_classes.py

import numpy as np

from ._base import _fit_liblinear, BaseSVC, BaseLibSVM
from ..base import BaseEstimator, RegressorMixin, OutlierMixin
from ..linear_model._base import LinearClassifierMixin, SparseCoefMixin, \
    LinearModel
from ..utils.validation import _num_samples
from ..utils.validation import _deprecate_positional_args
from ..utils.multiclass import check_classification_targets
from ..utils.deprecation import deprecated


class LinearSVC(BaseEstimator, LinearClassifierMixin,
                SparseCoefMixin):
    """Linear Support Vector Classification.

    Similar to SVC with parameter kernel='linear', but implemented in terms of
    liblinear rather than libsvm, so it has more flexibility in the choice of
    penalties and loss functions and should scale better to large numbers of
    samples.

    This class supports both dense and sparse input and the multiclass support
    is handled according to a one-vs-the-rest scheme.

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

    Parameters
    ----------
    penalty : {'l1', 'l2'}, default='l2'
        Specifies the norm used in the penalization. The 'l2'
        penalty is the standard used in SVC. The 'l1' leads to ``coef_``
        vectors that are sparse.

    loss : {'hinge', 'squared_hinge'}, default='squared_hinge'
        Specifies the loss function. 'hinge' is the standard SVM loss
        (used e.g. by the SVC class) while 'squared_hinge' is the
        square of the hinge loss.

    dual : bool, default=True
        Select the algorithm to either solve the dual or primal
        optimization problem. Prefer dual=False when n_samples > n_features.

    tol : float, default=1e-4
        Tolerance for stopping criteria.

    C : float, default=1.0
        Regularization parameter. The strength of the regularization is
        inversely proportional to C. Must be strictly positive.

    multi_class : {'ovr', 'crammer_singer'}, default='ovr'
        Determines the multi-class strategy if `y` contains more than
        two classes.
        ``"ovr"`` trains n_classes one-vs-rest classifiers, while
        ``"crammer_singer"`` optimizes a joint objective over all classes.
        While `crammer_singer` is interesting from a theoretical perspective
        as it is consistent, it is seldom used in practice as it rarely leads
        to better accuracy and is more expensive to compute.
        If ``"crammer_singer"`` is chosen, the options loss, penalty and dual
        will be ignored.

    fit_intercept : bool, default=True
        Whether to calculate the intercept for this model. If set
        to false, no intercept will be used in calculations
        (i.e. data is expected to be already centered).

    intercept_scaling : float, default=1
        When self.fit_intercept is True, instance vector x becomes
        ``[x, self.intercept_scaling]``,
        i.e. a "synthetic" feature with constant value equals to
        intercept_scaling is appended to the instance vector.
        The intercept becomes intercept_scaling * synthetic feature weight
        Note! the synthetic feature weight is subject to l1/l2 regularization
        as all other features.
        To lessen the effect of regularization on synthetic feature weight
        (and therefore on the intercept) intercept_scaling has to be increased.

    class_weight : dict or 'balanced', default=None
        Set the parameter C of class i to ``class_weight[i]*C`` for
        SVC. If not given, all classes are supposed to have
        weight one.
        The "balanced" mode uses the values of y to automatically adjust
        weights inversely proportional to class frequencies in the input data
        as ``n_samples / (n_classes * np.bincount(y))``.

    verbose : int, default=0
        Enable verbose output. Note that this setting takes advantage of a
        per-process runtime setting in liblinear that, if enabled, may not work
        properly in a multithreaded context.

    random_state : int or RandomState instance, default=None
        Controls the pseudo random number generation for shuffling the data for
        the dual coordinate descent (if ``dual=True``). When ``dual=False`` the
        underlying implementation of :class:`LinearSVC` is not random and
        ``random_state`` has no effect on the results.
        Pass an int for reproducible output across multiple function calls.
        See :term:`Glossary <random_state>`.

    max_iter : int, default=1000
        The maximum number of iterations to be run.

    Attributes
    ----------
    coef_ : ndarray of shape (1, n_features) if n_classes == 2 \
            else (n_classes, n_features)
        Weights assigned to the features (coefficients in the primal
        problem). This is only available in the case of a linear kernel.

        ``coef_`` is a readonly property derived from ``raw_coef_`` that
        follows the internal memory layout of liblinear.

    intercept_ : ndarray of shape (1,) if n_classes == 2 else (n_classes,)
        Constants in decision function.

    classes_ : ndarray of shape (n_classes,)
        The unique classes labels.

    n_iter_ : int
        Maximum number of iterations run across all classes.

    See Also
    --------
    SVC
        Implementation of Support Vector Machine classifier using libsvm:
        the kernel can be non-linear but its SMO algorithm does not
        scale to large number of samples as LinearSVC does.

        Furthermore SVC multi-class mode is implemented using one
        vs one scheme while LinearSVC uses one vs the rest. It is
        possible to implement one vs the rest with SVC by using the
        :class:`sklearn.multiclass.OneVsRestClassifier` wrapper.

        Finally SVC can fit dense data without memory copy if the input
        is C-contiguous. Sparse data will still incur memory copy though.

    sklearn.linear_model.SGDClassifier
        SGDClassifier can optimize the same cost function as LinearSVC
        by adjusting the penalty and loss parameters. In addition it requires
        less memory, allows incremental (online) learning, and implements
        various loss functions and regularization regimes.

    Notes
    -----
    The underlying C implementation uses a random number generator to
    select features when fitting the model. It is thus not uncommon
    to have slightly different results for the same input data. If
    that happens, try with a smaller ``tol`` parameter.

    The underlying implementation, liblinear, uses a sparse internal
    representation for the data that will incur a memory copy.

    Predict output may not match that of standalone liblinear in certain
    cases. See :ref:`differences from liblinear <liblinear_differences>`
    in the narrative documentation.

    References
    ----------
    `LIBLINEAR: A Library for Large Linear Classification
    <https://www.csie.ntu.edu.tw/~cjlin/liblinear/>`__

    Examples
    --------
    >>> from sklearn.svm import LinearSVC
    >>> from sklearn.pipeline import make_pipeline
    >>> from sklearn.preprocessing import StandardScaler
    >>> from sklearn.datasets import make_classification
    >>> X, y = make_classification(n_features=4, random_state=0)
    >>> clf = make_pipeline(StandardScaler(),
    ...                     LinearSVC(random_state=0, tol=1e-5))
    >>> clf.fit(X, y)
    Pipeline(steps=[('standardscaler', StandardScaler()),
                    ('linearsvc', LinearSVC(random_state=0, tol=1e-05))])

    >>> print(clf.named_steps['linearsvc'].coef_)
    [[0.141...   0.526... 0.679... 0.493...]]

    >>> print(clf.named_steps['linearsvc'].intercept_)
    [0.1693...]
    >>> print(clf.predict([[0, 0, 0, 0]]))
    [1]
    """
    @_deprecate_positional_args
    def __init__(self, penalty='l2', loss='squared_hinge', *, dual=True,
                 tol=1e-4, C=1.0, multi_class='ovr', fit_intercept=True,
                 intercept_scaling=1, class_weight=None, verbose=0,
                 random_state=None, max_iter=1000):
        self.dual = dual
        self.tol = tol
        self.C = C
        self.multi_class = multi_class
        self.fit_intercept = fit_intercept
        self.intercept_scaling = intercept_scaling
        self.class_weight = class_weight
        self.verbose = verbose
        self.random_state = random_state
        self.max_iter = max_iter
        self.penalty = penalty
        self.loss = loss

    def fit(self, X, y, sample_weight=None):
        """Fit the model according to the given training data.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            Training vector, where n_samples in the number of samples and
            n_features is the number of features.

        y : array-like of shape (n_samples,)
            Target vector relative to X.

        sample_weight : array-like of shape (n_samples,), default=None
            Array of weights that are assigned to individual
            samples. If not provided,
            then each sample is given unit weight.

            .. versionadded:: 0.18

        Returns
        -------
        self : object
            An instance of the estimator.
        """
        if self.C < 0:
            raise ValueError("Penalty term must be positive; got (C=%r)"
                             % self.C)

        X, y = self._validate_data(X, y, accept_sparse='csr',
                                   dtype=np.float64, order="C",
                                   accept_large_sparse=False)
        check_classification_targets(y)
        self.classes_ = np.unique(y)

        self.coef_, self.intercept_, self.n_iter_ = _fit_liblinear(
            X, y, self.C, self.fit_intercept, self.intercept_scaling,
            self.class_weight, self.penalty, self.dual, self.verbose,
            self.max_iter, self.tol, self.random_state, self.multi_class,
            self.loss, sample_weight=sample_weight)

        if self.multi_class == "crammer_singer" and len(self.classes_) == 2:
            self.coef_ = (self.coef_[1] - self.coef_[0]).reshape(1, -1)
            if self.fit_intercept:
                intercept = self.intercept_[1] - self.intercept_[0]
                self.intercept_ = np.array([intercept])

        return self


class LinearSVR(RegressorMixin, LinearModel):
    """Linear Support Vector Regression.

    Similar to SVR with parameter kernel='linear', but implemented in terms of
    liblinear rather than libsvm, so it has more flexibility in the choice of
    penalties and loss functions and should scale better to large numbers of
    samples.

    This class supports both dense and sparse input.

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

    .. versionadded:: 0.16

    Parameters
    ----------
    epsilon : float, default=0.0
        Epsilon parameter in the epsilon-insensitive loss function. Note
        that the value of this parameter depends on the scale of the target
        variable y. If unsure, set ``epsilon=0``.

    tol : float, default=1e-4
        Tolerance for stopping criteria.

    C : float, default=1.0
        Regularization parameter. The strength of the regularization is
        inversely proportional to C. Must be strictly positive.

    loss : {'epsilon_insensitive', 'squared_epsilon_insensitive'}, \
            default='epsilon_insensitive'
        Specifies the loss function. The epsilon-insensitive loss
        (standard SVR) is the L1 loss, while the squared epsilon-insensitive
        loss ('squared_epsilon_insensitive') is the L2 loss.

    fit_intercept : bool, default=True
        Whether to calculate the intercept for this model. If set
        to false, no intercept will be used in calculations
        (i.e. data is expected to be already centered).

    intercept_scaling : float, default=1.
        When self.fit_intercept is True, instance vector x becomes
        [x, self.intercept_scaling],
        i.e. a "synthetic" feature with constant value equals to
        intercept_scaling is appended to the instance vector.
        The intercept becomes intercept_scaling * synthetic feature weight
        Note! the synthetic feature weight is subject to l1/l2 regularization
        as all other features.
        To lessen the effect of regularization on synthetic feature weight
        (and therefore on the intercept) intercept_scaling has to be increased.

    dual : bool, default=True
        Select the algorithm to either solve the dual or primal
        optimization problem. Prefer dual=False when n_samples > n_features.

    verbose : int, default=0
        Enable verbose output. Note that this setting takes advantage of a
        per-process runtime setting in liblinear that, if enabled, may not work
        properly in a multithreaded context.

    random_state : int or RandomState instance, default=None
        Controls the pseudo random number generation for shuffling the data.
        Pass an int for reproducible output across multiple function calls.
        See :term:`Glossary <random_state>`.

    max_iter : int, default=1000
        The maximum number of iterations to be run.

    Attributes
    ----------
    coef_ : ndarray of shape (n_features) if n_classes == 2 \
            else (n_classes, n_features)
        Weights assigned to the features (coefficients in the primal
        problem). This is only available in the case of a linear kernel.

        `coef_` is a readonly property derived from `raw_coef_` that
        follows the internal memory layout of liblinear.

    intercept_ : ndarray of shape (1) if n_classes == 2 else (n_classes)
        Constants in decision function.

    n_iter_ : int
        Maximum number of iterations run across all classes.

    Examples
    --------
    >>> from sklearn.svm import LinearSVR
    >>> from sklearn.pipeline import make_pipeline
    >>> from sklearn.preprocessing import StandardScaler
    >>> from sklearn.datasets import make_regression
    >>> X, y = make_regression(n_features=4, random_state=0)
    >>> regr = make_pipeline(StandardScaler(),
    ...                      LinearSVR(random_state=0, tol=1e-5))
    >>> regr.fit(X, y)
    Pipeline(steps=[('standardscaler', StandardScaler()),
                    ('linearsvr', LinearSVR(random_state=0, tol=1e-05))])

    >>> print(regr.named_steps['linearsvr'].coef_)
    [18.582... 27.023... 44.357... 64.522...]
    >>> print(regr.named_steps['linearsvr'].intercept_)
    [-4...]
    >>> print(regr.predict([[0, 0, 0, 0]]))
    [-2.384...]


    See also
    --------
    LinearSVC
        Implementation of Support Vector Machine classifier using the
        same library as this class (liblinear).

    SVR
        Implementation of Support Vector Machine regression using libsvm:
        the kernel can be non-linear but its SMO algorithm does not
        scale to large number of samples as LinearSVC does.

    sklearn.linear_model.SGDRegressor
        SGDRegressor can optimize the same cost function as LinearSVR
        by adjusting the penalty and loss parameters. In addition it requires
        less memory, allows incremental (online) learning, and implements
        various loss functions and regularization regimes.
    """

    @_deprecate_positional_args
    def __init__(self, *, epsilon=0.0, tol=1e-4, C=1.0,
                 loss='epsilon_insensitive', fit_intercept=True,
                 intercept_scaling=1., dual=True, verbose=0,
                 random_state=None, max_iter=1000):
        self.tol = tol
        self.C = C
        self.epsilon = epsilon
        self.fit_intercept = fit_intercept
        self.intercept_scaling = intercept_scaling
        self.verbose = verbose
        self.random_state = random_state
        self.max_iter = max_iter
        self.dual = dual
        self.loss = loss

    def fit(self, X, y, sample_weight=None):
        """Fit the model according to the given training data.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            Training vector, where n_samples in the number of samples and
            n_features is the number of features.

        y : array-like of shape (n_samples,)
            Target vector relative to X

        sample_weight : array-like of shape (n_samples,), default=None
            Array of weights that are assigned to individual
            samples. If not provided,
            then each sample is given unit weight.

            .. versionadded:: 0.18

        Returns
        -------
        self : object
            An instance of the estimator.
        """
        if self.C < 0:
            raise ValueError("Penalty term must be positive; got (C=%r)"
                             % self.C)

        X, y = self._validate_data(X, y, accept_sparse='csr',
                                   dtype=np.float64, order="C",
                                   accept_large_sparse=False)
        penalty = 'l2'  # SVR only accepts l2 penalty
        self.coef_, self.intercept_, self.n_iter_ = _fit_liblinear(
            X, y, self.C, self.fit_intercept, self.intercept_scaling,
            None, penalty, self.dual, self.verbose,
            self.max_iter, self.tol, self.random_state, loss=self.loss,
            epsilon=self.epsilon, sample_weight=sample_weight)
        self.coef_ = self.coef_.ravel()

        return self


class SVC(BaseSVC):
    """C-Support Vector Classification.

    The implementation is based on libsvm. The fit time scales at least
    quadratically with the number of samples and may be impractical
    beyond tens of thousands of samples. For large datasets
    consider using :class:`sklearn.svm.LinearSVC` or
    :class:`sklearn.linear_model.SGDClassifier` instead, possibly after a
    :class:`sklearn.kernel_approximation.Nystroem` transformer.

    The multiclass support is handled according to a one-vs-one scheme.

    For details on the precise mathematical formulation of the provided
    kernel functions and how `gamma`, `coef0` and `degree` affect each
    other, see the corresponding section in the narrative documentation:
    :ref:`svm_kernels`.

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

    Parameters
    ----------
    C : float, default=1.0
        Regularization parameter. The strength of the regularization is
        inversely proportional to C. Must be strictly positive. The penalty
        is a squared l2 penalty.

    kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'}, default='rbf'
        Specifies the kernel type to be used in the algorithm.
        It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
        a callable.
        If none is given, 'rbf' will be used. If a callable is given it is
        used to pre-compute the kernel matrix from data matrices; that matrix
        should be an array of shape ``(n_samples, n_samples)``.

    degree : int, default=3
        Degree of the polynomial kernel function ('poly').
        Ignored by all other kernels.

    gamma : {'scale', 'auto'} or float, default='scale'
        Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.

        - if ``gamma='scale'`` (default) is passed then it uses
          1 / (n_features * X.var()) as value of gamma,
        - if 'auto', uses 1 / n_features.

        .. versionchanged:: 0.22
           The default value of ``gamma`` changed from 'auto' to 'scale'.

    coef0 : float, default=0.0
        Independent term in kernel function.
        It is only significant in 'poly' and 'sigmoid'.

    shrinking : bool, default=True
        Whether to use the shrinking heuristic.
        See the :ref:`User Guide <shrinking_svm>`.

    probability : bool, default=False
        Whether to enable probability estimates. This must be enabled prior
        to calling `fit`, will slow down that method as it internally uses
        5-fold cross-validation, and `predict_proba` may be inconsistent with
        `predict`. Read more in the :ref:`User Guide <scores_probabilities>`.

    tol : float, default=1e-3
        Tolerance for stopping criterion.

    cache_size : float, default=200
        Specify the size of the kernel cache (in MB).

    class_weight : dict or 'balanced', default=None
        Set the parameter C of class i to class_weight[i]*C for
        SVC. If not given, all classes are supposed to have
        weight one.
        The "balanced" mode uses the values of y to automatically adjust
        weights inversely proportional to class frequencies in the input data
        as ``n_samples / (n_classes * np.bincount(y))``

    verbose : bool, default=False
        Enable verbose output. Note that this setting takes advantage of a
        per-process runtime setting in libsvm that, if enabled, may not work
        properly in a multithreaded context.

    max_iter : int, default=-1
        Hard limit on iterations within solver, or -1 for no limit.

    decision_function_shape : {'ovo', 'ovr'}, default='ovr'
        Whether to return a one-vs-rest ('ovr') decision function of shape
        (n_samples, n_classes) as all other classifiers, or the original
        one-vs-one ('ovo') decision function of libsvm which has shape
        (n_samples, n_classes * (n_classes - 1) / 2). However, one-vs-one
        ('ovo') is always used as multi-class strategy. The parameter is
        ignored for binary classification.

        .. versionchanged:: 0.19
            decision_function_shape is 'ovr' by default.

        .. versionadded:: 0.17
           *decision_function_shape='ovr'* is recommended.

        .. versionchanged:: 0.17
           Deprecated *decision_function_shape='ovo' and None*.

    break_ties : bool, default=False
        If true, ``decision_function_shape='ovr'``, and number of classes > 2,
        :term:`predict` will break ties according to the confidence values of
        :term:`decision_function`; otherwise the first class among the tied
        classes is returned. Please note that breaking ties comes at a
        relatively high computational cost compared to a simple predict.

        .. versionadded:: 0.22

    random_state : int or RandomState instance, default=None
        Controls the pseudo random number generation for shuffling the data for
        probability estimates. Ignored when `probability` is False.
        Pass an int for reproducible output across multiple function calls.
        See :term:`Glossary <random_state>`.

    Attributes
    ----------
    support_ : ndarray of shape (n_SV,)
        Indices of support vectors.

    support_vectors_ : ndarray of shape (n_SV, n_features)
        Support vectors.

    n_support_ : ndarray of shape (n_class,), dtype=int32
        Number of support vectors for each class.

    dual_coef_ : ndarray of shape (n_class-1, n_SV)
        Dual coefficients of the support vector in the decision
        function (see :ref:`sgd_mathematical_formulation`), multiplied by
        their targets.
        For multiclass, coefficient for all 1-vs-1 classifiers.
        The layout of the coefficients in the multiclass case is somewhat
        non-trivial. See the :ref:`multi-class section of the User Guide
        <svm_multi_class>` for details.

    coef_ : ndarray of shape (n_class * (n_class-1) / 2, n_features)
        Weights assigned to the features (coefficients in the primal
        problem). This is only available in the case of a linear kernel.

        `coef_` is a readonly property derived from `dual_coef_` and
        `support_vectors_`.

    intercept_ : ndarray of shape (n_class * (n_class-1) / 2,)
        Constants in decision function.

    fit_status_ : int
        0 if correctly fitted, 1 otherwise (will raise warning)

    classes_ : ndarray of shape (n_classes,)
        The classes labels.

    probA_ : ndarray of shape (n_class * (n_class-1) / 2)
    probB_ : ndarray of shape (n_class * (n_class-1) / 2)
        If `probability=True`, it corresponds to the parameters learned in
        Platt scaling to produce probability estimates from decision values.
        If `probability=False`, it's an empty array. Platt scaling uses the
        logistic function
        ``1 / (1 + exp(decision_value * probA_ + probB_))``
        where ``probA_`` and ``probB_`` are learned from the dataset [2]_. For
        more information on the multiclass case and training procedure see
        section 8 of [1]_.

    class_weight_ : ndarray of shape (n_class,)
        Multipliers of parameter C for each class.
        Computed based on the ``class_weight`` parameter.

    shape_fit_ : tuple of int of shape (n_dimensions_of_X,)
        Array dimensions of training vector ``X``.

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.pipeline import make_pipeline
    >>> from sklearn.preprocessing import StandardScaler
    >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
    >>> y = np.array([1, 1, 2, 2])
    >>> from sklearn.svm import SVC
    >>> clf = make_pipeline(StandardScaler(), SVC(gamma='auto'))
    >>> clf.fit(X, y)
    Pipeline(steps=[('standardscaler', StandardScaler()),
                    ('svc', SVC(gamma='auto'))])

    >>> print(clf.predict([[-0.8, -1]]))
    [1]

    See also
    --------
    SVR
        Support Vector Machine for Regression implemented using libsvm.

    LinearSVC
        Scalable Linear Support Vector Machine for classification
        implemented using liblinear. Check the See also section of
        LinearSVC for more comparison element.

    References
    ----------
    .. [1] `LIBSVM: A Library for Support Vector Machines
        <http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf>`_

    .. [2] `Platt, John (1999). "Probabilistic outputs for support vector
        machines and comparison to regularizedlikelihood methods."
        <http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.1639>`_
    """

    _impl = 'c_svc'

    @_deprecate_positional_args
    def __init__(self, *, C=1.0, kernel='rbf', degree=3, gamma='scale',
                 coef0=0.0, shrinking=True, probability=False,
                 tol=1e-3, cache_size=200, class_weight=None,
                 verbose=False, max_iter=-1, decision_function_shape='ovr',
                 break_ties=False,
                 random_state=None):

        super().__init__(
            kernel=kernel, degree=degree, gamma=gamma,
            coef0=coef0, tol=tol, C=C, nu=0., shrinking=shrinking,
            probability=probability, cache_size=cache_size,
            class_weight=class_weight, verbose=verbose, max_iter=max_iter,
            decision_function_shape=decision_function_shape,
            break_ties=break_ties,
            random_state=random_state)


class NuSVC(BaseSVC):
    """Nu-Support Vector Classification.

    Similar to SVC but uses a parameter to control the number of support
    vectors.

    The implementation is based on libsvm.

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

    Parameters
    ----------
    nu : float, default=0.5
        An upper bound on the fraction of margin errors (see :ref:`User Guide
        <nu_svc>`) and a lower bound of the fraction of support vectors.
        Should be in the interval (0, 1].

    kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'}, default='rbf'
         Specifies the kernel type to be used in the algorithm.
         It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
         a callable.
         If none is given, 'rbf' will be used. If a callable is given it is
         used to precompute the kernel matrix.

    degree : int, default=3
        Degree of the polynomial kernel function ('poly').
        Ignored by all other kernels.

    gamma : {'scale', 'auto'} or float, default='scale'
        Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.

        - if ``gamma='scale'`` (default) is passed then it uses
          1 / (n_features * X.var()) as value of gamma,
        - if 'auto', uses 1 / n_features.

        .. versionchanged:: 0.22
           The default value of ``gamma`` changed from 'auto' to 'scale'.

    coef0 : float, default=0.0
        Independent term in kernel function.
        It is only significant in 'poly' and 'sigmoid'.

    shrinking : bool, default=True
        Whether to use the shrinking heuristic.
        See the :ref:`User Guide <shrinking_svm>`.

    probability : bool, default=False
        Whether to enable probability estimates. This must be enabled prior
        to calling `fit`, will slow down that method as it internally uses
        5-fold cross-validation, and `predict_proba` may be inconsistent with
        `predict`. Read more in the :ref:`User Guide <scores_probabilities>`.

    tol : float, default=1e-3
        Tolerance for stopping criterion.

    cache_size : float, default=200
        Specify the size of the kernel cache (in MB).

    class_weight : {dict, 'balanced'}, default=None
        Set the parameter C of class i to class_weight[i]*C for
        SVC. If not given, all classes are supposed to have
        weight one. The "balanced" mode uses the values of y to automatically
        adjust weights inversely proportional to class frequencies as
        ``n_samples / (n_classes * np.bincount(y))``

    verbose : bool, default=False
        Enable verbose output. Note that this setting takes advantage of a
        per-process runtime setting in libsvm that, if enabled, may not work
        properly in a multithreaded context.

    max_iter : int, default=-1
        Hard limit on iterations within solver, or -1 for no limit.

    decision_function_shape : {'ovo', 'ovr'}, default='ovr'
        Whether to return a one-vs-rest ('ovr') decision function of shape
        (n_samples, n_classes) as all other classifiers, or the original
        one-vs-one ('ovo') decision function of libsvm which has shape
        (n_samples, n_classes * (n_classes - 1) / 2). However, one-vs-one
        ('ovo') is always used as multi-class strategy. The parameter is
        ignored for binary classification.

        .. versionchanged:: 0.19
            decision_function_shape is 'ovr' by default.

        .. versionadded:: 0.17
           *decision_function_shape='ovr'* is recommended.

        .. versionchanged:: 0.17
           Deprecated *decision_function_shape='ovo' and None*.

    break_ties : bool, default=False
        If true, ``decision_function_shape='ovr'``, and number of classes > 2,
        :term:`predict` will break ties according to the confidence values of
        :term:`decision_function`; otherwise the first class among the tied
        classes is returned. Please note that breaking ties comes at a
        relatively high computational cost compared to a simple predict.

        .. versionadded:: 0.22

    random_state : int or RandomState instance, default=None
        Controls the pseudo random number generation for shuffling the data for
        probability estimates. Ignored when `probability` is False.
        Pass an int for reproducible output across multiple function calls.
        See :term:`Glossary <random_state>`.

    Attributes
    ----------
    support_ : ndarray of shape (n_SV,)
        Indices of support vectors.

    support_vectors_ : ndarray of shape (n_SV, n_features)
        Support vectors.

    n_support_ : ndarray of shape (n_class), dtype=int32
        Number of support vectors for each class.

    dual_coef_ : ndarray of shape (n_class-1, n_SV)
        Dual coefficients of the support vector in the decision
        function (see :ref:`sgd_mathematical_formulation`), multiplied by
        their targets.
        For multiclass, coefficient for all 1-vs-1 classifiers.
        The layout of the coefficients in the multiclass case is somewhat
        non-trivial. See the :ref:`multi-class section of the User Guide
        <svm_multi_class>` for details.

    coef_ : ndarray of shape (n_class * (n_class-1) / 2, n_features)
        Weights assigned to the features (coefficients in the primal
        problem). This is only available in the case of a linear kernel.

        `coef_` is readonly property derived from `dual_coef_` and
        `support_vectors_`.

    intercept_ : ndarray of shape (n_class * (n_class-1) / 2,)
        Constants in decision function.

    classes_ : ndarray of shape (n_classes,)
        The unique classes labels.

    fit_status_ : int
        0 if correctly fitted, 1 if the algorithm did not converge.

    probA_ : ndarray of shape (n_class * (n_class-1) / 2,)
    probB_ : ndarray of shape (n_class * (n_class-1) / 2,)
        If `probability=True`, it corresponds to the parameters learned in
        Platt scaling to produce probability estimates from decision values.
        If `probability=False`, it's an empty array. Platt scaling uses the
        logistic function
        ``1 / (1 + exp(decision_value * probA_ + probB_))``
        where ``probA_`` and ``probB_`` are learned from the dataset [2]_. For
        more information on the multiclass case and training procedure see
        section 8 of [1]_.

    class_weight_ : ndarray of shape (n_class,)
        Multipliers of parameter C of each class.
        Computed based on the ``class_weight`` parameter.

    shape_fit_ : tuple of int of shape (n_dimensions_of_X,)
        Array dimensions of training vector ``X``.

    Examples
    --------
    >>> import numpy as np
    >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
    >>> y = np.array([1, 1, 2, 2])
    >>> from sklearn.pipeline import make_pipeline
    >>> from sklearn.preprocessing import StandardScaler
    >>> from sklearn.svm import NuSVC
    >>> clf = make_pipeline(StandardScaler(), NuSVC())
    >>> clf.fit(X, y)
    Pipeline(steps=[('standardscaler', StandardScaler()), ('nusvc', NuSVC())])
    >>> print(clf.predict([[-0.8, -1]]))
    [1]

    See also
    --------
    SVC
        Support Vector Machine for classification using libsvm.

    LinearSVC
        Scalable linear Support Vector Machine for classification using
        liblinear.

    References
    ----------
    .. [1] `LIBSVM: A Library for Support Vector Machines
        <http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf>`_

    .. [2] `Platt, John (1999). "Probabilistic outputs for support vector
        machines and comparison to regularizedlikelihood methods."
        <http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.1639>`_
    """

    _impl = 'nu_svc'

    @_deprecate_positional_args
    def __init__(self, *, nu=0.5, kernel='rbf', degree=3, gamma='scale',
                 coef0=0.0, shrinking=True, probability=False, tol=1e-3,
                 cache_size=200, class_weight=None, verbose=False, max_iter=-1,
                 decision_function_shape='ovr', break_ties=False,
                 random_state=None):

        super().__init__(
            kernel=kernel, degree=degree, gamma=gamma,
            coef0=coef0, tol=tol, C=0., nu=nu, shrinking=shrinking,
            probability=probability, cache_size=cache_size,
            class_weight=class_weight, verbose=verbose, max_iter=max_iter,
            decision_function_shape=decision_function_shape,
            break_ties=break_ties,
            random_state=random_state)

    def _more_tags(self):
        return {
            '_xfail_checks': {
                'check_methods_subset_invariance':
                'fails for the decision_function method',
                'check_class_weight_classifiers': 'class_weight is ignored.'
            }
        }


class SVR(RegressorMixin, BaseLibSVM):
    """Epsilon-Support Vector Regression.

    The free parameters in the model are C and epsilon.

    The implementation is based on libsvm. The fit time complexity
    is more than quadratic with the number of samples which makes it hard
    to scale to datasets with more than a couple of 10000 samples. For large
    datasets consider using :class:`sklearn.svm.LinearSVR` or
    :class:`sklearn.linear_model.SGDRegressor` instead, possibly after a
    :class:`sklearn.kernel_approximation.Nystroem` transformer.

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

    Parameters
    ----------
    kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'}, default='rbf'
         Specifies the kernel type to be used in the algorithm.
         It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
         a callable.
         If none is given, 'rbf' will be used. If a callable is given it is
         used to precompute the kernel matrix.

    degree : int, default=3
        Degree of the polynomial kernel function ('poly').
        Ignored by all other kernels.

    gamma : {'scale', 'auto'} or float, default='scale'
        Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.

        - if ``gamma='scale'`` (default) is passed then it uses
          1 / (n_features * X.var()) as value of gamma,
        - if 'auto', uses 1 / n_features.

        .. versionchanged:: 0.22
           The default value of ``gamma`` changed from 'auto' to 'scale'.

    coef0 : float, default=0.0
        Independent term in kernel function.
        It is only significant in 'poly' and 'sigmoid'.

    tol : float, default=1e-3
        Tolerance for stopping criterion.

    C : float, default=1.0
        Regularization parameter. The strength of the regularization is
        inversely proportional to C. Must be strictly positive.
        The penalty is a squared l2 penalty.

    epsilon : float, default=0.1
         Epsilon in the epsilon-SVR model. It specifies the epsilon-tube
         within which no penalty is associated in the training loss function
         with points predicted within a distance epsilon from the actual
         value.

    shrinking : bool, default=True
        Whether to use the shrinking heuristic.
        See the :ref:`User Guide <shrinking_svm>`.

    cache_size : float, default=200
        Specify the size of the kernel cache (in MB).

    verbose : bool, default=False
        Enable verbose output. Note that this setting takes advantage of a
        per-process runtime setting in libsvm that, if enabled, may not work
        properly in a multithreaded context.

    max_iter : int, default=-1
        Hard limit on iterations within solver, or -1 for no limit.

    Attributes
    ----------
    support_ : ndarray of shape (n_SV,)
        Indices of support vectors.

    support_vectors_ : ndarray of shape (n_SV, n_features)
        Support vectors.

    dual_coef_ : ndarray of shape (1, n_SV)
        Coefficients of the support vector in the decision function.

    coef_ : ndarray of shape (1, n_features)
        Weights assigned to the features (coefficients in the primal
        problem). This is only available in the case of a linear kernel.

        `coef_` is readonly property derived from `dual_coef_` and
        `support_vectors_`.

    fit_status_ : int
        0 if correctly fitted, 1 otherwise (will raise warning)

    intercept_ : ndarray of shape (1,)
        Constants in decision function.

    Examples
    --------
    >>> from sklearn.svm import SVR
    >>> from sklearn.pipeline import make_pipeline
    >>> from sklearn.preprocessing import StandardScaler
    >>> import numpy as np
    >>> n_samples, n_features = 10, 5
    >>> rng = np.random.RandomState(0)
    >>> y = rng.randn(n_samples)
    >>> X = rng.randn(n_samples, n_features)
    >>> regr = make_pipeline(StandardScaler(), SVR(C=1.0, epsilon=0.2))
    >>> regr.fit(X, y)
    Pipeline(steps=[('standardscaler', StandardScaler()),
                    ('svr', SVR(epsilon=0.2))])


    See also
    --------
    NuSVR
        Support Vector Machine for regression implemented using libsvm
        using a parameter to control the number of support vectors.

    LinearSVR
        Scalable Linear Support Vector Machine for regression
        implemented using liblinear.

    Notes
    -----
    **References:**
    `LIBSVM: A Library for Support Vector Machines
    <http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf>`__
    """

    _impl = 'epsilon_svr'

    @_deprecate_positional_args
    def __init__(self, *, kernel='rbf', degree=3, gamma='scale',
                 coef0=0.0, tol=1e-3, C=1.0, epsilon=0.1, shrinking=True,
                 cache_size=200, verbose=False, max_iter=-1):

        super().__init__(
            kernel=kernel, degree=degree, gamma=gamma,
            coef0=coef0, tol=tol, C=C, nu=0., epsilon=epsilon, verbose=verbose,
            shrinking=shrinking, probability=False, cache_size=cache_size,
            class_weight=None, max_iter=max_iter, random_state=None)

    # mypy error: Decorated property not supported
    @deprecated(  # type: ignore
        "The probA_ attribute is deprecated in version 0.23 and will be "
        "removed in version 0.25.")
    @property
    def probA_(self):
        return self._probA

    # mypy error: Decorated property not supported
    @deprecated(  # type: ignore
        "The probB_ attribute is deprecated in version 0.23 and will be "
        "removed in version 0.25.")
    @property
    def probB_(self):
        return self._probB


class NuSVR(RegressorMixin, BaseLibSVM):
    """Nu Support Vector Regression.

    Similar to NuSVC, for regression, uses a parameter nu to control
    the number of support vectors. However, unlike NuSVC, where nu
    replaces C, here nu replaces the parameter epsilon of epsilon-SVR.

    The implementation is based on libsvm.

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

    Parameters
    ----------
    nu : float, default=0.5
        An upper bound on the fraction of training errors and a lower bound of
        the fraction of support vectors. Should be in the interval (0, 1].  By
        default 0.5 will be taken.

    C : float, default=1.0
        Penalty parameter C of the error term.

    kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'}, default='rbf'
         Specifies the kernel type to be used in the algorithm.
         It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
         a callable.
         If none is given, 'rbf' will be used. If a callable is given it is
         used to precompute the kernel matrix.

    degree : int, default=3
        Degree of the polynomial kernel function ('poly').
        Ignored by all other kernels.

    gamma : {'scale', 'auto'} or float, default='scale'
        Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.

        - if ``gamma='scale'`` (default) is passed then it uses
          1 / (n_features * X.var()) as value of gamma,
        - if 'auto', uses 1 / n_features.

        .. versionchanged:: 0.22
           The default value of ``gamma`` changed from 'auto' to 'scale'.

    coef0 : float, default=0.0
        Independent term in kernel function.
        It is only significant in 'poly' and 'sigmoid'.

    shrinking : bool, default=True
        Whether to use the shrinking heuristic.
        See the :ref:`User Guide <shrinking_svm>`.

    tol : float, default=1e-3
        Tolerance for stopping criterion.

    cache_size : float, default=200
        Specify the size of the kernel cache (in MB).

    verbose : bool, default=False
        Enable verbose output. Note that this setting takes advantage of a
        per-process runtime setting in libsvm that, if enabled, may not work
        properly in a multithreaded context.

    max_iter : int, default=-1
        Hard limit on iterations within solver, or -1 for no limit.

    Attributes
    ----------
    support_ : ndarray of shape (n_SV,)
        Indices of support vectors.

    support_vectors_ : ndarray of shape (n_SV, n_features)
        Support vectors.

    dual_coef_ : ndarray of shape (1, n_SV)
        Coefficients of the support vector in the decision function.

    coef_ : ndarray of shape (1, n_features)
        Weights assigned to the features (coefficients in the primal
        problem). This is only available in the case of a linear kernel.

        `coef_` is readonly property derived from `dual_coef_` and
        `support_vectors_`.

    intercept_ : ndarray of shape (1,)
        Constants in decision function.

    Examples
    --------
    >>> from sklearn.svm import NuSVR
    >>> from sklearn.pipeline import make_pipeline
    >>> from sklearn.preprocessing import StandardScaler
    >>> import numpy as np
    >>> n_samples, n_features = 10, 5
    >>> np.random.seed(0)
    >>> y = np.random.randn(n_samples)
    >>> X = np.random.randn(n_samples, n_features)
    >>> regr = make_pipeline(StandardScaler(), NuSVR(C=1.0, nu=0.1))
    >>> regr.fit(X, y)
    Pipeline(steps=[('standardscaler', StandardScaler()),
                    ('nusvr', NuSVR(nu=0.1))])

    See also
    --------
    NuSVC
        Support Vector Machine for classification implemented with libsvm
        with a parameter to control the number of support vectors.

    SVR
        epsilon Support Vector Machine for regression implemented with libsvm.

    Notes
    -----
    **References:**
    `LIBSVM: A Library for Support Vector Machines
    <http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf>`__
    """

    _impl = 'nu_svr'

    @_deprecate_positional_args
    def __init__(self, *, nu=0.5, C=1.0, kernel='rbf', degree=3,
                 gamma='scale', coef0=0.0, shrinking=True,
                 tol=1e-3, cache_size=200, verbose=False, max_iter=-1):

        super().__init__(
            kernel=kernel, degree=degree, gamma=gamma, coef0=coef0,
            tol=tol, C=C, nu=nu, epsilon=0., shrinking=shrinking,
            probability=False, cache_size=cache_size, class_weight=None,
            verbose=verbose, max_iter=max_iter, random_state=None)


class OneClassSVM(OutlierMixin, BaseLibSVM):
    """Unsupervised Outlier Detection.

    Estimate the support of a high-dimensional distribution.

    The implementation is based on libsvm.

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

    Parameters
    ----------
    kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'}, default='rbf'
         Specifies the kernel type to be used in the algorithm.
         It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
         a callable.
         If none is given, 'rbf' will be used. If a callable is given it is
         used to precompute the kernel matrix.

    degree : int, default=3
        Degree of the polynomial kernel function ('poly').
        Ignored by all other kernels.

    gamma : {'scale', 'auto'} or float, default='scale'
        Kernel coefficient for 'rbf', 'poly' and 'sigmoid'.

        - if ``gamma='scale'`` (default) is passed then it uses
          1 / (n_features * X.var()) as value of gamma,
        - if 'auto', uses 1 / n_features.

        .. versionchanged:: 0.22
           The default value of ``gamma`` changed from 'auto' to 'scale'.

    coef0 : float, default=0.0
        Independent term in kernel function.
        It is only significant in 'poly' and 'sigmoid'.

    tol : float, default=1e-3
        Tolerance for stopping criterion.

    nu : float, default=0.5
        An upper bound on the fraction of training
        errors and a lower bound of the fraction of support
        vectors. Should be in the interval (0, 1]. By default 0.5
        will be taken.

    shrinking : bool, default=True
        Whether to use the shrinking heuristic.
        See the :ref:`User Guide <shrinking_svm>`.

    cache_size : float, default=200
        Specify the size of the kernel cache (in MB).

    verbose : bool, default=False
        Enable verbose output. Note that this setting takes advantage of a
        per-process runtime setting in libsvm that, if enabled, may not work
        properly in a multithreaded context.

    max_iter : int, default=-1
        Hard limit on iterations within solver, or -1 for no limit.

    Attributes
    ----------
    support_ : ndarray of shape (n_SV,)
        Indices of support vectors.

    support_vectors_ : ndarray of shape (n_SV, n_features)
        Support vectors.

    dual_coef_ : ndarray of shape (1, n_SV)
        Coefficients of the support vectors in the decision function.

    coef_ : ndarray of shape (1, n_features)
        Weights assigned to the features (coefficients in the primal
        problem). This is only available in the case of a linear kernel.

        `coef_` is readonly property derived from `dual_coef_` and
        `support_vectors_`

    intercept_ : ndarray of shape (1,)
        Constant in the decision function.

    offset_ : float
        Offset used to define the decision function from the raw scores.
        We have the relation: decision_function = score_samples - `offset_`.
        The offset is the opposite of `intercept_` and is provided for
        consistency with other outlier detection algorithms.

        .. versionadded:: 0.20

    fit_status_ : int
        0 if correctly fitted, 1 otherwise (will raise warning)

    Examples
    --------
    >>> from sklearn.svm import OneClassSVM
    >>> X = [[0], [0.44], [0.45], [0.46], [1]]
    >>> clf = OneClassSVM(gamma='auto').fit(X)
    >>> clf.predict(X)
    array([-1,  1,  1,  1, -1])
    >>> clf.score_samples(X)
    array([1.7798..., 2.0547..., 2.0556..., 2.0561..., 1.7332...])
    """

    _impl = 'one_class'

    @_deprecate_positional_args
    def __init__(self, *, kernel='rbf', degree=3, gamma='scale',
                 coef0=0.0, tol=1e-3, nu=0.5, shrinking=True, cache_size=200,
                 verbose=False, max_iter=-1):

        super().__init__(
            kernel, degree, gamma, coef0, tol, 0., nu, 0.,
            shrinking, False, cache_size, None, verbose, max_iter,
            random_state=None)

    def fit(self, X, y=None, sample_weight=None, **params):
        """Detects the soft boundary of the set of samples X.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            Set of samples, where n_samples is the number of samples and
            n_features is the number of features.

        sample_weight : array-like of shape (n_samples,), default=None
            Per-sample weights. Rescale C per sample. Higher weights
            force the classifier to put more emphasis on these points.

        y : Ignored
            not used, present for API consistency by convention.

        Returns
        -------
        self : object

        Notes
        -----
        If X is not a C-ordered contiguous array it is copied.

        """
        super().fit(X, np.ones(_num_samples(X)),
                    sample_weight=sample_weight, **params)
        self.offset_ = -self._intercept_
        return self

    def decision_function(self, X):
        """Signed distance to the separating hyperplane.

        Signed distance is positive for an inlier and negative for an outlier.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            The data matrix.

        Returns
        -------
        dec : ndarray of shape (n_samples,)
            Returns the decision function of the samples.
        """
        dec = self._decision_function(X).ravel()
        return dec

    def score_samples(self, X):
        """Raw scoring function of the samples.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            The data matrix.

        Returns
        -------
        score_samples : ndarray of shape (n_samples,)
            Returns the (unshifted) scoring function of the samples.
        """
        return self.decision_function(X) + self.offset_

    def predict(self, X):
        """Perform classification on samples in X.

        For a one-class model, +1 or -1 is returned.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features) or \
                (n_samples_test, n_samples_train)
            For kernel="precomputed", the expected shape of X is
            (n_samples_test, n_samples_train).

        Returns
        -------
        y_pred : ndarray of shape (n_samples,)
            Class labels for samples in X.
        """
        y = super().predict(X)
        return np.asarray(y, dtype=np.intp)

    # mypy error: Decorated property not supported
    @deprecated(  # type: ignore
        "The probA_ attribute is deprecated in version 0.23 and will be "
        "removed in version 0.25.")
    @property
    def probA_(self):
        return self._probA

    # mypy error: Decorated property not supported
    @deprecated(  # type: ignore
        "The probB_ attribute is deprecated in version 0.23 and will be "
        "removed in version 0.25.")
    @property
    def probB_(self):
        return self._probB