns
-------
corr: 3D array in shape [num_processed_voxels, num_epochs, num_voxels]
the normalized correlation values of all subjects in all epochs
for the assigned values, in row-major | 4.064946 | 3.53786 | 1.148984 |
time1 = time.time()
(num_processed_voxels, num_epochs, _) = corr.shape
if isinstance(clf, sklearn.svm.SVC) and clf.kernel == 'precomputed':
# kernel matrices should be computed
kernel_matrices = np.zeros((num_processed_voxels, num_epochs,
num_epochs),
np.float32, order='C')
for i in range(num_processed_voxels):
blas.compute_kernel_matrix('L', 'T',
num_epochs, self.num_voxels2,
1.0, corr,
i, self.num_voxels2,
0.0, kernel_matrices[i, :, :],
num_epochs)
# shrink the values for getting more stable alpha values
# in SVM training iteration
num_digits = len(str(int(kernel_matrices[i, 0, 0])))
if num_digits > 2:
proportion = 10**(2-num_digits)
kernel_matrices[i, :, :] *= proportion
data = kernel_matrices
else:
data = corr
time2 = time.time()
logger.debug(
'cross validation data preparation takes %.2f s' %
(time2 - time1)
)
return data | def _prepare_for_cross_validation(self, corr, clf) | Prepare data for voxelwise cross validation.
If the classifier is sklearn.svm.SVC with precomputed kernel,
the kernel matrix of each voxel is computed, otherwise do nothing.
Parameters
----------
corr: 3D array in shape [num_processed_voxels, num_epochs, num_voxels]
the normalized correlation values of all subjects in all epochs
for the assigned values, in row-major
clf: classification function
the classifier to be used in cross validation
Returns
-------
data: 3D numpy array
If using sklearn.svm.SVC with precomputed kernel,
it is in shape [num_processed_voxels, num_epochs, num_epochs];
otherwise it is the input argument corr,
in shape [num_processed_voxels, num_epochs, num_voxels] | 4.42861 | 3.644763 | 1.215061 |
time1 = time.time()
if isinstance(clf, sklearn.svm.SVC) and clf.kernel == 'precomputed'\
and self.use_multiprocessing:
inlist = [(clf, i + task[0], self.num_folds, data[i, :, :],
self.labels) for i in range(task[1])]
with multiprocessing.Pool(self.process_num) as pool:
results = list(pool.starmap(_cross_validation_for_one_voxel,
inlist))
else:
results = []
for i in range(task[1]):
result = _cross_validation_for_one_voxel(clf, i + task[0],
self.num_folds,
data[i, :, :],
self.labels)
results.append(result)
time2 = time.time()
logger.debug(
'cross validation for %d voxels, takes %.2f s' %
(task[1], (time2 - time1))
)
return results | def _do_cross_validation(self, clf, data, task) | Run voxelwise cross validation based on correlation vectors.
clf: classification function
the classifier to be used in cross validation
data: 3D numpy array
If using sklearn.svm.SVC with precomputed kernel,
it is in shape [num_processed_voxels, num_epochs, num_epochs];
otherwise it is the input argument corr,
in shape [num_processed_voxels, num_epochs, num_voxels]
task: tuple (start_voxel_id, num_processed_voxels)
depicting the voxels assigned to compute
Returns
-------
results: list of tuple (voxel_id, accuracy)
the accuracy numbers of all voxels, in accuracy descending order
the length of array equals the number of assigned voxels | 2.844017 | 2.541203 | 1.119162 |
time1 = time.time()
# correlation computation
corr = self._correlation_computation(task)
# normalization
# corr = self._correlation_normalization(corr)
time3 = time.time()
fcma_extension.normalization(corr, self.epochs_per_subj)
time4 = time.time()
logger.debug(
'within-subject normalization for %d voxels '
'using C++, takes %.2f s' %
(task[1], (time4 - time3))
)
# cross validation
data = self._prepare_for_cross_validation(corr, clf)
if isinstance(clf, sklearn.svm.SVC) and clf.kernel == 'precomputed':
# to save memory so that the process can be forked
del corr
results = self._do_cross_validation(clf, data, task)
time2 = time.time()
logger.info(
'in rank %d, task %d takes %.2f s' %
(MPI.COMM_WORLD.Get_rank(),
(int(task[0] / self.voxel_unit)), (time2 - time1))
)
return results | def _voxel_scoring(self, task, clf) | The voxel selection process done in the worker node.
Take the task in,
do analysis on voxels specified by the task (voxel id, num_voxels)
It is a three-stage pipeline consisting of:
1. correlation computation
2. within-subject normalization
3. voxelwise cross validation
Parameters
----------
task: tuple (start_voxel_id, num_processed_voxels),
depicting the voxels assigned to compute
clf: classification function
the classifier to be used in cross validation
Returns
-------
results: list of tuple (voxel_id, accuracy)
the accuracy numbers of all voxels, in accuracy descending order
the length of array equals the number of assigned voxels | 5.239889 | 4.504151 | 1.163346 |
logger.info('Starting SS-SRM')
# Check that the alpha value is in range (0.0,1.0)
if 0.0 >= self.alpha or self.alpha >= 1.0:
raise ValueError("Alpha parameter should be in range (0.0, 1.0)")
# Check that the regularizer value is positive
if 0.0 >= self.gamma:
raise ValueError("Gamma parameter should be positive.")
# Check the number of subjects
if len(X) <= 1 or len(y) <= 1 or len(Z) <= 1:
raise ValueError("There are not enough subjects in the input "
"data to train the model.")
if not (len(X) == len(y)) or not (len(X) == len(Z)):
raise ValueError("Different number of subjects in data.")
# Check for input data sizes
if X[0].shape[1] < self.features:
raise ValueError(
"There are not enough samples to train the model with "
"{0:d} features.".format(self.features))
# Check if all subjects have same number of TRs for alignment
# and if alignment and classification data have the same number of
# voxels per subject. Also check that there labels for all the classif.
# sample
number_trs = X[0].shape[1]
number_subjects = len(X)
for subject in range(number_subjects):
assert_all_finite(X[subject])
assert_all_finite(Z[subject])
if X[subject].shape[1] != number_trs:
raise ValueError("Different number of alignment samples "
"between subjects.")
if X[subject].shape[0] != Z[subject].shape[0]:
raise ValueError("Different number of voxels between alignment"
" and classification data (subject {0:d})"
".".format(subject))
if Z[subject].shape[1] != y[subject].size:
raise ValueError("Different number of samples and labels in "
"subject {0:d}.".format(subject))
# Map the classes to [0..C-1]
new_y = self._init_classes(y)
# Run SS-SRM
self.w_, self.s_, self.theta_, self.bias_ = self._sssrm(X, Z, new_y)
return self | def fit(self, X, y, Z) | Compute the Semi-Supervised Shared Response Model
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, n_align]
Each element in the list contains the fMRI data for alignment of
one subject. There are n_align samples for each subject.
y : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in Z.
Z : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject
for training the MLR classifier. | 3.446848 | 3.195484 | 1.078662 |
self.classes_ = unique_labels(utils.concatenate_not_none(y))
new_y = [None] * len(y)
for s in range(len(y)):
new_y[s] = np.digitize(y[s], self.classes_) - 1
return new_y | def _init_classes(self, y) | Map all possible classes to the range [0,..,C-1]
Parameters
----------
y : list of arrays of int, each element has shape=[samples_i,]
Labels of the samples for each subject
Returns
-------
new_y : list of arrays of int, each element has shape=[samples_i,]
Mapped labels of the samples for each subject
Note
----
The mapping of the classes is saved in the attribute classes_. | 3.81769 | 3.318319 | 1.150489 |
# Check if the model exist
if hasattr(self, 'w_') is False:
raise NotFittedError("The model fit has not been run yet.")
# Check the number of subjects
if len(X) != len(self.w_):
raise ValueError("The number of subjects does not match the one"
" in the model.")
X_shared = self.transform(X)
p = [None] * len(X_shared)
for subject in range(len(X_shared)):
sumexp, _, exponents = utils.sumexp_stable(
self.theta_.T.dot(X_shared[subject]) + self.bias_)
p[subject] = self.classes_[
(exponents / sumexp[np.newaxis, :]).argmax(axis=0)]
return p | def predict(self, X) | Classify the output for given data
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject
The number of voxels should be according to each subject at
the moment of training the model.
Returns
-------
p: list of arrays, element i has shape=[samples_i]
Predictions for each data sample. | 3.997304 | 3.852075 | 1.037702 |
classes = self.classes_.size
# Initialization:
self.random_state_ = np.random.RandomState(self.rand_seed)
random_states = [
np.random.RandomState(self.random_state_.randint(2**32))
for i in range(len(data_align))]
# Set Wi's to a random orthogonal voxels by TRs
w, _ = srm._init_w_transforms(data_align, self.features, random_states)
# Initialize the shared response S
s = SSSRM._compute_shared_response(data_align, w)
# Initialize theta and bias
theta, bias = self._update_classifier(data_sup, labels, w, classes)
# calculate and print the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup, labels,
w, s, theta, bias)
logger.info('Objective function %f' % objective)
# Main loop:
for iteration in range(self.n_iter):
logger.info('Iteration %d' % (iteration + 1))
# Update the mappings Wi
w = self._update_w(data_align, data_sup, labels, w, s, theta, bias)
# Output the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup,
labels, w, s, theta, bias)
logger.info('Objective function after updating Wi %f'
% objective)
# Update the shared response S
s = SSSRM._compute_shared_response(data_align, w)
# Output the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup,
labels, w, s, theta, bias)
logger.info('Objective function after updating S %f'
% objective)
# Update the MLR classifier, theta and bias
theta, bias = self._update_classifier(data_sup, labels, w, classes)
# Output the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup,
labels, w, s, theta, bias)
logger.info('Objective function after updating MLR %f'
% objective)
return w, s, theta, bias | def _sssrm(self, data_align, data_sup, labels) | Block-Coordinate Descent algorithm for fitting SS-SRM.
Parameters
----------
data_align : list of 2D arrays, element i has shape=[voxels_i, n_align]
Each element in the list contains the fMRI data for alignment of
one subject. There are n_align samples for each subject.
data_sup : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in data_sup.
Returns
-------
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
s : array, shape=[features, samples]
The shared response. | 2.677859 | 2.503807 | 1.069515 |
# Stack the data and labels for training the classifier
data_stacked, labels_stacked, weights = \
SSSRM._stack_list(data, labels, w)
features = w[0].shape[1]
total_samples = weights.size
data_th = S.shared(data_stacked.astype(theano.config.floatX))
val_ = S.shared(labels_stacked)
total_samples_S = S.shared(total_samples)
theta_th = T.matrix(name='theta', dtype=theano.config.floatX)
bias_th = T.col(name='bias', dtype=theano.config.floatX)
constf2 = S.shared(self.alpha / self.gamma, allow_downcast=True)
weights_th = S.shared(weights)
log_p_y_given_x = \
T.log(T.nnet.softmax((theta_th.T.dot(data_th.T)).T + bias_th.T))
f = -constf2 * T.sum((log_p_y_given_x[T.arange(total_samples_S), val_])
/ weights_th) + 0.5 * T.sum(theta_th ** 2)
manifold = Product((Euclidean(features, classes),
Euclidean(classes, 1)))
problem = Problem(manifold=manifold, cost=f, arg=[theta_th, bias_th],
verbosity=0)
solver = ConjugateGradient(mingradnorm=1e-6)
solution = solver.solve(problem)
theta = solution[0]
bias = solution[1]
del constf2
del theta_th
del bias_th
del data_th
del val_
del solver
del solution
return theta, bias | def _update_classifier(self, data, labels, w, classes) | Update the classifier parameters theta and bias
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in data_sup.
w : list of 2D array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
classes : int
The number of classes in the classifier.
Returns
-------
theta : array, shape=[features, classes]
The MLR parameter for the class planes.
bias : array shape=[classes,]
The MLR parameter for class biases. | 3.98794 | 3.847744 | 1.036436 |
s = np.zeros((w[0].shape[1], data[0].shape[1]))
for m in range(len(w)):
s = s + w[m].T.dot(data[m])
s /= len(w)
return s | def _compute_shared_response(data, w) | Compute the shared response S
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples]
Each element in the list contains the fMRI data of one subject.
w : list of 2D arrays, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
Returns
-------
s : array, shape=[features, samples]
The shared response for the subjects data with the mappings in w. | 2.863352 | 2.609467 | 1.097294 |
subjects = len(data_align)
# Compute the SRM loss
f_val = 0.0
for subject in range(subjects):
samples = data_align[subject].shape[1]
f_val += (1 - self.alpha) * (0.5 / samples) \
* np.linalg.norm(data_align[subject] - w[subject].dot(s),
'fro')**2
# Compute the MLR loss
f_val += self._loss_lr(data_sup, labels, w, theta, bias)
return f_val | def _objective_function(self, data_align, data_sup, labels, w, s, theta,
bias) | Compute the objective function of the Semi-Supervised SRM
See :eq:`sssrm-eq`.
Parameters
----------
data_align : list of 2D arrays, element i has shape=[voxels_i, n_align]
Each element in the list contains the fMRI data for alignment of
one subject. There are n_align samples for each subject.
data_sup : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in data_sup.
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
s : array, shape=[features, samples]
The shared response.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
f_val : float
The SS-SRM objective function evaluated based on the parameters to
this function. | 4.038027 | 3.565099 | 1.132655 |
# Compute the SRM loss
f_val = 0.0
samples = data_align.shape[1]
f_val += (1 - self.alpha) * (0.5 / samples) \
* np.linalg.norm(data_align - w.dot(s), 'fro')**2
# Compute the MLR loss
f_val += self._loss_lr_subject(data_sup, labels, w, theta, bias)
return f_val | def _objective_function_subject(self, data_align, data_sup, labels, w, s,
theta, bias) | Compute the objective function for one subject.
.. math:: (1-C)*Loss_{SRM}_i(W_i,S;X_i)
.. math:: + C/\\gamma * Loss_{MLR_i}(\\theta, bias; {(W_i^T*Z_i, y_i})
.. math:: + R(\\theta)
Parameters
----------
data_align : 2D array, shape=[voxels_i, samples_align]
Contains the fMRI data for alignment of subject i.
data_sup : 2D array, shape=[voxels_i, samples_i]
Contains the fMRI data of one subject for the classification task.
labels : array of int, shape=[samples_i]
The labels for the data samples in data_sup.
w : array, shape=[voxels_i, features]
The orthogonal transform (mapping) :math:`W_i` for subject i.
s : array, shape=[features, samples]
The shared response.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
f_val : float
The SS-SRM objective function for subject i evaluated on the
parameters to this function. | 4.451812 | 3.707336 | 1.200811 |
if data is None:
return 0.0
samples = data.shape[1]
thetaT_wi_zi_plus_bias = theta.T.dot(w.T.dot(data)) + bias
sum_exp, max_value, _ = utils.sumexp_stable(thetaT_wi_zi_plus_bias)
sum_exp_values = np.log(sum_exp) + max_value
aux = 0.0
for sample in range(samples):
label = labels[sample]
aux += thetaT_wi_zi_plus_bias[label, sample]
return self.alpha / samples / self.gamma * (sum_exp_values.sum() - aux) | def _loss_lr_subject(self, data, labels, w, theta, bias) | Compute the Loss MLR for a single subject (without regularization)
Parameters
----------
data : array, shape=[voxels, samples]
The fMRI data of subject i for the classification task.
labels : array of int, shape=[samples]
The labels for the data samples in data.
w : array, shape=[voxels, features]
The orthogonal transform (mapping) :math:`W_i` for subject i.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
loss : float
The loss MLR for the subject | 4.241104 | 4.657131 | 0.910669 |
subjects = len(data)
loss = 0.0
for subject in range(subjects):
if labels[subject] is not None:
loss += self._loss_lr_subject(data[subject], labels[subject],
w[subject], theta, bias)
return loss + 0.5 * np.linalg.norm(theta, 'fro')**2 | def _loss_lr(self, data, labels, w, theta, bias) | Compute the Loss MLR (with the regularization)
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the samples in
data.
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
loss : float
The loss MLR for the SS-SRM model | 2.92911 | 3.024371 | 0.968502 |
labels_stacked = utils.concatenate_not_none(data_labels)
weights = np.empty((labels_stacked.size,))
data_shared = [None] * len(data)
curr_samples = 0
for s in range(len(data)):
if data[s] is not None:
subject_samples = data[s].shape[1]
curr_samples_end = curr_samples + subject_samples
weights[curr_samples:curr_samples_end] = subject_samples
data_shared[s] = w[s].T.dot(data[s])
curr_samples += data[s].shape[1]
data_stacked = utils.concatenate_not_none(data_shared, axis=1).T
return data_stacked, labels_stacked, weights | def _stack_list(data, data_labels, w) | Construct a numpy array by stacking arrays in a list
Parameter
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
data_labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the samples in
data.
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
Returns
-------
data_stacked : 2D array, shape=[samples, features]
The data samples from all subjects are stacked into a single
2D array, where "samples" is the sum of samples_i.
labels_stacked : array, shape=[samples,]
The labels from all subjects are stacked into a single
array, where "samples" is the sum of samples_i.
weights : array, shape=[samples,]
The number of samples of the subject that are related to that
sample. They become a weight per sample in the MLR loss. | 3.378434 | 3.010392 | 1.122257 |
voxel_fn = extra_params[0]
shape_mask = extra_params[1]
min_active_voxels_proportion = extra_params[2]
outmat = np.empty(msk.shape, dtype=np.object)[mysl_rad:-mysl_rad,
mysl_rad:-mysl_rad,
mysl_rad:-mysl_rad]
for i in range(0, outmat.shape[0]):
for j in range(0, outmat.shape[1]):
for k in range(0, outmat.shape[2]):
if msk[i+mysl_rad, j+mysl_rad, k+mysl_rad]:
searchlight_slice = np.s_[
i:i+2*mysl_rad+1,
j:j+2*mysl_rad+1,
k:k+2*mysl_rad+1]
voxel_fn_mask = msk[searchlight_slice] * shape_mask
if (min_active_voxels_proportion == 0
or np.count_nonzero(voxel_fn_mask) / voxel_fn_mask.size
> min_active_voxels_proportion):
outmat[i, j, k] = voxel_fn(
[ll[searchlight_slice] for ll in l],
msk[searchlight_slice] * shape_mask,
mysl_rad,
bcast_var)
return outmat | def _singlenode_searchlight(l, msk, mysl_rad, bcast_var, extra_params) | Run searchlight function on block data in parallel.
`extra_params` contains:
- Searchlight function.
- `Shape` mask.
- Minimum active voxels proportion required to run the searchlight
function. | 2.25598 | 2.018317 | 1.117753 |
rank = self.comm.rank
B = [(rank, idx) for (idx, c) in enumerate(data) if c is not None]
C = self.comm.allreduce(B)
ownership = [None] * len(data)
for c in C:
ownership[c[1]] = c[0]
return ownership | def _get_ownership(self, data) | Determine on which rank each subject currently resides
Parameters
----------
data: list of 4D arrays with subject data
Returns
-------
list of ranks indicating the owner of each subject | 4.349696 | 4.652554 | 0.934905 |
blocks = []
outerblk = self.max_blk_edge + 2*self.sl_rad
for i in range(0, mask.shape[0], self.max_blk_edge):
for j in range(0, mask.shape[1], self.max_blk_edge):
for k in range(0, mask.shape[2], self.max_blk_edge):
block_shape = mask[i:i+outerblk,
j:j+outerblk,
k:k+outerblk
].shape
if np.any(
mask[i+self.sl_rad:i+block_shape[0]-self.sl_rad,
j+self.sl_rad:j+block_shape[1]-self.sl_rad,
k+self.sl_rad:k+block_shape[2]-self.sl_rad]):
blocks.append(((i, j, k), block_shape))
return blocks | def _get_blocks(self, mask) | Divide the volume into a set of blocks
Ignore blocks that have no active voxels in the mask
Parameters
----------
mask: a boolean 3D array which is true at every active voxel
Returns
-------
list of tuples containing block information:
- a triple containing top left point of the block and
- a triple containing the size in voxels of the block | 2.197445 | 2.131971 | 1.030711 |
(pt, sz) = block
if len(mat.shape) == 3:
return mat[pt[0]:pt[0]+sz[0],
pt[1]:pt[1]+sz[1],
pt[2]:pt[2]+sz[2]].copy()
elif len(mat.shape) == 4:
return mat[pt[0]:pt[0]+sz[0],
pt[1]:pt[1]+sz[1],
pt[2]:pt[2]+sz[2],
:].copy() | def _get_block_data(self, mat, block) | Retrieve a block from a 3D or 4D volume
Parameters
----------
mat: a 3D or 4D volume
block: a tuple containing block information:
- a triple containing the lowest-coordinate voxel in the block
- a triple containing the size in voxels of the block
Returns
-------
In the case of a 3D array, a 3D subarray at the block location
In the case of a 4D array, a 4D subarray at the block location,
including the entire fourth dimension. | 1.804486 | 1.788728 | 1.00881 |
return [self._get_block_data(mat, block) for block in blocks] | def _split_volume(self, mat, blocks) | Convert a volume into a list of block data
Parameters
----------
mat: A 3D or 4D array to be split
blocks: a list of tuples containing block information:
- a triple containing the top left point of the block and
- a triple containing the size in voxels of the block
Returns
-------
A list of the subarrays corresponding to each block | 5.389194 | 6.491529 | 0.830189 |
rank = self.comm.rank
size = self.comm.size
subject_submatrices = []
nblocks = self.comm.bcast(len(data)
if rank == owner else None, root=owner)
# For each submatrix
for idx in range(0, nblocks, size):
padded = None
extra = max(0, idx+size - nblocks)
# Pad with "None" so scatter can go to all processes
if data is not None:
padded = data[idx:idx+size]
if extra > 0:
padded = padded + [None]*extra
# Scatter submatrices to all processes
mytrans = self.comm.scatter(padded, root=owner)
# Contribute submatrix to subject list
if mytrans is not None:
subject_submatrices += [mytrans]
return subject_submatrices | def _scatter_list(self, data, owner) | Distribute a list from one rank to other ranks in a cyclic manner
Parameters
----------
data: list of pickle-able data
owner: rank that owns the data
Returns
-------
A list containing the data in a cyclic layout across ranks | 4.662355 | 4.686542 | 0.994839 |
if mask.ndim != 3:
raise ValueError('mask should be a 3D array')
for (idx, subj) in enumerate(subjects):
if subj is not None:
if subj.ndim != 4:
raise ValueError('subjects[{}] must be 4D'.format(idx))
self.mask = mask
rank = self.comm.rank
# Get/set ownership
ownership = self._get_ownership(subjects)
all_blocks = self._get_blocks(mask) if rank == 0 else None
all_blocks = self.comm.bcast(all_blocks)
# Divide data and mask
splitsubj = [self._split_volume(s, all_blocks)
if s is not None else None
for s in subjects]
submasks = self._split_volume(mask, all_blocks)
# Scatter points, data, and mask
self.blocks = self._scatter_list(all_blocks, 0)
self.submasks = self._scatter_list(submasks, 0)
self.subproblems = [self._scatter_list(s, ownership[s_idx])
for (s_idx, s) in enumerate(splitsubj)] | def distribute(self, subjects, mask) | Distribute data to MPI ranks
Parameters
----------
subjects : list of 4D arrays containing data for one or more subjects.
Each entry of the list must be present on at most one rank,
and the other ranks contain a "None" at this list location.
For example, for 3 ranks you may lay out the data in the
following manner:
Rank 0: [Subj0, None, None]
Rank 1: [None, Subj1, None]
Rank 2: [None, None, Subj2]
Or alternatively, you may lay out the data in this manner:
Rank 0: [Subj0, Subj1, Subj2]
Rank 1: [None, None, None]
Rank 2: [None, None, None]
mask: 3D array with "True" entries at active vertices | 3.846568 | 3.718835 | 1.034348 |
rank = self.comm.rank
results = []
usable_cpus = usable_cpu_count()
if pool_size is None:
processes = usable_cpus
else:
processes = min(pool_size, usable_cpus)
if processes > 1:
with Pool(processes) as pool:
for idx, block in enumerate(self.blocks):
result = pool.apply_async(
block_fn,
([subproblem[idx] for subproblem in self.subproblems],
self.submasks[idx],
self.sl_rad,
self.bcast_var,
extra_block_fn_params))
results.append((block[0], result))
local_outputs = [(result[0], result[1].get())
for result in results]
else:
# If we only are using one CPU core, no need to create a Pool,
# cause an underlying fork(), and send the data to that process.
# Just do it here in serial. This will save copying the memory
# and will stop a fork() which can cause problems in some MPI
# implementations.
for idx, block in enumerate(self.blocks):
subprob_list = [subproblem[idx]
for subproblem in self.subproblems]
result = block_fn(
subprob_list,
self.submasks[idx],
self.sl_rad,
self.bcast_var,
extra_block_fn_params)
results.append((block[0], result))
local_outputs = [(result[0], result[1]) for result in results]
# Collect results
global_outputs = self.comm.gather(local_outputs)
# Coalesce results
outmat = np.empty(self.mask.shape, dtype=np.object)
if rank == 0:
for go_rank in global_outputs:
for (pt, mat) in go_rank:
coords = np.s_[
pt[0]+self.sl_rad:pt[0]+self.sl_rad+mat.shape[0],
pt[1]+self.sl_rad:pt[1]+self.sl_rad+mat.shape[1],
pt[2]+self.sl_rad:pt[2]+self.sl_rad+mat.shape[2]
]
outmat[coords] = mat
return outmat | def run_block_function(self, block_fn, extra_block_fn_params=None,
pool_size=None) | Perform a function for each block in a volume.
Parameters
----------
block_fn: function to apply to each block:
Parameters
data: list of 4D arrays containing subset of subject data,
which is padded with sl_rad voxels.
mask: 3D array containing subset of mask data
sl_rad: radius, in voxels, of the sphere inscribed in the
cube
bcast_var: shared data which is broadcast to all processes
extra_params: extra parameters
Returns
3D array which is the same size as the mask
input with padding removed
extra_block_fn_params: tuple
Extra parameters to pass to the block function
pool_size: int
Maximum number of processes running the block function in parallel.
If None, number of available hardware threads, considering cpusets
restrictions. | 3.302493 | 3.07704 | 1.07327 |
extra_block_fn_params = (voxel_fn, self.shape,
self.min_active_voxels_proportion)
block_fn_result = self.run_block_function(_singlenode_searchlight,
extra_block_fn_params,
pool_size)
return block_fn_result | def run_searchlight(self, voxel_fn, pool_size=None) | Perform a function at each voxel which is set to True in the
user-provided mask. The mask passed to the searchlight function will be
further masked by the user-provided searchlight shape.
Parameters
----------
voxel_fn: function to apply at each voxel
Must be `serializeable using pickle
<https://docs.python.org/3/library/pickle.html#what-can-be-pickled-and-unpickled>`_.
Parameters
subj: list of 4D arrays containing subset of subject data
mask: 3D array containing subset of mask data
sl_rad: radius, in voxels, of the sphere inscribed in the
cube
bcast_var: shared data which is broadcast to all processes
Returns
Value of any pickle-able type
Returns
-------
A volume which is the same size as the mask, however a number of voxels
equal to the searchlight radius has been removed from each border of
the volume. This volume contains the values returned from the
searchlight function at each voxel which was set to True in the mask,
and None elsewhere. | 6.31097 | 7.915668 | 0.797276 |
shape = data.shape
data = zscore(data, axis=axis, ddof=0)
# if zscore fails (standard deviation is zero),
# optionally set all values to be zero
if not return_nans:
data = np.nan_to_num(data)
data = data / math.sqrt(shape[axis])
return data | def _normalize_for_correlation(data, axis, return_nans=False) | normalize the data before computing correlation
The data will be z-scored and divided by sqrt(n)
along the assigned axis
Parameters
----------
data: 2D array
axis: int
specify which dimension of the data should be normalized
return_nans: bool, default:False
If False, return zeros for NaNs; if True, return NaNs
Returns
-------
data: 2D array
the normalized data | 4.524957 | 4.498696 | 1.005837 |
matrix1 = matrix1.astype(np.float32)
matrix2 = matrix2.astype(np.float32)
[r1, d1] = matrix1.shape
[r2, d2] = matrix2.shape
if d1 != d2:
raise ValueError('Dimension discrepancy')
# preprocess two components
matrix1 = _normalize_for_correlation(matrix1, 1,
return_nans=return_nans)
matrix2 = _normalize_for_correlation(matrix2, 1,
return_nans=return_nans)
corr_data = np.empty((r1, r2), dtype=np.float32, order='C')
# blas routine is column-major
blas.compute_single_matrix_multiplication('T', 'N',
r2, r1, d1,
1.0,
matrix2, d2,
matrix1, d1,
0.0,
corr_data,
r2)
return corr_data | def compute_correlation(matrix1, matrix2, return_nans=False) | compute correlation between two sets of variables
Correlate the rows of matrix1 with the rows of matrix2.
If matrix1 == matrix2, it is auto-correlation computation
resulting in a symmetric correlation matrix.
The number of columns MUST agree between set1 and set2.
The correlation being computed here is
the Pearson's correlation coefficient, which can be expressed as
.. math:: corr(X, Y) = \\frac{cov(X, Y)}{\\sigma_X\\sigma_Y}
where cov(X, Y) is the covariance of variable X and Y, and
.. math:: \\sigma_X
is the standard deviation of variable X
Reducing the correlation computation to matrix multiplication
and using BLAS GEMM API wrapped by Scipy can speedup the numpy built-in
correlation computation (numpy.corrcoef) by one order of magnitude
.. math::
corr(X, Y)
&= \\frac{\\sum\\limits_{i=1}^n (x_i-\\bar{x})(y_i-\\bar{y})}{(n-1)
\\sqrt{\\frac{\\sum\\limits_{j=1}^n x_j^2-n\\bar{x}}{n-1}}
\\sqrt{\\frac{\\sum\\limits_{j=1}^{n} y_j^2-n\\bar{y}}{n-1}}}\\\\
&= \\sum\\limits_{i=1}^n(\\frac{(x_i-\\bar{x})}
{\\sqrt{\\sum\\limits_{j=1}^n x_j^2-n\\bar{x}}}
\\frac{(y_i-\\bar{y})}{\\sqrt{\\sum\\limits_{j=1}^n y_j^2-n\\bar{y}}})
By default (return_nans=False), returns zeros for vectors with NaNs.
If return_nans=True, convert zeros to NaNs (np.nan) in output.
Parameters
----------
matrix1: 2D array in shape [r1, c]
MUST be continuous and row-major
matrix2: 2D array in shape [r2, c]
MUST be continuous and row-major
return_nans: bool, default:False
If False, return zeros for NaNs; if True, return NaNs
Returns
-------
corr_data: 2D array in shape [r1, r2]
continuous and row-major in np.float32 | 2.933596 | 2.955496 | 0.99259 |
alpha = 2
tau2 = (y_invK_y + 2 * tau_range**2) / (alpha * 2 + 2 + n_y)
log_ptau = scipy.stats.invgamma.logpdf(
tau2, scale=tau_range**2, a=2)
return tau2, log_ptau | def prior_GP_var_inv_gamma(y_invK_y, n_y, tau_range) | Imposing an inverse-Gamma prior onto the variance (tau^2)
parameter of a Gaussian Process, which is in turn a prior
imposed over an unknown function y = f(x).
The inverse-Gamma prior of tau^2, tau^2 ~ invgamma(shape, scale)
is described by a shape parameter alpha=2 and a scale parameter
beta=tau_range^2. tau_range describes the reasonable range of
tau in the inverse-Gamma prior.
The data y's at locations x's are assumed to follow Gaussian Process:
f(x, x') ~ N(0, K(x, x') / 2 tau^2), where K is a kernel
function defined on x. For n observations, K(x1, x2, ..., xn) is
an n by n positive definite matrix.
Given the prior parameter tau_range, number of observations
n_y, and y_invK_y = y * inv(K) * y',
the function returns the MAP estimate of tau^2 and
the log posterior probability of tau^2 at the MAP value:
log(p(tau^2|tau_range)).
This function is written primarily for BRSA but can also
be used elsewhere. y in this case corresponds to the log of
SNR in each voxel. GBRSA does not rely on this function.
An alternative form of prior is half-Cauchy prior on tau.
Inverse-Gamma prior penalizes for both very small and very
large values of tau, while half-Cauchy prior only penalizes
for very large values of tau.
For more information on usage, see description in BRSA class:
`.BRSA`
See also: `.prior_GP_var_half_cauchy`
Parameters
----------
y_invK_y: float
y * inv(K) * y^T, where y=f(x) is a vector of observations
of unknown function f at different locations x.
K is correlation matrix of f between different locations, based
on a Gaussian Process (GP) describing the smoothness property
of f. K fully incorporates the form of the kernel
and the length scale of the GP, but not the variance of the GP
(the purpose of this function is to estimate the variance).
n_y: int, number of observations
tau_range: float,
The reasonable range of tau, the standard deviation of the
Gaussian Process imposed on y=f(x). tau_range is parameter
of the inverse-Gamma prior. Say, if you expect the standard
deviation of the Gaussian process to be around 3, tau_range
can be set to 3.
The smaller it is, the more penalization is imposed
on large variation of y.
Returns
-------
tau2: The MAP estimation of tau^2 based on the prior on tau
and y_invK_y.
log_ptau: log(p(tau)) of the returned tau^2 based on the
inverse-Gamma prior. | 4.289187 | 3.707706 | 1.15683 |
tau2 = (y_invK_y - n_y * tau_range**2
+ np.sqrt(n_y**2 * tau_range**4 + (2 * n_y + 8)
* tau_range**2 * y_invK_y + y_invK_y**2))\
/ 2 / (n_y + 2)
log_ptau = scipy.stats.halfcauchy.logpdf(
tau2**0.5, scale=tau_range)
return tau2, log_ptau | def prior_GP_var_half_cauchy(y_invK_y, n_y, tau_range) | Imposing a half-Cauchy prior onto the standard deviation (tau)
of the Gaussian Process which is in turn a prior imposed over
a function y = f(x).
The scale parameter of the half-Cauchy prior is tau_range.
The function returns the MAP estimate of tau^2 and
log(p(tau|tau_range)) for the MAP value of tau^2,
where tau_range describes the reasonable range of tau
in the half-Cauchy prior.
An alternative form of prior is inverse-Gamma prior on tau^2.
Inverse-Gamma prior penalizes for both very small and very
large values of tau, while half-Cauchy prior only penalizes
for very large values of tau.
For more information on usage, see description in BRSA class:
`.BRSA` | 3.434268 | 3.430038 | 1.001233 |
beta = X.shape[0] / X.shape[1]
if beta > 1:
beta = 1 / beta
omega = 0.56 * beta ** 3 - 0.95 * beta ** 2 + 1.82 * beta + 1.43
if zscore:
sing = np.linalg.svd(_zscore(X), False, False)
else:
sing = np.linalg.svd(X, False, False)
thresh = omega * np.median(sing)
ncomp = int(np.sum(np.logical_and(sing > thresh, np.logical_not(
np.isclose(sing, thresh)))))
# In the line above, we look for the singular values larger than
# the threshold but excluding those that happen to be "just" larger
# than the threshold by an amount close to the numerical precision.
# This is to prevent close-to-zero singular values to be included if
# the median of the eigenvalues is close to 0 (which could happen
# when the input X has lower rank than its minimal size.
return ncomp | def Ncomp_SVHT_MG_DLD_approx(X, zscore=True) | This function implements the approximate calculation of the
optimal hard threshold for singular values, by Matan Gavish
and David L. Donoho:
"The optimal hard threshold for singular values is 4 / sqrt(3)"
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6846297
Parameters
----------
X: 2-D numpy array of size [n_T, n_V]
The data to estimate the optimal rank for selecting principal
components.
zscore: Boolean
Whether to z-score the data before calculating number of components.
Returns
-------
ncomp: integer
The optimal number of components determined by the method of MG
and DLD | 5.37253 | 5.586894 | 0.961631 |
assert a.ndim > 1, 'a must have more than one dimensions'
zscore = scipy.stats.zscore(a, axis=0)
zscore[:, np.logical_not(np.all(np.isfinite(zscore), axis=0))] = 0
return zscore | def _zscore(a) | Calculating z-score of data on the first axis.
If the numbers in any column are all equal, scipy.stats.zscore
will return NaN for this column. We shall correct them all to
be zeros.
Parameters
----------
a: numpy array
Returns
-------
zscore: numpy array
The z-scores of input "a", with any columns including non-finite
numbers replaced by all zeros. | 2.968623 | 2.956703 | 1.004031 |
assert X.ndim == 2 and X.shape[1] == self.beta_.shape[1], \
'The shape of X is not consistent with the shape of data '\
'used in the fitting step. They should have the same number '\
'of voxels'
assert scan_onsets is None or (scan_onsets.ndim == 1 and
0 in scan_onsets), \
'scan_onsets should either be None or an array of indices '\
'If it is given, it should include at least 0'
if scan_onsets is None:
scan_onsets = np.array([0], dtype=int)
else:
scan_onsets = np.int32(scan_onsets)
ts, ts0, log_p = self._transform(
Y=X, scan_onsets=scan_onsets, beta=self.beta_,
beta0=self.beta0_, rho_e=self.rho_, sigma_e=self.sigma_,
rho_X=self._rho_design_, sigma2_X=self._sigma2_design_,
rho_X0=self._rho_X0_, sigma2_X0=self._sigma2_X0_)
return ts, ts0 | def transform(self, X, y=None, scan_onsets=None) | Use the model to estimate the time course of response to
each condition (ts), and the time course unrelated to task
(ts0) which is spread across the brain.
This is equivalent to "decoding" the design matrix and
nuisance regressors from a new dataset different from the
training dataset on which fit() was applied. An AR(1) smooth
prior is imposed on the decoded ts and ts0 with the AR(1)
parameters learnt from the corresponding time courses in the
training data.
Notice: if you set the rank to be lower than the number of
experimental conditions (number of columns in the design
matrix), the recovered task-related activity will have
collinearity (the recovered time courses of some conditions
can be linearly explained by the recovered time courses
of other conditions).
Parameters
----------
X : numpy arrays, shape=[time_points, voxels]
fMRI data of new data of the same subject. The voxels should
match those used in the fit() function. If data are z-scored
(recommended) when fitting the model, data should be z-scored
as well when calling transform()
y : not used (as it is unsupervised learning)
scan_onsets : numpy array, shape=[number of runs].
A list of indices corresponding to the onsets of
scans in the data X. If not provided, data will be assumed
to be acquired in a continuous scan.
Returns
-------
ts : numpy arrays, shape = [time_points, condition]
The estimated response to the task conditions which have the
response amplitudes estimated during the fit step.
ts0: numpy array, shape = [time_points, n_nureg]
The estimated time course spread across the brain, with the
loading weights estimated during the fit step. | 3.472832 | 3.171684 | 1.094949 |
assert X.ndim == 2 and X.shape[1] == self.beta_.shape[1], \
'The shape of X is not consistent with the shape of data '\
'used in the fitting step. They should have the same number '\
'of voxels'
assert scan_onsets is None or (scan_onsets.ndim == 1 and
0 in scan_onsets), \
'scan_onsets should either be None or an array of indices '\
'If it is given, it should include at least 0'
if scan_onsets is None:
scan_onsets = np.array([0], dtype=int)
else:
scan_onsets = np.int32(scan_onsets)
ll = self._score(Y=X, design=design, beta=self.beta_,
scan_onsets=scan_onsets, beta0=self.beta0_,
rho_e=self.rho_, sigma_e=self.sigma_,
rho_X0=self._rho_X0_, sigma2_X0=self._sigma2_X0_)
ll_null = self._score(Y=X, design=None, beta=None,
scan_onsets=scan_onsets, beta0=self.beta0_,
rho_e=self.rho_, sigma_e=self.sigma_,
rho_X0=self._rho_X0_,
sigma2_X0=self._sigma2_X0_)
return ll, ll_null | def score(self, X, design, scan_onsets=None) | Use the model and parameters estimated by fit function
from some data of a participant to evaluate the log
likelihood of some new data of the same participant.
Design matrix of the same set of experimental
conditions in the testing data should be provided, with each
column corresponding to the same condition as that column
in the design matrix of the training data.
Unknown nuisance time series will be marginalized, assuming
they follow the same spatial pattern as in the training
data. The hypothetical response captured by the design matrix
will be subtracted from data before the marginalization
when evaluating the log likelihood. For null model,
nothing will be subtracted before marginalization.
There is a difference between the form of likelihood function
used in fit() and score(). In fit(), the response amplitude
beta to design matrix X and the modulation beta0 by nuisance
regressor X0 are both marginalized, with X provided and X0
estimated from data. In score(), posterior estimation of
beta and beta0 from the fitting step are assumed unchanged
to testing data and X0 is marginalized.
The logic underlying score() is to transfer
as much as what we can learn from training data when
calculating a likelihood score for testing data.
If you z-scored your data during fit step, you should
z-score them for score function as well. If you did not
z-score in fitting, you should not z-score here either.
Parameters
----------
X : numpy arrays, shape=[time_points, voxels]
fMRI data of new data of the same subject. The voxels should
match those used in the fit() function. If data are z-scored
(recommended) when fitting the model, data should be z-scored
as well when calling transform()
design : numpy array, shape=[time_points, conditions]
Design matrix expressing the hypothetical response of
the task conditions in data X.
scan_onsets : numpy array, shape=[number of runs].
A list of indices corresponding to the onsets of
scans in the data X. If not provided, data will be assumed
to be acquired in a continuous scan.
Returns
-------
ll: float.
The log likelihood of the new data based on the model and its
parameters fit to the training data.
ll_null: float.
The log likelihood of the new data based on a null model
which assumes the same as the full model for everything
except for that there is no response to any of the
task conditions. | 2.685309 | 2.454894 | 1.093859 |
run_TRs, n_run = self._run_TR_from_scan_onsets(n_T, scan_onsets)
D_ele = map(self._D_gen, run_TRs)
F_ele = map(self._F_gen, run_TRs)
D = scipy.linalg.block_diag(*D_ele)
F = scipy.linalg.block_diag(*F_ele)
# D and F above are templates for constructing
# the inverse of temporal covariance matrix of noise
return D, F, run_TRs, n_run | def _prepare_DF(self, n_T, scan_onsets=None) | Prepare the essential template matrices D and F for
pre-calculating some terms to be re-used.
The inverse covariance matrix of AR(1) noise is
sigma^-2 * (I - rho1*D + rho1**2 * F).
And we denote A = I - rho1*D + rho1**2 * F | 4.413514 | 3.966551 | 1.112683 |
XTY, XTDY, XTFY = self._make_templates(D, F, X, Y)
YTY_diag = np.sum(Y * Y, axis=0)
YTDY_diag = np.sum(Y * np.dot(D, Y), axis=0)
YTFY_diag = np.sum(Y * np.dot(F, Y), axis=0)
XTX, XTDX, XTFX = self._make_templates(D, F, X, X)
return XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, \
XTDX, XTFX | def _prepare_data_XY(self, X, Y, D, F) | Prepares different forms of products of design matrix X
and data Y, or between themselves.
These products are re-used a lot during fitting.
So we pre-calculate them. Because these are reused,
it is in principle possible to update the fitting
as new data come in, by just incrementally adding
the products of new data and their corresponding parts
of design matrix to these pre-calculated terms. | 2.080883 | 2.126164 | 0.978703 |
X_DC = self._gen_X_DC(run_TRs)
reg_sol = np.linalg.lstsq(X_DC, X)
if np.any(np.isclose(reg_sol[1], 0)):
raise ValueError('Your design matrix appears to have '
'included baseline time series.'
'Either remove them, or move them to'
' nuisance regressors.')
X_DC, X_base, idx_DC = self._merge_DC_to_base(X_DC, X_base,
no_DC)
if X_res is None:
X0 = X_base
else:
X0 = np.concatenate((X_base, X_res), axis=1)
n_X0 = X0.shape[1]
X0TX0, X0TDX0, X0TFX0 = self._make_templates(D, F, X0, X0)
XTX0, XTDX0, XTFX0 = self._make_templates(D, F, X, X0)
X0TY, X0TDY, X0TFY = self._make_templates(D, F, X0, Y)
return X0TX0, X0TDX0, X0TFX0, XTX0, XTDX0, XTFX0, \
X0TY, X0TDY, X0TFY, X0, X_base, n_X0, idx_DC | def _prepare_data_XYX0(self, X, Y, X_base, X_res, D, F, run_TRs,
no_DC=False) | Prepares different forms of products between design matrix X or
data Y or nuisance regressors X0.
These products are re-used a lot during fitting.
So we pre-calculate them.
no_DC means not inserting regressors for DC components
into nuisance regressor.
It will only take effect if X_base is not None. | 2.880663 | 2.741368 | 1.050812 |
if X_base is not None:
reg_sol = np.linalg.lstsq(X_DC, X_base)
if not no_DC:
if not np.any(np.isclose(reg_sol[1], 0)):
# No columns in X_base can be explained by the
# baseline regressors. So we insert them.
X_base = np.concatenate((X_DC, X_base), axis=1)
idx_DC = np.arange(0, X_DC.shape[1])
else:
logger.warning('Provided regressors for uninteresting '
'time series already include baseline. '
'No additional baseline is inserted.')
idx_DC = np.where(np.isclose(reg_sol[1], 0))[0]
else:
idx_DC = np.where(np.isclose(reg_sol[1], 0))[0]
else:
# If a set of regressors for non-interested signals is not
# provided, then we simply include one baseline for each run.
X_base = X_DC
idx_DC = np.arange(0, X_base.shape[1])
logger.info('You did not provide time series of no interest '
'such as DC component. Trivial regressors of'
' DC component are included for further modeling.'
' The final covariance matrix won''t '
'reflect these components.')
return X_DC, X_base, idx_DC | def _merge_DC_to_base(self, X_DC, X_base, no_DC) | Merge DC components X_DC to the baseline time series
X_base (By baseline, this means any fixed nuisance
regressors not updated during fitting, including DC
components and any nuisance regressors provided by
the user.
X_DC is always in the first few columns of X_base. | 4.236484 | 4.05469 | 1.044835 |
idx_param_sing = {'Cholesky': np.arange(n_l), 'a1': n_l}
# for simplified fitting
idx_param_fitU = {'Cholesky': np.arange(n_l),
'a1': np.arange(n_l, n_l + n_V)}
# for the likelihood function when we fit U (the shared covariance).
idx_param_fitV = {'log_SNR2': np.arange(n_V - 1),
'c_space': n_V - 1, 'c_inten': n_V,
'c_both': np.arange(n_V - 1, n_V - 1 + n_smooth)}
# for the likelihood function when we fit V (reflected by SNR of
# each voxel)
return idx_param_sing, idx_param_fitU, idx_param_fitV | def _build_index_param(self, n_l, n_V, n_smooth) | Build dictionaries to retrieve each parameter
from the combined parameters. | 5.054386 | 4.927182 | 1.025817 |
chol = np.linalg.cholesky(M)
if M.ndim == 2:
return np.sum(np.log(np.abs(np.diag(chol))))
else:
return np.sum(np.log(np.abs(np.diagonal(
chol, axis1=-2, axis2=-1))), axis=-1) | def _half_log_det(self, M) | Return log(|M|)*0.5. For positive definite matrix M
of more than 2 dimensions, calculate this for the
last two dimension and return a value corresponding
to each element in the first few dimensions. | 2.244925 | 2.114244 | 1.06181 |
logger.info('Transforming new data.')
# Constructing the transition matrix and the variance of
# innovation noise as prior for the latent variable X and X0
# in new data.
n_C = beta.shape[0]
n_T = Y.shape[0]
weight = np.concatenate((beta, beta0), axis=0)
T_X = np.diag(np.concatenate((rho_X, rho_X0)))
Var_X = np.concatenate((sigma2_X / (1 - rho_X**2),
sigma2_X0 / (1 - rho_X0**2)))
Var_dX = np.concatenate((sigma2_X, sigma2_X0))
sigma2_e = sigma_e ** 2
scan_onsets = np.setdiff1d(scan_onsets, n_T)
n_scan = scan_onsets.size
X = [None] * scan_onsets.size
X0 = [None] * scan_onsets.size
total_log_p = 0
for scan, onset in enumerate(scan_onsets):
# Forward step
if scan == n_scan - 1:
offset = n_T
else:
offset = scan_onsets[scan + 1]
mu, mu_Gamma_inv, Gamma_inv, log_p_data, Lambda_0, \
Lambda_1, H, deltaY, deltaY_sigma2inv_rho_weightT = \
self._forward_step(Y[onset:offset, :],
T_X, Var_X, Var_dX, rho_e, sigma2_e,
weight)
total_log_p += log_p_data
# Backward step
mu_hat, mu_Gamma_inv_hat, Gamma_inv_hat \
= self._backward_step(
deltaY, deltaY_sigma2inv_rho_weightT, sigma2_e,
weight, mu, mu_Gamma_inv, Gamma_inv,
Lambda_0, Lambda_1, H)
X[scan] = np.concatenate(
[mu_t[None, :n_C] for mu_t in mu_hat])
X0[scan] = np.concatenate(
[mu_t[None, n_C:] for mu_t in mu_hat])
X = np.concatenate(X)
X0 = np.concatenate(X0)
return X, X0, total_log_p | def _transform(self, Y, scan_onsets, beta, beta0,
rho_e, sigma_e, rho_X, sigma2_X, rho_X0, sigma2_X0) | Given the data Y and the response amplitudes beta and beta0
estimated in the fit step, estimate the corresponding X and X0.
It is done by a forward-backward algorithm.
We assume X and X0 both are vector autoregressive (VAR)
processes, to capture temporal smoothness. Their VAR
parameters are estimated from training data at the fit stage. | 2.88857 | 2.851804 | 1.012892 |
logger.info('Estimating cross-validated score for new data.')
n_T = Y.shape[0]
if design is not None:
Y = Y - np.dot(design, beta)
# The function works for both full model and null model.
# If design matrix is not provided, the whole data is
# used as input for _forward_step. If design matrix is provided,
# residual after subtracting design * beta is fed to _forward_step
T_X = np.diag(rho_X0)
Var_X = sigma2_X0 / (1 - rho_X0**2)
Var_dX = sigma2_X0
# Prior parmeters for X0: T_X is transitioning matrix, Var_X
# is the marginal variance of the first time point. Var_dX is the
# variance of the updating noise.
sigma2_e = sigma_e ** 2
# variance of voxel-specific updating noise component
scan_onsets = np.setdiff1d(scan_onsets, n_T).astype(int)
n_scan = scan_onsets.size
total_log_p = 0
for scan, onset in enumerate(scan_onsets):
# Forward step
if scan == n_scan - 1:
offset = n_T
else:
offset = scan_onsets[scan + 1]
_, _, _, log_p_data, _, _, _, _, _ = \
self._forward_step(
Y[onset:offset, :], T_X, Var_X, Var_dX, rho_e, sigma2_e,
beta0)
total_log_p += log_p_data
return total_log_p | def _score(self, Y, design, beta, scan_onsets, beta0, rho_e, sigma_e,
rho_X0, sigma2_X0) | Given the data Y, and the spatial pattern beta0
of nuisance time series, return the cross-validated score
of the data Y given all parameters of the subject estimated
during the first step.
It is assumed that the user has design matrix built for the
data Y. Both beta and beta0 are posterior expectation estimated
from training data with the estimated covariance matrix U and
SNR serving as prior. We marginalize X0 instead of fitting
it in this function because this function is for the purpose
of evaluating model no new data. We should avoid doing any
additional fitting when performing cross-validation.
The hypothetic response to the task will be subtracted, and
the unknown nuisance activity which contributes to the data
through beta0 will be marginalized. | 4.577852 | 4.407941 | 1.038547 |
if same_para:
n_c = x.shape[1]
x = np.reshape(x, x.size, order='F')
rho, sigma2 = alg.AR_est_YW(x, 1)
# We concatenate all the design matrix to estimate common AR(1)
# parameters. This creates some bias because the end of one column
# and the beginning of the next column of the design matrix are
# treated as consecutive samples.
rho = np.ones(n_c) * rho
sigma2 = np.ones(n_c) * sigma2
else:
rho = np.zeros(np.shape(x)[1])
sigma2 = np.zeros(np.shape(x)[1])
for c in np.arange(np.shape(x)[1]):
rho[c], sigma2[c] = alg.AR_est_YW(x[:, c], 1)
return rho, sigma2 | def _est_AR1(self, x, same_para=False) | Estimate the AR(1) parameters of input x.
Each column of x is assumed as independent from other columns,
and each column is treated as an AR(1) process.
If same_para is set as True, then all columns of x
are concatenated and a single set of AR(1) parameters
is estimated. Strictly speaking the breaking point
between each concatenated column should be considered.
But for long time series, this is ignored. | 3.814788 | 3.441514 | 1.108462 |
n_T = len(Gamma_inv)
# All the terms with hat before are parameters of posterior
# distributions of X conditioned on data from all time points,
# whereas the ones without hat calculated by _forward_step
# are mean and covariance of posterior of X conditioned on
# data up to the time point.
Gamma_inv_hat = [None] * n_T
mu_Gamma_inv_hat = [None] * n_T
mu_hat = [None] * n_T
mu_hat[-1] = mu[-1].copy()
mu_Gamma_inv_hat[-1] = mu_Gamma_inv[-1].copy()
Gamma_inv_hat[-1] = Gamma_inv[-1].copy()
for t in np.arange(n_T - 2, -1, -1):
tmp = np.linalg.solve(Gamma_inv_hat[t + 1] - Gamma_inv[t + 1]
+ Lambda_1, H)
Gamma_inv_hat[t] = Gamma_inv[t] + Lambda_0 - np.dot(H.T, tmp)
mu_Gamma_inv_hat[t] = mu_Gamma_inv[t] \
- deltaY_sigma2inv_rho_weightT[t, :] + np.dot(
mu_Gamma_inv_hat[t + 1] - mu_Gamma_inv[t + 1]
+ np.dot(deltaY[t, :] / sigma2_e, weight.T), tmp)
mu_hat[t] = np.linalg.solve(Gamma_inv_hat[t],
mu_Gamma_inv_hat[t])
return mu_hat, mu_Gamma_inv_hat, Gamma_inv_hat | def _backward_step(self, deltaY, deltaY_sigma2inv_rho_weightT,
sigma2_e, weight, mu, mu_Gamma_inv, Gamma_inv,
Lambda_0, Lambda_1, H) | backward step for HMM, assuming both the hidden state and noise
have 1-step dependence on the previous value. | 2.754465 | 2.780325 | 0.990699 |
X = self._check_data_GBRSA(X, for_fit=False)
scan_onsets = self._check_scan_onsets_GBRSA(scan_onsets, X)
assert len(X) == self.n_subj_
ts = [None] * self.n_subj_
ts0 = [None] * self.n_subj_
log_p = [None] * self.n_subj_
for i, x in enumerate(X):
if x is not None:
s = scan_onsets[i]
ts[i], ts0[i], log_p[i] = self._transform(
Y=x, scan_onsets=s, beta=self.beta_[i],
beta0=self.beta0_[i], rho_e=self.rho_[i],
sigma_e=self.sigma_[i], rho_X=self._rho_design_[i],
sigma2_X=self._sigma2_design_[i],
rho_X0=self._rho_X0_[i], sigma2_X0=self._sigma2_X0_[i])
return ts, ts0 | def transform(self, X, y=None, scan_onsets=None) | Use the model to estimate the time course of response to
each condition (ts), and the time course unrelated to task
(ts0) which is spread across the brain.
This is equivalent to "decoding" the design matrix and
nuisance regressors from a new dataset different from the
training dataset on which fit() was applied. An AR(1) smooth
prior is imposed on the decoded ts and ts0 with the AR(1)
parameters learnt from the corresponding time courses in the
training data.
Parameters
----------
X : list of 2-D arrays. For each item, shape=[time_points, voxels]
New fMRI data of the same subjects. The voxels should
match those used in the fit() function.
The size of the list should match the size of the list X fed
to fit(), with each item in the list corresponding to data
from the same subject in the X fed to fit(). If you do not
need to transform some subjects' data, leave the entry
corresponding to that subject as None.
If data are z-scored when fitting the model,
data should be z-scored as well when calling transform()
y : not used (as it is unsupervised learning)
scan_onsets : list of 1-D numpy arrays,
Each array corresponds to the onsets of
scans in the data X for the particular subject.
If not provided, data will be assumed
to be acquired in a continuous scan.
Returns
-------
ts : list of 2-D arrays. For each, shape = [time_points, condition]
The estimated response to the cognitive dimensions
（task dimensions) whose response amplitudes were estimated
during the fit step.
One item for each subject. If some subjects' data are
not provided, None will be returned.
ts0: list of 2-D array. For each, shape = [time_points, n_nureg]
The estimated time courses spread across the brain, with the
loading weights estimated during the fit step.
One item for each subject. If some subjects' data are
not provided, None will be returned. | 2.993141 | 2.753137 | 1.087175 |
boundaries = np.flip(scipy.stats.expon.isf(
np.linspace(0, 1, n_bin + 1),
scale=scale), axis=0)
bins = np.empty(n_bin)
for i in np.arange(n_bin):
bins[i] = utils.center_mass_exp(
(boundaries[i], boundaries[i + 1]), scale=scale)
return bins | def _bin_exp(self, n_bin, scale=1.0) | Calculate the bin locations to approximate exponential distribution.
It breaks the cumulative probability of exponential distribution
into n_bin equal bins, each covering 1 / n_bin probability. Then it
calculates the center of mass in each bins and returns the
centers of mass. So, it approximates the exponential distribution
with n_bin of Delta function weighted by 1 / n_bin, at the
locations of these centers of mass.
Parameters:
-----------
n_bin: int
The number of bins to approximate the exponential distribution
scale: float.
The scale parameter of the exponential distribution, defined in
the same way as scipy.stats. It does not influence the ratios
between the bins, but just controls the spacing between the bins.
So generally users should not change its default.
Returns:
--------
bins: numpy array of size [n_bin,]
The centers of mass for each segment of the
exponential distribution. | 3.181073 | 3.119428 | 1.019762 |
if self.SNR_prior == 'unif':
SNR_grids = np.linspace(0, 1, self.SNR_bins)
SNR_weights = np.ones(self.SNR_bins) / (self.SNR_bins - 1)
SNR_weights[0] = SNR_weights[0] / 2.0
SNR_weights[-1] = SNR_weights[-1] / 2.0
elif self.SNR_prior == 'lognorm':
dist = scipy.stats.lognorm
alphas = np.arange(np.mod(self.SNR_bins, 2),
self.SNR_bins + 2, 2) / self.SNR_bins
# The goal here is to divide the area under the pdf curve
# to segments representing equal probabilities.
bounds = dist.interval(alphas, (self.logS_range,))
bounds = np.unique(bounds)
# bounds contain the boundaries which equally separate
# the probability mass of the distribution
SNR_grids = np.zeros(self.SNR_bins)
for i in np.arange(self.SNR_bins):
SNR_grids[i] = dist.expect(
lambda x: x, args=(self.logS_range,),
lb=bounds[i], ub=bounds[i + 1]) * self.SNR_bins
# Center of mass of each segment between consecutive
# bounds are set as the grids for SNR.
SNR_weights = np.ones(self.SNR_bins) / self.SNR_bins
elif self.SNR_prior == 'exp':
SNR_grids = self._bin_exp(self.SNR_bins)
SNR_weights = np.ones(self.SNR_bins) / self.SNR_bins
else:
SNR_grids = np.ones(1)
SNR_weights = np.ones(1)
SNR_weights = SNR_weights / np.sum(SNR_weights)
return SNR_grids, SNR_weights | def _set_SNR_grids(self) | Set the grids and weights for SNR used in numerical integration
of SNR parameters. | 2.982758 | 2.924313 | 1.019986 |
rho_grids = np.arange(self.rho_bins) * 2 / self.rho_bins - 1 \
+ 1 / self.rho_bins
rho_weights = np.ones(self.rho_bins) / self.rho_bins
return rho_grids, rho_weights | def _set_rho_grids(self) | Set the grids and weights for rho used in numerical integration
of AR(1) parameters. | 3.101884 | 2.79876 | 1.108306 |
half_log_det_X0TAX0 = np.reshape(
np.repeat(self._half_log_det(X0TAX0)[None, :],
self.SNR_bins, axis=0), n_grid)
X0TAX0 = np.reshape(
np.repeat(X0TAX0[None, :, :, :],
self.SNR_bins, axis=0),
(n_grid, n_X0, n_X0))
X0TAX0_i = np.reshape(np.repeat(
X0TAX0_i[None, :, :, :],
self.SNR_bins, axis=0),
(n_grid, n_X0, n_X0))
s2XTAcorrX = np.reshape(
SNR_grids[:, None, None, None]**2 * XTAcorrX,
(n_grid, n_C, n_C))
YTAcorrY_diag = np.reshape(np.repeat(
YTAcorrY_diag[None, :, :],
self.SNR_bins, axis=0), (n_grid, n_V))
sXTAcorrY = np.reshape(SNR_grids[:, None, None, None]
* XTAcorrY, (n_grid, n_C, n_V))
X0TAY = np.reshape(np.repeat(X0TAY[None, :, :, :],
self.SNR_bins, axis=0),
(n_grid, n_X0, n_V))
XTAX0 = np.reshape(np.repeat(XTAX0[None, :, :, :],
self.SNR_bins, axis=0),
(n_grid, n_C, n_X0))
return half_log_det_X0TAX0, X0TAX0, X0TAX0_i, s2XTAcorrX, \
YTAcorrY_diag, sXTAcorrY, X0TAY, XTAX0 | def _matrix_flattened_grid(self, X0TAX0, X0TAX0_i, SNR_grids, XTAcorrX,
YTAcorrY_diag, XTAcorrY, X0TAY, XTAX0,
n_C, n_V, n_X0, n_grid) | We need to integrate parameters SNR and rho on 2-d discrete grids.
This function generates matrices which have only one dimension for
these two parameters, with each slice in that dimension
corresponding to each combination of the discrete grids of SNR
and discrete grids of rho. | 1.601341 | 1.634348 | 0.979804 |
logger.info('Starting RSRM')
# Check that the regularizer value is positive
if 0.0 >= self.lam:
raise ValueError("Gamma parameter should be positive.")
# Check the number of subjects
if len(X) <= 1:
raise ValueError("There are not enough subjects in the input "
"data to train the model.")
# Check for input data sizes
if X[0].shape[1] < self.features:
raise ValueError(
"There are not enough timepoints to train the model with "
"{0:d} features.".format(self.features))
# Check if all subjects have same number of TRs for alignment
number_trs = X[0].shape[1]
number_subjects = len(X)
for subject in range(number_subjects):
assert_all_finite(X[subject])
if X[subject].shape[1] != number_trs:
raise ValueError("Different number of alignment timepoints "
"between subjects.")
# Create a new random state
self.random_state_ = np.random.RandomState(self.rand_seed)
# Run RSRM
self.w_, self.r_, self.s_ = self._rsrm(X)
return self | def fit(self, X) | Compute the Robust Shared Response Model
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, timepoints]
Each element in the list contains the fMRI data of one subject. | 4.041771 | 3.812639 | 1.060098 |
# Check if the model exist
if hasattr(self, 'w_') is False:
raise NotFittedError("The model fit has not been run yet.")
# Check the number of subjects
if len(X) != len(self.w_):
raise ValueError("The number of subjects does not match the one"
" in the model.")
r = [None] * len(X)
s = [None] * len(X)
for subject in range(len(X)):
if X[subject] is not None:
r[subject], s[subject] = self._transform_new_data(X[subject],
subject)
return r, s | def transform(self, X) | Use the model to transform new data to Shared Response space
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, timepoints_i]
Each element in the list contains the fMRI data of one subject.
Returns
-------
r : list of 2D arrays, element i has shape=[features_i, timepoints_i]
Shared responses from input data (X)
s : list of 2D arrays, element i has shape=[voxels_i, timepoints_i]
Individual data obtained from fitting model to input data (X) | 3.250835 | 2.840767 | 1.144351 |
S = np.zeros_like(X)
R = None
for i in range(self.n_iter):
R = self.w_[subject].T.dot(X - S)
S = self._shrink(X - self.w_[subject].dot(R), self.lam)
return R, S | def _transform_new_data(self, X, subject) | Transform new data for a subjects by projecting to the shared subspace and
computing the individual information.
Parameters
----------
X : array, shape=[voxels, timepoints]
The fMRI data of the subject.
subject : int
The subject id.
Returns
-------
R : array, shape=[features, timepoints]
Shared response from input data (X)
S : array, shape=[voxels, timepoints]
Individual data obtained from fitting model to input data (X) | 4.374014 | 4.463033 | 0.980054 |
# Check if the model exist
if hasattr(self, 'w_') is False:
raise NotFittedError("The model fit has not been run yet.")
# Check the number of TRs in the subject
if X.shape[1] != self.r_.shape[1]:
raise ValueError("The number of timepoints(TRs) does not match the"
"one in the model.")
s = np.zeros_like(X)
for i in range(self.n_iter):
w = self._update_transform_subject(X, s, self.r_)
s = self._shrink(X - w.dot(self.r_), self.lam)
return w, s | def transform_subject(self, X) | Transform a new subject using the existing model
Parameters
----------
X : 2D array, shape=[voxels, timepoints]
The fMRI data of the new subject.
Returns
-------
w : 2D array, shape=[voxels, features]
Orthogonal mapping `W_{new}` for new subject
s : 2D array, shape=[voxels, timepoints]
Individual term `S_{new}` for new subject | 4.722648 | 4.079994 | 1.157513 |
subjs = len(X)
voxels = [X[i].shape[0] for i in range(subjs)]
TRs = X[0].shape[1]
features = self.features
# Initialization
W = self._init_transforms(subjs, voxels, features, self.random_state_)
S = self._init_individual(subjs, voxels, TRs)
R = self._update_shared_response(X, S, W, features)
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(X, W, R, S, self.lam)
logger.info('Objective function %f' % objective)
# Main loop
for i in range(self.n_iter):
W = self._update_transforms(X, S, R)
S = self._update_individual(X, W, R, self.lam)
R = self._update_shared_response(X, S, W, features)
# Print objective function every iteration
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(X, W, R, S, self.lam)
logger.info('Objective function %f' % objective)
return W, R, S | def _rsrm(self, X) | Block-Coordinate Descent algorithm for fitting RSRM.
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, timepoints]
Each element in the list contains the fMRI data for alignment of
one subject.
Returns
-------
W : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
R : array, shape=[features, timepoints]
The shared response.
S : list of array, element i has shape=[voxels_i, timepoints]
The individual component :math:`S_i` for each subject. | 2.891613 | 2.388194 | 1.210795 |
# Init the Random seed generator
np.random.seed(self.rand_seed)
# Draw a random W for each subject
W = [random_state.random_sample((voxels[i], features))
for i in range(subjs)]
# Make it orthogonal it with QR decomposition
for i in range(subjs):
W[i], _ = np.linalg.qr(W[i])
return W | def _init_transforms(self, subjs, voxels, features, random_state) | Initialize the mappings (Wi) with random orthogonal matrices.
Parameters
----------
subjs : int
The number of subjects.
voxels : list of int
A list with the number of voxels per subject.
features : int
The number of features in the model.
random_state : `RandomState`
A random state to draw the mappings.
Returns
-------
W : list of array, element i has shape=[voxels_i, features]
The initialized orthogonal transforms (mappings) :math:`W_i` for
each subject.
Note
----
Not thread safe. | 5.602273 | 4.219152 | 1.32782 |
subjs = len(X)
func = .0
for i in range(subjs):
func += 0.5 * np.sum((X[i] - W[i].dot(R) - S[i])**2) \
+ gamma * np.sum(np.abs(S[i]))
return func | def _objective_function(X, W, R, S, gamma) | Evaluate the objective function.
.. math:: \\sum_{i=1}^{N} 1/2 \\| X_i - W_i R - S_i \\|_F^2
.. math:: + /\\gamma * \\|S_i\\|_1
Parameters
----------
X : list of array, element i has shape=[voxels_i, timepoints]
Each element in the list contains the fMRI data for alignment of
one subject.
W : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
R : array, shape=[features, timepoints]
The shared response.
S : list of array, element i has shape=[voxels_i, timepoints]
The individual component :math:`S_i` for each subject.
gamma : float, default: 1.0
Regularization parameter for the sparseness of the individual
components.
Returns
-------
func : float
The RSRM objective function evaluated on the parameters to this
function. | 3.461295 | 3.17733 | 1.089372 |
subjs = len(X)
S = []
for i in range(subjs):
S.append(RSRM._shrink(X[i] - W[i].dot(R), gamma))
return S | def _update_individual(X, W, R, gamma) | Update the individual components `S_i`.
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, timepoints]
Each element in the list contains the fMRI data for alignment of
one subject.
W : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
R : array, shape=[features, timepoints]
The shared response.
gamma : float, default: 1.0
Regularization parameter for the sparseness of the individual
components.
Returns
-------
S : list of array, element i has shape=[voxels_i, timepoints]
The individual component :math:`S_i` for each subject. | 6.909562 | 6.814937 | 1.013885 |
return [np.zeros((voxels[i], TRs)) for i in range(subjs)] | def _init_individual(subjs, voxels, TRs) | Initializes the individual components `S_i` to empty (all zeros).
Parameters
----------
subjs : int
The number of subjects.
voxels : list of int
A list with the number of voxels per subject.
TRs : int
The number of timepoints in the data.
Returns
-------
S : list of 2D array, element i has shape=[voxels_i, timepoints]
The individual component :math:`S_i` for each subject initialized
to zero. | 5.644478 | 4.345129 | 1.299036 |
subjs = len(X)
TRs = X[0].shape[1]
R = np.zeros((features, TRs))
# Project the subject data with the individual component removed into
# the shared subspace and average over all subjects.
for i in range(subjs):
R += W[i].T.dot(X[i]-S[i])
R /= subjs
return R | def _update_shared_response(X, S, W, features) | Update the shared response `R`.
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, timepoints]
Each element in the list contains the fMRI data for alignment of
one subject.
S : list of array, element i has shape=[voxels_i, timepoints]
The individual component :math:`S_i` for each subject.
W : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
features : int
The number of features in the model.
Returns
-------
R : array, shape=[features, timepoints]
The updated shared response. | 6.525561 | 5.181515 | 1.259392 |
A = Xi.dot(R.T)
A -= Si.dot(R.T)
# Solve the Procrustes problem
U, _, V = np.linalg.svd(A, full_matrices=False)
return U.dot(V) | def _update_transform_subject(Xi, Si, R) | Updates the mappings `W_i` for one subject.
Parameters
----------
Xi : array, shape=[voxels, timepoints]
The fMRI data :math:`X_i` for aligning the subject.
Si : array, shape=[voxels, timepoints]
The individual component :math:`S_i` for the subject.
R : array, shape=[features, timepoints]
The shared response.
Returns
-------
Wi : array, shape=[voxels, features]
The orthogonal transform (mapping) :math:`W_i` for the subject. | 3.485839 | 4.19272 | 0.831403 |
subjs = len(X)
W = []
for i in range(subjs):
W.append(RSRM._update_transform_subject(X[i], S[i], R))
return W | def _update_transforms(X, S, R) | Updates the mappings `W_i` for each subject.
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, timepoints]
Each element in the list contains the fMRI data for alignment of
one subject.ß
S : list of array, element i has shape=[voxels_i, timepoints]
The individual component :math:`S_i` for each subject.
R : array, shape=[features, timepoints]
The shared response.
Returns
-------
W : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject. | 5.833858 | 5.593774 | 1.04292 |
pos = v > gamma
neg = v < -gamma
v[pos] -= gamma
v[neg] += gamma
v[np.logical_and(~pos, ~neg)] = .0
return v | def _shrink(v, gamma) | Soft-shrinkage of an array with parameter gamma.
Parameters
----------
v : array
Array containing the values to be applied to the shrinkage operator
gamma : float
Shrinkage parameter.
Returns
-------
v : array
The same input array after the shrinkage operator was applied. | 3.573369 | 4.209385 | 0.848905 |
import matplotlib.pyplot as plt
import math
plt.figure()
subjects = len(cm)
root_subjects = math.sqrt(subjects)
cols = math.ceil(root_subjects)
rows = math.ceil(subjects/cols)
classes = cm[0].shape[0]
for subject in range(subjects):
plt.subplot(rows, cols, subject+1)
plt.imshow(cm[subject], interpolation='nearest', cmap=plt.cm.bone)
plt.xticks(np.arange(classes), range(1, classes+1))
plt.yticks(np.arange(classes), range(1, classes+1))
cbar = plt.colorbar(ticks=[0.0, 1.0], shrink=0.6)
cbar.set_clim(0.0, 1.0)
plt.xlabel("Predicted")
plt.ylabel("True label")
plt.title("{0:d}".format(subject + 1))
plt.suptitle(title)
plt.tight_layout()
plt.show() | def plot_confusion_matrix(cm, title="Confusion Matrix") | Plots a confusion matrix for each subject | 2.122406 | 2.025687 | 1.047746 |
image_data = image.get_data()
if image_data.shape[:3] != mask.shape:
raise ValueError("Image data and mask have different shapes.")
if data_type is not None:
cast_data = image_data.astype(data_type)
else:
cast_data = image_data
return cast_data[mask] | def mask_image(image: SpatialImage, mask: np.ndarray, data_type: type = None
) -> np.ndarray | Mask image after optionally casting its type.
Parameters
----------
image
Image to mask. Can include time as the last dimension.
mask
Mask to apply. Must have the same shape as the image data.
data_type
Type to cast image to.
Returns
-------
np.ndarray
Masked image.
Raises
------
ValueError
Image data and masks have different shapes. | 2.580355 | 2.721519 | 0.94813 |
for image in images:
yield [mask_image(image, mask, image_type) for mask in masks] | def multimask_images(images: Iterable[SpatialImage],
masks: Sequence[np.ndarray], image_type: type = None
) -> Iterable[Sequence[np.ndarray]] | Mask images with multiple masks.
Parameters
----------
images:
Images to mask.
masks:
Masks to apply.
image_type:
Type to cast images to.
Yields
------
Sequence[np.ndarray]
For each mask, a masked image. | 3.522394 | 4.730463 | 0.744619 |
for images in multimask_images(images, (mask,), image_type):
yield images[0] | def mask_images(images: Iterable[SpatialImage], mask: np.ndarray,
image_type: type = None) -> Iterable[np.ndarray] | Mask images.
Parameters
----------
images:
Images to mask.
mask:
Mask to apply.
image_type:
Type to cast images to.
Yields
------
np.ndarray
Masked image. | 10.208649 | 13.025961 | 0.783716 |
images_iterator = iter(masked_images)
first_image = next(images_iterator)
first_image_shape = first_image.T.shape
result = np.empty((first_image_shape[0], first_image_shape[1],
n_subjects))
for n_images, image in enumerate(itertools.chain([first_image],
images_iterator)):
image = image.T
if image.shape != first_image_shape:
raise ValueError("Image {} has different shape from first "
"image: {} != {}".format(n_images,
image.shape,
first_image_shape))
result[:, :, n_images] = image
n_images += 1
if n_images != n_subjects:
raise ValueError("n_subjects != number of images: {} != {}"
.format(n_subjects, n_images))
return result.view(cls) | def from_masked_images(cls: Type[T], masked_images: Iterable[np.ndarray],
n_subjects: int) -> T | Create a new instance of MaskedMultiSubjecData from masked images.
Parameters
----------
masked_images : iterator
Images from multiple subjects to stack along 3rd dimension
n_subjects : int
Number of subjects; must match the number of images
Returns
-------
T
A new instance of MaskedMultiSubjectData
Raises
------
ValueError
Images have different shapes.
The number of images differs from n_subjects. | 2.237546 | 2.440391 | 0.91688 |
condition_idxs, epoch_idxs, _ = np.where(self)
_, unique_epoch_idxs = np.unique(epoch_idxs, return_index=True)
return condition_idxs[unique_epoch_idxs] | def extract_labels(self) -> np.ndarray | Extract condition labels.
Returns
-------
np.ndarray
The condition label of each epoch. | 5.093973 | 4.101325 | 1.242031 |
w = []
subjects = len(data)
voxels = np.empty(subjects, dtype=int)
# Set Wi to a random orthogonal voxels by features matrix
for subject in range(subjects):
if data[subject] is not None:
voxels[subject] = data[subject].shape[0]
rnd_matrix = random_states[subject].random_sample((
voxels[subject], features))
q, r = np.linalg.qr(rnd_matrix)
w.append(q)
else:
voxels[subject] = 0
w.append(None)
voxels = comm.allreduce(voxels, op=MPI.SUM)
return w, voxels | def _init_w_transforms(data, features, random_states, comm=MPI.COMM_SELF) | Initialize the mappings (Wi) for the SRM with random orthogonal matrices.
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples]
Each element in the list contains the fMRI data of one subject.
features : int
The number of features in the model.
random_states : list of `RandomState`s
One `RandomState` instance per subject.
comm : mpi4py.MPI.Intracomm
The MPI communicator containing the data
Returns
-------
w : list of array, element i has shape=[voxels_i, features]
The initialized orthogonal transforms (mappings) :math:`W_i` for each
subject.
voxels : list of int
A list with the number of voxels per subject.
Note
----
This function assumes that the numpy random number generator was
initialized.
Not thread safe. | 3.641288 | 2.986872 | 1.219097 |
logger.info('Starting Probabilistic SRM')
# Check the number of subjects
if len(X) <= 1:
raise ValueError("There are not enough subjects "
"({0:d}) to train the model.".format(len(X)))
# Check for input data sizes
number_subjects = len(X)
number_subjects_vec = self.comm.allgather(number_subjects)
for rank in range(self.comm.Get_size()):
if number_subjects_vec[rank] != number_subjects:
raise ValueError(
"Not all ranks have same number of subjects")
# Collect size information
shape0 = np.zeros((number_subjects,), dtype=np.int)
shape1 = np.zeros((number_subjects,), dtype=np.int)
for subject in range(number_subjects):
if X[subject] is not None:
assert_all_finite(X[subject])
shape0[subject] = X[subject].shape[0]
shape1[subject] = X[subject].shape[1]
shape0 = self.comm.allreduce(shape0, op=MPI.SUM)
shape1 = self.comm.allreduce(shape1, op=MPI.SUM)
# Check if all subjects have same number of TRs
number_trs = np.min(shape1)
for subject in range(number_subjects):
if shape1[subject] < self.features:
raise ValueError(
"There are not enough samples to train the model with "
"{0:d} features.".format(self.features))
if shape1[subject] != number_trs:
raise ValueError("Different number of samples between subjects"
".")
# Run SRM
self.sigma_s_, self.w_, self.mu_, self.rho2_, self.s_ = self._srm(X)
return self | def fit(self, X, y=None) | Compute the probabilistic Shared Response Model
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, samples]
Each element in the list contains the fMRI data of one subject.
y : not used | 3.114107 | 2.987892 | 1.042242 |
# Check if the model exist
if hasattr(self, 'w_') is False:
raise NotFittedError("The model fit has not been run yet.")
# Check the number of subjects
if len(X) != len(self.w_):
raise ValueError("The number of subjects does not match the one"
" in the model.")
s = [None] * len(X)
for subject in range(len(X)):
if X[subject] is not None:
s[subject] = self.w_[subject].T.dot(X[subject])
return s | def transform(self, X, y=None) | Use the model to transform matrix to Shared Response space
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject
note that number of voxels and samples can vary across subjects
y : not used (as it is unsupervised learning)
Returns
-------
s : list of 2D arrays, element i has shape=[features_i, samples_i]
Shared responses from input data (X) | 3.186861 | 2.809292 | 1.1344 |
A = Xi.dot(S.T)
# Solve the Procrustes problem
U, _, V = np.linalg.svd(A, full_matrices=False)
return U.dot(V) | def _update_transform_subject(Xi, S) | Updates the mappings `W_i` for one subject.
Parameters
----------
Xi : array, shape=[voxels, timepoints]
The fMRI data :math:`X_i` for aligning the subject.
S : array, shape=[features, timepoints]
The shared response.
Returns
-------
Wi : array, shape=[voxels, features]
The orthogonal transform (mapping) :math:`W_i` for the subject. | 3.751317 | 4.576279 | 0.819731 |
# Check if the model exist
if hasattr(self, 'w_') is False:
raise NotFittedError("The model fit has not been run yet.")
# Check the number of TRs in the subject
if X.shape[1] != self.s_.shape[1]:
raise ValueError("The number of timepoints(TRs) does not match the"
"one in the model.")
w = self._update_transform_subject(X, self.s_)
return w | def transform_subject(self, X) | Transform a new subject using the existing model.
The subject is assumed to have recieved equivalent stimulation
Parameters
----------
X : 2D array, shape=[voxels, timepoints]
The fMRI data of the new subject.
Returns
-------
w : 2D array, shape=[voxels, features]
Orthogonal mapping `W_{new}` for new subject | 5.400873 | 4.850527 | 1.113461 |
subjects = len(data)
self.random_state_ = np.random.RandomState(self.rand_seed)
random_states = [
np.random.RandomState(self.random_state_.randint(2 ** 32))
for i in range(len(data))]
# Initialization step: initialize the outputs with initial values,
# voxels with the number of voxels in each subject.
w, _ = _init_w_transforms(data, self.features, random_states)
shared_response = self._compute_shared_response(data, w)
if logger.isEnabledFor(logging.INFO):
# Calculate the current objective function value
objective = self._objective_function(data, w, shared_response)
logger.info('Objective function %f' % objective)
# Main loop of the algorithm
for iteration in range(self.n_iter):
logger.info('Iteration %d' % (iteration + 1))
# Update each subject's mapping transform W_i:
for subject in range(subjects):
a_subject = data[subject].dot(shared_response.T)
perturbation = np.zeros(a_subject.shape)
np.fill_diagonal(perturbation, 0.001)
u_subject, _, v_subject = np.linalg.svd(
a_subject + perturbation, full_matrices=False)
w[subject] = u_subject.dot(v_subject)
# Update the shared response:
shared_response = self._compute_shared_response(data, w)
if logger.isEnabledFor(logging.INFO):
# Calculate the current objective function value
objective = self._objective_function(data, w, shared_response)
logger.info('Objective function %f' % objective)
return w, shared_response | def _srm(self, data) | Expectation-Maximization algorithm for fitting the probabilistic SRM.
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples]
Each element in the list contains the fMRI data of one subject.
Returns
-------
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
s : array, shape=[features, samples]
The shared response. | 3.125122 | 2.763078 | 1.131029 |
X = copy.deepcopy(X)
if type(X) is not list:
X = check_array(X)
X = [X]
n_train = len(X)
for i in range(n_train):
X[i] = X[i].T
self.classes_ = np.arange(self.n_events)
n_dim = X[0].shape[0]
for i in range(n_train):
assert (X[i].shape[0] == n_dim)
# Double-check that data is z-scored in time
for i in range(n_train):
X[i] = stats.zscore(X[i], axis=1, ddof=1)
# Initialize variables for fitting
log_gamma = []
for i in range(n_train):
log_gamma.append(np.zeros((X[i].shape[1],
self.n_events)))
step = 1
best_ll = float("-inf")
self.ll_ = np.empty((0, n_train))
while step <= self.n_iter:
iteration_var = self.step_var(step)
# Based on the current segmentation, compute the mean pattern
# for each event
seg_prob = [np.exp(lg) / np.sum(np.exp(lg), axis=0)
for lg in log_gamma]
mean_pat = np.empty((n_train, n_dim, self.n_events))
for i in range(n_train):
mean_pat[i, :, :] = X[i].dot(seg_prob[i])
mean_pat = np.mean(mean_pat, axis=0)
# Based on the current mean patterns, compute the event
# segmentation
self.ll_ = np.append(self.ll_, np.empty((1, n_train)), axis=0)
for i in range(n_train):
logprob = self._logprob_obs(X[i],
mean_pat, iteration_var)
log_gamma[i], self.ll_[-1, i] = self._forward_backward(logprob)
# If log-likelihood has started decreasing, undo last step and stop
if np.mean(self.ll_[-1, :]) < best_ll:
self.ll_ = self.ll_[:-1, :]
break
self.segments_ = [np.exp(lg) for lg in log_gamma]
self.event_var_ = iteration_var
self.event_pat_ = mean_pat
best_ll = np.mean(self.ll_[-1, :])
logger.debug("Fitting step %d, LL=%f", step, best_ll)
step += 1
return self | def fit(self, X, y=None) | Learn a segmentation on training data
Fits event patterns and a segmentation to training data. After
running this function, the learned event patterns can be used to
segment other datasets using find_events
Parameters
----------
X: time by voxel ndarray, or a list of such ndarrays
fMRI data to be segmented. If a list is given, then all datasets
are segmented simultaneously with the same event patterns
y: not used (added to comply with BaseEstimator definition)
Returns
-------
self: the EventSegment object | 2.871782 | 2.816127 | 1.019763 |
n_vox = data.shape[0]
t = data.shape[1]
# z-score both data and mean patterns in space, so that Gaussians
# are measuring Pearson correlations and are insensitive to overall
# activity changes
data_z = stats.zscore(data, axis=0, ddof=1)
mean_pat_z = stats.zscore(mean_pat, axis=0, ddof=1)
logprob = np.empty((t, self.n_events))
if type(var) is not np.ndarray:
var = var * np.ones(self.n_events)
for k in range(self.n_events):
logprob[:, k] = -0.5 * n_vox * np.log(
2 * np.pi * var[k]) - 0.5 * np.sum(
(data_z.T - mean_pat_z[:, k]).T ** 2, axis=0) / var[k]
logprob /= n_vox
return logprob | def _logprob_obs(self, data, mean_pat, var) | Log probability of observing each timepoint under each event model
Computes the log probability of each observed timepoint being
generated by the Gaussian distribution for each event pattern
Parameters
----------
data: voxel by time ndarray
fMRI data on which to compute log probabilities
mean_pat: voxel by event ndarray
Centers of the Gaussians for each event
var: float or 1D array of length equal to the number of events
Variance of the event Gaussians. If scalar, all events are
assumed to have the same variance
Returns
-------
logprob : time by event ndarray
Log probability of each timepoint under each event Gaussian | 3.178005 | 2.800354 | 1.134858 |
logprob = copy.copy(logprob)
t = logprob.shape[0]
logprob = np.hstack((logprob, float("-inf") * np.ones((t, 1))))
# Initialize variables
log_scale = np.zeros(t)
log_alpha = np.zeros((t, self.n_events + 1))
log_beta = np.zeros((t, self.n_events + 1))
# Set up transition matrix, with final sink state
self.p_start = np.zeros(self.n_events + 1)
self.p_end = np.zeros(self.n_events + 1)
self.P = np.zeros((self.n_events + 1, self.n_events + 1))
label_ind = np.unique(self.event_chains, return_inverse=True)[1]
n_chains = np.max(label_ind) + 1
# For each chain of events, link them together and then to sink state
for c in range(n_chains):
chain_ind = np.nonzero(label_ind == c)[0]
self.p_start[chain_ind[0]] = 1 / n_chains
self.p_end[chain_ind[-1]] = 1 / n_chains
p_trans = (len(chain_ind) - 1) / t
if p_trans >= 1:
raise ValueError('Too few timepoints')
for i in range(len(chain_ind)):
self.P[chain_ind[i], chain_ind[i]] = 1 - p_trans
if i < len(chain_ind) - 1:
self.P[chain_ind[i], chain_ind[i+1]] = p_trans
else:
self.P[chain_ind[i], -1] = p_trans
self.P[-1, -1] = 1
# Forward pass
for i in range(t):
if i == 0:
log_alpha[0, :] = self._log(self.p_start) + logprob[0, :]
else:
log_alpha[i, :] = self._log(np.exp(log_alpha[i - 1, :])
.dot(self.P)) + logprob[i, :]
log_scale[i] = np.logaddexp.reduce(log_alpha[i, :])
log_alpha[i] -= log_scale[i]
# Backward pass
log_beta[-1, :] = self._log(self.p_end) - log_scale[-1]
for i in reversed(range(t - 1)):
obs_weighted = log_beta[i + 1, :] + logprob[i + 1, :]
offset = np.max(obs_weighted)
log_beta[i, :] = offset + self._log(
np.exp(obs_weighted - offset).dot(self.P.T)) - log_scale[i]
# Combine and normalize
log_gamma = log_alpha + log_beta
log_gamma -= np.logaddexp.reduce(log_gamma, axis=1, keepdims=True)
ll = np.sum(log_scale[:(t - 1)]) + np.logaddexp.reduce(
log_alpha[-1, :] + log_scale[-1] + self._log(self.p_end))
log_gamma = log_gamma[:, :-1]
return log_gamma, ll | def _forward_backward(self, logprob) | Runs forward-backward algorithm on observation log probs
Given the log probability of each timepoint being generated by
each event, run the HMM forward-backward algorithm to find the
probability that each timepoint belongs to each event (based on the
transition priors in p_start, p_end, and P)
See https://en.wikipedia.org/wiki/Forward-backward_algorithm for
mathematical details
Parameters
----------
logprob : time by event ndarray
Log probability of each timepoint under each event Gaussian
Returns
-------
log_gamma : time by event ndarray
Log probability of each timepoint belonging to each event
ll : float
Log-likelihood of fit | 2.225715 | 2.12108 | 1.049331 |
xshape = x.shape
_x = x.flatten()
y = utils.masked_log(_x)
return y.reshape(xshape) | def _log(self, x) | Modified version of np.log that manually sets values <=0 to -inf
Parameters
----------
x: ndarray of floats
Input to the log function
Returns
-------
log_ma: ndarray of floats
log of x, with x<=0 values replaced with -inf | 7.410101 | 7.695527 | 0.96291 |
if event_pat.shape[1] != self.n_events:
raise ValueError(("Number of columns of event_pat must match "
"number of events"))
self.event_pat_ = event_pat.copy() | def set_event_patterns(self, event_pat) | Set HMM event patterns manually
Rather than fitting the event patterns automatically using fit(), this
function allows them to be set explicitly. They can then be used to
find corresponding events in a new dataset, using find_events().
Parameters
----------
event_pat: voxel by event ndarray | 3.741298 | 4.02105 | 0.930428 |
if var is None:
if not hasattr(self, 'event_var_'):
raise NotFittedError(("Event variance must be provided, if "
"not previously set by fit()"))
else:
var = self.event_var_
if not hasattr(self, 'event_pat_'):
raise NotFittedError(("The event patterns must first be set "
"by fit() or set_event_patterns()"))
if scramble:
mean_pat = self.event_pat_[:, np.random.permutation(self.n_events)]
else:
mean_pat = self.event_pat_
logprob = self._logprob_obs(testing_data.T, mean_pat, var)
lg, test_ll = self._forward_backward(logprob)
segments = np.exp(lg)
return segments, test_ll | def find_events(self, testing_data, var=None, scramble=False) | Applies learned event segmentation to new testing dataset
After fitting an event segmentation using fit() or setting event
patterns directly using set_event_patterns(), this function finds the
same sequence of event patterns in a new testing dataset.
Parameters
----------
testing_data: timepoint by voxel ndarray
fMRI data to segment based on previously-learned event patterns
var: float or 1D ndarray of length equal to the number of events
default: uses variance that maximized training log-likelihood
Variance of the event Gaussians. If scalar, all events are
assumed to have the same variance. If fit() has not previously
been run, this must be specifed (cannot be None).
scramble: bool : default False
If true, the order of the learned events are shuffled before
fitting, to give a null distribution
Returns
-------
segments : time by event ndarray
The resulting soft segmentation. segments[t,e] = probability
that timepoint t is in event e
test_ll : float
Log-likelihood of model fit | 3.954244 | 3.125794 | 1.265037 |
check_is_fitted(self, ["event_pat_", "event_var_"])
X = check_array(X)
segments, test_ll = self.find_events(X)
return np.argmax(segments, axis=1) | def predict(self, X) | Applies learned event segmentation to new testing dataset
Alternative function for segmenting a new dataset after using
fit() to learn a sequence of events, to comply with the sklearn
Classifier interface
Parameters
----------
X: timepoint by voxel ndarray
fMRI data to segment based on previously-learned event patterns
Returns
-------
Event label for each timepoint | 6.450968 | 8.547134 | 0.754752 |
Dz = stats.zscore(D, axis=1, ddof=1)
ev_var = np.empty(event_pat.shape[1])
for e in range(event_pat.shape[1]):
# Only compute variances for weights > 0.1% of max weight
nz = weights[:, e] > np.max(weights[:, e])/1000
sumsq = np.dot(weights[nz, e],
np.sum(np.square(Dz[nz, :] -
event_pat[:, e]), axis=1))
ev_var[e] = sumsq/(np.sum(weights[nz, e]) -
np.sum(np.square(weights[nz, e])) /
np.sum(weights[nz, e]))
ev_var = ev_var / D.shape[1]
return ev_var | def calc_weighted_event_var(self, D, weights, event_pat) | Computes normalized weighted variance around event pattern
Utility function for computing variance in a training set of weighted
event examples. For each event, the sum of squared differences for all
timepoints from the event pattern is computed, and then the weights
specify how much each of these differences contributes to the
variance (normalized by the number of voxels).
Parameters
----------
D : timepoint by voxel ndarray
fMRI data for which to compute event variances
weights : timepoint by event ndarray
specifies relative weights of timepoints for each event
event_pat : voxel by event ndarray
mean event patterns to compute variance around
Returns
-------
ev_var : ndarray of variances for each event | 3.085838 | 2.874753 | 1.073427 |
lg, test_ll = self._forward_backward(np.zeros((t, self.n_events)))
segments = np.exp(lg)
return segments, test_ll | def model_prior(self, t) | Returns the prior probability of the HMM
Runs forward-backward without any data, showing the prior distribution
of the model (for comparison with a posterior).
Parameters
----------
t: int
Number of timepoints
Returns
-------
segments : time by event ndarray
segments[t,e] = prior probability that timepoint t is in event e
test_ll : float
Log-likelihood of model (data-independent term) | 13.940866 | 6.086598 | 2.29042 |
try:
return _resolve_value(safe_chain_getattr(obj, attr))
except AttributeError:
return value | def chain_getattr(obj, attr, value=None) | Get chain attribute for an object. | 6.212589 | 6.629694 | 0.937085 |
if split is None:
sl = 0
join = False
else:
sl = len(split)
join = True
result = []
rl = 0
for element in iterable:
element = prefix + element + postfix
el = len(element)
if len(result) > 0:
el += sl
rl += el
if rl <= limit:
result.append(element)
else:
break
if join:
result = split.join(result)
return result | def trim_iterable(iterable, limit, *, split=None, prefix='', postfix='') | trim the list to make total length no more than limit.If split specified,a string is return.
:return: | 2.907312 | 2.990264 | 0.972259 |
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