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Vehicle-Anti-Theft-Face-Rec.../venv/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 time
import sys
import itertools
from math import ceil
import numpy as np
from scipy import linalg
from joblib import Parallel, delayed, effective_n_jobs
from ..base import BaseEstimator, TransformerMixin
from ..utils import (check_array, check_random_state, gen_even_slices,
gen_batches)
from ..utils.extmath import randomized_svd, row_norms
from ..utils.validation import check_is_fitted, _deprecate_positional_args
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 : array of shape (n_samples, n_features)
Data matrix.
dictionary : array 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 : None | array, shape=(n_components, n_components)
Precomputed Gram matrix, dictionary * dictionary'
gram can be None if method is 'threshold'.
cov : array, shape=(n_components, n_samples)
Precomputed covariance, dictionary * X'
algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}
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 | float
The regularization parameter. It corresponds to alpha when
algorithm is 'lasso_lars', 'lasso_cd' or 'threshold'.
Otherwise it corresponds to n_nonzero_coefs.
init : array of shape (n_samples, n_components)
Initialization value of the sparse code. Only used if
`algorithm='lasso_cd'`.
max_iter : int, 1000 by default
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`lasso_lars`.
copy_cov : boolean, optional
Whether to copy the precomputed covariance matrix; if False, it may be
overwritten.
check_input : boolean, optional
If False, the input arrays X and dictionary will not be checked.
verbose : int
Controls the verbosity; the higher, the more messages. Defaults to 0.
positive: boolean
Whether to enforce a positivity constraint on the sparse code.
.. versionadded:: 0.20
Returns
-------
code : array 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=False,
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
@_deprecate_positional_args
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 of shape (n_samples, n_features)
Data matrix
dictionary : array 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, shape=(n_components, n_components)
Precomputed Gram matrix, dictionary * dictionary'
cov : array, shape=(n_components, n_samples)
Precomputed covariance, dictionary' * X
algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'}
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'
n_nonzero_coefs : int, 0.1 * n_features by default
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.
alpha : float, 1. by default
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`.
copy_cov : boolean, optional
Whether to copy the precomputed covariance matrix; if False, it may be
overwritten.
init : array of shape (n_samples, n_components)
Initialization value of the sparse codes. Only used if
`algorithm='lasso_cd'`.
max_iter : int, 1000 by default
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`lasso_lars`.
n_jobs : int or None, optional (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 : boolean, optional
If False, the input arrays X and dictionary will not be checked.
verbose : int, optional
Controls the verbosity; the higher, the more messages. Defaults to 0.
positive : boolean, optional
Whether to enforce positivity when finding the encoding.
.. versionadded:: 0.20
Returns
-------
code : array 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.
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, verbose=False, return_r2=False,
random_state=None, positive=False):
"""Update the dense dictionary factor in place.
Parameters
----------
dictionary : array of shape (n_features, n_components)
Value of the dictionary at the previous iteration.
Y : array of shape (n_features, n_samples)
Data matrix.
code : array of shape (n_components, n_samples)
Sparse coding of the data against which to optimize the dictionary.
verbose:
Degree of output the procedure will print.
return_r2 : bool
Whether to compute and return the residual sum of squares corresponding
to the computed solution.
random_state : int, RandomState instance, default=None
Used for randomly initializing the dictionary. Pass an int for
reproducible results across multiple function calls.
See :term:`Glossary <random_state>`.
positive : boolean, optional
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
Returns
-------
dictionary : array of shape (n_features, n_components)
Updated dictionary.
"""
n_components = len(code)
n_features = Y.shape[0]
random_state = check_random_state(random_state)
# Get BLAS functions
gemm, = linalg.get_blas_funcs(('gemm',), (dictionary, code, Y))
ger, = linalg.get_blas_funcs(('ger',), (dictionary, code))
nrm2, = linalg.get_blas_funcs(('nrm2',), (dictionary,))
# Residuals, computed with BLAS for speed and efficiency
# R <- -1.0 * U * V^T + 1.0 * Y
# Outputs R as Fortran array for efficiency
R = gemm(-1.0, dictionary, code, 1.0, Y)
for k in range(n_components):
# R <- 1.0 * U_k * V_k^T + R
R = ger(1.0, dictionary[:, k], code[k, :], a=R, overwrite_a=True)
dictionary[:, k] = np.dot(R, code[k, :])
if positive:
np.clip(dictionary[:, k], 0, None, out=dictionary[:, k])
# Scale k'th atom
# (U_k * U_k) ** 0.5
atom_norm = nrm2(dictionary[:, k])
if atom_norm < 1e-10:
if verbose == 1:
sys.stdout.write("+")
sys.stdout.flush()
elif verbose:
print("Adding new random atom")
dictionary[:, k] = random_state.randn(n_features)
if positive:
np.clip(dictionary[:, k], 0, None, out=dictionary[:, k])
# Setting corresponding coefs to 0
code[k, :] = 0.0
# (U_k * U_k) ** 0.5
atom_norm = nrm2(dictionary[:, k])
dictionary[:, k] /= atom_norm
else:
dictionary[:, k] /= atom_norm
# R <- -1.0 * U_k * V_k^T + R
R = ger(-1.0, dictionary[:, k], code[k, :], a=R, overwrite_a=True)
if return_r2:
R = nrm2(R) ** 2.0
return dictionary, R
return dictionary
@_deprecate_positional_args
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 ||_2^2 + alpha * || U ||_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.
Read more in the :ref:`User Guide <DictionaryLearning>`.
Parameters
----------
X : array 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,
Maximum number of iterations to perform.
tol : float,
Tolerance for the stopping condition.
method : {'lars', 'cd'}
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 or None, optional (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 : array of shape (n_components, n_features),
Initial value for the dictionary for warm restart scenarios.
code_init : array of shape (n_samples, n_components),
Initial value for the sparse code for warm restart scenarios.
callback : callable or None, optional (default: None)
Callable that gets invoked every five iterations
verbose : bool, optional (default: False)
To control the verbosity of the procedure.
random_state : int, RandomState instance or None, optional (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
Whether or not to return the number of iterations.
positive_dict : bool
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
positive_code : bool
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
method_max_iter : int, optional (default=1000)
Maximum number of iterations to perform.
.. versionadded:: 0.22
Returns
-------
code : array of shape (n_samples, n_components)
The sparse code factor in the matrix factorization.
dictionary : array 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)
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, as we are going to access its row vectors
dictionary = np.array(dictionary, order='F')
residuals = 0
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
dictionary, residuals = _update_dict(dictionary.T, X.T, code.T,
verbose=verbose, return_r2=True,
random_state=random_state,
positive=positive_dict)
dictionary = dictionary.T
# Cost function
current_cost = 0.5 * residuals + 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
@_deprecate_positional_args
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 ||_2^2 + alpha * || U ||_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. 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 of shape (n_samples, n_features)
Data matrix.
n_components : int,
Number of dictionary atoms to extract.
alpha : float,
Sparsity controlling parameter.
n_iter : int,
Number of mini-batch iterations to perform.
return_code : boolean,
Whether to also return the code U or just the dictionary V.
dict_init : array of shape (n_components, n_features),
Initial value for the dictionary for warm restart scenarios.
callback : callable or None, optional (default: None)
callable that gets invoked every five iterations
batch_size : int,
The number of samples to take in each batch.
verbose : bool, optional (default: False)
To control the verbosity of the procedure.
shuffle : boolean,
Whether to shuffle the data before splitting it in batches.
n_jobs : int or None, optional (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'}
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, optional (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 : boolean, optional
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
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
Whether or not to return the number of iterations.
positive_dict : bool
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
positive_code : bool
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
method_max_iter : int, optional (default=1000)
Maximum number of iterations to perform when solving the lasso problem.
.. versionadded:: 0.22
Returns
-------
code : array of shape (n_samples, n_components),
the sparse code (only returned if `return_code=True`)
dictionary : array 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
dictionary = check_array(dictionary.T, 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. / verbose) == 0:
print("Iteration % 3i (elapsed time: % 3is, % 4.1fmn)"
% (ii, dt, dt / 60))
this_code = sparse_encode(this_X, dictionary.T, algorithm=method,
alpha=alpha, n_jobs=n_jobs,
check_input=False,
positive=positive_code,
max_iter=method_max_iter, verbose=verbose).T
# 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, this_code.T)
B *= beta
B += np.dot(this_X.T, this_code.T)
# Update dictionary
dictionary = _update_dict(dictionary, B, A, verbose=verbose,
random_state=random_state,
positive=positive_dict)
# XXX: Can the residuals be of any use?
# 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.T, (A, B), ii - iter_offset + 1
else:
return dictionary.T, (A, B)
if return_code:
if verbose > 1:
print('Learning code...', end=' ')
elif verbose == 1:
print('|', end=' ')
code = sparse_encode(X, dictionary.T, algorithm=method, alpha=alpha,
n_jobs=n_jobs, check_input=False,
positive=positive_code, max_iter=method_max_iter,
verbose=verbose)
if verbose > 1:
dt = (time.time() - t0)
print('done (total time: % 3is, % 4.1fmn)' % (dt, dt / 60))
if return_n_iter:
return code, dictionary.T, ii - iter_offset + 1
else:
return code, dictionary.T
if return_n_iter:
return dictionary.T, ii - iter_offset + 1
else:
return dictionary.T
class SparseCodingMixin(TransformerMixin):
"""Sparse coding mixin"""
def _set_sparse_coding_params(self, n_components,
transform_algorithm='omp',
transform_n_nonzero_coefs=None,
transform_alpha=None, split_sign=False,
n_jobs=None, positive_code=False,
transform_max_iter=1000):
self.n_components = n_components
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):
"""Encode the data as a sparse combination of the dictionary atoms.
Coding method is determined by the object parameter
`transform_algorithm`.
Parameters
----------
X : array 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 : array, shape (n_samples, n_components)
Transformed data
"""
check_is_fitted(self)
X = check_array(X)
code = sparse_encode(
X, self.components_, algorithm=self.transform_algorithm,
n_nonzero_coefs=self.transform_n_nonzero_coefs,
alpha=self.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
class SparseCoder(SparseCodingMixin, 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 : array, [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=0.1*n_features
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.
transform_alpha : float, default=1.
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`.
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 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.
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
----------
components_ : array, [n_components, n_features]
The unchanged dictionary atoms
See also
--------
DictionaryLearning
MiniBatchDictionaryLearning
SparsePCA
MiniBatchSparsePCA
sparse_encode
"""
_required_parameters = ["dictionary"]
@_deprecate_positional_args
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):
self._set_sparse_coding_params(dictionary.shape[0],
transform_algorithm,
transform_n_nonzero_coefs,
transform_alpha, split_sign, n_jobs,
positive_code, transform_max_iter)
self.components_ = 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
y : Ignored
Returns
-------
self : object
Returns the object itself
"""
return self
@property
def n_features_in_(self):
return self.components_.shape[1]
class DictionaryLearning(SparseCodingMixin, BaseEstimator):
"""Dictionary learning
Finds a dictionary (a set of atoms) that can best be used to represent data
using a sparse code.
Solves the optimization problem::
(U^*,V^*) = argmin 0.5 || Y - U V ||_2^2 + alpha * || U ||_1
(U,V)
with || V_k ||_2 = 1 for all 0 <= k < n_components
Read more in the :ref:`User Guide <DictionaryLearning>`.
Parameters
----------
n_components : int, default=n_features
number of dictionary elements to extract
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
(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.
.. 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 (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'``
.. versionadded:: 0.17
*lasso_cd* coordinate descent method to improve speed.
transform_n_nonzero_coefs : int, default=0.1*n_features
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.
transform_alpha : float, default=1.0
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`.
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 : array of shape (n_samples, n_components), default=None
initial value for the code, for warm restart
dict_init : array of shape (n_components, n_features), default=None
initial values for the dictionary, for warm restart
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, optional (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_ : array, [n_components, n_features]
dictionary atoms extracted from the data
error_ : array
vector of errors at each iteration
n_iter_ : int
Number of iterations run.
Notes
-----
**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)
See also
--------
SparseCoder
MiniBatchDictionaryLearning
SparsePCA
MiniBatchSparsePCA
"""
@_deprecate_positional_args
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, verbose=False,
split_sign=False, random_state=None, positive_code=False,
positive_dict=False, transform_max_iter=1000):
self._set_sparse_coding_params(n_components, transform_algorithm,
transform_n_nonzero_coefs,
transform_alpha, split_sign, n_jobs,
positive_code, transform_max_iter)
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.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, shape (n_samples, n_features)
Training vector, where n_samples in the number of samples
and n_features is the number of features.
y : Ignored
Returns
-------
self : object
Returns the object itself
"""
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=self.fit_algorithm,
method_max_iter=self.transform_max_iter,
n_jobs=self.n_jobs,
code_init=self.code_init,
dict_init=self.dict_init,
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 self
class MiniBatchDictionaryLearning(SparseCodingMixin, BaseEstimator):
"""Mini-batch dictionary learning
Finds a dictionary (a set of atoms) that can best be used to represent data
using a sparse code.
Solves the optimization problem::
(U^*,V^*) = argmin 0.5 || Y - U V ||_2^2 + alpha * || U ||_1
(U,V)
with || V_k ||_2 = 1 for all 0 <= k < n_components
Read more in the :ref:`User Guide <DictionaryLearning>`.
Parameters
----------
n_components : int,
number of dictionary elements to extract
alpha : float,
sparsity controlling parameter
n_iter : int,
total number of iterations to perform
fit_algorithm : {'lars', 'cd'}
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 or None, optional (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,
number of samples in each mini-batch
shuffle : bool,
whether to shuffle the samples before forming batches
dict_init : array of shape (n_components, n_features),
initial value of the dictionary for warm restart scenarios
transform_algorithm : {'lasso_lars', 'lasso_cd', 'lars', 'omp', \
'threshold'}
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, ``0.1 * n_features`` by default
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.
transform_alpha : float, 1. by default
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`.
verbose : bool, optional (default: False)
To control the verbosity of the procedure.
split_sign : bool, False by default
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, optional (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
Whether to enforce positivity when finding the code.
.. versionadded:: 0.20
positive_dict : bool
Whether to enforce positivity when finding the dictionary.
.. versionadded:: 0.20
transform_max_iter : int, optional (default=1000)
Maximum number of iterations to perform if `algorithm='lasso_cd'` or
`lasso_lars`.
.. versionadded:: 0.22
Attributes
----------
components_ : array, [n_components, n_features]
components extracted from the data
inner_stats_ : tuple of (A, B) ndarrays
Internal sufficient statistics that are kept by the algorithm.
Keeping them is useful in online settings, to avoid losing the
history of the evolution, but they shouldn't have any use for the
end user.
A (n_components, n_components) is the dictionary covariance matrix.
B (n_features, n_components) is the data approximation matrix
n_iter_ : int
Number of iterations run.
iter_offset_ : int
The number of iteration on data batches that has been
performed before.
random_state_ : RandomState
RandomState instance that is generated either from a seed, the random
number generattor or by `np.random`.
Notes
-----
**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)
See also
--------
SparseCoder
DictionaryLearning
SparsePCA
MiniBatchSparsePCA
"""
@_deprecate_positional_args
def __init__(self, n_components=None, *, alpha=1, n_iter=1000,
fit_algorithm='lars', n_jobs=None, batch_size=3, 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):
self._set_sparse_coding_params(n_components, transform_algorithm,
transform_n_nonzero_coefs,
transform_alpha, split_sign, n_jobs,
positive_code, transform_max_iter)
self.alpha = alpha
self.n_iter = n_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
def fit(self, X, y=None):
"""Fit the model from data in X.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Training vector, where n_samples in the number of samples
and n_features is the number of features.
y : Ignored
Returns
-------
self : object
Returns the instance itself.
"""
random_state = check_random_state(self.random_state)
X = self._validate_data(X)
U, (A, B), self.n_iter_ = dict_learning_online(
X, self.n_components, alpha=self.alpha,
n_iter=self.n_iter, return_code=False,
method=self.fit_algorithm,
method_max_iter=self.transform_max_iter,
n_jobs=self.n_jobs, dict_init=self.dict_init,
batch_size=self.batch_size, shuffle=self.shuffle,
verbose=self.verbose, random_state=random_state,
return_inner_stats=True,
return_n_iter=True,
positive_dict=self.positive_dict,
positive_code=self.positive_code)
self.components_ = U
# Keep track of the state of the algorithm to be able to do
# some online fitting (partial_fit)
self.inner_stats_ = (A, B)
self.iter_offset_ = self.n_iter
self.random_state_ = random_state
return self
def partial_fit(self, X, y=None, iter_offset=None):
"""Updates the model using the data in X as a mini-batch.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Training vector, where n_samples in the number of samples
and n_features is the number of features.
y : Ignored
iter_offset : integer, optional
The number of iteration on data batches that has been
performed before this call to partial_fit. This is optional:
if no number is passed, the memory of the object is
used.
Returns
-------
self : object
Returns the instance itself.
"""
if not hasattr(self, 'random_state_'):
self.random_state_ = check_random_state(self.random_state)
X = check_array(X)
if hasattr(self, 'components_'):
dict_init = self.components_
else:
dict_init = self.dict_init
inner_stats = getattr(self, 'inner_stats_', None)
if iter_offset is None:
iter_offset = getattr(self, 'iter_offset_', 0)
U, (A, B) = dict_learning_online(
X, self.n_components, alpha=self.alpha,
n_iter=1, method=self.fit_algorithm,
method_max_iter=self.transform_max_iter,
n_jobs=self.n_jobs, dict_init=dict_init,
batch_size=len(X), shuffle=False,
verbose=self.verbose, return_code=False,
iter_offset=iter_offset, random_state=self.random_state_,
return_inner_stats=True, inner_stats=inner_stats,
positive_dict=self.positive_dict,
positive_code=self.positive_code)
self.components_ = U
# Keep track of the state of the algorithm to be able to do
# some online fitting (partial_fit)
self.inner_stats_ = (A, B)
self.iter_offset_ = iter_offset + 1
return self
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