"""Matrix factorization with Sparse PCA""" # Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort # License: BSD 3 clause import warnings import numpy as np from ..utils import check_random_state, check_array from ..utils.validation import check_is_fitted from ..linear_model import ridge_regression from ..base import BaseEstimator, TransformerMixin from .dict_learning import dict_learning, dict_learning_online class SparsePCA(BaseEstimator, TransformerMixin): """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, 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 ` 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. .. versionadded:: 0.20 .. deprecated:: 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)``. 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) # doctest: +ELLIPSIS SparsePCA(...) >>> X_transformed = transformer.transform(X) >>> X_transformed.shape (200, 5) >>> # most values in the components_ are zero (sparsity) >>> np.mean(transformer.components_ == 0) # doctest: +ELLIPSIS 0.9666... See also -------- PCA MiniBatchSparsePCA DictionaryLearning """ 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, normalize_components=False): 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 self.normalize_components = normalize_components def fit(self, 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. """ random_state = check_random_state(self.random_state) X = check_array(X) if self.normalize_components: self.mean_ = X.mean(axis=0) X = X - self.mean_ else: warnings.warn("normalize_components=False is a " "backward-compatible setting that implements a " "non-standard definition of sparse PCA. This " "compatibility mode will be removed in 0.22.", DeprecationWarning) 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, 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 if self.normalize_components: components_norm = \ np.linalg.norm(self.components_, axis=1)[:, np.newaxis] components_norm[components_norm == 0] = 1 self.components_ /= components_norm self.error_ = E return self def transform(self, 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:: 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. """ check_is_fitted(self, 'components_') X = check_array(X) if ridge_alpha != 'deprecated': warnings.warn("The ridge_alpha parameter on transform() is " "deprecated since 0.19 and will be removed in 0.21. " "Specify ridge_alpha in the SparsePCA constructor.", DeprecationWarning) if ridge_alpha is None: ridge_alpha = self.ridge_alpha else: ridge_alpha = self.ridge_alpha if self.normalize_components: X = X - self.mean_ U = ridge_regression(self.components_.T, X.T, ridge_alpha, solver='cholesky') if not self.normalize_components: s = np.sqrt((U ** 2).sum(axis=0)) s[s == 0] = 1 U /= s 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, number of sparse atoms to extract alpha : int, 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. n_iter : int, number of iterations to perform for each mini batch callback : callable or None, optional (default: None) callable that gets invoked every five iterations batch_size : int, the number of features to take in each mini batch verbose : int Controls the verbosity; the higher, the more messages. Defaults to 0. shuffle : boolean, whether to shuffle the data before splitting it in batches 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 ` for more details. 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. 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. .. versionadded:: 0.20 .. deprecated:: 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. 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 MiniBatchSparsePCA >>> X, _ = make_friedman1(n_samples=200, n_features=30, random_state=0) >>> transformer = MiniBatchSparsePCA(n_components=5, ... batch_size=50, ... normalize_components=True, ... random_state=0) >>> transformer.fit(X) # doctest: +ELLIPSIS 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 """ 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, normalize_components=False): super(MiniBatchSparsePCA, self).__init__( n_components=n_components, alpha=alpha, verbose=verbose, ridge_alpha=ridge_alpha, n_jobs=n_jobs, method=method, random_state=random_state, normalize_components=normalize_components) 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, 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 = check_array(X) if self.normalize_components: self.mean_ = X.mean(axis=0) X = X - self.mean_ else: warnings.warn("normalize_components=False is a " "backward-compatible setting that implements a " "non-standard definition of sparse PCA. This " "compatibility mode will be removed in 0.22.", DeprecationWarning) 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 if self.normalize_components: components_norm = \ np.linalg.norm(self.components_, axis=1)[:, np.newaxis] components_norm[components_norm == 0] = 1 self.components_ /= components_norm return self