165 lines
5.6 KiB
Python
165 lines
5.6 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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import numpy as np
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from scipy import linalg
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from ..base import BaseEstimator, TransformerMixin, ClassNamePrefixFeaturesOutMixin
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from ..utils.validation import check_is_fitted
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from abc import ABCMeta, abstractmethod
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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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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_ * np.sqrt(exp_var[:, np.newaxis])
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exp_var_diff = np.maximum(exp_var - self.noise_variance_, 0.0)
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cov = np.dot(components_.T * exp_var_diff, components_)
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cov.flat[:: len(cov) + 1] += self.noise_variance_ # modify diag inplace
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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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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 np.eye(n_features) / self.noise_variance_
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if np.isclose(self.noise_variance_, 0.0, atol=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_ * np.sqrt(exp_var[:, np.newaxis])
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exp_var_diff = np.maximum(exp_var - self.noise_variance_, 0.0)
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precision = np.dot(components_, components_.T) / self.noise_variance_
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precision.flat[:: len(precision) + 1] += 1.0 / exp_var_diff
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precision = np.dot(components_.T, np.dot(linalg.inv(precision), components_))
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precision /= -(self.noise_variance_**2)
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precision.flat[:: len(precision) + 1] += 1.0 / self.noise_variance_
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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 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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check_is_fitted(self)
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X = self._validate_data(X, dtype=[np.float64, np.float32], reset=False)
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if self.mean_ is not None:
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X = X - self.mean_
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X_transformed = np.dot(X, self.components_.T)
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if self.whiten:
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X_transformed /= np.sqrt(self.explained_variance_)
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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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if self.whiten:
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return (
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np.dot(
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X,
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np.sqrt(self.explained_variance_[:, np.newaxis]) * self.components_,
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)
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+ self.mean_
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)
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else:
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return np.dot(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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