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, 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 : 'scale', 'auto'
or float, optional (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, 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.
probability : boolean, optional (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, 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_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 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*.
break_ties : bool, optional (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, RandomState instance or None, optional (default=None) The seed of the pseudo random number generator used when shuffling the data for probability estimates. 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 of shape (n_SV) Indices of support vectors.
support_vectors_ : array-like of 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 * (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_ : array of shape (n_classes,) The unique classes labels.
fit_status_ : int 0 if correctly fitted, 1 if the algorithm did not converge.
probA_ : ndarray, shape of (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.svm import NuSVC >>> clf = NuSVC() >>> clf.fit(X, y) 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>`_