"""Matrix factorization with Sparse PCA.""" # Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort # License: BSD 3 clause import numpy as np from ..utils import check_random_state from ..utils.validation import check_is_fitted from ..utils.validation import _deprecate_positional_args from ..linear_model import ridge_regression from ..base import BaseEstimator, TransformerMixin from ._dict_learning import dict_learning, dict_learning_online class SparsePCA(TransformerMixin, BaseEstimator): """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 `. Parameters ---------- n_components : int, default=None Number of sparse atoms to extract. alpha : float, default=1 Sparsity controlling parameter. Higher values lead to sparser components. ridge_alpha : float, default=0.01 Amount of ridge shrinkage to apply in order to improve conditioning when calling the transform method. max_iter : int, default=1000 Maximum number of iterations to perform. tol : float, default=1e-8 Tolerance for the stopping condition. method : {'lars', 'cd'}, default='lars' 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, 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 ` for more details. U_init : ndarray of shape (n_samples, n_components), default=None Initial values for the loadings for warm restart scenarios. Only used if `U_init` and `V_init` are not None. V_init : ndarray of shape (n_components, n_features), default=None Initial values for the components for warm restart scenarios. Only used if `U_init` and `V_init` are not None. verbose : int or bool, default=False Controls the verbosity; the higher, the more messages. Defaults to 0. random_state : int, RandomState instance or None, default=None Used during dictionary learning. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. 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. .. versionadded:: 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 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 """ @_deprecate_positional_args def __init__(self, n_components=None, *, alpha=1, ridge_alpha=0.01, max_iter=1000, tol=1e-8, method='lars', n_jobs=None, U_init=None, V_init=None, verbose=False, random_state=None): self.n_components = n_components self.alpha = alpha self.ridge_alpha = ridge_alpha self.max_iter = max_iter self.tol = tol self.method = method self.n_jobs = n_jobs self.U_init = U_init self.V_init = V_init self.verbose = verbose self.random_state = random_state def fit(self, X, y=None): """Fit the model from data in X. Parameters ---------- X : array-like of 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. """ random_state = check_random_state(self.random_state) X = self._validate_data(X) self.mean_ = X.mean(axis=0) X = X - self.mean_ if self.n_components is None: n_components = X.shape[1] else: n_components = self.n_components code_init = self.V_init.T if self.V_init is not None else None dict_init = self.U_init.T if self.U_init is not None else None Vt, _, E, self.n_iter_ = dict_learning(X.T, n_components, alpha=self.alpha, tol=self.tol, max_iter=self.max_iter, method=self.method, n_jobs=self.n_jobs, verbose=self.verbose, random_state=random_state, code_init=code_init, dict_init=dict_init, return_n_iter=True) self.components_ = Vt.T components_norm = np.linalg.norm( self.components_, axis=1)[:, np.newaxis] components_norm[components_norm == 0] = 1 self.components_ /= components_norm self.n_components_ = len(self.components_) self.error_ = E return self def transform(self, X): """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 : ndarray 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 : ndarray of shape (n_samples, n_components) Transformed data. """ check_is_fitted(self) X = self._validate_data(X, reset=False) X = X - self.mean_ U = ridge_regression(self.components_.T, X.T, self.ridge_alpha, solver='cholesky') return U class MiniBatchSparsePCA(SparsePCA): """Mini-batch Sparse Principal Components Analysis 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 `. Parameters ---------- n_components : int, default=None number of sparse atoms to extract alpha : int, default=1 Sparsity controlling parameter. Higher values lead to sparser components. ridge_alpha : float, default=0.01 Amount of ridge shrinkage to apply in order to improve conditioning when calling the transform method. n_iter : int, default=100 number of iterations to perform for each mini batch callback : callable, default=None callable that gets invoked every five iterations batch_size : int, default=3 the number of features to take in each mini batch verbose : int or bool, default=False Controls the verbosity; the higher, the more messages. Defaults to 0. shuffle : bool, default=True whether to shuffle the data before splitting it in batches n_jobs : int, 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 ` for more details. method : {'lars', 'cd'}, default='lars' 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. random_state : int, RandomState instance or None, default=None Used for random shuffling when ``shuffle`` is set to ``True``, during online dictionary learning. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. Attributes ---------- components_ : ndarray of shape (n_components, n_features) Sparse components extracted from the data. n_components_ : int Estimated number of components. .. versionadded:: 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 to ``X.mean(axis=0)``. Examples -------- >>> import numpy as np >>> from sklearn.datasets import make_friedman1 >>> from sklearn.decomposition import MiniBatchSparsePCA >>> X, _ = make_friedman1(n_samples=200, n_features=30, random_state=0) >>> transformer = MiniBatchSparsePCA(n_components=5, batch_size=50, ... random_state=0) >>> transformer.fit(X) MiniBatchSparsePCA(...) >>> X_transformed = transformer.transform(X) >>> X_transformed.shape (200, 5) >>> # most values in the components_ are zero (sparsity) >>> np.mean(transformer.components_ == 0) 0.94 See Also -------- PCA SparsePCA DictionaryLearning """ @_deprecate_positional_args def __init__(self, n_components=None, *, alpha=1, ridge_alpha=0.01, n_iter=100, callback=None, batch_size=3, verbose=False, shuffle=True, n_jobs=None, method='lars', random_state=None): super().__init__( n_components=n_components, alpha=alpha, verbose=verbose, ridge_alpha=ridge_alpha, n_jobs=n_jobs, method=method, random_state=random_state) self.n_iter = n_iter self.callback = callback self.batch_size = batch_size self.shuffle = shuffle def fit(self, X, y=None): """Fit the model from data in X. Parameters ---------- X : array-like of 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. """ random_state = check_random_state(self.random_state) X = self._validate_data(X) self.mean_ = X.mean(axis=0) X = X - self.mean_ if self.n_components is None: n_components = X.shape[1] else: n_components = self.n_components Vt, _, self.n_iter_ = dict_learning_online( X.T, n_components, alpha=self.alpha, n_iter=self.n_iter, return_code=True, dict_init=None, verbose=self.verbose, callback=self.callback, batch_size=self.batch_size, shuffle=self.shuffle, n_jobs=self.n_jobs, method=self.method, random_state=random_state, return_n_iter=True) self.components_ = Vt.T components_norm = np.linalg.norm( self.components_, axis=1)[:, np.newaxis] components_norm[components_norm == 0] = 1 self.components_ /= components_norm self.n_components_ = len(self.components_) return self