sklearn.decomposition.SparsePCA

class sklearn.decomposition.SparsePCA(n_components=None, alpha=1, ridge_alpha=0.01, max_iter=1000, tol=1e-08, method='lars', n_jobs=None, U_init=None, V_init=None, verbose=False, random_state=None, normalize_components=False)

Sparse Principal Components Analysis (SparsePCA)

Finds the set of sparse components that can optimally reconstruct the data. The amount of sparseness is controllable by the coefficient of the L1 penalty, given by the parameter alpha.

Read more in the User Guide.

Parameters:

n_components : int,

Number of sparse atoms to extract.

alpha : float,

Sparsity controlling parameter. Higher values lead to sparser components.

ridge_alpha : float,

Amount of ridge shrinkage to apply in order to improve conditioning when calling the transform method.

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 joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

U_init : array of shape (n_samples, n_components),

Initial values for the loadings for warm restart scenarios.

V_init : array of shape (n_components, n_features),

Initial values for the components for warm restart scenarios.

verbose : int

Controls the verbosity; the higher, the more messages. Defaults to 0.

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.

normalize_components : boolean, optional (default=False)

• if False, use a version of Sparse PCA without components normalization and without data centering. This is likely a bug and even though it’s the default for backward compatibility, this should not be used.
• if True, use a version of Sparse PCA with components normalization and data centering.

New in version 0.20.

Deprecated since version 0.22: normalize_components was added and set to False for backward compatibility. It would be set to True from 0.22 onwards.

Attributes:

components_ : array, [n_components, n_features]

Sparse components extracted from the data.

error_ : array

Vector of errors at each iteration.

n_iter_ : int

Number of iterations run.

mean_ : array, shape (n_features,)

Per-feature empirical mean, estimated from the training set. Equal to X.mean(axis=0).

See also

PCA, MiniBatchSparsePCA, DictionaryLearning

Examples

>>> import numpy as np
>>> from sklearn.datasets import make_friedman1
>>> from sklearn.decomposition import SparsePCA
>>> X, _ = make_friedman1(n_samples=200, n_features=30, random_state=0)
>>> transformer = SparsePCA(n_components=5,
...         normalize_components=True,
...         random_state=0)
>>> transformer.fit(X) 
SparsePCA(...)
>>> X_transformed = transformer.transform(X)
>>> X_transformed.shape
(200, 5)
>>> # most values in the components_ are zero (sparsity)
>>> np.mean(transformer.components_ == 0) 
0.9666...

Methods

fit(X[, y])	Fit the model from data in X.
fit_transform(X[, y])	Fit to data, then transform it.
get_params([deep])	Get parameters for this estimator.
set_params(**params)	Set the parameters of this estimator.
transform(X[, ridge_alpha])	Least Squares projection of the data onto the sparse components.

__init__(n_components=None, alpha=1, ridge_alpha=0.01, max_iter=1000, tol=1e-08, method='lars', n_jobs=None, U_init=None, V_init=None, verbose=False, random_state=None, normalize_components=False)

fit(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.

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns:

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep : boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

params : mapping of string to any

Parameter names mapped to their values.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:

self

transform(X, ridge_alpha='deprecated')

Least Squares projection of the data onto the sparse components.

To avoid instability issues in case the system is under-determined, regularization can be applied (Ridge regression) via the ridge_alpha parameter.

Note that Sparse PCA components orthogonality is not enforced as in PCA hence one cannot use a simple linear projection.

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.

ridge_alpha : float, default: 0.01

Amount of ridge shrinkage to apply in order to improve conditioning.

Deprecated since version 0.19: This parameter will be removed in 0.21. Specify ridge_alpha in the SparsePCA constructor.

Returns:

X_new array, shape (n_samples, n_components)

Transformed data.