"""Matrix factorization with Sparse PCA.""" # Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort # License: BSD 3 clause from numbers import Integral, Real import numpy as np from ..base import ( BaseEstimator, ClassNamePrefixFeaturesOutMixin, TransformerMixin, _fit_context, ) from ..linear_model import ridge_regression from ..utils import check_random_state from ..utils._param_validation import Hidden, Interval, StrOptions from ..utils.extmath import svd_flip from ..utils.validation import check_array, check_is_fitted from ._dict_learning import MiniBatchDictionaryLearning, dict_learning class _BaseSparsePCA(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator): """Base class for SparsePCA and MiniBatchSparsePCA""" _parameter_constraints: dict = { "n_components": [None, Interval(Integral, 1, None, closed="left")], "alpha": [Interval(Real, 0.0, None, closed="left")], "ridge_alpha": [Interval(Real, 0.0, None, closed="left")], "max_iter": [Interval(Integral, 0, None, closed="left")], "tol": [Interval(Real, 0.0, None, closed="left")], "method": [StrOptions({"lars", "cd"})], "n_jobs": [Integral, None], "verbose": ["verbose"], "random_state": ["random_state"], } def __init__( self, n_components=None, *, alpha=1, ridge_alpha=0.01, max_iter=1000, tol=1e-8, method="lars", n_jobs=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.verbose = verbose self.random_state = random_state @_fit_context(prefer_skip_nested_validation=True) 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` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present here for API consistency by convention. 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 return self._fit(X, n_components, random_state) 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 def inverse_transform(self, X): """Transform data from the latent space to the original space. This inversion is an approximation due to the loss of information induced by the forward decomposition. .. versionadded:: 1.2 Parameters ---------- X : ndarray of shape (n_samples, n_components) Data in the latent space. Returns ------- X_original : ndarray of shape (n_samples, n_features) Reconstructed data in the original space. """ check_is_fitted(self) X = check_array(X) return (X @ self.components_) + self.mean_ @property def _n_features_out(self): """Number of transformed output features.""" return self.components_.shape[0] def _more_tags(self): return { "preserves_dtype": [np.float64, np.float32], } class SparsePCA(_BaseSparsePCA): """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. If None, then ``n_components`` is set to ``n_features``. 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' 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 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)``. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- PCA : Principal Component Analysis implementation. MiniBatchSparsePCA : Mini batch variant of `SparsePCA` that is faster but less accurate. DictionaryLearning : Generic dictionary learning problem using a sparse code. 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... """ _parameter_constraints: dict = { **_BaseSparsePCA._parameter_constraints, "U_init": [None, np.ndarray], "V_init": [None, np.ndarray], } 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, ): super().__init__( n_components=n_components, alpha=alpha, ridge_alpha=ridge_alpha, max_iter=max_iter, tol=tol, method=method, n_jobs=n_jobs, verbose=verbose, random_state=random_state, ) self.U_init = U_init self.V_init = V_init def _fit(self, X, n_components, random_state): """Specialized `fit` for SparsePCA.""" 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 code, dictionary, 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, ) # flip eigenvectors' sign to enforce deterministic output code, dictionary = svd_flip(code, dictionary, u_based_decision=True) self.components_ = code.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 class MiniBatchSparsePCA(_BaseSparsePCA): """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. For an example comparing sparse PCA to PCA, see :ref:`sphx_glr_auto_examples_decomposition_plot_faces_decomposition.py` Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, default=None Number of sparse atoms to extract. If None, then ``n_components`` is set to ``n_features``. 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. max_iter : int, default=1_000 Maximum number of iterations over the complete dataset before stopping independently of any early stopping criterion heuristics. .. versionadded:: 1.2 .. deprecated:: 1.4 `max_iter=None` is deprecated in 1.4 and will be removed in 1.6. Use the default value (i.e. `100`) instead. 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' 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 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 `. tol : float, default=1e-3 Control early stopping based on the norm of the differences in the dictionary between 2 steps. To disable early stopping based on changes in the dictionary, set `tol` to 0.0. .. versionadded:: 1.1 max_no_improvement : int or None, default=10 Control early stopping based on the consecutive number of mini batches that does not yield an improvement on the smoothed cost function. To disable convergence detection based on cost function, set `max_no_improvement` to `None`. .. versionadded:: 1.1 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)``. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- DictionaryLearning : Find a dictionary that sparsely encodes data. IncrementalPCA : Incremental principal components analysis. PCA : Principal component analysis. SparsePCA : Sparse Principal Components Analysis. TruncatedSVD : Dimensionality reduction using truncated SVD. 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, ... max_iter=10, 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) 0.9... """ _parameter_constraints: dict = { **_BaseSparsePCA._parameter_constraints, "max_iter": [Interval(Integral, 0, None, closed="left"), Hidden(None)], "callback": [None, callable], "batch_size": [Interval(Integral, 1, None, closed="left")], "shuffle": ["boolean"], "max_no_improvement": [Interval(Integral, 0, None, closed="left"), None], } def __init__( self, n_components=None, *, alpha=1, ridge_alpha=0.01, max_iter=1_000, callback=None, batch_size=3, verbose=False, shuffle=True, n_jobs=None, method="lars", random_state=None, tol=1e-3, max_no_improvement=10, ): super().__init__( n_components=n_components, alpha=alpha, ridge_alpha=ridge_alpha, max_iter=max_iter, tol=tol, method=method, n_jobs=n_jobs, verbose=verbose, random_state=random_state, ) self.callback = callback self.batch_size = batch_size self.shuffle = shuffle self.max_no_improvement = max_no_improvement def _fit(self, X, n_components, random_state): """Specialized `fit` for MiniBatchSparsePCA.""" transform_algorithm = "lasso_" + self.method est = MiniBatchDictionaryLearning( n_components=n_components, alpha=self.alpha, max_iter=self.max_iter, dict_init=None, batch_size=self.batch_size, shuffle=self.shuffle, n_jobs=self.n_jobs, fit_algorithm=self.method, random_state=random_state, transform_algorithm=transform_algorithm, transform_alpha=self.alpha, verbose=self.verbose, callback=self.callback, tol=self.tol, max_no_improvement=self.max_no_improvement, ) est.set_output(transform="default") est.fit(X.T) self.components_, self.n_iter_ = est.transform(X.T).T, est.n_iter_ 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