def test_warnings(self):
with pytest.warns(
VisibleDeprecationWarning,
match=f"The argument `learning_rate` has been deprecated"):
_ = orpca(self.X, rank=self.rank, learning_rate=0.1)
with pytest.warns(
VisibleDeprecationWarning,
match=f"The argument `momentum` has been deprecated"):
_ = orpca(self.X, rank=self.rank, momentum=0.1)
def test_init_mat(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, store_error=True, init=self.U)
compare_norms(X, self.A)
with pytest.raises(ValueError, match=f"has to be a two-dimensional matrix"):
mat = np.zeros(self.m)
_ = orpca(self.X, rank=self.rank, init=mat)
with pytest.raises(ValueError, match=f"has to be of shape"):
mat = np.zeros((self.m, self.rank - 1))
_ = orpca(self.X, rank=self.rank, init=mat)
def test_training(self, rank, training_samples):
X, E, U, S, V = orpca(
self.X,
rank=rank,
store_error=True,
init="qr",
training_samples=training_samples,
)
compare_norms(X, self.A)
with pytest.raises(ValueError, match=f"must be >="):
_ = orpca(self.X, rank=self.rank, init="qr", training_samples=self.rank - 1)
def test_method_MomentumSGD(self, subspace_momentum):
X, E, U, S, V = orpca(
self.X,
rank=self.rank,
store_error=True,
method="MomentumSGD",
subspace_learning_rate=1.1,
subspace_momentum=subspace_momentum,
)
compare_norms(X, self.A)
with pytest.raises(ValueError, match=f"must be a float between 0 and 1"):
_ = orpca(
self.X, rank=self.rank, method="MomentumSGD", subspace_momentum=1.9
)
def test_init(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, init='rand')
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
assert normX < self.tol
with pytest.raises(ValueError,
match=f"has to be a two-dimensional matrix"):
mat = np.zeros(self.m)
_ = orpca(self.X, rank=self.rank, init=mat)
with pytest.raises(ValueError, match=f"has to be of shape"):
mat = np.zeros((self.m, self.rank - 1))
_ = orpca(self.X, rank=self.rank, init=mat)
def test_method_SGD(self):
X, E, U, S, V = orpca(self.X, rank=self.rank,
method='SGD', learning_rate=self.learning_rate)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def test_training(self):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
init='qr',
training_samples=self.training_samples)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
print(normX)
assert normX < self.tol
with pytest.raises(ValueError, match=f"must be >="):
_ = orpca(self.X,
rank=self.rank,
init='qr',
training_samples=self.rank - 1)
def test_training(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, init='qr',
training_samples=self.training_samples)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
print(normX)
nt.assert_true(normX < self.tol)
def test_fast(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, fast=True)
# Only check shapes
assert X.shape == (self.m, self.n)
assert E.shape == (self.m, self.n)
assert U.shape == (self.m, self.rank)
assert S.shape == (self.rank, )
assert V.shape == (self.n, self.rank)
def test_regularization(self):
X, E, U, S, V = orpca(self.X, rank=self.rank,
lambda1=self.lambda1,
lambda2=self.lambda2)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def test_method_MomentumSGD(self, subspace_momentum):
X, E, U, S, V = orpca(
self.X,
rank=self.rank,
method='MomentumSGD',
subspace_learning_rate=self.subspace_learning_rate,
subspace_momentum=subspace_momentum)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
assert normX < self.tol
with pytest.raises(ValueError,
match=f"must be a float between 0 and 1"):
_ = orpca(self.X,
rank=self.rank,
method='MomentumSGD',
subspace_momentum=1.9)
def test_method_SGD(self, subspace_learning_rate):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
method='SGD',
subspace_learning_rate=subspace_learning_rate)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
assert normX < self.tol
def test_method_SGD(self, subspace_learning_rate):
X, E, U, S, V = orpca(
self.X,
rank=self.rank,
store_error=True,
method="SGD",
subspace_learning_rate=subspace_learning_rate,
)
compare_norms(X, self.A)
def test_regularization(self):
X, E, U, S, V = orpca(
self.X,
rank=self.rank,
store_error=True,
lambda1=0.01,
lambda2=0.02,
)
compare_norms(X, self.A)
def test_method_MomentumSGD(self):
X, E, U, S, V = orpca(self.X, rank=self.rank,
method='MomentumSGD',
learning_rate=self.learning_rate,
momentum=self.momentum)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
assert normX < self.tol
def test_method_SGD(self):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
method='SGD',
learning_rate=self.learning_rate)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def test_regularization(self):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
lambda1=self.lambda1,
lambda2=self.lambda2)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def test_method_MomentumSGD(self):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
method='MomentumSGD',
learning_rate=self.learning_rate,
momentum=self.momentum)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
assert normX < self.tol
def test_training(self):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
init='qr',
training_samples=self.training_samples)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
print(normX)
nt.assert_true(normX < self.tol)
def test_default(self):
X, E, U, S, V = orpca(self.X, rank=self.rank)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
assert normX < self.tol
def test_method_BCD(self):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
store_error=True,
method="BCD")
compare_norms(X, self.A)
def test_batch_size(self):
L, R = orpca(self.X, rank=self.rank, batch_size=2)
assert L.shape == (self.m, self.rank)
assert R.shape == (self.rank, self.n)
def test_project(self):
L, R = orpca(self.X, rank=self.rank, project=True)
assert L.shape == (self.m, self.rank)
assert R.shape == (self.rank, self.n)
def test_default(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, store_error=True)
compare_norms(X, self.A)
def decomposition(self,
normalize_poissonian_noise=False,
algorithm='svd',
output_dimension=None,
centre=None,
auto_transpose=True,
navigation_mask=None,
signal_mask=None,
var_array=None,
var_func=None,
polyfit=None,
reproject=None,
return_info=False,
**kwargs):
"""Decomposition with a choice of algorithms
The results are stored in self.learning_results
Parameters
----------
normalize_poissonian_noise : bool
If True, scale the SI to normalize Poissonian noise
algorithm : 'svd' | 'fast_svd' | 'mlpca' | 'fast_mlpca' | 'nmf' |
'sparse_pca' | 'mini_batch_sparse_pca' | 'RPCA_GoDec' | 'ORPCA'
output_dimension : None or int
number of components to keep/calculate
centre : None | 'variables' | 'trials'
If None no centring is applied. If 'variable' the centring will be
performed in the variable axis. If 'trials', the centring will be
performed in the 'trials' axis. It only has effect when using the
svd or fast_svd algorithms
auto_transpose : bool
If True, automatically transposes the data to boost performance.
Only has effect when using the svd of fast_svd algorithms.
navigation_mask : boolean numpy array
The navigation locations marked as True are not used in the
decompostion.
signal_mask : boolean numpy array
The signal locations marked as True are not used in the
decomposition.
var_array : numpy array
Array of variance for the maximum likelihood PCA algorithm
var_func : function or numpy array
If function, it will apply it to the dataset to obtain the
var_array. Alternatively, it can a an array with the coefficients
of a polynomial.
reproject : None | signal | navigation | both
If not None, the results of the decomposition will be projected in
the selected masked area.
return_info: bool, default False
The result of the decomposition is stored internally. However, some algorithms generate some extra
information that is not stored. If True (the default is False) return any extra information if available
Returns
-------
(X, E) : (numpy array, numpy array)
If 'algorithm' == 'RPCA_GoDec' or 'ORPCA' and 'return_info' is True,
returns the low-rank (X) and sparse (E) matrices from robust PCA.
See also
--------
plot_decomposition_factors, plot_decomposition_loadings, plot_lev
"""
to_return = None
# Check if it is the wrong data type
if self.data.dtype.char not in ['e', 'f', 'd']: # If not float
_logger.warning(
'To perform a decomposition the data must be of the float '
'type. You can change the type using the change_dtype method'
' e.g. s.change_dtype(\'float64\')\n'
'Nothing done.')
return
if self.axes_manager.navigation_size < 2:
raise AttributeError("It is not possible to decompose a dataset "
"with navigation_size < 2")
# backup the original data
self._data_before_treatments = self.data.copy()
# set the output target (peak results or not?)
target = LearningResults()
if algorithm == 'mlpca':
if normalize_poissonian_noise is True:
_logger.warning(
"It makes no sense to do normalize_poissonian_noise with "
"the MLPCA algorithm. Therefore, "
"normalize_poissonian_noise is set to False")
normalize_poissonian_noise = False
if output_dimension is None:
raise ValueError("With the MLPCA algorithm the "
"output_dimension must be specified")
if algorithm == 'RPCA_GoDec' or algorithm == 'ORPCA':
if output_dimension is None:
raise ValueError(
"With the robust PCA algorithms ('RPCA_GoDec' "
"and 'ORPCA'), the output_dimension "
"must be specified")
# Apply pre-treatments
# Transform the data in a line spectrum
self._unfolded4decomposition = self.unfold()
try:
if hasattr(navigation_mask, 'ravel'):
navigation_mask = navigation_mask.ravel()
if hasattr(signal_mask, 'ravel'):
signal_mask = signal_mask.ravel()
# Normalize the poissonian noise
# TODO this function can change the masks and this can cause
# problems when reprojecting
if normalize_poissonian_noise is True:
self.normalize_poissonian_noise(
navigation_mask=navigation_mask,
signal_mask=signal_mask,
)
_logger.info('Performing decomposition analysis')
# The rest of the code assumes that the first data axis
# is the navigation axis. We transpose the data if that is not the
# case.
dc = (self.data
if self.axes_manager[0].index_in_array == 0 else self.data.T)
# Transform the None masks in slices to get the right behaviour
if navigation_mask is None:
navigation_mask = slice(None)
else:
navigation_mask = ~navigation_mask
if signal_mask is None:
signal_mask = slice(None)
else:
signal_mask = ~signal_mask
# WARNING: signal_mask and navigation_mask values are now their
# negaties i.e. True -> False and viceversa. However, the
# stored value (at the end of the method) coincides with the
# input masks
# Reset the explained_variance which is not set by all the
# algorithms
explained_variance = None
explained_variance_ratio = None
mean = None
if algorithm == 'svd':
factors, loadings, explained_variance, mean = svd_pca(
dc[:, signal_mask][navigation_mask, :],
centre=centre,
auto_transpose=auto_transpose)
elif algorithm == 'fast_svd':
factors, loadings, explained_variance, mean = svd_pca(
dc[:, signal_mask][navigation_mask, :],
fast=True,
output_dimension=output_dimension,
centre=centre,
auto_transpose=auto_transpose)
elif algorithm == 'sklearn_pca':
if import_sklearn.sklearn_installed is False:
raise ImportError('sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.PCA(**kwargs)
sk.n_components = output_dimension
loadings = sk.fit_transform(
(dc[:, signal_mask][navigation_mask, :]))
factors = sk.components_.T
explained_variance = sk.explained_variance_
mean = sk.mean_
centre = 'trials'
if return_info:
to_return = sk
elif algorithm == 'nmf':
if import_sklearn.sklearn_installed is False:
raise ImportError('sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.NMF(**kwargs)
sk.n_components = output_dimension
loadings = sk.fit_transform(
(dc[:, signal_mask][navigation_mask, :]))
factors = sk.components_.T
if return_info:
to_return = sk
elif algorithm == 'sparse_pca':
if import_sklearn.sklearn_installed is False:
raise ImportError('sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.SparsePCA(
output_dimension, **kwargs)
loadings = sk.fit_transform(
dc[:, signal_mask][navigation_mask, :])
factors = sk.components_.T
if return_info:
to_return = sk
elif algorithm == 'mini_batch_sparse_pca':
if import_sklearn.sklearn_installed is False:
raise ImportError('sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.MiniBatchSparsePCA(
output_dimension, **kwargs)
loadings = sk.fit_transform(
dc[:, signal_mask][navigation_mask, :])
factors = sk.components_.T
if return_info:
to_return = sk
elif algorithm == 'mlpca' or algorithm == 'fast_mlpca':
_logger.info("Performing the MLPCA training")
if output_dimension is None:
raise ValueError("For MLPCA it is mandatory to define the "
"output_dimension")
if var_array is None and var_func is None:
_logger.info('No variance array provided.'
'Assuming poissonian data')
var_array = dc[:, signal_mask][navigation_mask, :]
if var_array is not None and var_func is not None:
raise ValueError(
"You have defined both the var_func and var_array "
"keywords."
"Please, define just one of them")
if var_func is not None:
if hasattr(var_func, '__call__'):
var_array = var_func(dc[signal_mask,
...][:, navigation_mask])
else:
try:
var_array = np.polyval(
polyfit, dc[signal_mask, navigation_mask])
except:
raise ValueError(
'var_func must be either a function or an '
'array defining the coefficients of a polynom')
if algorithm == 'mlpca':
fast = False
else:
fast = True
U, S, V, Sobj, ErrFlag = mlpca(
dc[:, signal_mask][navigation_mask, :],
var_array,
output_dimension,
fast=fast)
loadings = U * S
factors = V
explained_variance_ratio = S**2 / Sobj
explained_variance = S**2 / len(factors)
elif algorithm == 'RPCA_GoDec':
_logger.info("Performing Robust PCA with GoDec")
X, E, G, U, S, V = rpca_godec(
dc[:, signal_mask][navigation_mask, :],
rank=output_dimension,
fast=True,
**kwargs)
loadings = U * S
factors = V
explained_variance = S**2 / len(factors)
if return_info:
to_return = (X, E)
elif algorithm == 'ORPCA':
_logger.info("Performing Online Robust PCA")
X, E, U, S, V = orpca(dc[:, signal_mask][navigation_mask, :],
rank=output_dimension,
fast=True,
**kwargs)
loadings = U * S
factors = V
explained_variance = S**2 / len(factors)
if return_info:
to_return = (X, E)
else:
raise ValueError('Algorithm not recognised. ' 'Nothing done')
# We must calculate the ratio here because otherwise the sum
# information can be lost if the user call
# crop_decomposition_dimension
if explained_variance is not None and \
explained_variance_ratio is None:
explained_variance_ratio = \
explained_variance / explained_variance.sum()
# Store the results in learning_results
target.factors = factors
target.loadings = loadings
target.explained_variance = explained_variance
target.explained_variance_ratio = explained_variance_ratio
target.decomposition_algorithm = algorithm
target.poissonian_noise_normalized = \
normalize_poissonian_noise
target.output_dimension = output_dimension
target.unfolded = self._unfolded4decomposition
target.centre = centre
target.mean = mean
if output_dimension and factors.shape[1] != output_dimension:
target.crop_decomposition_dimension(output_dimension)
# Delete the unmixing information, because it'll refer to a
# previous decomposition
target.unmixing_matrix = None
target.bss_algorithm = None
if self._unfolded4decomposition is True:
folding = \
self.metadata._HyperSpy.Folding
target.original_shape = folding.original_shape
# Reproject
if mean is None:
mean = 0
if reproject in ('navigation', 'both'):
if algorithm not in ('nmf', 'sparse_pca',
'mini_batch_sparse_pca'):
loadings_ = np.dot(dc[:, signal_mask] - mean, factors)
else:
loadings_ = sk.transform(dc[:, signal_mask])
target.loadings = loadings_
if reproject in ('signal', 'both'):
if algorithm not in ('nmf', 'sparse_pca',
'mini_batch_sparse_pca'):
factors = np.dot(np.linalg.pinv(loadings),
dc[navigation_mask, :] - mean).T
target.factors = factors
else:
_logger.info("Reprojecting the signal is not yet "
"supported for this algorithm")
if reproject == 'both':
reproject = 'signal'
else:
reproject = None
# Rescale the results if the noise was normalized
if normalize_poissonian_noise is True:
target.factors[:] *= self._root_bH.T
target.loadings[:] *= self._root_aG
# Set the pixels that were not processed to nan
if not isinstance(signal_mask, slice):
# Store the (inverted, as inputed) signal mask
target.signal_mask = ~signal_mask.reshape(
self.axes_manager._signal_shape_in_array)
if reproject not in ('both', 'signal'):
factors = np.zeros((dc.shape[-1], target.factors.shape[1]))
factors[signal_mask, :] = target.factors
factors[~signal_mask, :] = np.nan
target.factors = factors
if not isinstance(navigation_mask, slice):
# Store the (inverted, as inputed) navigation mask
target.navigation_mask = ~navigation_mask.reshape(
self.axes_manager._navigation_shape_in_array)
if reproject not in ('both', 'navigation'):
loadings = np.zeros(
(dc.shape[0], target.loadings.shape[1]))
loadings[navigation_mask, :] = target.loadings
loadings[~navigation_mask, :] = np.nan
target.loadings = loadings
finally:
if self._unfolded4decomposition is True:
self.fold()
self._unfolded4decomposition is False
self.learning_results.__dict__.update(target.__dict__)
# undo any pre-treatments
self.undo_treatments()
return to_return
def test_method_BCD(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, method='BCD')
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def test_init(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, init='rand')
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def test_init_rand(self):
X, E, U, S, V = orpca(self.X,
rank=self.rank,
store_error=True,
init="rand")
compare_norms(X, self.A)
def test_init(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, init='rand')
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def test_exception_method(self):
with pytest.raises(ValueError, match=f"'method' not recognised"):
_ = orpca(self.X, rank=self.rank, method="uniform")
def test_method_BCD(self):
X, E, U, S, V = orpca(self.X, rank=self.rank, method='BCD')
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
nt.assert_true(normX < self.tol)
def VCA(R, p, verbose='on', snr_input=0, compress='svd', **kwargs):
from math import sqrt, log10
import time
import numpy as np
from scipy.linalg import svd
from hyperspy.learn.rpca import orpca
start_time = time.clock()
L, N = R.shape
print('Shape of R is: ', R.shape)
if p < 0 or p > L or (p % 1) != 0:
raise ValueError('ENDMEMBER parameter must be integer between 1 and L')
if snr_input == 0:
r_m = np.mean(R, 1)[:, np.newaxis]
R_m = np.tile(r_m, N)
R_o = R - R_m
if compress == 'svd':
Ud, Sd, Vd = svd(np.dot(R_o, R_o.T) / N)
Ud = Ud[:, :p]
del Sd, Vd
elif compress == 'orpca':
X, E, Ud, Sd, Vd = orpca(np.dot(R_o, R_o.T) / N,
rank=p,
fast=True,
**kwargs)
del X, E, Sd, Vd
x_p = np.dot(Ud.T, R_o)
SNR = estimate_snr(R, r_m, x_p)
else:
SNR = snr_input
SNR_th = 15 + 10 * log10(p)
if SNR < SNR_th:
d = p - 1
if snr_input == 0:
Ud = Ud[:, :d]
else:
r_m = np.mean(R, 1)[:, np.newaxis]
R_m = np.tile(r_m, N)
R_o = R - R_m
Ud, Sd, Vd = svd(np.dot(R_o, R_o.T) / N)
Ud = Ud[:, :d]
x_p = np.dot(Ud.T, R_o)
Rp = np.dot(Ud, x_p[0:d, :]) + np.tile(r_m, N)
x = x_p[0:d, :]
c = np.max(np.sum(x**2, axis=0))**0.5
c_arr_temp = c * np.ones((1, N))
y = np.array(x, copy=True)
y = np.append(y, c_arr_temp, axis=0)
else:
d = p
Ud, Sd, Vd = svd(np.dot(R, R.T) / N)
Ud = Ud[:, :d]
x_p = np.dot(Ud.T, R)
Rp = np.dot(Ud, x_p[:d, :])
x = np.dot(Ud.T, R)
u = np.mean(x, 1)[:, np.newaxis]
y = x / np.tile(
np.sum(x * np.tile(u, N), axis=0)[np.newaxis, :], (d, 1))
indice = np.zeros((1, p), dtype=int)
A = np.zeros((p, p))
A[p - 1, 0] = 1
for i in range(p):
Ip = np.eye(p)
mean = np.zeros(p)
w = np.random.rand(p, 1)
f = w - np.dot(np.dot(A, np.linalg.pinv(A)), w)
f = f / sqrt(np.sum(f**2))
v = np.dot(f.T, y)
v = np.absolute(v)
indice[0, i] = v.argmax()
A[:, i] = y[:, indice[0, i]]
if SNR < SNR_th:
Ae = np.dot(Ud, x[:, indice[0]]) + np.tile(r_m, p)
else:
Ae = np.dot(Ud, x[:, indice[0]])
loadings = np.dot(np.dot(np.linalg.pinv(np.dot(Ae.T, Ae)), Ae.T), R)
print("Execution Time---%s seconds ---" % (time.clock() - start_time))
return Ae, loadings, SNR
def decomposition(self,
normalize_poissonian_noise=False,
algorithm='svd',
output_dimension=None,
centre=None,
auto_transpose=True,
navigation_mask=None,
signal_mask=None,
var_array=None,
var_func=None,
polyfit=None,
reproject=None,
return_info=False,
**kwargs):
"""Decomposition with a choice of algorithms
The results are stored in self.learning_results
Parameters
----------
normalize_poissonian_noise : bool
If True, scale the SI to normalize Poissonian noise
algorithm : 'svd' | 'fast_svd' | 'mlpca' | 'fast_mlpca' | 'nmf' |
'sparse_pca' | 'mini_batch_sparse_pca' | 'RPCA_GoDec' | 'ORPCA'
output_dimension : None or int
number of components to keep/calculate
centre : None | 'variables' | 'trials'
If None no centring is applied. If 'variable' the centring will be
performed in the variable axis. If 'trials', the centring will be
performed in the 'trials' axis. It only has effect when using the
svd or fast_svd algorithms
auto_transpose : bool
If True, automatically transposes the data to boost performance.
Only has effect when using the svd of fast_svd algorithms.
navigation_mask : boolean numpy array
The navigation locations marked as True are not used in the
decompostion.
signal_mask : boolean numpy array
The signal locations marked as True are not used in the
decomposition.
var_array : numpy array
Array of variance for the maximum likelihood PCA algorithm
var_func : function or numpy array
If function, it will apply it to the dataset to obtain the
var_array. Alternatively, it can a an array with the coefficients
of a polynomial.
reproject : None | signal | navigation | both
If not None, the results of the decomposition will be projected in
the selected masked area.
return_info: bool, default False
The result of the decomposition is stored internally. However, some algorithms generate some extra
information that is not stored. If True (the default is False) return any extra information if available
Returns
-------
(X, E) : (numpy array, numpy array)
If 'algorithm' == 'RPCA_GoDec' or 'ORPCA' and 'return_info' is True,
returns the low-rank (X) and sparse (E) matrices from robust PCA.
See also
--------
plot_decomposition_factors, plot_decomposition_loadings, plot_lev
"""
to_return = None
# Check if it is the wrong data type
if self.data.dtype.char not in ['e', 'f', 'd']: # If not float
_logger.warning(
'To perform a decomposition the data must be of the float '
'type. You can change the type using the change_dtype method'
' e.g. s.change_dtype(\'float64\')\n'
'Nothing done.')
return
if self.axes_manager.navigation_size < 2:
raise AttributeError("It is not possible to decompose a dataset "
"with navigation_size < 2")
# backup the original data
self._data_before_treatments = self.data.copy()
# set the output target (peak results or not?)
target = LearningResults()
if algorithm == 'mlpca':
if normalize_poissonian_noise is True:
_logger.warning(
"It makes no sense to do normalize_poissonian_noise with "
"the MLPCA algorithm. Therefore, "
"normalize_poissonian_noise is set to False")
normalize_poissonian_noise = False
if output_dimension is None:
raise ValueError("With the MLPCA algorithm the "
"output_dimension must be specified")
if algorithm == 'RPCA_GoDec' or algorithm == 'ORPCA':
if output_dimension is None:
raise ValueError("With the robust PCA algorithms ('RPCA_GoDec' "
"and 'ORPCA'), the output_dimension "
"must be specified")
# Apply pre-treatments
# Transform the data in a line spectrum
self._unfolded4decomposition = self.unfold()
try:
if hasattr(navigation_mask, 'ravel'):
navigation_mask = navigation_mask.ravel()
if hasattr(signal_mask, 'ravel'):
signal_mask = signal_mask.ravel()
# Normalize the poissonian noise
# TODO this function can change the masks and this can cause
# problems when reprojecting
if normalize_poissonian_noise is True:
self.normalize_poissonian_noise(
navigation_mask=navigation_mask,
signal_mask=signal_mask,)
_logger.info('Performing decomposition analysis')
# The rest of the code assumes that the first data axis
# is the navigation axis. We transpose the data if that is not the
# case.
dc = (self.data if self.axes_manager[0].index_in_array == 0
else self.data.T)
# Transform the None masks in slices to get the right behaviour
if navigation_mask is None:
navigation_mask = slice(None)
else:
navigation_mask = ~navigation_mask
if signal_mask is None:
signal_mask = slice(None)
else:
signal_mask = ~signal_mask
# WARNING: signal_mask and navigation_mask values are now their
# negaties i.e. True -> False and viceversa. However, the
# stored value (at the end of the method) coincides with the
# input masks
# Reset the explained_variance which is not set by all the
# algorithms
explained_variance = None
explained_variance_ratio = None
mean = None
if algorithm == 'svd':
factors, loadings, explained_variance, mean = svd_pca(
dc[:, signal_mask][navigation_mask, :], centre=centre,
auto_transpose=auto_transpose)
elif algorithm == 'fast_svd':
factors, loadings, explained_variance, mean = svd_pca(
dc[:, signal_mask][navigation_mask, :],
fast=True,
output_dimension=output_dimension,
centre=centre,
auto_transpose=auto_transpose)
elif algorithm == 'sklearn_pca':
if import_sklearn.sklearn_installed is False:
raise ImportError(
'sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.PCA(**kwargs)
sk.n_components = output_dimension
loadings = sk.fit_transform((
dc[:, signal_mask][navigation_mask, :]))
factors = sk.components_.T
explained_variance = sk.explained_variance_
mean = sk.mean_
centre = 'trials'
if return_info:
to_return = sk
elif algorithm == 'nmf':
if import_sklearn.sklearn_installed is False:
raise ImportError(
'sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.NMF(**kwargs)
sk.n_components = output_dimension
loadings = sk.fit_transform((
dc[:, signal_mask][navigation_mask, :]))
factors = sk.components_.T
if return_info:
to_return = sk
elif algorithm == 'sparse_pca':
if import_sklearn.sklearn_installed is False:
raise ImportError(
'sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.SparsePCA(
output_dimension, **kwargs)
loadings = sk.fit_transform(
dc[:, signal_mask][navigation_mask, :])
factors = sk.components_.T
if return_info:
to_return = sk
elif algorithm == 'mini_batch_sparse_pca':
if import_sklearn.sklearn_installed is False:
raise ImportError(
'sklearn is not installed. Nothing done')
sk = import_sklearn.sklearn.decomposition.MiniBatchSparsePCA(
output_dimension, **kwargs)
loadings = sk.fit_transform(
dc[:, signal_mask][navigation_mask, :])
factors = sk.components_.T
if return_info:
to_return = sk
elif algorithm == 'mlpca' or algorithm == 'fast_mlpca':
_logger.info("Performing the MLPCA training")
if output_dimension is None:
raise ValueError(
"For MLPCA it is mandatory to define the "
"output_dimension")
if var_array is None and var_func is None:
_logger.info('No variance array provided.'
'Assuming poissonian data')
var_array = dc[:, signal_mask][navigation_mask, :]
if var_array is not None and var_func is not None:
raise ValueError(
"You have defined both the var_func and var_array "
"keywords."
"Please, define just one of them")
if var_func is not None:
if hasattr(var_func, '__call__'):
var_array = var_func(
dc[signal_mask, ...][:, navigation_mask])
else:
try:
var_array = np.polyval(
polyfit, dc[
signal_mask, navigation_mask])
except:
raise ValueError(
'var_func must be either a function or an '
'array defining the coefficients of a polynom')
if algorithm == 'mlpca':
fast = False
else:
fast = True
U, S, V, Sobj, ErrFlag = mlpca(
dc[:, signal_mask][navigation_mask, :],
var_array, output_dimension, fast=fast)
loadings = U * S
factors = V
explained_variance_ratio = S ** 2 / Sobj
explained_variance = S ** 2 / len(factors)
elif algorithm == 'RPCA_GoDec':
_logger.info("Performing Robust PCA with GoDec")
X, E, G, U, S, V = rpca_godec(
dc[:, signal_mask][navigation_mask, :],
rank=output_dimension, fast=True, **kwargs)
loadings = U * S
factors = V
explained_variance = S ** 2 / len(factors)
if return_info:
to_return = (X, E)
elif algorithm == 'ORPCA':
_logger.info("Performing Online Robust PCA")
X, E, U, S, V = orpca(
dc[:, signal_mask][navigation_mask, :],
rank=output_dimension, fast=True, **kwargs)
loadings = U * S
factors = V
explained_variance = S ** 2 / len(factors)
if return_info:
to_return = (X, E)
else:
raise ValueError('Algorithm not recognised. '
'Nothing done')
# We must calculate the ratio here because otherwise the sum
# information can be lost if the user call
# crop_decomposition_dimension
if explained_variance is not None and \
explained_variance_ratio is None:
explained_variance_ratio = \
explained_variance / explained_variance.sum()
# Store the results in learning_results
target.factors = factors
target.loadings = loadings
target.explained_variance = explained_variance
target.explained_variance_ratio = explained_variance_ratio
target.decomposition_algorithm = algorithm
target.poissonian_noise_normalized = \
normalize_poissonian_noise
target.output_dimension = output_dimension
target.unfolded = self._unfolded4decomposition
target.centre = centre
target.mean = mean
if output_dimension and factors.shape[1] != output_dimension:
target.crop_decomposition_dimension(output_dimension)
# Delete the unmixing information, because it'll refer to a
# previous decomposition
target.unmixing_matrix = None
target.bss_algorithm = None
if self._unfolded4decomposition is True:
folding = \
self.metadata._HyperSpy.Folding
target.original_shape = folding.original_shape
# Reproject
if mean is None:
mean = 0
if reproject in ('navigation', 'both'):
if algorithm not in ('nmf', 'sparse_pca',
'mini_batch_sparse_pca'):
loadings_ = np.dot(dc[:, signal_mask] - mean, factors)
else:
loadings_ = sk.transform(dc[:, signal_mask])
target.loadings = loadings_
if reproject in ('signal', 'both'):
if algorithm not in ('nmf', 'sparse_pca',
'mini_batch_sparse_pca'):
factors = np.dot(np.linalg.pinv(loadings),
dc[navigation_mask, :] - mean).T
target.factors = factors
else:
_logger.info("Reprojecting the signal is not yet "
"supported for this algorithm")
if reproject == 'both':
reproject = 'signal'
else:
reproject = None
# Rescale the results if the noise was normalized
if normalize_poissonian_noise is True:
target.factors[:] *= self._root_bH.T
target.loadings[:] *= self._root_aG
# Set the pixels that were not processed to nan
if not isinstance(signal_mask, slice):
# Store the (inverted, as inputed) signal mask
target.signal_mask = ~signal_mask.reshape(
self.axes_manager._signal_shape_in_array)
if reproject not in ('both', 'signal'):
factors = np.zeros((dc.shape[-1], target.factors.shape[1]))
factors[signal_mask, :] = target.factors
factors[~signal_mask, :] = np.nan
target.factors = factors
if not isinstance(navigation_mask, slice):
# Store the (inverted, as inputed) navigation mask
target.navigation_mask = ~navigation_mask.reshape(
self.axes_manager._navigation_shape_in_array)
if reproject not in ('both', 'navigation'):
loadings = np.zeros(
(dc.shape[0], target.loadings.shape[1]))
loadings[navigation_mask, :] = target.loadings
loadings[~navigation_mask, :] = np.nan
target.loadings = loadings
finally:
if self._unfolded4decomposition is True:
self.fold()
self._unfolded4decomposition is False
self.learning_results.__dict__.update(target.__dict__)
# undo any pre-treatments
self.undo_treatments()
return to_return
def test_exception_init(self):
with pytest.raises(ValueError, match=f"'init' not recognised"):
_ = orpca(self.X, rank=self.rank, init="uniform")
def test_default(self):
X, E, U, S, V = orpca(self.X, rank=self.rank)
# Check the low-rank component MSE
normX = np.linalg.norm(X - self.A) / (self.m * self.n)
assert normX < self.tol