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_dict_learning.py
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_dict_learning.py
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""" Dictionary learning.
"""
# Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort
# License: BSD 3 clause
import time
import sys
import itertools
import warnings
from math import ceil
import numpy as np
from scipy import linalg
from joblib import Parallel, effective_n_jobs
from ..base import BaseEstimator, TransformerMixin
from ..utils import deprecated
from ..utils import check_array, check_random_state, gen_even_slices, gen_batches
from ..utils.extmath import randomized_svd, row_norms, svd_flip
from ..utils.validation import check_is_fitted
from ..utils.fixes import delayed
from ..linear_model import Lasso, orthogonal_mp_gram, LassoLars, Lars
def _check_positive_coding(method, positive):
if positive and method in ["omp", "lars"]:
raise ValueError(
"Positive constraint not supported for '{}' coding method.".format(method)
)
def _sparse_encode(
X,
dictionary,
gram,
cov=None,
algorithm="lasso_lars",
regularization=None,
copy_cov=True,
init=None,
max_iter=1000,
check_input=True,
verbose=0,
positive=False,
):
"""Generic sparse coding.
Each column of the result is the solution to a Lasso problem.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Data matrix.
dictionary : ndarray of shape (n_components, n_features)
The dictionary matrix against which to solve the sparse coding of
the data. Some of the algorithms assume normalized rows.
gram : ndarray of shape (n_components, n_components) or None
Precomputed Gram matrix, `dictionary * dictionary'`
gram can be `None` if method is 'threshold'.
cov : ndarray of shape (n_components, n_samples), default=None
Precomputed covariance, `dictionary * X'`.
algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}, \
default='lasso_lars'
The algorithm used:
* `'lars'`: uses the least angle regression method
(`linear_model.lars_path`);
* `'lasso_lars'`: uses Lars to compute the Lasso solution;
* `'lasso_cd'`: uses the coordinate descent method to compute the
Lasso solution (`linear_model.Lasso`). lasso_lars will be faster if
the estimated components are sparse;
* `'omp'`: uses orthogonal matching pursuit to estimate the sparse
solution;
* `'threshold'`: squashes to zero all coefficients less than
regularization from the projection `dictionary * data'`.
regularization : int or float, default=None
The regularization parameter. It corresponds to alpha when
algorithm is `'lasso_lars'`, `'lasso_cd'` or `'threshold'`.
Otherwise it corresponds to `n_nonzero_coefs`.
init : ndarray of shape (n_samples, n_components), default=None
Initialization value of the sparse code. Only used if
`algorithm='lasso_cd'`.
max_iter : int, default=1000
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`'lasso_lars'`.
copy_cov : bool, default=True
Whether to copy the precomputed covariance matrix; if `False`, it may
be overwritten.
check_input : bool, default=True
If `False`, the input arrays `X` and dictionary will not be checked.
verbose : int, default=0
Controls the verbosity; the higher, the more messages.
positive: bool, default=False
Whether to enforce a positivity constraint on the sparse code.
.. versionadded:: 0.20
Returns
-------
code : ndarray of shape (n_components, n_features)
The sparse codes.
See Also
--------
sklearn.linear_model.lars_path
sklearn.linear_model.orthogonal_mp
sklearn.linear_model.Lasso
SparseCoder
"""
if X.ndim == 1:
X = X[:, np.newaxis]
n_samples, n_features = X.shape
n_components = dictionary.shape[0]
if dictionary.shape[1] != X.shape[1]:
raise ValueError(
"Dictionary and X have different numbers of features:"
"dictionary.shape: {} X.shape{}".format(dictionary.shape, X.shape)
)
if cov is None and algorithm != "lasso_cd":
# overwriting cov is safe
copy_cov = False
cov = np.dot(dictionary, X.T)
_check_positive_coding(algorithm, positive)
if algorithm == "lasso_lars":
alpha = float(regularization) / n_features # account for scaling
try:
err_mgt = np.seterr(all="ignore")
# Not passing in verbose=max(0, verbose-1) because Lars.fit already
# corrects the verbosity level.
lasso_lars = LassoLars(
alpha=alpha,
fit_intercept=False,
verbose=verbose,
normalize=False,
precompute=gram,
fit_path=False,
positive=positive,
max_iter=max_iter,
)
lasso_lars.fit(dictionary.T, X.T, Xy=cov)
new_code = lasso_lars.coef_
finally:
np.seterr(**err_mgt)
elif algorithm == "lasso_cd":
alpha = float(regularization) / n_features # account for scaling
# TODO: Make verbosity argument for Lasso?
# sklearn.linear_model.coordinate_descent.enet_path has a verbosity
# argument that we could pass in from Lasso.
clf = Lasso(
alpha=alpha,
fit_intercept=False,
normalize="deprecated", # as it was False by default
precompute=gram,
max_iter=max_iter,
warm_start=True,
positive=positive,
)
if init is not None:
clf.coef_ = init
clf.fit(dictionary.T, X.T, check_input=check_input)
new_code = clf.coef_
elif algorithm == "lars":
try:
err_mgt = np.seterr(all="ignore")
# Not passing in verbose=max(0, verbose-1) because Lars.fit already
# corrects the verbosity level.
lars = Lars(
fit_intercept=False,
verbose=verbose,
normalize=False,
precompute=gram,
n_nonzero_coefs=int(regularization),
fit_path=False,
)
lars.fit(dictionary.T, X.T, Xy=cov)
new_code = lars.coef_
finally:
np.seterr(**err_mgt)
elif algorithm == "threshold":
new_code = (np.sign(cov) * np.maximum(np.abs(cov) - regularization, 0)).T
if positive:
np.clip(new_code, 0, None, out=new_code)
elif algorithm == "omp":
new_code = orthogonal_mp_gram(
Gram=gram,
Xy=cov,
n_nonzero_coefs=int(regularization),
tol=None,
norms_squared=row_norms(X, squared=True),
copy_Xy=copy_cov,
).T
else:
raise ValueError(
'Sparse coding method must be "lasso_lars" '
'"lasso_cd", "lasso", "threshold" or "omp", got %s.' % algorithm
)
if new_code.ndim != 2:
return new_code.reshape(n_samples, n_components)
return new_code
# XXX : could be moved to the linear_model module
def sparse_encode(
X,
dictionary,
*,
gram=None,
cov=None,
algorithm="lasso_lars",
n_nonzero_coefs=None,
alpha=None,
copy_cov=True,
init=None,
max_iter=1000,
n_jobs=None,
check_input=True,
verbose=0,
positive=False,
):
"""Sparse coding
Each row of the result is the solution to a sparse coding problem.
The goal is to find a sparse array `code` such that::
X ~= code * dictionary
Read more in the :ref:`User Guide <SparseCoder>`.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Data matrix.
dictionary : ndarray of shape (n_components, n_features)
The dictionary matrix against which to solve the sparse coding of
the data. Some of the algorithms assume normalized rows for meaningful
output.
gram : ndarray of shape (n_components, n_components), default=None
Precomputed Gram matrix, `dictionary * dictionary'`.
cov : ndarray of shape (n_components, n_samples), default=None
Precomputed covariance, `dictionary' * X`.
algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}, \
default='lasso_lars'
The algorithm used:
* `'lars'`: uses the least angle regression method
(`linear_model.lars_path`);
* `'lasso_lars'`: uses Lars to compute the Lasso solution;
* `'lasso_cd'`: uses the coordinate descent method to compute the
Lasso solution (`linear_model.Lasso`). lasso_lars will be faster if
the estimated components are sparse;
* `'omp'`: uses orthogonal matching pursuit to estimate the sparse
solution;
* `'threshold'`: squashes to zero all coefficients less than
regularization from the projection `dictionary * data'`.
n_nonzero_coefs : int, default=None
Number of nonzero coefficients to target in each column of the
solution. This is only used by `algorithm='lars'` and `algorithm='omp'`
and is overridden by `alpha` in the `omp` case. If `None`, then
`n_nonzero_coefs=int(n_features / 10)`.
alpha : float, default=None
If `algorithm='lasso_lars'` or `algorithm='lasso_cd'`, `alpha` is the
penalty applied to the L1 norm.
If `algorithm='threshold'`, `alpha` is the absolute value of the
threshold below which coefficients will be squashed to zero.
If `algorithm='omp'`, `alpha` is the tolerance parameter: the value of
the reconstruction error targeted. In this case, it overrides
`n_nonzero_coefs`.
If `None`, default to 1.
copy_cov : bool, default=True
Whether to copy the precomputed covariance matrix; if `False`, it may
be overwritten.
init : ndarray of shape (n_samples, n_components), default=None
Initialization value of the sparse codes. Only used if
`algorithm='lasso_cd'`.
max_iter : int, default=1000
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`'lasso_lars'`.
n_jobs : int, default=None
Number of parallel jobs to run.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
check_input : bool, default=True
If `False`, the input arrays X and dictionary will not be checked.
verbose : int, default=0
Controls the verbosity; the higher, the more messages.
positive : bool, default=False
Whether to enforce positivity when finding the encoding.
.. versionadded:: 0.20
Returns
-------
code : ndarray of shape (n_samples, n_components)
The sparse codes
See Also
--------
sklearn.linear_model.lars_path
sklearn.linear_model.orthogonal_mp
sklearn.linear_model.Lasso
SparseCoder
"""
if check_input:
if algorithm == "lasso_cd":
dictionary = check_array(dictionary, order="C", dtype="float64")
X = check_array(X, order="C", dtype="float64")
else:
dictionary = check_array(dictionary)
X = check_array(X)
n_samples, n_features = X.shape
n_components = dictionary.shape[0]
if gram is None and algorithm != "threshold":
gram = np.dot(dictionary, dictionary.T)
if cov is None and algorithm != "lasso_cd":
copy_cov = False
cov = np.dot(dictionary, X.T)
if algorithm in ("lars", "omp"):
regularization = n_nonzero_coefs
if regularization is None:
regularization = min(max(n_features / 10, 1), n_components)
else:
regularization = alpha
if regularization is None:
regularization = 1.0
if effective_n_jobs(n_jobs) == 1 or algorithm == "threshold":
code = _sparse_encode(
X,
dictionary,
gram,
cov=cov,
algorithm=algorithm,
regularization=regularization,
copy_cov=copy_cov,
init=init,
max_iter=max_iter,
check_input=False,
verbose=verbose,
positive=positive,
)
return code
# Enter parallel code block
code = np.empty((n_samples, n_components))
slices = list(gen_even_slices(n_samples, effective_n_jobs(n_jobs)))
code_views = Parallel(n_jobs=n_jobs, verbose=verbose)(
delayed(_sparse_encode)(
X[this_slice],
dictionary,
gram,
cov[:, this_slice] if cov is not None else None,
algorithm,
regularization=regularization,
copy_cov=copy_cov,
init=init[this_slice] if init is not None else None,
max_iter=max_iter,
check_input=False,
verbose=verbose,
positive=positive,
)
for this_slice in slices
)
for this_slice, this_view in zip(slices, code_views):
code[this_slice] = this_view
return code
def _update_dict(
dictionary,
Y,
code,
A=None,
B=None,
verbose=False,
random_state=None,
positive=False,
):
"""Update the dense dictionary factor in place.
Parameters
----------
dictionary : ndarray of shape (n_components, n_features)
Value of the dictionary at the previous iteration.
Y : ndarray of shape (n_samples, n_features)
Data matrix.
code : ndarray of shape (n_samples, n_components)
Sparse coding of the data against which to optimize the dictionary.
A : ndarray of shape (n_components, n_components), default=None
Together with `B`, sufficient stats of the online model to update the
dictionary.
B : ndarray of shape (n_features, n_components), default=None
Together with `A`, sufficient stats of the online model to update the
dictionary.
verbose: bool, default=False
Degree of output the procedure will print.
random_state : int, RandomState instance or None, default=None
Used for randomly initializing the dictionary. Pass an int for
reproducible results across multiple function calls.
See :term:`Glossary <random_state>`.
positive : bool, default=False
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
"""
n_samples, n_components = code.shape
random_state = check_random_state(random_state)
if A is None:
A = code.T @ code
if B is None:
B = Y.T @ code
n_unused = 0
for k in range(n_components):
if A[k, k] > 1e-6:
# 1e-6 is arbitrary but consistent with the spams implementation
dictionary[k] += (B[:, k] - A[k] @ dictionary) / A[k, k]
else:
# kth atom is almost never used -> sample a new one from the data
newd = Y[random_state.choice(n_samples)]
# add small noise to avoid making the sparse coding ill conditioned
noise_level = 0.01 * (newd.std() or 1) # avoid 0 std
noise = random_state.normal(0, noise_level, size=len(newd))
dictionary[k] = newd + noise
code[:, k] = 0
n_unused += 1
if positive:
np.clip(dictionary[k], 0, None, out=dictionary[k])
# Projection on the constraint set ||V_k|| == 1
dictionary[k] /= linalg.norm(dictionary[k])
if verbose and n_unused > 0:
print(f"{n_unused} unused atoms resampled.")
def dict_learning(
X,
n_components,
*,
alpha,
max_iter=100,
tol=1e-8,
method="lars",
n_jobs=None,
dict_init=None,
code_init=None,
callback=None,
verbose=False,
random_state=None,
return_n_iter=False,
positive_dict=False,
positive_code=False,
method_max_iter=1000,
):
"""Solves a dictionary learning matrix factorization problem.
Finds the best dictionary and the corresponding sparse code for
approximating the data matrix X by solving::
(U^*, V^*) = argmin 0.5 || X - U V ||_Fro^2 + alpha * || U ||_1,1
(U,V)
with || V_k ||_2 = 1 for all 0 <= k < n_components
where V is the dictionary and U is the sparse code. ||.||_Fro stands for
the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm
which is the sum of the absolute values of all the entries in the matrix.
Read more in the :ref:`User Guide <DictionaryLearning>`.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Data matrix.
n_components : int
Number of dictionary atoms to extract.
alpha : int
Sparsity controlling parameter.
max_iter : int, default=100
Maximum number of iterations to perform.
tol : float, default=1e-8
Tolerance for the stopping condition.
method : {'lars', 'cd'}, default='lars'
The method used:
* `'lars'`: uses the least angle regression method to solve the lasso
problem (`linear_model.lars_path`);
* `'cd'`: uses the coordinate descent method to compute the
Lasso solution (`linear_model.Lasso`). Lars will be faster if
the estimated components are sparse.
n_jobs : int, default=None
Number of parallel jobs to run.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
dict_init : ndarray of shape (n_components, n_features), default=None
Initial value for the dictionary for warm restart scenarios. Only used
if `code_init` and `dict_init` are not None.
code_init : ndarray of shape (n_samples, n_components), default=None
Initial value for the sparse code for warm restart scenarios. Only used
if `code_init` and `dict_init` are not None.
callback : callable, default=None
Callable that gets invoked every five iterations
verbose : bool, default=False
To control the verbosity of the procedure.
random_state : int, RandomState instance or None, default=None
Used for randomly initializing the dictionary. Pass an int for
reproducible results across multiple function calls.
See :term:`Glossary <random_state>`.
return_n_iter : bool, default=False
Whether or not to return the number of iterations.
positive_dict : bool, default=False
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
positive_code : bool, default=False
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
method_max_iter : int, default=1000
Maximum number of iterations to perform.
.. versionadded:: 0.22
Returns
-------
code : ndarray of shape (n_samples, n_components)
The sparse code factor in the matrix factorization.
dictionary : ndarray of shape (n_components, n_features),
The dictionary factor in the matrix factorization.
errors : array
Vector of errors at each iteration.
n_iter : int
Number of iterations run. Returned only if `return_n_iter` is
set to True.
See Also
--------
dict_learning_online
DictionaryLearning
MiniBatchDictionaryLearning
SparsePCA
MiniBatchSparsePCA
"""
if method not in ("lars", "cd"):
raise ValueError("Coding method %r not supported as a fit algorithm." % method)
_check_positive_coding(method, positive_code)
method = "lasso_" + method
t0 = time.time()
# Avoid integer division problems
alpha = float(alpha)
random_state = check_random_state(random_state)
# Init the code and the dictionary with SVD of Y
if code_init is not None and dict_init is not None:
code = np.array(code_init, order="F")
# Don't copy V, it will happen below
dictionary = dict_init
else:
code, S, dictionary = linalg.svd(X, full_matrices=False)
# flip the initial code's sign to enforce deterministic output
code, dictionary = svd_flip(code, dictionary)
dictionary = S[:, np.newaxis] * dictionary
r = len(dictionary)
if n_components <= r: # True even if n_components=None
code = code[:, :n_components]
dictionary = dictionary[:n_components, :]
else:
code = np.c_[code, np.zeros((len(code), n_components - r))]
dictionary = np.r_[
dictionary, np.zeros((n_components - r, dictionary.shape[1]))
]
# Fortran-order dict better suited for the sparse coding which is the
# bottleneck of this algorithm.
dictionary = np.asfortranarray(dictionary)
errors = []
current_cost = np.nan
if verbose == 1:
print("[dict_learning]", end=" ")
# If max_iter is 0, number of iterations returned should be zero
ii = -1
for ii in range(max_iter):
dt = time.time() - t0
if verbose == 1:
sys.stdout.write(".")
sys.stdout.flush()
elif verbose:
print(
"Iteration % 3i (elapsed time: % 3is, % 4.1fmn, current cost % 7.3f)"
% (ii, dt, dt / 60, current_cost)
)
# Update code
code = sparse_encode(
X,
dictionary,
algorithm=method,
alpha=alpha,
init=code,
n_jobs=n_jobs,
positive=positive_code,
max_iter=method_max_iter,
verbose=verbose,
)
# Update dictionary in place
_update_dict(
dictionary,
X,
code,
verbose=verbose,
random_state=random_state,
positive=positive_dict,
)
# Cost function
current_cost = 0.5 * np.sum((X - code @ dictionary) ** 2) + alpha * np.sum(
np.abs(code)
)
errors.append(current_cost)
if ii > 0:
dE = errors[-2] - errors[-1]
# assert(dE >= -tol * errors[-1])
if dE < tol * errors[-1]:
if verbose == 1:
# A line return
print("")
elif verbose:
print("--- Convergence reached after %d iterations" % ii)
break
if ii % 5 == 0 and callback is not None:
callback(locals())
if return_n_iter:
return code, dictionary, errors, ii + 1
else:
return code, dictionary, errors
def dict_learning_online(
X,
n_components=2,
*,
alpha=1,
n_iter=100,
return_code=True,
dict_init=None,
callback=None,
batch_size=3,
verbose=False,
shuffle=True,
n_jobs=None,
method="lars",
iter_offset=0,
random_state=None,
return_inner_stats=False,
inner_stats=None,
return_n_iter=False,
positive_dict=False,
positive_code=False,
method_max_iter=1000,
):
"""Solves a dictionary learning matrix factorization problem online.
Finds the best dictionary and the corresponding sparse code for
approximating the data matrix X by solving::
(U^*, V^*) = argmin 0.5 || X - U V ||_Fro^2 + alpha * || U ||_1,1
(U,V)
with || V_k ||_2 = 1 for all 0 <= k < n_components
where V is the dictionary and U is the sparse code. ||.||_Fro stands for
the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm
which is the sum of the absolute values of all the entries in the matrix.
This is accomplished by repeatedly iterating over mini-batches by slicing
the input data.
Read more in the :ref:`User Guide <DictionaryLearning>`.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Data matrix.
n_components : int, default=2
Number of dictionary atoms to extract.
alpha : float, default=1
Sparsity controlling parameter.
n_iter : int, default=100
Number of mini-batch iterations to perform.
return_code : bool, default=True
Whether to also return the code U or just the dictionary `V`.
dict_init : ndarray of shape (n_components, n_features), default=None
Initial value for the dictionary for warm restart scenarios.
callback : callable, default=None
callable that gets invoked every five iterations.
batch_size : int, default=3
The number of samples to take in each batch.
verbose : bool, default=False
To control the verbosity of the procedure.
shuffle : bool, default=True
Whether to shuffle the data before splitting it in batches.
n_jobs : int, default=None
Number of parallel jobs to run.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
method : {'lars', 'cd'}, default='lars'
* `'lars'`: uses the least angle regression method to solve the lasso
problem (`linear_model.lars_path`);
* `'cd'`: uses the coordinate descent method to compute the
Lasso solution (`linear_model.Lasso`). Lars will be faster if
the estimated components are sparse.
iter_offset : int, default=0
Number of previous iterations completed on the dictionary used for
initialization.
random_state : int, RandomState instance or None, default=None
Used for initializing the dictionary when ``dict_init`` is not
specified, randomly shuffling the data when ``shuffle`` is set to
``True``, and updating the dictionary. Pass an int for reproducible
results across multiple function calls.
See :term:`Glossary <random_state>`.
return_inner_stats : bool, default=False
Return the inner statistics A (dictionary covariance) and B
(data approximation). Useful to restart the algorithm in an
online setting. If `return_inner_stats` is `True`, `return_code` is
ignored.
inner_stats : tuple of (A, B) ndarrays, default=None
Inner sufficient statistics that are kept by the algorithm.
Passing them at initialization is useful in online settings, to
avoid losing the history of the evolution.
`A` `(n_components, n_components)` is the dictionary covariance matrix.
`B` `(n_features, n_components)` is the data approximation matrix.
return_n_iter : bool, default=False
Whether or not to return the number of iterations.
positive_dict : bool, default=False
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
positive_code : bool, default=False
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
method_max_iter : int, default=1000
Maximum number of iterations to perform when solving the lasso problem.
.. versionadded:: 0.22
Returns
-------
code : ndarray of shape (n_samples, n_components),
The sparse code (only returned if `return_code=True`).
dictionary : ndarray of shape (n_components, n_features),
The solutions to the dictionary learning problem.
n_iter : int
Number of iterations run. Returned only if `return_n_iter` is
set to `True`.
See Also
--------
dict_learning
DictionaryLearning
MiniBatchDictionaryLearning
SparsePCA
MiniBatchSparsePCA
"""
if n_components is None:
n_components = X.shape[1]
if method not in ("lars", "cd"):
raise ValueError("Coding method not supported as a fit algorithm.")
_check_positive_coding(method, positive_code)
method = "lasso_" + method
t0 = time.time()
n_samples, n_features = X.shape
# Avoid integer division problems
alpha = float(alpha)
random_state = check_random_state(random_state)
# Init V with SVD of X
if dict_init is not None:
dictionary = dict_init
else:
_, S, dictionary = randomized_svd(X, n_components, random_state=random_state)
dictionary = S[:, np.newaxis] * dictionary
r = len(dictionary)
if n_components <= r:
dictionary = dictionary[:n_components, :]
else:
dictionary = np.r_[
dictionary, np.zeros((n_components - r, dictionary.shape[1]))
]
if verbose == 1:
print("[dict_learning]", end=" ")
if shuffle:
X_train = X.copy()
random_state.shuffle(X_train)
else:
X_train = X
# Fortran-order dict better suited for the sparse coding which is the
# bottleneck of this algorithm.
dictionary = check_array(dictionary, order="F", dtype=np.float64, copy=False)
dictionary = np.require(dictionary, requirements="W")
X_train = check_array(X_train, order="C", dtype=np.float64, copy=False)
batches = gen_batches(n_samples, batch_size)
batches = itertools.cycle(batches)
# The covariance of the dictionary
if inner_stats is None:
A = np.zeros((n_components, n_components))
# The data approximation
B = np.zeros((n_features, n_components))
else:
A = inner_stats[0].copy()
B = inner_stats[1].copy()
# If n_iter is zero, we need to return zero.
ii = iter_offset - 1
for ii, batch in zip(range(iter_offset, iter_offset + n_iter), batches):
this_X = X_train[batch]
dt = time.time() - t0
if verbose == 1:
sys.stdout.write(".")
sys.stdout.flush()
elif verbose:
if verbose > 10 or ii % ceil(100.0 / verbose) == 0:
print(
"Iteration % 3i (elapsed time: % 3is, % 4.1fmn)" % (ii, dt, dt / 60)
)
this_code = sparse_encode(
this_X,
dictionary,
algorithm=method,
alpha=alpha,
n_jobs=n_jobs,
check_input=False,
positive=positive_code,
max_iter=method_max_iter,
verbose=verbose,
)
# Update the auxiliary variables
if ii < batch_size - 1:
theta = float((ii + 1) * batch_size)
else:
theta = float(batch_size ** 2 + ii + 1 - batch_size)
beta = (theta + 1 - batch_size) / (theta + 1)
A *= beta
A += np.dot(this_code.T, this_code)
B *= beta
B += np.dot(this_X.T, this_code)
# Update dictionary in place
_update_dict(
dictionary,
this_X,
this_code,
A,
B,
verbose=verbose,
random_state=random_state,
positive=positive_dict,
)
# Maybe we need a stopping criteria based on the amount of
# modification in the dictionary
if callback is not None:
callback(locals())
if return_inner_stats:
if return_n_iter:
return dictionary, (A, B), ii - iter_offset + 1
else:
return dictionary, (A, B)
if return_code:
if verbose > 1:
print("Learning code...", end=" ")
elif verbose == 1:
print("|", end=" ")
code = sparse_encode(
X,
dictionary,
algorithm=method,
alpha=alpha,
n_jobs=n_jobs,
check_input=False,
positive=positive_code,
max_iter=method_max_iter,
verbose=verbose,