<commit_before>"""Kernel Principal Components Analysis"""

# Author: <NAME> <<EMAIL>>
# License: BSD 3 clause

import numpy as np
from scipy import linalg
from scipy.sparse.linalg import eigsh

from ..utils import check_random_state
from ..utils.extmath import svd_flip
from ..utils.validation import check_is_fitted, _check_psd_eigenvalues
from ..exceptions import NotFittedError
from ..base import BaseEstimator, TransformerMixin
from ..preprocessing import KernelCenterer
from ..metrics.pairwise import pairwise_kernels
from ..utils.validation import _deprecate_positional_args


class KernelPCA(TransformerMixin, BaseEstimator):
    """Kernel Principal component analysis (KPCA)

    Non-linear dimensionality reduction through the use of kernels (see
    :ref:`metrics`).

    Read more in the :ref:`User Guide <kernel_PCA>`.

    Parameters
    ----------
    n_components : int, default=None
        Number of components. If None, all non-zero components are kept.

    kernel : "linear" | "poly" | "rbf" | "sigmoid" | "cosine" | "precomputed"
        Kernel. Default="linear".

    gamma : float, default=1/n_features
        Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other
        kernels.

    degree : int, default=3
        Degree for poly kernels. Ignored by other kernels.

    coef0 : float, default=1
        Independent term in poly and sigmoid kernels.
        Ignored by other kernels.

    kernel_params : mapping of string to any, default=None
        Parameters (keyword arguments) and values for kernel passed as
        callable object. Ignored by other kernels.

    alpha : int, default=1.0
        Hyperparameter of the ridge regression that learns the
        inverse transform (when fit_inverse_transform=True).

    fit_inverse_transform : bool, default=False
        Learn the inverse transform for non-precomputed kernels.
        (i.e. learn to find the pre-image of a point)

    eigen_solver : string ['auto'|'dense'|'arpack'], default='auto'
        Select eigensolver to use. If n_components is much less than
        the number of training samples, arpack may be more efficient
        than the dense eigensolver.

    tol : float, default=0
        Convergence tolerance for arpack.
        If 0, optimal value will be chosen by arpack.

    max_iter : int, default=None
        Maximum number of iterations for arpack.
        If None, optimal value will be chosen by arpack.

    remove_zero_eig : boolean, default=False
        If True, then all components with zero eigenvalues are removed, so
        that the number of components in the output may be < n_components
        (and sometimes even zero due to numerical instability).
        When n_components is None, this parameter is ignored and components
        with zero eigenvalues are removed regardless.

    random_state : int, RandomState instance, default=None
        Used when ``eigen_solver`` == 'arpack'. Pass an int for reproducible
        results across multiple function calls.
        See :term:`Glossary <random_state>`.

        .. versionadded:: 0.18

    copy_X : boolean, default=True
        If True, input X is copied and stored by the model in the `X_fit_`
        attribute. If no further changes will be done to X, setting
        `copy_X=False` saves memory by storing a reference.

        .. versionadded:: 0.18

    n_jobs : int or None, optional (default=None)
        The number of parallel jobs to run.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

        .. versionadded:: 0.18

    Attributes
    ----------
    lambdas_ : array, (n_components,)
        Eigenvalues of the centered kernel matrix in decreasing order.
        If `n_components` and `remove_zero_eig` are not set,
        then all values are stored.

    alphas_ : array, (n_samples, n_components)
        Eigenvectors of the centered kernel matrix. If `n_components` and
        `remove_zero_eig` are not set, then all components are stored.

    dual_coef_ : array, (n_samples, n_features)
        Inverse transform matrix. Only available when
        ``fit_inverse_transform`` is True.

    X_transformed_fit_ : array, (n_samples, n_components)
        Projection of the fitted data on the kernel principal components.
        Only available when ``fit_inverse_transform`` is True.

    X_fit_ : (n_samples, n_features)
        The data used to fit the model. If `copy_X=False`, then `X_fit_` is
        a reference. This attribute is used for the calls to transform.

    Examples
    --------
    >>> from sklearn.datasets import load_digits
    >>> from sklearn.decomposition import KernelPCA
    >>> X, _ = load_digits(return_X_y=True)
    >>> transformer = KernelPCA(n_components=7, kernel='linear')
    >>> X_transformed = transformer.fit_transform(X)
    >>> X_transformed.shape
    (1797, 7)<commit_msg>DOC improve attributes and parameters descriptions in KernelPCA (#17747)<commit_after>"""Kernel Principal Components Analysis"""

# Author: <NAME> <<EMAIL>>
# License: BSD 3 clause

import numpy as np
from scipy import linalg
from scipy.sparse.linalg import eigsh

from ..utils import check_random_state
from ..utils.extmath import svd_flip
from ..utils.validation import check_is_fitted, _check_psd_eigenvalues
from ..exceptions import NotFittedError
from ..base import BaseEstimator, TransformerMixin
from ..preprocessing import KernelCenterer
from ..metrics.pairwise import pairwise_kernels
from ..utils.validation import _deprecate_positional_args


class KernelPCA(TransformerMixin, BaseEstimator):
    """Kernel Principal component analysis (KPCA)

    Non-linear dimensionality reduction through the use of kernels (see
    :ref:`metrics`).

    Read more in the :ref:`User Guide <kernel_PCA>`.

    Parameters
    ----------
    n_components : int, default=None
        Number of components. If None, all non-zero components are kept.

    kernel : {'linear', 'poly', \
            'rbf', 'sigmoid', 'cosine', 'precomputed'}, default='linear'
        Kernel used for PCA.

    gamma : float, default=1/n_features
        Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other
        kernels.

    degree : int, default=3
        Degree for poly kernels. Ignored by other kernels.

    coef0 : float, default=1
        Independent term in poly and sigmoid kernels.
        Ignored by other kernels.

    kernel_params : dict, default=None
        Parameters (keyword arguments) and
        values for kernel passed as callable object.
        Ignored by other kernels.

    alpha : float, default=1.0
        Hyperparameter of the ridge regression that learns the
        inverse transform (when fit_inverse_transform=True).

    fit_inverse_transform : bool, default=False
        Learn the inverse transform for non-precomputed kernels.
        (i.e. learn to find the pre-image of a point)

    eigen_solver : {'auto', 'dense', 'arpack'}, default='auto'
        Select eigensolver to use. If n_components is much less than
        the number of training samples, arpack may be more efficient
        than the dense eigensolver.

    tol : float, default=0
        Convergence tolerance for arpack.
        If 0, optimal value will be chosen by arpack.

    max_iter : int, default=None
        Maximum number of iterations for arpack.
        If None, optimal value will be chosen by arpack.

    remove_zero_eig : bool, default=False
        If True, then all components with zero eigenvalues are removed, so
        that the number of components in the output may be < n_components
        (and sometimes even zero due to numerical instability).
        When n_components is None, this parameter is ignored and components
        with zero eigenvalues are removed regardless.

    random_state : int, RandomState instance, default=None
        Used when ``eigen_solver`` == 'arpack'. Pass an int for reproducible
        results across multiple function calls.
        See :term:`Glossary <random_state>`.

        .. versionadded:: 0.18

    copy_X : bool, default=True
        If True, input X is copied and stored by the model in the `X_fit_`
        attribute. If no further changes will be done to X, setting
        `copy_X=False` saves memory by storing a reference.

        .. versionadded:: 0.18

    n_jobs : int, default=None
        The number of parallel jobs to run.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

        .. versionadded:: 0.18

    Attributes
    ----------
    lambdas_ : ndarray of shape (n_components,)
        Eigenvalues of the centered kernel matrix in decreasing order.
        If `n_components` and `remove_zero_eig` are not set,
        then all values are stored.

    alphas_ : ndarray of shape (n_samples, n_components)
        Eigenvectors of the centered kernel matrix. If `n_components` and
        `remove_zero_eig` are not set, then all components are stored.

    dual_coef_ : ndarray of shape (n_samples, n_features)
        Inverse transform matrix. Only available when
        ``fit_inverse_transform`` is True.

    X_transformed_fit_ : ndarray of shape (n_samples, n_components)
        Projection of the fitted data on the kernel principal components.
        Only available when ``fit_inverse_transform`` is True.

    X_fit_ : ndarray of shape (n_samples, n_features)
        The data used to fit the model. If `copy_X=False`, then `X_fit_` is
        a reference. This attribute is used for the calls to transform.

    Examples
    --------
    >>> from sklearn.datasets import load_digits
    >>> from sklearn.decomposition import KernelPCA
    >>> X, _ = load_digits(return_X_y=True)
    >>> transformer = KernelPCA(n_components=7, kernel='linear')
    >>> X_transformed = transformer.fit_transform(X)
    >>> X_transformed.shape
    (1797, 7)
{'fraction_non_alphanumeric': 0.07676969092721835, 'fraction_numerical': 0.005682951146560319, 'mean_word_length': 2.916829363529871, 'pattern_counts': {'":': 0, '<': 17, '<?xml version=': 0, '>': 51, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '5612145', 'n_tokens_mistral': 2902, 'n_tokens_neox': 2695, 'n_words': 1079}