# 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='deprecated')[source]

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_componentsint,

Number of sparse atoms to extract.

alphafloat,

Sparsity controlling parameter. Higher values lead to sparser components.

ridge_alphafloat,

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

max_iterint,

Maximum number of iterations to perform.

tolfloat,

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_jobsint 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_initarray of shape (n_samples, n_components),

V_initarray of shape (n_components, n_features),

Initial values for the components for warm restart scenarios.

verboseint

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

random_stateint, 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‘deprecated’

This parameter does not have any effect. The components are always normalized.

New in version 0.20.

Deprecated since version 0.22: normalize_components is deprecated in 0.22 and will be removed in 0.24.

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).

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

Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y=None)[source]

Fit the model from data in X.

Parameters
Xarray-like, shape (n_samples, n_features)

Training vector, where n_samples in the number of samples and n_features is the number of features.

yIgnored
Returns
selfobject

Returns the instance itself.

fit_transform(self, X, y=None, **fit_params)[source]

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
Xnumpy array of shape [n_samples, n_features]

Training set.

ynumpy array of shape [n_samples]

Target values.

Returns
X_newnumpy array of shape [n_samples, n_features_new]

Transformed array.

get_params(self, deep=True)[source]

Get parameters for this estimator.

Parameters
deepboolean, optional

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

Returns
paramsmapping of string to any

Parameter names mapped to their values.

set_params(self, **params)[source]

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(self, X)[source]

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
Xarray 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.