365 lines
12 KiB
Python
365 lines
12 KiB
Python
"""Matrix factorization with Sparse PCA."""
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# Author: Vlad Niculae, Gael Varoquaux, Alexandre Gramfort
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# License: BSD 3 clause
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import numpy as np
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from ..utils import check_random_state
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from ..utils.validation import check_is_fitted
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from ..utils.validation import _deprecate_positional_args
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from ..linear_model import ridge_regression
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from ..base import BaseEstimator, TransformerMixin
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from ._dict_learning import dict_learning, dict_learning_online
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class SparsePCA(TransformerMixin, BaseEstimator):
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"""Sparse Principal Components Analysis (SparsePCA).
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Finds the set of sparse components that can optimally reconstruct
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the data. The amount of sparseness is controllable by the coefficient
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of the L1 penalty, given by the parameter alpha.
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Read more in the :ref:`User Guide <SparsePCA>`.
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Parameters
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----------
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n_components : int, default=None
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Number of sparse atoms to extract.
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alpha : float, default=1
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Sparsity controlling parameter. Higher values lead to sparser
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components.
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ridge_alpha : float, default=0.01
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Amount of ridge shrinkage to apply in order to improve
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conditioning when calling the transform method.
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max_iter : int, default=1000
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Maximum number of iterations to perform.
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tol : float, default=1e-8
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Tolerance for the stopping condition.
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method : {'lars', 'cd'}, default='lars'
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lars: uses the least angle regression method to solve the lasso problem
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(linear_model.lars_path)
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cd: uses the coordinate descent method to compute the
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Lasso solution (linear_model.Lasso). Lars will be faster if
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the estimated components are sparse.
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n_jobs : int, default=None
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Number of parallel jobs to run.
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``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
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``-1`` means using all processors. See :term:`Glossary <n_jobs>`
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for more details.
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U_init : ndarray of shape (n_samples, n_components), default=None
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Initial values for the loadings for warm restart scenarios. Only used
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if `U_init` and `V_init` are not None.
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V_init : ndarray of shape (n_components, n_features), default=None
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Initial values for the components for warm restart scenarios. Only used
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if `U_init` and `V_init` are not None.
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verbose : int or bool, default=False
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Controls the verbosity; the higher, the more messages. Defaults to 0.
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random_state : int, RandomState instance or None, default=None
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Used during dictionary learning. Pass an int for reproducible results
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across multiple function calls.
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See :term:`Glossary <random_state>`.
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Attributes
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----------
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components_ : ndarray of shape (n_components, n_features)
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Sparse components extracted from the data.
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error_ : ndarray
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Vector of errors at each iteration.
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n_components_ : int
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Estimated number of components.
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.. versionadded:: 0.23
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n_iter_ : int
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Number of iterations run.
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mean_ : ndarray of shape (n_features,)
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Per-feature empirical mean, estimated from the training set.
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Equal to ``X.mean(axis=0)``.
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Examples
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--------
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>>> import numpy as np
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>>> from sklearn.datasets import make_friedman1
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>>> from sklearn.decomposition import SparsePCA
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>>> X, _ = make_friedman1(n_samples=200, n_features=30, random_state=0)
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>>> transformer = SparsePCA(n_components=5, random_state=0)
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>>> transformer.fit(X)
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SparsePCA(...)
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>>> X_transformed = transformer.transform(X)
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>>> X_transformed.shape
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(200, 5)
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>>> # most values in the components_ are zero (sparsity)
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>>> np.mean(transformer.components_ == 0)
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0.9666...
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See Also
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--------
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PCA
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MiniBatchSparsePCA
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DictionaryLearning
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"""
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@_deprecate_positional_args
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def __init__(self, n_components=None, *, alpha=1, ridge_alpha=0.01,
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max_iter=1000, tol=1e-8, method='lars', n_jobs=None,
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U_init=None, V_init=None, verbose=False, random_state=None):
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self.n_components = n_components
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self.alpha = alpha
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self.ridge_alpha = ridge_alpha
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self.max_iter = max_iter
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self.tol = tol
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self.method = method
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self.n_jobs = n_jobs
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self.U_init = U_init
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self.V_init = V_init
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self.verbose = verbose
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self.random_state = random_state
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def fit(self, X, y=None):
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"""Fit the model from data in X.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Training vector, where n_samples in the number of samples
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and n_features is the number of features.
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y : Ignored
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Returns
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-------
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self : object
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Returns the instance itself.
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"""
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random_state = check_random_state(self.random_state)
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X = self._validate_data(X)
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self.mean_ = X.mean(axis=0)
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X = X - self.mean_
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if self.n_components is None:
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n_components = X.shape[1]
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else:
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n_components = self.n_components
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code_init = self.V_init.T if self.V_init is not None else None
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dict_init = self.U_init.T if self.U_init is not None else None
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Vt, _, E, self.n_iter_ = dict_learning(X.T, n_components,
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alpha=self.alpha,
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tol=self.tol,
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max_iter=self.max_iter,
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method=self.method,
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n_jobs=self.n_jobs,
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verbose=self.verbose,
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random_state=random_state,
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code_init=code_init,
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dict_init=dict_init,
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return_n_iter=True)
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self.components_ = Vt.T
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components_norm = np.linalg.norm(
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self.components_, axis=1)[:, np.newaxis]
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components_norm[components_norm == 0] = 1
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self.components_ /= components_norm
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self.n_components_ = len(self.components_)
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self.error_ = E
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return self
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def transform(self, X):
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"""Least Squares projection of the data onto the sparse components.
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To avoid instability issues in case the system is under-determined,
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regularization can be applied (Ridge regression) via the
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`ridge_alpha` parameter.
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Note that Sparse PCA components orthogonality is not enforced as in PCA
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hence one cannot use a simple linear projection.
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Parameters
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----------
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X : ndarray of shape (n_samples, n_features)
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Test data to be transformed, must have the same number of
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features as the data used to train the model.
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Returns
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-------
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X_new : ndarray of shape (n_samples, n_components)
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Transformed data.
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"""
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check_is_fitted(self)
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X = self._validate_data(X, reset=False)
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X = X - self.mean_
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U = ridge_regression(self.components_.T, X.T, self.ridge_alpha,
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solver='cholesky')
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return U
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class MiniBatchSparsePCA(SparsePCA):
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"""Mini-batch Sparse Principal Components Analysis
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Finds the set of sparse components that can optimally reconstruct
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the data. The amount of sparseness is controllable by the coefficient
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of the L1 penalty, given by the parameter alpha.
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Read more in the :ref:`User Guide <SparsePCA>`.
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Parameters
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----------
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n_components : int, default=None
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number of sparse atoms to extract
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alpha : int, default=1
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Sparsity controlling parameter. Higher values lead to sparser
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components.
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ridge_alpha : float, default=0.01
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Amount of ridge shrinkage to apply in order to improve
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conditioning when calling the transform method.
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n_iter : int, default=100
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number of iterations to perform for each mini batch
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callback : callable, default=None
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callable that gets invoked every five iterations
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batch_size : int, default=3
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the number of features to take in each mini batch
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verbose : int or bool, default=False
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Controls the verbosity; the higher, the more messages. Defaults to 0.
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shuffle : bool, default=True
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whether to shuffle the data before splitting it in batches
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n_jobs : int, default=None
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Number of parallel jobs to run.
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``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
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``-1`` means using all processors. See :term:`Glossary <n_jobs>`
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for more details.
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method : {'lars', 'cd'}, default='lars'
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lars: uses the least angle regression method to solve the lasso problem
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(linear_model.lars_path)
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cd: uses the coordinate descent method to compute the
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Lasso solution (linear_model.Lasso). Lars will be faster if
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the estimated components are sparse.
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random_state : int, RandomState instance or None, default=None
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Used for random shuffling when ``shuffle`` is set to ``True``,
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during online dictionary learning. Pass an int for reproducible results
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across multiple function calls.
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See :term:`Glossary <random_state>`.
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Attributes
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----------
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components_ : ndarray of shape (n_components, n_features)
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Sparse components extracted from the data.
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n_components_ : int
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Estimated number of components.
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.. versionadded:: 0.23
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n_iter_ : int
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Number of iterations run.
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mean_ : ndarray of shape (n_features,)
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Per-feature empirical mean, estimated from the training set.
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Equal to ``X.mean(axis=0)``.
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Examples
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--------
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>>> import numpy as np
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>>> from sklearn.datasets import make_friedman1
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>>> from sklearn.decomposition import MiniBatchSparsePCA
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>>> X, _ = make_friedman1(n_samples=200, n_features=30, random_state=0)
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>>> transformer = MiniBatchSparsePCA(n_components=5, batch_size=50,
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... random_state=0)
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>>> transformer.fit(X)
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MiniBatchSparsePCA(...)
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>>> X_transformed = transformer.transform(X)
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>>> X_transformed.shape
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(200, 5)
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>>> # most values in the components_ are zero (sparsity)
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>>> np.mean(transformer.components_ == 0)
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0.94
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See Also
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--------
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PCA
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SparsePCA
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DictionaryLearning
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"""
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@_deprecate_positional_args
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def __init__(self, n_components=None, *, alpha=1, ridge_alpha=0.01,
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n_iter=100, callback=None, batch_size=3, verbose=False,
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shuffle=True, n_jobs=None, method='lars', random_state=None):
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super().__init__(
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n_components=n_components, alpha=alpha, verbose=verbose,
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ridge_alpha=ridge_alpha, n_jobs=n_jobs, method=method,
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random_state=random_state)
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self.n_iter = n_iter
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self.callback = callback
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self.batch_size = batch_size
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self.shuffle = shuffle
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def fit(self, X, y=None):
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"""Fit the model from data in X.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Training vector, where n_samples in the number of samples
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and n_features is the number of features.
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y : Ignored
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Returns
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-------
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self : object
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Returns the instance itself.
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"""
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random_state = check_random_state(self.random_state)
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X = self._validate_data(X)
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self.mean_ = X.mean(axis=0)
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X = X - self.mean_
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if self.n_components is None:
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n_components = X.shape[1]
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else:
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n_components = self.n_components
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Vt, _, self.n_iter_ = dict_learning_online(
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X.T, n_components, alpha=self.alpha,
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n_iter=self.n_iter, return_code=True,
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dict_init=None, verbose=self.verbose,
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callback=self.callback,
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batch_size=self.batch_size,
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shuffle=self.shuffle,
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n_jobs=self.n_jobs, method=self.method,
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random_state=random_state,
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return_n_iter=True)
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self.components_ = Vt.T
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components_norm = np.linalg.norm(
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self.components_, axis=1)[:, np.newaxis]
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components_norm[components_norm == 0] = 1
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self.components_ /= components_norm
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self.n_components_ = len(self.components_)
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return self
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