def test_safe_min():
msg = ("safe_min is deprecated in version 0.22 and will be removed "
"in version 0.24.")
with pytest.warns(FutureWarning, match=msg):
safe_min(np.ones(10))
def non_negative_factorization(lam,
N,
D,
X,
W=None,
H=None,
n_components=None,
init='warn',
update_H=True,
solver='mu',
beta_loss='KL',
tol=1e-4,
max_iter=400,
alpha=0.,
l1_ratio=0.,
regularization=None,
random_state=None,
verbose=0,
shuffle=False):
X = check_array(X, accept_sparse=('csr', 'csc'), dtype=float)
check_non_negative(X, "NMF (input X)")
beta_loss = _check_string_param(solver, regularization, beta_loss, init)
if safe_min(X) == 0 and beta_loss <= 0:
raise ValueError("When beta_loss <= 0 and X contains zeros, "
"the solver may diverge. Please add small values to "
"X, or use a positive beta_loss.")
n_samples, n_features = X.shape
if n_components is None:
n_components = n_features
if not isinstance(n_components, INTEGER_TYPES) or n_components <= 0:
raise ValueError("Number of components must be a positive integer;"
" got (n_components=%r)" % n_components)
if not isinstance(max_iter, INTEGER_TYPES) or max_iter < 0:
raise ValueError("Maximum number of iterations must be a positive "
"integer; got (max_iter=%r)" % max_iter)
if not isinstance(tol, numbers.Number) or tol < 0:
raise ValueError("Tolerance for stopping criteria must be "
"positive; got (tol=%r)" % tol)
if init == "warn":
if n_components < n_features:
warnings.warn(
"The default value of init will change from "
"random to None in 0.23 to make it consistent "
"with decomposition.NMF.", FutureWarning)
init = "random"
# check W and H, or initialize them
if init == 'custom' and update_H:
_check_init(H, (n_components, n_features), "NMF (input H)")
_check_init(W, (n_samples, n_components), "NMF (input W)")
elif not update_H:
_check_init(H, (n_components, n_features), "NMF (input H)")
avg = np.sqrt(X.mean() / n_components)
W = np.full((n_samples, n_components), avg)
else:
W, H = _initialize_nmf(X,
n_components,
init=init,
random_state=random_state)
l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H = _compute_regularization(
alpha, l1_ratio, regularization)
W, H, n_iter = _fit_multiplicative_update(lam, N, D, X, W, H, beta_loss,
max_iter, tol, l1_reg_W,
l1_reg_H, l2_reg_W, l2_reg_H,
update_H, verbose)
if n_iter == max_iter and tol > 0:
warnings.warn(
"Maximum number of iteration %d reached. Increase it to"
" improve convergence." % max_iter, ConvergenceWarning)
return W, H, n_iter
def non_negative_factorization(X, W=None, H=None, n_components=None,
init='random', update_H=True, solver='cd',
beta_loss='frobenius', tol=1e-4,
max_iter=200, alpha=0., l1_ratio=0.,
regularization=None, random_state=None,
verbose=0, shuffle=False):
"""Compute Non-negative Matrix Factorization (NMF)
Find two non-negative matrices (W, H) whose product approximates the non-
negative matrix X. This factorization can be used for example for
dimensionality reduction, source separation or topic extraction.
The objective function is::
0.5 * ||X - WH||_Fro^2
+ alpha * l1_ratio * ||vec(W)||_1
+ alpha * l1_ratio * ||vec(H)||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
+ 0.5 * alpha * (1 - l1_ratio) * ||H||_Fro^2
Where::
||A||_Fro^2 = \sum_{i,j} A_{ij}^2 (Frobenius norm)
||vec(A)||_1 = \sum_{i,j} abs(A_{ij}) (Elementwise L1 norm)
For multiplicative-update ('mu') solver, the Frobenius norm
(0.5 * ||X - WH||_Fro^2) can be changed into another beta-divergence loss,
by changing the beta_loss parameter.
The objective function is minimized with an alternating minimization of W
and H. If H is given and update_H=False, it solves for W only.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Constant matrix.
W : array-like, shape (n_samples, n_components)
If init='custom', it is used as initial guess for the solution.
H : array-like, shape (n_components, n_features)
If init='custom', it is used as initial guess for the solution.
If update_H=False, it is used as a constant, to solve for W only.
n_components : integer
Number of components, if n_components is not set all features
are kept.
init : None | 'random' | 'nndsvd' | 'nndsvda' | 'nndsvdar' | 'custom'
Method used to initialize the procedure.
Default: 'nndsvd' if n_components < n_features, otherwise random.
Valid options:
- 'random': non-negative random matrices, scaled with:
sqrt(X.mean() / n_components)
- 'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
initialization (better for sparseness)
- 'nndsvda': NNDSVD with zeros filled with the average of X
(better when sparsity is not desired)
- 'nndsvdar': NNDSVD with zeros filled with small random values
(generally faster, less accurate alternative to NNDSVDa
for when sparsity is not desired)
- 'custom': use custom matrices W and H
update_H : boolean, default: True
Set to True, both W and H will be estimated from initial guesses.
Set to False, only W will be estimated.
solver : 'cd' | 'mu'
Numerical solver to use:
'cd' is a Coordinate Descent solver.
'mu' is a Multiplicative Update solver.
.. versionadded:: 0.17
Coordinate Descent solver.
.. versionadded:: 0.19
Multiplicative Update solver.
beta_loss : float or string, default 'frobenius'
String must be in {'frobenius', 'kullback-leibler', 'itakura-saito'}.
Beta divergence to be minimized, measuring the distance between X
and the dot product WH. Note that values different from 'frobenius'
(or 2) and 'kullback-leibler' (or 1) lead to significantly slower
fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
matrix X cannot contain zeros. Used only in 'mu' solver.
.. versionadded:: 0.19
tol : float, default: 1e-4
Tolerance of the stopping condition.
max_iter : integer, default: 200
Maximum number of iterations before timing out.
alpha : double, default: 0.
Constant that multiplies the regularization terms.
l1_ratio : double, default: 0.
The regularization mixing parameter, with 0 <= l1_ratio <= 1.
For l1_ratio = 0 the penalty is an elementwise L2 penalty
(aka Frobenius Norm).
For l1_ratio = 1 it is an elementwise L1 penalty.
For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
regularization : 'both' | 'components' | 'transformation' | None
Select whether the regularization affects the components (H), the
transformation (W), both or none of them.
random_state : integer seed, RandomState instance, or None (default)
Random number generator seed control.
verbose : integer, default: 0
The verbosity level.
shuffle : boolean, default: False
If true, randomize the order of coordinates in the CD solver.
Returns
-------
W : array-like, shape (n_samples, n_components)
Solution to the non-negative least squares problem.
H : array-like, shape (n_components, n_features)
Solution to the non-negative least squares problem.
n_iter : int
Actual number of iterations.
Examples
--------
>>> import numpy as np
>>> X = np.array([[1,1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
>>> from sklearn.decomposition import non_negative_factorization
>>> W, H, n_iter = non_negative_factorization(X, n_components=2, \
init='random', random_state=0)
References
----------
Cichocki, Andrzej, and P. H. A. N. Anh-Huy. "Fast local algorithms for
large scale nonnegative matrix and tensor factorizations."
IEICE transactions on fundamentals of electronics, communications and
computer sciences 92.3: 708-721, 2009.
Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix
factorization with the beta-divergence. Neural Computation, 23(9).
"""
X = check_array(X, accept_sparse=('csr', 'csc'), force_all_finite=False)
check_non_negative(X, "NMF (input X)", accept_nan=True)
beta_loss = _check_string_param(solver, regularization, beta_loss, init)
if sp.issparse(X) and np.any(np.isnan(X.data)):
raise ValueError("X contains NaN values, and NMF with missing "
"values is not implemented for sparse matrices.")
if not sp.issparse(X) and np.any(np.isnan(X)) and solver != 'mu':
raise ValueError("NMF solver '%s' cannot handle missing values. "
"Use 'mu' solver or remove NaN from the input X."
% solver)
if safe_min(X) == 0 and beta_loss <= 0:
raise ValueError("When beta_loss <= 0 and X contains zeros, "
"the solver may diverge. Please add small values to "
"X, or use a positive beta_loss.")
n_samples, n_features = X.shape
if n_components is None:
n_components = n_features
if not isinstance(n_components, INTEGER_TYPES) or n_components <= 0:
raise ValueError("Number of components must be a positive integer;"
" got (n_components=%r)" % n_components)
if not isinstance(max_iter, INTEGER_TYPES) or max_iter < 0:
raise ValueError("Maximum number of iterations must be a positive "
"integer; got (max_iter=%r)" % max_iter)
if not isinstance(tol, numbers.Number) or tol < 0:
raise ValueError("Tolerance for stopping criteria must be "
"positive; got (tol=%r)" % tol)
# check W and H, or initialize them
if init == 'custom' and update_H:
_check_init(H, (n_components, n_features), "NMF (input H)")
_check_init(W, (n_samples, n_components), "NMF (input W)")
elif not update_H:
_check_init(H, (n_components, n_features), "NMF (input H)")
# 'mu' solver should not be initialized by zeros
if solver == 'mu':
avg = np.sqrt(X.mean() / n_components)
W = avg * np.ones((n_samples, n_components))
else:
W = np.zeros((n_samples, n_components))
else:
W, H = _initialize_nmf(X, n_components, init=init,
random_state=random_state)
l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H = _compute_regularization(
alpha, l1_ratio, regularization)
if solver == 'cd':
W, H, n_iter = _fit_coordinate_descent(X, W, H, tol, max_iter,
l1_reg_W, l1_reg_H,
l2_reg_W, l2_reg_H,
update_H=update_H,
verbose=verbose,
shuffle=shuffle,
random_state=random_state)
elif solver == 'mu':
W, H, n_iter = _fit_multiplicative_update(X, W, H, beta_loss, max_iter,
tol, l1_reg_W, l1_reg_H,
l2_reg_W, l2_reg_H, update_H,
verbose)
else:
raise ValueError("Invalid solver parameter '%s'." % solver)
if n_iter == max_iter and tol > 0:
warnings.warn("Maximum number of iteration %d reached. Increase it to"
" improve convergence." % max_iter, ConvergenceWarning)
return W, H, n_iter
def non_negative_factorization(X, W=None, H=None, n_components=None,
init='random', update_H=True, solver='cd',
beta_loss='frobenius', tol=1e-4,
max_iter=200, alpha=0., l1_ratio=0.,
regularization=None, random_state=None,
verbose=0, shuffle=False, distribution = 'gaussian', N=None, D=None):
r"""Compute Non-negative Matrix Factorization (NMF)
Find two non-negative matrices (W, H) whose product approximates the non-
negative matrix X. This factorization can be used for example for
dimensionality reduction, source separation or topic extraction.
The objective function is::
0.5 * ||X - WH||_Fro^2
+ alpha * l1_ratio * ||vec(W)||_1
+ alpha * l1_ratio * ||vec(H)||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
+ 0.5 * alpha * (1 - l1_ratio) * ||H||_Fro^2
Where::
||A||_Fro^2 = \sum_{i,j} A_{ij}^2 (Frobenius norm)
||vec(A)||_1 = \sum_{i,j} abs(A_{ij}) (Elementwise L1 norm)
For multiplicative-update ('mu') solver, the Frobenius norm
(0.5 * ||X - WH||_Fro^2) can be changed into another beta-divergence loss,
by changing the beta_loss parameter.
The objective function is minimized with an alternating minimization of W
and H. If H is given and update_H=False, it solves for W only.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Constant matrix.
W : array-like, shape (n_samples, n_components)
If init='custom', it is used as initial guess for the solution.
H : array-like, shape (n_components, n_features)
If init='custom', it is used as initial guess for the solution.
If update_H=False, it is used as a constant, to solve for W only.
n_components : integer
Number of components, if n_components is not set all features
are kept.
init : None | 'random' | 'nndsvd' | 'nndsvda' | 'nndsvdar' | 'custom'
Method used to initialize the procedure.
Default: 'random'.
Valid options:
- 'random': non-negative random matrices, scaled with:
sqrt(X.mean() / n_components)
- 'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
initialization (better for sparseness)
- 'nndsvda': NNDSVD with zeros filled with the average of X
(better when sparsity is not desired)
- 'nndsvdar': NNDSVD with zeros filled with small random values
(generally faster, less accurate alternative to NNDSVDa
for when sparsity is not desired)
- 'custom': use custom matrices W and H
update_H : boolean, default: True
Set to True, both W and H will be estimated from initial guesses.
Set to False, only W will be estimated.
solver : 'cd' | 'mu'
Numerical solver to use:
'cd' is a Coordinate Descent solver that uses Fast Hierarchical
Alternating Least Squares (Fast HALS).
'mu' is a Multiplicative Update solver.
.. versionadded:: 0.17
Coordinate Descent solver.
.. versionadded:: 0.19
Multiplicative Update solver.
beta_loss : float or string, default 'frobenius'
String must be in {'frobenius', 'kullback-leibler', 'itakura-saito'}.
Beta divergence to be minimized, measuring the distance between X
and the dot product WH. Note that values different from 'frobenius'
(or 2) and 'kullback-leibler' (or 1) lead to significantly slower
fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
matrix X cannot contain zeros. Used only in 'mu' solver.
.. versionadded:: 0.19
tol : float, default: 1e-4
Tolerance of the stopping condition.
max_iter : integer, default: 200
Maximum number of iterations before timing out.
alpha : double, default: 0.
Constant that multiplies the regularization terms.
l1_ratio : double, default: 0.
The regularization mixing parameter, with 0 <= l1_ratio <= 1.
For l1_ratio = 0 the penalty is an elementwise L2 penalty
(aka Frobenius Norm).
For l1_ratio = 1 it is an elementwise L1 penalty.
For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
regularization : 'both' | 'components' | 'transformation' | None
Select whether the regularization affects the components (H), the
transformation (W), both or none of them.
random_state : int, RandomState instance or None, optional, default: None
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
verbose : integer, default: 0
The verbosity level.
shuffle : boolean, default: False
If true, randomize the order of coordinates in the CD solver.
Returns
-------
W : array-like, shape (n_samples, n_components)
Solution to the non-negative least squares problem.
H : array-like, shape (n_components, n_features)
Solution to the non-negative least squares problem.
n_iter : int
Actual number of iterations.
Examples
--------
>>> import numpy as np
>>> X = np.array([[1,1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
>>> from sklearn.decomposition import non_negative_factorization
>>> W, H, n_iter = non_negative_factorization(X, n_components=2,
... init='random', random_state=0)
References
----------
Cichocki, Andrzej, and P. H. A. N. Anh-Huy. "Fast local algorithms for
large scale nonnegative matrix and tensor factorizations."
IEICE transactions on fundamentals of electronics, communications and
computer sciences 92.3: 708-721, 2009.
Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix
factorization with the beta-divergence. Neural Computation, 23(9).
"""
#print('My Non negative Factorization')
X = check_array(X, accept_sparse=('csr', 'csc'), dtype=float)
check_non_negative(X, "NMF (input X)")
beta_loss = _check_string_param(solver, regularization, beta_loss, init)
if safe_min(X) == 0 and beta_loss <= 0:
raise ValueError("When beta_loss <= 0 and X contains zeros, "
"the solver may diverge. Please add small values to "
"X, or use a positive beta_loss.")
n_samples, n_features = X.shape
if n_components is None:
n_components = n_features
if not isinstance(n_components, INTEGER_TYPES) or n_components <= 0:
raise ValueError("Number of components must be a positive integer;"
" got (n_components=%r)" % n_components)
if not isinstance(max_iter, INTEGER_TYPES) or max_iter < 0:
raise ValueError("Maximum number of iterations must be a positive "
"integer; got (max_iter=%r)" % max_iter)
if not isinstance(tol, numbers.Number) or tol < 0:
raise ValueError("Tolerance for stopping criteria must be "
"positive; got (tol=%r)" % tol)
# check W and H, or initialize them
if init == 'custom' and update_H:
_check_init(H, (n_components, n_features), "NMF (input H)")
_check_init(W, (n_samples, n_components), "NMF (input W)")
elif not update_H:
_check_init(H, (n_components, n_features), "NMF (input H)")
# 'mu' solver should not be initialized by zeros
if solver == 'mu':
avg = np.sqrt(X.mean() / n_components)
W = np.full((n_samples, n_components), avg)
else:
W = np.zeros((n_samples, n_components))
else:
W, H = _initialize_nmf(X, n_components, init=init,
random_state=random_state)
l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H = _compute_regularization(
alpha, l1_ratio, regularization)
W, H, n_iter = update(X, W, H, max_iter, distribution, N , D)
if n_iter == max_iter and tol > 0:
warnings.warn("Maximum number of iteration %d reached. Increase it to"
" improve convergence." % max_iter, ConvergenceWarning)
return W, H, n_iter
