204 lines
7.1 KiB
Python
204 lines
7.1 KiB
Python
"""Principal Component Analysis Base Classes"""
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# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# Olivier Grisel <olivier.grisel@ensta.org>
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# Mathieu Blondel <mathieu@mblondel.org>
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# Denis A. Engemann <denis-alexander.engemann@inria.fr>
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# Kyle Kastner <kastnerkyle@gmail.com>
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#
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# License: BSD 3 clause
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from abc import ABCMeta, abstractmethod
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import numpy as np
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from scipy import linalg
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from ..base import BaseEstimator, ClassNamePrefixFeaturesOutMixin, TransformerMixin
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from ..utils._array_api import _add_to_diagonal, device, get_namespace
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from ..utils.validation import check_is_fitted
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class _BasePCA(
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ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator, metaclass=ABCMeta
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):
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"""Base class for PCA methods.
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Warning: This class should not be used directly.
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Use derived classes instead.
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"""
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def get_covariance(self):
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"""Compute data covariance with the generative model.
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``cov = components_.T * S**2 * components_ + sigma2 * eye(n_features)``
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where S**2 contains the explained variances, and sigma2 contains the
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noise variances.
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Returns
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-------
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cov : array of shape=(n_features, n_features)
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Estimated covariance of data.
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"""
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xp, _ = get_namespace(self.components_)
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components_ = self.components_
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exp_var = self.explained_variance_
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if self.whiten:
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components_ = components_ * xp.sqrt(exp_var[:, np.newaxis])
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exp_var_diff = exp_var - self.noise_variance_
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exp_var_diff = xp.where(
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exp_var > self.noise_variance_,
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exp_var_diff,
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xp.asarray(0.0, device=device(exp_var)),
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)
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cov = (components_.T * exp_var_diff) @ components_
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_add_to_diagonal(cov, self.noise_variance_, xp)
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return cov
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def get_precision(self):
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"""Compute data precision matrix with the generative model.
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Equals the inverse of the covariance but computed with
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the matrix inversion lemma for efficiency.
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Returns
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-------
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precision : array, shape=(n_features, n_features)
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Estimated precision of data.
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"""
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xp, is_array_api_compliant = get_namespace(self.components_)
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n_features = self.components_.shape[1]
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# handle corner cases first
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if self.n_components_ == 0:
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return xp.eye(n_features) / self.noise_variance_
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if is_array_api_compliant:
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linalg_inv = xp.linalg.inv
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else:
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linalg_inv = linalg.inv
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if self.noise_variance_ == 0.0:
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return linalg_inv(self.get_covariance())
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# Get precision using matrix inversion lemma
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components_ = self.components_
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exp_var = self.explained_variance_
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if self.whiten:
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components_ = components_ * xp.sqrt(exp_var[:, np.newaxis])
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exp_var_diff = exp_var - self.noise_variance_
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exp_var_diff = xp.where(
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exp_var > self.noise_variance_,
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exp_var_diff,
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xp.asarray(0.0, device=device(exp_var)),
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)
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precision = components_ @ components_.T / self.noise_variance_
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_add_to_diagonal(precision, 1.0 / exp_var_diff, xp)
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precision = components_.T @ linalg_inv(precision) @ components_
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precision /= -(self.noise_variance_**2)
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_add_to_diagonal(precision, 1.0 / self.noise_variance_, xp)
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return precision
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@abstractmethod
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def fit(self, X, y=None):
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"""Placeholder for fit. Subclasses should implement this method!
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Fit the model with 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 data, where `n_samples` is the number of samples and
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`n_features` is the number of features.
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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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def transform(self, X):
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"""Apply dimensionality reduction to X.
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X is projected on the first principal components previously extracted
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from a training set.
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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New data, where `n_samples` is the number of samples
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and `n_features` is the number of features.
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Returns
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-------
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X_new : array-like of shape (n_samples, n_components)
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Projection of X in the first principal components, where `n_samples`
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is the number of samples and `n_components` is the number of the components.
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"""
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xp, _ = get_namespace(X, self.components_, self.explained_variance_)
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check_is_fitted(self)
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X = self._validate_data(
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X, dtype=[xp.float64, xp.float32], accept_sparse=("csr", "csc"), reset=False
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)
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return self._transform(X, xp=xp, x_is_centered=False)
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def _transform(self, X, xp, x_is_centered=False):
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X_transformed = X @ self.components_.T
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if not x_is_centered:
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# Apply the centering after the projection.
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# For dense X this avoids copying or mutating the data passed by
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# the caller.
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# For sparse X it keeps sparsity and avoids having to wrap X into
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# a linear operator.
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X_transformed -= xp.reshape(self.mean_, (1, -1)) @ self.components_.T
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if self.whiten:
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# For some solvers (such as "arpack" and "covariance_eigh"), on
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# rank deficient data, some components can have a variance
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# arbitrarily close to zero, leading to non-finite results when
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# whitening. To avoid this problem we clip the variance below.
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scale = xp.sqrt(self.explained_variance_)
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min_scale = xp.finfo(scale.dtype).eps
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scale[scale < min_scale] = min_scale
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X_transformed /= scale
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return X_transformed
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def inverse_transform(self, X):
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"""Transform data back to its original space.
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In other words, return an input `X_original` whose transform would be X.
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Parameters
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----------
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X : array-like of shape (n_samples, n_components)
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New data, where `n_samples` is the number of samples
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and `n_components` is the number of components.
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Returns
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-------
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X_original array-like of shape (n_samples, n_features)
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Original data, where `n_samples` is the number of samples
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and `n_features` is the number of features.
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Notes
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-----
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If whitening is enabled, inverse_transform will compute the
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exact inverse operation, which includes reversing whitening.
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"""
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xp, _ = get_namespace(X)
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if self.whiten:
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scaled_components = (
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xp.sqrt(self.explained_variance_[:, np.newaxis]) * self.components_
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)
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return X @ scaled_components + self.mean_
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else:
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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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