import warnings import numpy as np from .base import _fit_liblinear, BaseSVC, BaseLibSVM from ..base import BaseEstimator, RegressorMixin from ..linear_model.base import LinearClassifierMixin, SparseCoefMixin, \ LinearModel from ..utils import check_X_y from ..utils.validation import _num_samples from ..utils.multiclass import check_classification_targets 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 `. Parameters ---------- penalty : string, 'l1' or '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 : string, 'hinge' or '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, optional (default=1e-4) Tolerance for stopping criteria. C : float, optional (default=1.0) Penalty parameter C of the error term. multi_class : string, 'ovr' or '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 : boolean, optional (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, optional (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, 'balanced'}, optional 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, RandomState instance or None, optional (default=None) The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. max_iter : int, (default=1000) The maximum number of iterations to be run. Attributes ---------- coef_ : array, 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_ : array, shape = [1] if n_classes == 2 else [n_classes] Constants in decision function. Examples -------- >>> from sklearn.svm import LinearSVC >>> from sklearn.datasets import make_classification >>> X, y = make_classification(n_features=4, random_state=0) >>> clf = LinearSVC(random_state=0) >>> clf.fit(X, y) LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True, intercept_scaling=1, loss='squared_hinge', max_iter=1000, multi_class='ovr', penalty='l2', random_state=0, tol=0.0001, verbose=0) >>> print(clf.coef_) [[ 0.08551385 0.39414796 0.49847831 0.37513797]] >>> print(clf.intercept_) [ 0.28418066] >>> print(clf.predict([[0, 0, 0, 0]])) [1] 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 ` in the narrative documentation. References ---------- `LIBLINEAR: A Library for Large Linear Classification `__ 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. """ 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}, 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, shape = [n_samples] Target vector relative to X sample_weight : array-like, shape = [n_samples], optional Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- self : object Returns self. """ # FIXME Remove l1/l2 support in 1.0 ----------------------------------- msg = ("loss='%s' has been deprecated in favor of " "loss='%s' as of 0.16. Backward compatibility" " for the loss='%s' will be removed in %s") if self.loss in ('l1', 'l2'): old_loss = self.loss self.loss = {'l1': 'hinge', 'l2': 'squared_hinge'}.get(self.loss) warnings.warn(msg % (old_loss, self.loss, old_loss, '1.0'), DeprecationWarning) # --------------------------------------------------------------------- if self.C < 0: raise ValueError("Penalty term must be positive; got (C=%r)" % self.C) X, y = check_X_y(X, y, accept_sparse='csr', dtype=np.float64, order="C") 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(LinearModel, RegressorMixin): """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 `. Parameters ---------- C : float, optional (default=1.0) Penalty parameter C of the error term. The penalty is a squared l2 penalty. The bigger this parameter, the less regularization is used. loss : string, 'epsilon_insensitive' or 'squared_epsilon_insensitive' (default='epsilon_insensitive') Specifies the loss function. 'l1' is the epsilon-insensitive loss (standard SVR) while 'l2' is the squared epsilon-insensitive loss. epsilon : float, optional (default=0.1) 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``. 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, optional (default=1e-4) Tolerance for stopping criteria. fit_intercept : boolean, optional (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, optional (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. 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, RandomState instance or None, optional (default=None) The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. max_iter : int, (default=1000) The maximum number of iterations to be run. Attributes ---------- coef_ : array, 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_ : array, shape = [1] if n_classes == 2 else [n_classes] Constants in decision function. Examples -------- >>> from sklearn.svm import LinearSVR >>> from sklearn.datasets import make_regression >>> X, y = make_regression(n_features=4, random_state=0) >>> regr = LinearSVR(random_state=0) >>> regr.fit(X, y) LinearSVR(C=1.0, dual=True, epsilon=0.0, fit_intercept=True, intercept_scaling=1.0, loss='epsilon_insensitive', max_iter=1000, random_state=0, tol=0.0001, verbose=0) >>> print(regr.coef_) [ 16.35750999 26.91499923 42.30652207 60.47843124] >>> print(regr.intercept_) [-4.29756543] >>> print(regr.predict([[0, 0, 0, 0]])) [-4.29756543] 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. """ 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}, 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, shape = [n_samples] Target vector relative to X sample_weight : array-like, shape = [n_samples], optional Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- self : object Returns self. """ # FIXME Remove l1/l2 support in 1.0 ----------------------------------- msg = ("loss='%s' has been deprecated in favor of " "loss='%s' as of 0.16. Backward compatibility" " for the loss='%s' will be removed in %s") if self.loss in ('l1', 'l2'): old_loss = self.loss self.loss = {'l1': 'epsilon_insensitive', 'l2': 'squared_epsilon_insensitive' }.get(self.loss) warnings.warn(msg % (old_loss, self.loss, old_loss, '1.0'), DeprecationWarning) # --------------------------------------------------------------------- if self.C < 0: raise ValueError("Penalty term must be positive; got (C=%r)" % self.C) X, y = check_X_y(X, y, accept_sparse='csr', dtype=np.float64, order="C") 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 complexity is more than quadratic with the number of samples which makes it hard to scale to dataset with more than a couple of 10000 samples. 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 `. Parameters ---------- C : float, optional (default=1.0) Penalty parameter C of the error term. kernel : string, optional (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, optional (default=3) Degree of the polynomial kernel function ('poly'). Ignored by all other kernels. gamma : float, optional (default='auto') Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. If gamma is 'auto' then 1/n_features will be used instead. coef0 : float, optional (default=0.0) Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. probability : boolean, optional (default=False) Whether to enable probability estimates. This must be enabled prior to calling `fit`, and will slow down that method. shrinking : boolean, optional (default=True) Whether to use the shrinking heuristic. tol : float, optional (default=1e-3) Tolerance for stopping criterion. cache_size : float, optional Specify the size of the kernel cache (in MB). class_weight : {dict, 'balanced'}, optional 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, optional (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). .. 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*. random_state : int, RandomState instance or None, optional (default=None) The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Attributes ---------- support_ : array-like, shape = [n_SV] Indices of support vectors. support_vectors_ : array-like, shape = [n_SV, n_features] Support vectors. n_support_ : array-like, dtype=int32, shape = [n_class] Number of support vectors for each class. dual_coef_ : array, shape = [n_class-1, n_SV] Coefficients of the support vector in the decision function. For multiclass, coefficient for all 1-vs-1 classifiers. The layout of the coefficients in the multiclass case is somewhat non-trivial. See the section about multi-class classification in the SVM section of the User Guide for details. coef_ : array, shape = [n_class-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 a readonly property derived from `dual_coef_` and `support_vectors_`. intercept_ : array, shape = [n_class * (n_class-1) / 2] Constants in decision function. 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.svm import SVC >>> clf = SVC() >>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf', max_iter=-1, probability=False, random_state=None, shrinking=True, tol=0.001, verbose=False) >>> 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. """ def __init__(self, C=1.0, kernel='rbf', degree=3, gamma='auto', 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', random_state=None): super(SVC, self).__init__( impl='c_svc', 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, 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 `. Parameters ---------- nu : float, optional (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]. kernel : string, optional (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, optional (default=3) Degree of the polynomial kernel function ('poly'). Ignored by all other kernels. gamma : float, optional (default='auto') Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. If gamma is 'auto' then 1/n_features will be used instead. coef0 : float, optional (default=0.0) Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. probability : boolean, optional (default=False) Whether to enable probability estimates. This must be enabled prior to calling `fit`, and will slow down that method. shrinking : boolean, optional (default=True) Whether to use the shrinking heuristic. tol : float, optional (default=1e-3) Tolerance for stopping criterion. cache_size : float, optional Specify the size of the kernel cache (in MB). class_weight : {dict, 'balanced'}, optional 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, optional (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). .. 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*. random_state : int, RandomState instance or None, optional (default=None) The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Attributes ---------- support_ : array-like, shape = [n_SV] Indices of support vectors. support_vectors_ : array-like, shape = [n_SV, n_features] Support vectors. n_support_ : array-like, dtype=int32, shape = [n_class] Number of support vectors for each class. dual_coef_ : array, shape = [n_class-1, n_SV] Coefficients of the support vector in the decision function. For multiclass, coefficient for all 1-vs-1 classifiers. The layout of the coefficients in the multiclass case is somewhat non-trivial. See the section about multi-class classification in the SVM section of the User Guide for details. coef_ : array, shape = [n_class-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_ : array, shape = [n_class * (n_class-1) / 2] Constants in decision function. 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.svm import NuSVC >>> clf = NuSVC() >>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE NuSVC(cache_size=200, class_weight=None, coef0=0.0, decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf', max_iter=-1, nu=0.5, probability=False, random_state=None, shrinking=True, tol=0.001, verbose=False) >>> 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. """ def __init__(self, nu=0.5, kernel='rbf', degree=3, gamma='auto', 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', random_state=None): super(NuSVC, self).__init__( impl='nu_svc', 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, random_state=random_state) class SVR(BaseLibSVM, RegressorMixin): """Epsilon-Support Vector Regression. The free parameters in the model are C and epsilon. The implementation is based on libsvm. Read more in the :ref:`User Guide `. Parameters ---------- C : float, optional (default=1.0) Penalty parameter C of the error term. epsilon : float, optional (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. kernel : string, optional (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, optional (default=3) Degree of the polynomial kernel function ('poly'). Ignored by all other kernels. gamma : float, optional (default='auto') Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. If gamma is 'auto' then 1/n_features will be used instead. coef0 : float, optional (default=0.0) Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. shrinking : boolean, optional (default=True) Whether to use the shrinking heuristic. tol : float, optional (default=1e-3) Tolerance for stopping criterion. cache_size : float, optional 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, optional (default=-1) Hard limit on iterations within solver, or -1 for no limit. Attributes ---------- support_ : array-like, shape = [n_SV] Indices of support vectors. support_vectors_ : array-like, shape = [nSV, n_features] Support vectors. dual_coef_ : array, shape = [1, n_SV] Coefficients of the support vector in the decision function. coef_ : array, 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_ : array, shape = [1] Constants in decision function. sample_weight : array-like, shape = [n_samples] Individual weights for each sample Examples -------- >>> from sklearn.svm import SVR >>> 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) >>> clf = SVR(C=1.0, epsilon=0.2) >>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.2, gamma='auto', kernel='rbf', max_iter=-1, shrinking=True, tol=0.001, verbose=False) 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. """ def __init__(self, kernel='rbf', degree=3, gamma='auto', coef0=0.0, tol=1e-3, C=1.0, epsilon=0.1, shrinking=True, cache_size=200, verbose=False, max_iter=-1): super(SVR, self).__init__( 'epsilon_svr', 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) class NuSVR(BaseLibSVM, RegressorMixin): """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 `. Parameters ---------- C : float, optional (default=1.0) Penalty parameter C of the error term. nu : float, optional 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. kernel : string, optional (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, optional (default=3) Degree of the polynomial kernel function ('poly'). Ignored by all other kernels. gamma : float, optional (default='auto') Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. If gamma is 'auto' then 1/n_features will be used instead. coef0 : float, optional (default=0.0) Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. shrinking : boolean, optional (default=True) Whether to use the shrinking heuristic. tol : float, optional (default=1e-3) Tolerance for stopping criterion. cache_size : float, optional 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, optional (default=-1) Hard limit on iterations within solver, or -1 for no limit. Attributes ---------- support_ : array-like, shape = [n_SV] Indices of support vectors. support_vectors_ : array-like, shape = [nSV, n_features] Support vectors. dual_coef_ : array, shape = [1, n_SV] Coefficients of the support vector in the decision function. coef_ : array, 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_ : array, shape = [1] Constants in decision function. Examples -------- >>> from sklearn.svm import NuSVR >>> 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) >>> clf = NuSVR(C=1.0, nu=0.1) >>> clf.fit(X, y) #doctest: +NORMALIZE_WHITESPACE NuSVR(C=1.0, cache_size=200, coef0=0.0, degree=3, gamma='auto', kernel='rbf', max_iter=-1, nu=0.1, shrinking=True, tol=0.001, verbose=False) 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. """ def __init__(self, nu=0.5, C=1.0, kernel='rbf', degree=3, gamma='auto', coef0=0.0, shrinking=True, tol=1e-3, cache_size=200, verbose=False, max_iter=-1): super(NuSVR, self).__init__( 'nu_svr', 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(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 `. Parameters ---------- kernel : string, optional (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. nu : float, optional 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. degree : int, optional (default=3) Degree of the polynomial kernel function ('poly'). Ignored by all other kernels. gamma : float, optional (default='auto') Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. If gamma is 'auto' then 1/n_features will be used instead. coef0 : float, optional (default=0.0) Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. tol : float, optional Tolerance for stopping criterion. shrinking : boolean, optional Whether to use the shrinking heuristic. cache_size : float, optional 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, optional (default=-1) Hard limit on iterations within solver, or -1 for no limit. random_state : int, RandomState instance or None, optional (default=None) The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Attributes ---------- support_ : array-like, shape = [n_SV] Indices of support vectors. support_vectors_ : array-like, shape = [nSV, n_features] Support vectors. dual_coef_ : array, shape = [1, n_SV] Coefficients of the support vectors in the decision function. coef_ : array, 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_ : array, shape = [1,] Constant in the decision function. """ def __init__(self, kernel='rbf', degree=3, gamma='auto', coef0=0.0, tol=1e-3, nu=0.5, shrinking=True, cache_size=200, verbose=False, max_iter=-1, random_state=None): super(OneClassSVM, self).__init__( 'one_class', kernel, degree, gamma, coef0, tol, 0., nu, 0., shrinking, False, cache_size, None, verbose, max_iter, random_state) 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}, 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, shape (n_samples,) Per-sample weights. Rescale C per sample. Higher weights force the classifier to put more emphasis on these points. Returns ------- self : object Returns self. Notes ----- If X is not a C-ordered contiguous array it is copied. """ super(OneClassSVM, self).fit(X, np.ones(_num_samples(X)), sample_weight=sample_weight, **params) 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, shape (n_samples, n_features) Returns ------- X : array-like, shape (n_samples,) Returns the decision function of the samples. """ dec = self._decision_function(X) return dec def predict(self, X): """ Perform classification on samples in X. For an one-class model, +1 or -1 is returned. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) For kernel="precomputed", the expected shape of X is [n_samples_test, n_samples_train] Returns ------- y_pred : array, shape (n_samples,) Class labels for samples in X. """ y = super(OneClassSVM, self).predict(X) return np.asarray(y, dtype=np.intp)