"""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, 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, Number of parallel jobs to run. 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 : Degree of verbosity of the printed output. random_state : int or RandomState Pseudo number generator state used for random sampling. 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. 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=1, 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, shape (n_samples, n_features) Training vector, where n_samples in the number of samples and n_features is the number of features. Returns ------- self : object Returns the instance itself. """ random_state = check_random_state(self.random_state) X = check_array(X) 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 self.error_ = E return self def transform(self, X, ridge_alpha=None): """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. Returns ------- X_new array, shape (n_samples, n_components) Transformed data. """ check_is_fitted(self, 'components_') X = check_array(X) ridge_alpha = self.ridge_alpha if ridge_alpha is None else ridge_alpha U = ridge_regression(self.components_.T, X.T, ridge_alpha, solver='cholesky') 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, callable that gets invoked every five iterations batch_size : int, the number of features to take in each mini batch verbose : degree of output the procedure will print shuffle : boolean, whether to shuffle the data before splitting it in batches n_jobs : int, number of parallel jobs to run, or -1 to autodetect. 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 or RandomState Pseudo number generator state used for random sampling. 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. 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=1, method='lars', random_state=None): self.n_components = n_components self.alpha = alpha self.ridge_alpha = ridge_alpha self.n_iter = n_iter self.callback = callback self.batch_size = batch_size self.verbose = verbose self.shuffle = shuffle self.n_jobs = n_jobs self.method = method self.random_state = random_state 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. Returns ------- self : object Returns the instance itself. """ random_state = check_random_state(self.random_state) X = check_array(X) 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 return self