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 :ref:`User Guide <SparsePCA>`.
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 :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary <n_jobs>` 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, default=None Used during dictionary learning. Pass an int for reproducible results across multiple function calls. See :term:`Glossary <random_state>`.
normalize_components : 'deprecated' This parameter does not have any effect. The components are always normalized.
.. versionadded:: 0.20
.. deprecated:: 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_components_ : int Estimated number of components.
.. versionadded:: 0.23
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...
See also -------- PCA MiniBatchSparsePCA DictionaryLearning