554 lines
18 KiB
Python
554 lines
18 KiB
Python
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"""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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from numbers import Integral, Real
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import numpy as np
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from ..utils import check_random_state
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from ..utils.extmath import svd_flip
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from ..utils._param_validation import Hidden, Interval, StrOptions
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from ..utils.validation import check_array, check_is_fitted
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from ..linear_model import ridge_regression
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from ..base import BaseEstimator, TransformerMixin, ClassNamePrefixFeaturesOutMixin
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from ._dict_learning import dict_learning, MiniBatchDictionaryLearning
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class _BaseSparsePCA(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
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"""Base class for SparsePCA and MiniBatchSparsePCA"""
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_parameter_constraints: dict = {
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"n_components": [None, Interval(Integral, 1, None, closed="left")],
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"alpha": [Interval(Real, 0.0, None, closed="left")],
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"ridge_alpha": [Interval(Real, 0.0, None, closed="left")],
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"max_iter": [Interval(Integral, 0, None, closed="left")],
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"tol": [Interval(Real, 0.0, None, closed="left")],
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"method": [StrOptions({"lars", "cd"})],
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"n_jobs": [Integral, None],
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"verbose": ["verbose"],
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"random_state": ["random_state"],
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}
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def __init__(
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self,
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n_components=None,
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*,
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alpha=1,
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ridge_alpha=0.01,
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max_iter=1000,
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tol=1e-8,
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method="lars",
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n_jobs=None,
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verbose=False,
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random_state=None,
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):
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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.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` is 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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Not used, present here for API consistency by convention.
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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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self._validate_params()
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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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return self._fit(X, n_components, random_state)
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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(
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self.components_.T, X.T, self.ridge_alpha, solver="cholesky"
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)
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return U
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def inverse_transform(self, X):
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"""Transform data from the latent space to the original space.
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This inversion is an approximation due to the loss of information
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induced by the forward decomposition.
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.. versionadded:: 1.2
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Parameters
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----------
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X : ndarray of shape (n_samples, n_components)
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Data in the latent space.
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Returns
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-------
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X_original : ndarray of shape (n_samples, n_features)
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Reconstructed data in the original space.
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"""
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check_is_fitted(self)
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X = check_array(X)
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return (X @ self.components_) + self.mean_
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@property
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def _n_features_out(self):
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"""Number of transformed output features."""
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return self.components_.shape[0]
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def _more_tags(self):
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return {
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"preserves_dtype": [np.float64, np.float32],
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}
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class SparsePCA(_BaseSparsePCA):
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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. If None, then ``n_components``
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is set to ``n_features``.
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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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Method to be used for optimization.
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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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n_features_in_ : int
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Number of features seen during :term:`fit`.
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.. versionadded:: 0.24
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
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Names of features seen during :term:`fit`. Defined only when `X`
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has feature names that are all strings.
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.. versionadded:: 1.0
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See Also
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--------
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PCA : Principal Component Analysis implementation.
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MiniBatchSparsePCA : Mini batch variant of `SparsePCA` that is faster but less
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accurate.
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DictionaryLearning : Generic dictionary learning problem using a sparse code.
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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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"""
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_parameter_constraints: dict = {
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**_BaseSparsePCA._parameter_constraints,
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"U_init": [None, np.ndarray],
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"V_init": [None, np.ndarray],
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}
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def __init__(
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self,
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n_components=None,
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*,
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alpha=1,
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ridge_alpha=0.01,
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max_iter=1000,
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tol=1e-8,
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method="lars",
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n_jobs=None,
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U_init=None,
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V_init=None,
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verbose=False,
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random_state=None,
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):
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super().__init__(
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n_components=n_components,
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alpha=alpha,
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ridge_alpha=ridge_alpha,
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max_iter=max_iter,
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tol=tol,
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method=method,
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n_jobs=n_jobs,
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verbose=verbose,
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random_state=random_state,
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)
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self.U_init = U_init
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self.V_init = V_init
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def _fit(self, X, n_components, random_state):
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"""Specialized `fit` for SparsePCA."""
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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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code, dictionary, E, self.n_iter_ = dict_learning(
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X.T,
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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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)
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# flip eigenvectors' sign to enforce deterministic output
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code, dictionary = svd_flip(code, dictionary, u_based_decision=False)
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self.components_ = code.T
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components_norm = np.linalg.norm(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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class MiniBatchSparsePCA(_BaseSparsePCA):
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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. If None, then ``n_components``
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is set to ``n_features``.
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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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.. deprecated:: 1.2
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`n_iter` is deprecated in 1.2 and will be removed in 1.4. Use
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`max_iter` instead.
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max_iter : int, default=None
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Maximum number of iterations over the complete dataset before
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stopping independently of any early stopping criterion heuristics.
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If `max_iter` is not `None`, `n_iter` is ignored.
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.. versionadded:: 1.2
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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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Method to be used for optimization.
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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
|
||
|
|
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 <random_state>`.
|
||
|
|
|
||
|
|
tol : float, default=1e-3
|
||
|
|
Control early stopping based on the norm of the differences in the
|
||
|
|
dictionary between 2 steps. Used only if `max_iter` is not None.
|
||
|
|
|
||
|
|
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. Used only if
|
||
|
|
`max_iter` is not None.
|
||
|
|
|
||
|
|
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"), None],
|
||
|
|
"n_iter": [
|
||
|
|
Interval(Integral, 0, None, closed="left"),
|
||
|
|
Hidden(StrOptions({"deprecated"})),
|
||
|
|
],
|
||
|
|
"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,
|
||
|
|
n_iter="deprecated",
|
||
|
|
max_iter=None,
|
||
|
|
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.n_iter = n_iter
|
||
|
|
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,
|
||
|
|
n_iter=self.n_iter,
|
||
|
|
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,
|
||
|
|
).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
|