8.26.1.2. sklearn.svm.LinearSVC

class sklearn.svm.LinearSVC(penalty='l2', loss='l2', dual=True, tol=0.0001, C=None, multi_class='ovr', fit_intercept=True, intercept_scaling=1, scale_C=True, class_weight=None)

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.

Parameters :

C : float or None, optional (default=None)

Penalty parameter C of the error term. If None then C is set to n_samples.

loss : string, ‘l1’ or ‘l2’ (default=’l2’)

Specifies the loss function. ‘l1’ is the hinge loss (standard SVM) while ‘l2’ is the squared hinge loss.

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.

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

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 an theoretical perspective as it is consistent it is seldom used in practice and rarely leads to better accuracy and is more expensive to compute. If crammer_singer is choosen, 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 (e.g. 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, ‘auto’}, 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 ‘auto’ mode uses the values of y to automatically adjust weights inversely proportional to class frequencies.

scale_C : bool, default: True

Scale C with number of samples. It makes the setting of C independent of the number of samples. To match liblinear commandline one should use scale_C=False. WARNING: scale_C will disappear in version 0.12.

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 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. Furthermore SGDClassifier is scalable to large number of samples as it uses a Stochastic Gradient Descent optimizer. Finally SGDClassifier can fit both dense and sparse data without memory copy if the input is C-contiguous or CSR.

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.

References: LIBLINEAR: A Library for Large Linear Classification

Attributes

coef_	array, shape = [n_features] if n_classes == 2 else [n_classes, n_features]	Weights asigned to the features (coefficients in the primal problem). This is only available in the case of linear kernel. coef_ is 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.
scaled_C_	float	The C value passed to liblinear.

Methods

decision_function(X)	Decision function value for X according to the trained model.
fit(X, y[, class_weight])	Fit the model according to the given training data.
fit_transform(X[, y])	Fit to data, then transform it
get_params([deep])	Get parameters for the estimator
predict(X)	Predict target values of X according to the fitted model.
score(X, y)	Returns the mean accuracy on the given test data and labels.
set_params(**params)	Set the parameters of the estimator.
transform(X[, threshold])	Reduce X to its most important features.

__init__(penalty='l2', loss='l2', dual=True, tol=0.0001, C=None, multi_class='ovr', fit_intercept=True, intercept_scaling=1, scale_C=True, class_weight=None)

decision_function(X)

Decision function value for X according to the trained model.

Parameters :

X : array-like, shape = [n_samples, n_features]

Returns :

T : array-like, shape = [n_samples, n_class]

Returns the decision function of the sample for each class in the model.

fit(X, y, class_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

class_weight : {dict, ‘auto’}, optional

Weights associated with classes. If not given, all classes are supposed to have weight one.

Returns :

self : object

Returns self.

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters :

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns :

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

Notes

This method just calls fit and transform consecutively, i.e., it is not an optimized implementation of fit_transform, unlike other transformers such as PCA.

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

If True, will return the parameters for this estimator and contained subobjects that are estimators.

predict(X)

Predict target values of X according to the fitted model.

Parameters :X : {array-like, sparse matrix}, shape = [n_samples, n_features] Returns :C : array, shape = [n_samples]

score(X, y)

Returns the mean accuracy on the given test data and labels.

Parameters :

X : array-like, shape = [n_samples, n_features]

Training set.

y : array-like, shape = [n_samples]

Labels for X.

Returns :

z : float

set_params(**params)

Set the parameters of the estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns :self :

transform(X, threshold=None)

Reduce X to its most important features.

Parameters :

X : array or scipy sparse matrix of shape [n_samples, n_features]

The input samples.

threshold : string, float or None, optional (default=None)

The threshold value to use for feature selection. Features whose importance is greater or equal are kept while the others are discarded. If “median” (resp. “mean”), then the threshold value is the median (resp. the mean) of the feature importances. A scaling factor (e.g., “1.25*mean”) may also be used. If None and if available, the object attribute threshold is used. Otherwise, “mean” is used by default.

Returns :

X_r : array of shape [n_samples, n_selected_features]

The input samples with only the selected features.