LinearSVC

• Corresponde al modelo SVC con kernel lineal.

• Sus parámetros se calculan solucionando la ecuación:

\min_{w,b} \frac{1}{2} w^T w + C \sum_{i=1}^n \max \left(0, 1-y_i \left( w^T \phi(x_i)+ b \right) \right)

• Se usa la función de hinge (o hinge2) como métrica de error.

from sklearn.datasets import make_blobs

NPOINTS = 150

X, d = make_blobs(
    n_samples=NPOINTS,
    n_features=2,
    centers=3,
    cluster_std=0.8,
    shuffle=False,
    random_state=12345,
)

from sklearn.svm import LinearSVC

linearSVC = LinearSVC(
    # --------------------------------------------------------------------------
    # Specifies the norm used in the penalization {'l1', 'l2'}. The ‘l2’
    # penalty is the standard used in SVC.
    penalty='l2',
    # --------------------------------------------------------------------------
    # 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.
    # The combination of penalty='l1' and loss='hinge' is not supported.
    loss='hinge',
    # --------------------------------------------------------------------------
    # Tolerance for stopping criterion.
    tol=1e-3,
    # --------------------------------------------------------------------------
    # Regularization parameter. The strength of the regularization is inversely
    # proportional to C. Must be strictly positive.
    # penalty.
    C=1,
    # --------------------------------------------------------------------------
    # Whether to calculate the intercept for this model. If set to false, no
    # intercept will be used in calculations
    fit_intercept=True,
    # --------------------------------------------------------------------------
    # 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.
    intercept_scaling=1.0,
    # --------------------------------------------------------------------------
    # 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)).
    class_weight=None,
    # --------------------------------------------------------------------------
    # The maximum number of iterations to be run.
    max_iter=1000,
)

linearSVC.fit(X, d)
linearSVC.predict(X)

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])

linearSVC.score(X, d)

1.0

linearSVC.coef_

array([[ 0.23076305, -0.21562713],
       [-0.33610822, -0.30659105],
       [-0.07930195,  0.56635286]])

linearSVC.intercept_

array([-1.34329076, -0.70744767,  0.79081926])

linearSVC.classes_

array([0, 1, 2])