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Traktor/myenv/Lib/site-packages/sklearn/decomposition/_dict_learning.py

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"""Dictionary learning."""
# Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort
# License: BSD 3 clause
import itertools
import sys
import time
from numbers import Integral, Real
from warnings import warn
import numpy as np
from joblib import effective_n_jobs
from scipy import linalg
from ..base import (
BaseEstimator,
ClassNamePrefixFeaturesOutMixin,
TransformerMixin,
_fit_context,
)
from ..linear_model import Lars, Lasso, LassoLars, orthogonal_mp_gram
from ..utils import check_array, check_random_state, gen_batches, gen_even_slices
from ..utils._param_validation import Hidden, Interval, StrOptions, validate_params
from ..utils.extmath import randomized_svd, row_norms, svd_flip
from ..utils.parallel import Parallel, delayed
from ..utils.validation import check_is_fitted
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_precomputed(
X,
dictionary,
*,
gram=None,
cov=None,
algorithm="lasso_lars",
regularization=None,
copy_cov=True,
init=None,
max_iter=1000,
verbose=0,
positive=False,
):
"""Generic sparse coding with precomputed Gram and/or covariance matrices.
Each row 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), default=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.
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.
"""
n_samples, n_features = X.shape
n_components = dictionary.shape[0]
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,
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,
precompute=gram,
max_iter=max_iter,
warm_start=True,
positive=positive,
)
if init is not None:
# In some workflows using coordinate descent algorithms:
# - users might provide NumPy arrays with read-only buffers
# - `joblib` might memmap arrays making their buffer read-only
# TODO: move this handling (which is currently too broad)
# closer to the actual private function which need buffers to be writable.
if not init.flags["WRITEABLE"]:
init = np.array(init)
clf.coef_ = init
clf.fit(dictionary.T, X.T, check_input=False)
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,
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
return new_code.reshape(n_samples, n_components)
@validate_params(
{
"X": ["array-like"],
"dictionary": ["array-like"],
"gram": ["array-like", None],
"cov": ["array-like", None],
"algorithm": [
StrOptions({"lasso_lars", "lasso_cd", "lars", "omp", "threshold"})
],
"n_nonzero_coefs": [Interval(Integral, 1, None, closed="left"), None],
"alpha": [Interval(Real, 0, None, closed="left"), None],
"copy_cov": ["boolean"],
"init": ["array-like", None],
"max_iter": [Interval(Integral, 0, None, closed="left")],
"n_jobs": [Integral, None],
"check_input": ["boolean"],
"verbose": ["verbose"],
"positive": ["boolean"],
},
prefer_skip_nested_validation=True,
)
# 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 : array-like of shape (n_samples, n_features)
Data matrix.
dictionary : array-like 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 : array-like of shape (n_components, n_components), default=None
Precomputed Gram matrix, `dictionary * dictionary'`.
cov : array-like 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 : Compute Least Angle Regression or Lasso
path using LARS algorithm.
sklearn.linear_model.orthogonal_mp : Solves Orthogonal Matching Pursuit problems.
sklearn.linear_model.Lasso : Train Linear Model with L1 prior as regularizer.
SparseCoder : Find a sparse representation of data from a fixed precomputed
dictionary.
Examples
--------
>>> import numpy as np
>>> from sklearn.decomposition import sparse_encode
>>> X = np.array([[-1, -1, -1], [0, 0, 3]])
>>> dictionary = np.array(
... [[0, 1, 0],
... [-1, -1, 2],
... [1, 1, 1],
... [0, 1, 1],
... [0, 2, 1]],
... dtype=np.float64
... )
>>> sparse_encode(X, dictionary, alpha=1e-10)
array([[ 0., 0., -1., 0., 0.],
[ 0., 1., 1., 0., 0.]])
"""
if check_input:
if algorithm == "lasso_cd":
dictionary = check_array(
dictionary, order="C", dtype=[np.float64, np.float32]
)
X = check_array(X, order="C", dtype=[np.float64, np.float32])
else:
dictionary = check_array(dictionary)
X = check_array(X)
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)
)
_check_positive_coding(algorithm, positive)
return _sparse_encode(
X,
dictionary,
gram=gram,
cov=cov,
algorithm=algorithm,
n_nonzero_coefs=n_nonzero_coefs,
alpha=alpha,
copy_cov=copy_cov,
init=init,
max_iter=max_iter,
n_jobs=n_jobs,
verbose=verbose,
positive=positive,
)
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,
verbose=0,
positive=False,
):
"""Sparse coding without input/parameter validation."""
n_samples, n_features = X.shape
n_components = dictionary.shape[0]
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 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 effective_n_jobs(n_jobs) == 1 or algorithm == "threshold":
code = _sparse_encode_precomputed(
X,
dictionary,
gram=gram,
cov=cov,
algorithm=algorithm,
regularization=regularization,
copy_cov=copy_cov,
init=init,
max_iter=max_iter,
verbose=verbose,
positive=positive,
)
return code
# Enter parallel code block
n_samples = X.shape[0]
n_components = dictionary.shape[0]
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_precomputed)(
X[this_slice],
dictionary,
gram=gram,
cov=cov[:, this_slice] if cov is not None else None,
algorithm=algorithm,
regularization=regularization,
copy_cov=copy_cov,
init=init[this_slice] if init is not None else None,
max_iter=max_iter,
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] /= max(linalg.norm(dictionary[k]), 1)
if verbose and n_unused > 0:
print(f"{n_unused} unused atoms resampled.")
def _dict_learning(
X,
n_components,
*,
alpha,
max_iter,
tol,
method,
n_jobs,
dict_init,
code_init,
callback,
verbose,
random_state,
return_n_iter,
positive_dict,
positive_code,
method_max_iter,
):
"""Main dictionary learning algorithm"""
t0 = time.time()
# 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
@validate_params(
{
"X": ["array-like"],
"return_code": ["boolean"],
"method": [StrOptions({"cd", "lars"})],
"method_max_iter": [Interval(Integral, 0, None, closed="left")],
},
prefer_skip_nested_validation=False,
)
def dict_learning_online(
X,
n_components=2,
*,
alpha=1,
max_iter=100,
return_code=True,
dict_init=None,
callback=None,
batch_size=256,
verbose=False,
shuffle=True,
n_jobs=None,
method="lars",
random_state=None,
positive_dict=False,
positive_code=False,
method_max_iter=1000,
tol=1e-3,
max_no_improvement=10,
):
"""Solve 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 : array-like of shape (n_samples, n_features)
Data matrix.
n_components : int or None, default=2
Number of dictionary atoms to extract. If None, then ``n_components``
is set to ``n_features``.
alpha : float, default=1
Sparsity controlling parameter.
max_iter : int, default=100
Maximum number of iterations over the complete dataset before
stopping independently of any early stopping criterion heuristics.
.. versionadded:: 1.1
.. deprecated:: 1.4
`max_iter=None` is deprecated in 1.4 and will be removed in 1.6.
Use the default value (i.e. `100`) instead.
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 values for the dictionary for warm restart scenarios.
If `None`, the initial values for the dictionary are created
with an SVD decomposition of the data via
:func:`~sklearn.utils.extmath.randomized_svd`.
callback : callable, default=None
A callable that gets invoked at the end of each iteration.
batch_size : int, default=256
The number of samples to take in each batch.
.. versionchanged:: 1.3
The default value of `batch_size` changed from 3 to 256 in version 1.3.
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.
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>`.
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
tol : float, default=1e-3
Control early stopping based on the norm of the differences in the
dictionary between 2 steps.
To disable early stopping based on changes in the dictionary, set
`tol` to 0.0.
.. versionadded:: 1.1
max_no_improvement : int, default=10
Control early stopping based on the consecutive number of mini batches
that does not yield an improvement on the smoothed cost function.
To disable convergence detection based on cost function, set
`max_no_improvement` to None.
.. versionadded:: 1.1
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 : Solve a dictionary learning matrix factorization problem.
DictionaryLearning : Find a dictionary that sparsely encodes data.
MiniBatchDictionaryLearning : A faster, less accurate, version of the dictionary
learning algorithm.
SparsePCA : Sparse Principal Components Analysis.
MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
Examples
--------
>>> import numpy as np
>>> from sklearn.datasets import make_sparse_coded_signal
>>> from sklearn.decomposition import dict_learning_online
>>> X, _, _ = make_sparse_coded_signal(
... n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10,
... random_state=42,
... )
>>> U, V = dict_learning_online(
... X, n_components=15, alpha=0.2, max_iter=20, batch_size=3, random_state=42
... )
We can check the level of sparsity of `U`:
>>> np.mean(U == 0)
0.53...
We can compare the average squared euclidean norm of the reconstruction
error of the sparse coded signal relative to the squared euclidean norm of
the original signal:
>>> X_hat = U @ V
>>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1))
0.05...
"""
# TODO(1.6): remove in 1.6
if max_iter is None:
warn(
(
"`max_iter=None` is deprecated in version 1.4 and will be removed in "
"version 1.6. Use the default value (i.e. `100`) instead."
),
FutureWarning,
)
max_iter = 100
transform_algorithm = "lasso_" + method
est = MiniBatchDictionaryLearning(
n_components=n_components,
alpha=alpha,
max_iter=max_iter,
n_jobs=n_jobs,
fit_algorithm=method,
batch_size=batch_size,
shuffle=shuffle,
dict_init=dict_init,
random_state=random_state,
transform_algorithm=transform_algorithm,
transform_alpha=alpha,
positive_code=positive_code,
positive_dict=positive_dict,
transform_max_iter=method_max_iter,
verbose=verbose,
callback=callback,
tol=tol,
max_no_improvement=max_no_improvement,
).fit(X)
if not return_code:
return est.components_
else:
code = est.transform(X)
return code, est.components_
@validate_params(
{
"X": ["array-like"],
"method": [StrOptions({"lars", "cd"})],
"return_n_iter": ["boolean"],
"method_max_iter": [Interval(Integral, 0, None, closed="left")],
},
prefer_skip_nested_validation=False,
)
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,
):
"""Solve 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 : array-like of shape (n_samples, n_features)
Data matrix.
n_components : int
Number of dictionary atoms to extract.
alpha : int or float
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 : Solve a dictionary learning matrix factorization
problem online.
DictionaryLearning : Find a dictionary that sparsely encodes data.
MiniBatchDictionaryLearning : A faster, less accurate version
of the dictionary learning algorithm.
SparsePCA : Sparse Principal Components Analysis.
MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
Examples
--------
>>> import numpy as np
>>> from sklearn.datasets import make_sparse_coded_signal
>>> from sklearn.decomposition import dict_learning
>>> X, _, _ = make_sparse_coded_signal(
... n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10,
... random_state=42,
... )
>>> U, V, errors = dict_learning(X, n_components=15, alpha=0.1, random_state=42)
We can check the level of sparsity of `U`:
>>> np.mean(U == 0)
0.6...
We can compare the average squared euclidean norm of the reconstruction
error of the sparse coded signal relative to the squared euclidean norm of
the original signal:
>>> X_hat = U @ V
>>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1))
0.01...
"""
estimator = DictionaryLearning(
n_components=n_components,
alpha=alpha,
max_iter=max_iter,
tol=tol,
fit_algorithm=method,
n_jobs=n_jobs,
dict_init=dict_init,
callback=callback,
code_init=code_init,
verbose=verbose,
random_state=random_state,
positive_code=positive_code,
positive_dict=positive_dict,
transform_max_iter=method_max_iter,
).set_output(transform="default")
code = estimator.fit_transform(X)
if return_n_iter:
return (
code,
estimator.components_,
estimator.error_,
estimator.n_iter_,
)
return code, estimator.components_, estimator.error_
class _BaseSparseCoding(ClassNamePrefixFeaturesOutMixin, TransformerMixin):
"""Base class from SparseCoder and DictionaryLearning algorithms."""
def __init__(
self,
transform_algorithm,
transform_n_nonzero_coefs,
transform_alpha,
split_sign,
n_jobs,
positive_code,
transform_max_iter,
):
self.transform_algorithm = transform_algorithm
self.transform_n_nonzero_coefs = transform_n_nonzero_coefs
self.transform_alpha = transform_alpha
self.transform_max_iter = transform_max_iter
self.split_sign = split_sign
self.n_jobs = n_jobs
self.positive_code = positive_code
def _transform(self, X, dictionary):
"""Private method allowing to accommodate both DictionaryLearning and
SparseCoder."""
X = self._validate_data(X, reset=False)
if hasattr(self, "alpha") and self.transform_alpha is None:
transform_alpha = self.alpha
else:
transform_alpha = self.transform_alpha
code = sparse_encode(
X,
dictionary,
algorithm=self.transform_algorithm,
n_nonzero_coefs=self.transform_n_nonzero_coefs,
alpha=transform_alpha,
max_iter=self.transform_max_iter,
n_jobs=self.n_jobs,
positive=self.positive_code,
)
if self.split_sign:
# feature vector is split into a positive and negative side
n_samples, n_features = code.shape
split_code = np.empty((n_samples, 2 * n_features))
split_code[:, :n_features] = np.maximum(code, 0)
split_code[:, n_features:] = -np.minimum(code, 0)
code = split_code
return code
def transform(self, X):
"""Encode the data as a sparse combination of the dictionary atoms.
Coding method is determined by the object parameter
`transform_algorithm`.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Test data to be transformed, must have the same number of
features as the data used to train the model.
Returns
-------
X_new : ndarray of shape (n_samples, n_components)
Transformed data.
"""
check_is_fitted(self)
return self._transform(X, self.components_)
class SparseCoder(_BaseSparseCoding, BaseEstimator):
"""Sparse coding.
Finds a sparse representation of data against a fixed, precomputed
dictionary.
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
----------
dictionary : ndarray of shape (n_components, n_features)
The dictionary atoms used for sparse coding. Lines are assumed to be
normalized to unit norm.
transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \
'threshold'}, default='omp'
Algorithm used to transform the data:
- `'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 alpha from
the projection ``dictionary * X'``.
transform_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
`transform_n_nonzero_coefs=int(n_features / 10)`.
transform_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.
split_sign : bool, default=False
Whether to split the sparse feature vector into the concatenation of
its negative part and its positive part. This can improve the
performance of downstream classifiers.
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.
positive_code : bool, default=False
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
transform_max_iter : int, default=1000
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`lasso_lars`.
.. versionadded:: 0.22
Attributes
----------
n_components_ : int
Number of atoms.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
See Also
--------
DictionaryLearning : Find a dictionary that sparsely encodes data.
MiniBatchDictionaryLearning : A faster, less accurate, version of the
dictionary learning algorithm.
MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
SparsePCA : Sparse Principal Components Analysis.
sparse_encode : Sparse coding where each row of the result is the solution
to a sparse coding problem.
Examples
--------
>>> import numpy as np
>>> from sklearn.decomposition import SparseCoder
>>> X = np.array([[-1, -1, -1], [0, 0, 3]])
>>> dictionary = np.array(
... [[0, 1, 0],
... [-1, -1, 2],
... [1, 1, 1],
... [0, 1, 1],
... [0, 2, 1]],
... dtype=np.float64
... )
>>> coder = SparseCoder(
... dictionary=dictionary, transform_algorithm='lasso_lars',
... transform_alpha=1e-10,
... )
>>> coder.transform(X)
array([[ 0., 0., -1., 0., 0.],
[ 0., 1., 1., 0., 0.]])
"""
_required_parameters = ["dictionary"]
def __init__(
self,
dictionary,
*,
transform_algorithm="omp",
transform_n_nonzero_coefs=None,
transform_alpha=None,
split_sign=False,
n_jobs=None,
positive_code=False,
transform_max_iter=1000,
):
super().__init__(
transform_algorithm,
transform_n_nonzero_coefs,
transform_alpha,
split_sign,
n_jobs,
positive_code,
transform_max_iter,
)
self.dictionary = dictionary
def fit(self, X, y=None):
"""Do nothing and return the estimator unchanged.
This method is just there to implement the usual API and hence
work in pipelines.
Parameters
----------
X : Ignored
Not used, present for API consistency by convention.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
Returns the instance itself.
"""
return self
def transform(self, X, y=None):
"""Encode the data as a sparse combination of the dictionary atoms.
Coding method is determined by the object parameter
`transform_algorithm`.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Training vector, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
X_new : ndarray of shape (n_samples, n_components)
Transformed data.
"""
return super()._transform(X, self.dictionary)
def _more_tags(self):
return {
"requires_fit": False,
"preserves_dtype": [np.float64, np.float32],
}
@property
def n_components_(self):
"""Number of atoms."""
return self.dictionary.shape[0]
@property
def n_features_in_(self):
"""Number of features seen during `fit`."""
return self.dictionary.shape[1]
@property
def _n_features_out(self):
"""Number of transformed output features."""
return self.n_components_
class DictionaryLearning(_BaseSparseCoding, BaseEstimator):
"""Dictionary learning.
Finds a dictionary (a set of atoms) that performs well at sparsely
encoding the fitted data.
Solves the optimization problem::
(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
||.||_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
----------
n_components : int, default=None
Number of dictionary elements to extract. If None, then ``n_components``
is set to ``n_features``.
alpha : float, default=1.0
Sparsity controlling parameter.
max_iter : int, default=1000
Maximum number of iterations to perform.
tol : float, default=1e-8
Tolerance for numerical error.
fit_algorithm : {'lars', 'cd'}, default='lars'
* `'lars'`: uses the least angle regression method to solve the lasso
problem (:func:`~sklearn.linear_model.lars_path`);
* `'cd'`: uses the coordinate descent method to compute the
Lasso solution (:class:`~sklearn.linear_model.Lasso`). Lars will be
faster if the estimated components are sparse.
.. versionadded:: 0.17
*cd* coordinate descent method to improve speed.
transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \
'threshold'}, default='omp'
Algorithm used to transform the data:
- `'lars'`: uses the least angle regression method
(:func:`~sklearn.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 (:class:`~sklearn.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 alpha from
the projection ``dictionary * X'``.
.. versionadded:: 0.17
*lasso_cd* coordinate descent method to improve speed.
transform_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'`. If `None`, then
`transform_n_nonzero_coefs=int(n_features / 10)`.
transform_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 `None`, defaults to `alpha`.
.. versionchanged:: 1.2
When None, default value changed from 1.0 to `alpha`.
n_jobs : int or None, 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.
code_init : ndarray of shape (n_samples, n_components), default=None
Initial value for the code, for warm restart. Only used if `code_init`
and `dict_init` are not None.
dict_init : ndarray of shape (n_components, n_features), default=None
Initial values for the dictionary, for warm restart. Only used if
`code_init` and `dict_init` are not None.
callback : callable, default=None
Callable that gets invoked every five iterations.
.. versionadded:: 1.3
verbose : bool, default=False
To control the verbosity of the procedure.
split_sign : bool, default=False
Whether to split the sparse feature vector into the concatenation of
its negative part and its positive part. This can improve the
performance of downstream classifiers.
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>`.
positive_code : bool, default=False
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
positive_dict : bool, default=False
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
transform_max_iter : int, default=1000
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`'lasso_lars'`.
.. versionadded:: 0.22
Attributes
----------
components_ : ndarray of shape (n_components, n_features)
dictionary atoms extracted from the data
error_ : array
vector of errors at each iteration
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
n_iter_ : int
Number of iterations run.
See Also
--------
MiniBatchDictionaryLearning: A faster, less accurate, version of the
dictionary learning algorithm.
MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
SparseCoder : Find a sparse representation of data from a fixed,
precomputed dictionary.
SparsePCA : Sparse Principal Components Analysis.
References
----------
J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning
for sparse coding (https://www.di.ens.fr/sierra/pdfs/icml09.pdf)
Examples
--------
>>> import numpy as np
>>> from sklearn.datasets import make_sparse_coded_signal
>>> from sklearn.decomposition import DictionaryLearning
>>> X, dictionary, code = make_sparse_coded_signal(
... n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10,
... random_state=42,
... )
>>> dict_learner = DictionaryLearning(
... n_components=15, transform_algorithm='lasso_lars', transform_alpha=0.1,
... random_state=42,
... )
>>> X_transformed = dict_learner.fit(X).transform(X)
We can check the level of sparsity of `X_transformed`:
>>> np.mean(X_transformed == 0)
0.52...
We can compare the average squared euclidean norm of the reconstruction
error of the sparse coded signal relative to the squared euclidean norm of
the original signal:
>>> X_hat = X_transformed @ dict_learner.components_
>>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1))
0.05...
"""
_parameter_constraints: dict = {
"n_components": [Interval(Integral, 1, None, closed="left"), None],
"alpha": [Interval(Real, 0, None, closed="left")],
"max_iter": [Interval(Integral, 0, None, closed="left")],
"tol": [Interval(Real, 0, None, closed="left")],
"fit_algorithm": [StrOptions({"lars", "cd"})],
"transform_algorithm": [
StrOptions({"lasso_lars", "lasso_cd", "lars", "omp", "threshold"})
],
"transform_n_nonzero_coefs": [Interval(Integral, 1, None, closed="left"), None],
"transform_alpha": [Interval(Real, 0, None, closed="left"), None],
"n_jobs": [Integral, None],
"code_init": [np.ndarray, None],
"dict_init": [np.ndarray, None],
"callback": [callable, None],
"verbose": ["verbose"],
"split_sign": ["boolean"],
"random_state": ["random_state"],
"positive_code": ["boolean"],
"positive_dict": ["boolean"],
"transform_max_iter": [Interval(Integral, 0, None, closed="left")],
}
def __init__(
self,
n_components=None,
*,
alpha=1,
max_iter=1000,
tol=1e-8,
fit_algorithm="lars",
transform_algorithm="omp",
transform_n_nonzero_coefs=None,
transform_alpha=None,
n_jobs=None,
code_init=None,
dict_init=None,
callback=None,
verbose=False,
split_sign=False,
random_state=None,
positive_code=False,
positive_dict=False,
transform_max_iter=1000,
):
super().__init__(
transform_algorithm,
transform_n_nonzero_coefs,
transform_alpha,
split_sign,
n_jobs,
positive_code,
transform_max_iter,
)
self.n_components = n_components
self.alpha = alpha
self.max_iter = max_iter
self.tol = tol
self.fit_algorithm = fit_algorithm
self.code_init = code_init
self.dict_init = dict_init
self.callback = callback
self.verbose = verbose
self.random_state = random_state
self.positive_dict = positive_dict
def fit(self, X, y=None):
"""Fit the model from data in X.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vector, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
Returns the instance itself.
"""
self.fit_transform(X)
return self
@_fit_context(prefer_skip_nested_validation=True)
def fit_transform(self, X, y=None):
"""Fit the model from data in X and return the transformed data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vector, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
V : ndarray of shape (n_samples, n_components)
Transformed data.
"""
_check_positive_coding(method=self.fit_algorithm, positive=self.positive_code)
method = "lasso_" + self.fit_algorithm
random_state = check_random_state(self.random_state)
X = self._validate_data(X)
if self.n_components is None:
n_components = X.shape[1]
else:
n_components = self.n_components
V, U, E, self.n_iter_ = _dict_learning(
X,
n_components,
alpha=self.alpha,
tol=self.tol,
max_iter=self.max_iter,
method=method,
method_max_iter=self.transform_max_iter,
n_jobs=self.n_jobs,
code_init=self.code_init,
dict_init=self.dict_init,
callback=self.callback,
verbose=self.verbose,
random_state=random_state,
return_n_iter=True,
positive_dict=self.positive_dict,
positive_code=self.positive_code,
)
self.components_ = U
self.error_ = E
return V
@property
def _n_features_out(self):
"""Number of transformed output features."""
return self.components_.shape[0]
def _more_tags(self):
return {
"preserves_dtype": [np.float64, np.float32],
}
class MiniBatchDictionaryLearning(_BaseSparseCoding, BaseEstimator):
"""Mini-batch dictionary learning.
Finds a dictionary (a set of atoms) that performs well at sparsely
encoding the fitted data.
Solves the optimization problem::
(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
||.||_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
----------
n_components : int, default=None
Number of dictionary elements to extract.
alpha : float, default=1
Sparsity controlling parameter.
max_iter : int, default=1_000
Maximum number of iterations over the complete dataset before
stopping independently of any early stopping criterion heuristics.
.. versionadded:: 1.1
.. deprecated:: 1.4
`max_iter=None` is deprecated in 1.4 and will be removed in 1.6.
Use the default value (i.e. `1_000`) instead.
fit_algorithm : {'lars', 'cd'}, default='lars'
The algorithm 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.
batch_size : int, default=256
Number of samples in each mini-batch.
.. versionchanged:: 1.3
The default value of `batch_size` changed from 3 to 256 in version 1.3.
shuffle : bool, default=True
Whether to shuffle the samples before forming batches.
dict_init : ndarray of shape (n_components, n_features), default=None
Initial value of the dictionary for warm restart scenarios.
transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \
'threshold'}, default='omp'
Algorithm used to transform the data:
- `'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 alpha from
the projection ``dictionary * X'``.
transform_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'`. If `None`, then
`transform_n_nonzero_coefs=int(n_features / 10)`.
transform_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 `None`, defaults to `alpha`.
.. versionchanged:: 1.2
When None, default value changed from 1.0 to `alpha`.
verbose : bool or int, default=False
To control the verbosity of the procedure.
split_sign : bool, default=False
Whether to split the sparse feature vector into the concatenation of
its negative part and its positive part. This can improve the
performance of downstream classifiers.
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>`.
positive_code : bool, default=False
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
positive_dict : bool, default=False
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
transform_max_iter : int, default=1000
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`'lasso_lars'`.
.. versionadded:: 0.22
callback : callable, default=None
A callable that gets invoked at the end of each iteration.
.. versionadded:: 1.1
tol : float, default=1e-3
Control early stopping based on the norm of the differences in the
dictionary between 2 steps.
To disable early stopping based on changes in the dictionary, set
`tol` to 0.0.
.. versionadded:: 1.1
max_no_improvement : int, default=10
Control early stopping based on the consecutive number of mini batches
that does not yield an improvement on the smoothed cost function.
To disable convergence detection based on cost function, set
`max_no_improvement` to None.
.. versionadded:: 1.1
Attributes
----------
components_ : ndarray of shape (n_components, n_features)
Components extracted from the data.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
n_iter_ : int
Number of iterations over the full dataset.
n_steps_ : int
Number of mini-batches processed.
.. versionadded:: 1.1
See Also
--------
DictionaryLearning : Find a dictionary that sparsely encodes data.
MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
SparseCoder : Find a sparse representation of data from a fixed,
precomputed dictionary.
SparsePCA : Sparse Principal Components Analysis.
References
----------
J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning
for sparse coding (https://www.di.ens.fr/sierra/pdfs/icml09.pdf)
Examples
--------
>>> import numpy as np
>>> from sklearn.datasets import make_sparse_coded_signal
>>> from sklearn.decomposition import MiniBatchDictionaryLearning
>>> X, dictionary, code = make_sparse_coded_signal(
... n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10,
... random_state=42)
>>> dict_learner = MiniBatchDictionaryLearning(
... n_components=15, batch_size=3, transform_algorithm='lasso_lars',
... transform_alpha=0.1, max_iter=20, random_state=42)
>>> X_transformed = dict_learner.fit_transform(X)
We can check the level of sparsity of `X_transformed`:
>>> np.mean(X_transformed == 0) > 0.5
True
We can compare the average squared euclidean norm of the reconstruction
error of the sparse coded signal relative to the squared euclidean norm of
the original signal:
>>> X_hat = X_transformed @ dict_learner.components_
>>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1))
0.052...
"""
_parameter_constraints: dict = {
"n_components": [Interval(Integral, 1, None, closed="left"), None],
"alpha": [Interval(Real, 0, None, closed="left")],
"max_iter": [Interval(Integral, 0, None, closed="left"), Hidden(None)],
"fit_algorithm": [StrOptions({"cd", "lars"})],
"n_jobs": [None, Integral],
"batch_size": [Interval(Integral, 1, None, closed="left")],
"shuffle": ["boolean"],
"dict_init": [None, np.ndarray],
"transform_algorithm": [
StrOptions({"lasso_lars", "lasso_cd", "lars", "omp", "threshold"})
],
"transform_n_nonzero_coefs": [Interval(Integral, 1, None, closed="left"), None],
"transform_alpha": [Interval(Real, 0, None, closed="left"), None],
"verbose": ["verbose"],
"split_sign": ["boolean"],
"random_state": ["random_state"],
"positive_code": ["boolean"],
"positive_dict": ["boolean"],
"transform_max_iter": [Interval(Integral, 0, None, closed="left")],
"callback": [None, callable],
"tol": [Interval(Real, 0, None, closed="left")],
"max_no_improvement": [Interval(Integral, 0, None, closed="left"), None],
}
def __init__(
self,
n_components=None,
*,
alpha=1,
max_iter=1_000,
fit_algorithm="lars",
n_jobs=None,
batch_size=256,
shuffle=True,
dict_init=None,
transform_algorithm="omp",
transform_n_nonzero_coefs=None,
transform_alpha=None,
verbose=False,
split_sign=False,
random_state=None,
positive_code=False,
positive_dict=False,
transform_max_iter=1000,
callback=None,
tol=1e-3,
max_no_improvement=10,
):
super().__init__(
transform_algorithm,
transform_n_nonzero_coefs,
transform_alpha,
split_sign,
n_jobs,
positive_code,
transform_max_iter,
)
self.n_components = n_components
self.alpha = alpha
self.max_iter = max_iter
self.fit_algorithm = fit_algorithm
self.dict_init = dict_init
self.verbose = verbose
self.shuffle = shuffle
self.batch_size = batch_size
self.split_sign = split_sign
self.random_state = random_state
self.positive_dict = positive_dict
self.callback = callback
self.max_no_improvement = max_no_improvement
self.tol = tol
def _check_params(self, X):
# n_components
self._n_components = self.n_components
if self._n_components is None:
self._n_components = X.shape[1]
# fit_algorithm
_check_positive_coding(self.fit_algorithm, self.positive_code)
self._fit_algorithm = "lasso_" + self.fit_algorithm
# batch_size
self._batch_size = min(self.batch_size, X.shape[0])
def _initialize_dict(self, X, random_state):
"""Initialization of the dictionary."""
if self.dict_init is not None:
dictionary = self.dict_init
else:
# Init V with SVD of X
_, S, dictionary = randomized_svd(
X, self._n_components, random_state=random_state
)
dictionary = S[:, np.newaxis] * dictionary
if self._n_components <= len(dictionary):
dictionary = dictionary[: self._n_components, :]
else:
dictionary = np.concatenate(
(
dictionary,
np.zeros(
(self._n_components - len(dictionary), dictionary.shape[1]),
dtype=dictionary.dtype,
),
)
)
dictionary = check_array(dictionary, order="F", dtype=X.dtype, copy=False)
dictionary = np.require(dictionary, requirements="W")
return dictionary
def _update_inner_stats(self, X, code, batch_size, step):
"""Update the inner stats inplace."""
if step < batch_size - 1:
theta = (step + 1) * batch_size
else:
theta = batch_size**2 + step + 1 - batch_size
beta = (theta + 1 - batch_size) / (theta + 1)
self._A *= beta
self._A += code.T @ code / batch_size
self._B *= beta
self._B += X.T @ code / batch_size
def _minibatch_step(self, X, dictionary, random_state, step):
"""Perform the update on the dictionary for one minibatch."""
batch_size = X.shape[0]
# Compute code for this batch
code = _sparse_encode(
X,
dictionary,
algorithm=self._fit_algorithm,
alpha=self.alpha,
n_jobs=self.n_jobs,
positive=self.positive_code,
max_iter=self.transform_max_iter,
verbose=self.verbose,
)
batch_cost = (
0.5 * ((X - code @ dictionary) ** 2).sum()
+ self.alpha * np.sum(np.abs(code))
) / batch_size
# Update inner stats
self._update_inner_stats(X, code, batch_size, step)
# Update dictionary
_update_dict(
dictionary,
X,
code,
self._A,
self._B,
verbose=self.verbose,
random_state=random_state,
positive=self.positive_dict,
)
return batch_cost
def _check_convergence(
self, X, batch_cost, new_dict, old_dict, n_samples, step, n_steps
):
"""Helper function to encapsulate the early stopping logic.
Early stopping is based on two factors:
- A small change of the dictionary between two minibatch updates. This is
controlled by the tol parameter.
- No more improvement on a smoothed estimate of the objective function for a
a certain number of consecutive minibatch updates. This is controlled by
the max_no_improvement parameter.
"""
batch_size = X.shape[0]
# counts steps starting from 1 for user friendly verbose mode.
step = step + 1
# Ignore 100 first steps or 1 epoch to avoid initializing the ewa_cost with a
# too bad value
if step <= min(100, n_samples / batch_size):
if self.verbose:
print(f"Minibatch step {step}/{n_steps}: mean batch cost: {batch_cost}")
return False
# Compute an Exponentially Weighted Average of the cost function to
# monitor the convergence while discarding minibatch-local stochastic
# variability: https://en.wikipedia.org/wiki/Moving_average
if self._ewa_cost is None:
self._ewa_cost = batch_cost
else:
alpha = batch_size / (n_samples + 1)
alpha = min(alpha, 1)
self._ewa_cost = self._ewa_cost * (1 - alpha) + batch_cost * alpha
if self.verbose:
print(
f"Minibatch step {step}/{n_steps}: mean batch cost: "
f"{batch_cost}, ewa cost: {self._ewa_cost}"
)
# Early stopping based on change of dictionary
dict_diff = linalg.norm(new_dict - old_dict) / self._n_components
if self.tol > 0 and dict_diff <= self.tol:
if self.verbose:
print(f"Converged (small dictionary change) at step {step}/{n_steps}")
return True
# Early stopping heuristic due to lack of improvement on smoothed
# cost function
if self._ewa_cost_min is None or self._ewa_cost < self._ewa_cost_min:
self._no_improvement = 0
self._ewa_cost_min = self._ewa_cost
else:
self._no_improvement += 1
if (
self.max_no_improvement is not None
and self._no_improvement >= self.max_no_improvement
):
if self.verbose:
print(
"Converged (lack of improvement in objective function) "
f"at step {step}/{n_steps}"
)
return True
return False
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y=None):
"""Fit the model from data in X.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vector, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
Returns the instance itself.
"""
X = self._validate_data(
X, dtype=[np.float64, np.float32], order="C", copy=False
)
self._check_params(X)
self._random_state = check_random_state(self.random_state)
dictionary = self._initialize_dict(X, self._random_state)
old_dict = dictionary.copy()
if self.shuffle:
X_train = X.copy()
self._random_state.shuffle(X_train)
else:
X_train = X
n_samples, n_features = X_train.shape
if self.verbose:
print("[dict_learning]")
# Inner stats
self._A = np.zeros(
(self._n_components, self._n_components), dtype=X_train.dtype
)
self._B = np.zeros((n_features, self._n_components), dtype=X_train.dtype)
# TODO(1.6): remove in 1.6
if self.max_iter is None:
warn(
(
"`max_iter=None` is deprecated in version 1.4 and will be removed"
" in version 1.6. Use the default value (i.e. `1_000`) instead."
),
FutureWarning,
)
max_iter = 1_000
else:
max_iter = self.max_iter
# Attributes to monitor the convergence
self._ewa_cost = None
self._ewa_cost_min = None
self._no_improvement = 0
batches = gen_batches(n_samples, self._batch_size)
batches = itertools.cycle(batches)
n_steps_per_iter = int(np.ceil(n_samples / self._batch_size))
n_steps = max_iter * n_steps_per_iter
i = -1 # to allow max_iter = 0
for i, batch in zip(range(n_steps), batches):
X_batch = X_train[batch]
batch_cost = self._minibatch_step(
X_batch, dictionary, self._random_state, i
)
if self._check_convergence(
X_batch, batch_cost, dictionary, old_dict, n_samples, i, n_steps
):
break
# XXX callback param added for backward compat in #18975 but a common
# unified callback API should be preferred
if self.callback is not None:
self.callback(locals())
old_dict[:] = dictionary
self.n_steps_ = i + 1
self.n_iter_ = np.ceil(self.n_steps_ / n_steps_per_iter)
self.components_ = dictionary
return self
@_fit_context(prefer_skip_nested_validation=True)
def partial_fit(self, X, y=None):
"""Update the model using the data in X as a mini-batch.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vector, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
Return the instance itself.
"""
has_components = hasattr(self, "components_")
X = self._validate_data(
X, dtype=[np.float64, np.float32], order="C", reset=not has_components
)
if not has_components:
# This instance has not been fitted yet (fit or partial_fit)
self._check_params(X)
self._random_state = check_random_state(self.random_state)
dictionary = self._initialize_dict(X, self._random_state)
self.n_steps_ = 0
self._A = np.zeros((self._n_components, self._n_components), dtype=X.dtype)
self._B = np.zeros((X.shape[1], self._n_components), dtype=X.dtype)
else:
dictionary = self.components_
self._minibatch_step(X, dictionary, self._random_state, self.n_steps_)
self.components_ = dictionary
self.n_steps_ += 1
return self
@property
def _n_features_out(self):
"""Number of transformed output features."""
return self.components_.shape[0]
def _more_tags(self):
return {
"preserves_dtype": [np.float64, np.float32],
}
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