decreases for higher degrees in practicethe mathematical details behind the kernel svm are not that importantthoughand how an svm with an rbf kernel makes decision can be summarized quite easily--we'll do so in the next section understanding svms during trainingthe svm learns how important each of the training data points is to represent the decision boundary between the two classes typically only subset of the training points matter for defining the decision boundarythe ones that lie on the border between the classes these are called support vectors and give the support vector machine its name to make prediction for new pointthe distance to each of the support vectors is measured classification decision is made based on the distances to the support vectorand the importance of the support vectors that was learned during training (stored in the dual_coef_ attribute of svcthe distance between data points is measured by the gaussian kernelkrbf( exp ( || || herex and are data points| |denotes euclidean distanceand (gammais parameter that controls the width of the gaussian kernel figure - shows the result of training support vector machine on twodimensional two-class dataset the decision boundary is shown in blackand the support vectors are larger points with the wide outline the following code creates this plot by training an svm on the forge datasetin[ ]from sklearn svm import svc xy mglearn tools make_handcrafted_dataset(svm svc(kernel='rbf' = gamma= fit(xymglearn plots plot_ d_separator(svmxeps mglearn discrete_scatter( [: ] [: ]yplot support vectors sv svm support_vectors_ class labels of support vectors are given by the sign of the dual coefficients sv_labels svm dual_coef_ ravel( mglearn discrete_scatter(sv[: ]sv[: ]sv_labelss= markeredgewidth= plt xlabel("feature "plt ylabel("feature " this follows from the taylor expansion of the exponential map supervised learning