SparsePCA#

classsklearn.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)[source]#

Sparse Principal Components Analysis (SparsePCA).

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

Read more in theUser Guide.

Parameters:

n_componentsint, default=None

Number of sparse atoms to extract. If None, thenn_componentsis set ton_features.

alphafloat, default=1

Sparsity controlling parameter. Higher values lead to sparsercomponents.

ridge_alphafloat, default=0.01

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

max_iterint, default=1000

Maximum number of iterations to perform.

tolfloat, default=1e-8

Tolerance for the stopping condition.

method{‘lars’, ‘cd’}, default=’lars’

Method to be used for optimization.lars: uses the least angle regression method to solve the lasso problem(linear_model.lars_path)cd: uses the coordinate descent method to compute theLasso solution (linear_model.Lasso). Lars will be faster ifthe estimated components are sparse.

n_jobsint, default=None

Number of parallel jobs to run.None means 1 unless in ajoblib.parallel_backend context.-1 means using all processors. SeeGlossaryfor more details.

U_initndarray of shape (n_samples, n_components), default=None

Initial values for the loadings for warm restart scenarios. Only usedifU_init andV_init are not None.

V_initndarray of shape (n_components, n_features), default=None

Initial values for the components for warm restart scenarios. Only usedifU_init andV_init are not None.

verboseint or bool, default=False

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

random_stateint, RandomState instance or None, default=None

Used during dictionary learning. Pass an int for reproducible resultsacross multiple function calls.SeeGlossary.

Attributes:

components_ndarray of shape (n_components, n_features)

Sparse components extracted from the data.

error_ndarray

Vector of errors at each iteration.

n_components_int

Estimated number of components.

Added in version 0.23.

n_iter_int

Number of iterations run.

mean_ndarray of shape (n_features,)

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

n_features_in_int

Number of features seen duringfit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen duringfit. Defined only whenXhas feature names that are all strings.

Added in version 1.0.

See also

PCA

Principal Component Analysis implementation.

MiniBatchSparsePCA

Mini batch variant ofSparsePCA that is faster but less accurate.

DictionaryLearning

Generic dictionary learning problem using a sparse code.

Examples

>>>importnumpyasnp>>>fromsklearn.datasetsimportmake_friedman1>>>fromsklearn.decompositionimportSparsePCA>>>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)np.float64(0.9666)

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

Fit the model from data in X.

Parameters:

Xarray-like of shape (n_samples, n_features)

Training vector, wheren_samples is the number of samplesandn_features is the number of features.

yIgnored

Not used, present here for API consistency by convention.

Returns:

selfobject

Returns the instance itself.

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

Fit to data, then transform it.

Fits transformer toX andy with optional parametersfit_paramsand returns a transformed version ofX.

Parameters:

Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Additional fit parameters.

Returns:

X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

get_feature_names_out(input_features=None)[source]#

Get output feature names for transformation.

The feature names out will prefixed by the lowercased class name. Forexample, if the transformer outputs 3 features, then the feature namesout are:["class_name0","class_name1","class_name2"].

Parameters:

input_featuresarray-like of str or None, default=None

Only used to validate feature names with the names seen infit.

Returns:

feature_names_outndarray of str objects

Transformed feature names.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Returns:

routingMetadataRequest

AMetadataRequest encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True

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

Returns:

paramsdict

Parameter names mapped to their values.

inverse_transform(X)[source]#

Transform data from the latent space to the original space.

This inversion is an approximation due to the loss of informationinduced by the forward decomposition.

Added in version 1.2.

Parameters:

Xndarray of shape (n_samples, n_components)

Data in the latent space.

Returns:

X_originalndarray of shape (n_samples, n_features)

Reconstructed data in the original space.

set_output(*,transform=None)[source]#

Set output container.

SeeIntroducing the set_output APIfor an example on how to use the API.

Parameters:

transform{“default”, “pandas”, “polars”}, default=None

Configure output oftransform andfit_transform.

• "default": Default output format of a transformer

• "pandas": DataFrame output

• "polars": Polars output

• None: Transform configuration is unchanged

Added in version 1.4:"polars" option was added.

Returns:

selfestimator instance

Estimator instance.

set_params(**params)[source]#

Set the parameters of this estimator.

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

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

transform(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 theridge_alpha parameter.

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

Parameters:

Xndarray of shape (n_samples, n_features)

Test data to be transformed, must have the same number offeatures as the data used to train the model.

Returns:

X_newndarray of shape (n_samples, n_components)

Transformed data.

Gallery examples#

Faces dataset decompositions

Faces dataset decompositions