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_weighti
*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>`_