_base.py

"""Principal Component Analysis Base Classes"""

# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#         Olivier Grisel <olivier.grisel@ensta.org>
#         Mathieu Blondel <mathieu@mblondel.org>
#         Denis A. Engemann <denis-alexander.engemann@inria.fr>
#         Kyle Kastner <kastnerkyle@gmail.com>
#
# License: BSD 3 clause

import numpy as np
from scipy import linalg

from ..base import BaseEstimator, TransformerMixin, ClassNamePrefixFeaturesOutMixin
from ..utils.validation import check_is_fitted
from abc import ABCMeta, abstractmethod


class _BasePCA(
    ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator, metaclass=ABCMeta
):
    """Base class for PCA methods.

    Warning: This class should not be used directly.
    Use derived classes instead.
    """

    def get_covariance(self):
        """Compute data covariance with the generative model.

        ``cov = components_.T * S**2 * components_ + sigma2 * eye(n_features)``
        where S**2 contains the explained variances, and sigma2 contains the
        noise variances.

        Returns
        -------
        cov : array of shape=(n_features, n_features)
            Estimated covariance of data.
        """
        components_ = self.components_
        exp_var = self.explained_variance_
        if self.whiten:
            components_ = components_ * np.sqrt(exp_var[:, np.newaxis])
        exp_var_diff = np.maximum(exp_var - self.noise_variance_, 0.0)
        cov = np.dot(components_.T * exp_var_diff, components_)
        cov.flat[:: len(cov) + 1] += self.noise_variance_  # modify diag inplace
        return cov

    def get_precision(self):
        """Compute data precision matrix with the generative model.

        Equals the inverse of the covariance but computed with
        the matrix inversion lemma for efficiency.

        Returns
        -------
        precision : array, shape=(n_features, n_features)
            Estimated precision of data.
        """
        n_features = self.components_.shape[1]

        # handle corner cases first
        if self.n_components_ == 0:
            return np.eye(n_features) / self.noise_variance_

        if np.isclose(self.noise_variance_, 0.0, atol=0.0):
            return linalg.inv(self.get_covariance())

        # Get precision using matrix inversion lemma
        components_ = self.components_
        exp_var = self.explained_variance_
        if self.whiten:
            components_ = components_ * np.sqrt(exp_var[:, np.newaxis])
        exp_var_diff = np.maximum(exp_var - self.noise_variance_, 0.0)
        precision = np.dot(components_, components_.T) / self.noise_variance_
        precision.flat[:: len(precision) + 1] += 1.0 / exp_var_diff
        precision = np.dot(components_.T, np.dot(linalg.inv(precision), components_))
        precision /= -(self.noise_variance_**2)
        precision.flat[:: len(precision) + 1] += 1.0 / self.noise_variance_
        return precision

    @abstractmethod
    def fit(self, X, y=None):
        """Placeholder for fit. Subclasses should implement this method!

        Fit the model with X.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Training data, where `n_samples` is the number of samples and
            `n_features` is the number of features.

        Returns
        -------
        self : object
            Returns the instance itself.
        """

    def transform(self, X):
        """Apply dimensionality reduction to X.

        X is projected on the first principal components previously extracted
        from a training set.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            New data, where `n_samples` is the number of samples
            and `n_features` is the number of features.

        Returns
        -------
        X_new : array-like of shape (n_samples, n_components)
            Projection of X in the first principal components, where `n_samples`
            is the number of samples and `n_components` is the number of the components.
        """
        check_is_fitted(self)

        X = self._validate_data(X, dtype=[np.float64, np.float32], reset=False)
        if self.mean_ is not None:
            X = X - self.mean_
        X_transformed = np.dot(X, self.components_.T)
        if self.whiten:
            X_transformed /= np.sqrt(self.explained_variance_)
        return X_transformed

    def inverse_transform(self, X):
        """Transform data back to its original space.

        In other words, return an input `X_original` whose transform would be X.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_components)
            New data, where `n_samples` is the number of samples
            and `n_components` is the number of components.

        Returns
        -------
        X_original array-like of shape (n_samples, n_features)
            Original data, where `n_samples` is the number of samples
            and `n_features` is the number of features.

        Notes
        -----
        If whitening is enabled, inverse_transform will compute the
        exact inverse operation, which includes reversing whitening.
        """
        if self.whiten:
            return (
                np.dot(
                    X,
                    np.sqrt(self.explained_variance_[:, np.newaxis]) * self.components_,
                )
                + self.mean_
            )
        else:
            return np.dot(X, self.components_) + self.mean_

    @property
    def _n_features_out(self):
        """Number of transformed output features."""
        return self.components_.shape[0]