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Plot different SVM classifiers in the iris dataset¶
Comparison of different linear SVM classifiers on a 2D projection of the iris dataset. We only consider the first 2 features of this dataset:
This example shows how to plot the decision surface for four SVM classifiers with different kernels.
The linear models
SVC(kernel='linear') yield slightly
different decision boundaries. This can be a consequence of the following
LinearSVCminimizes the squared hinge loss while
SVCminimizes the regular hinge loss.
LinearSVCuses the One-vs-All (also known as One-vs-Rest) multiclass reduction while
SVCuses the One-vs-One multiclass reduction.
Both linear models have linear decision boundaries (intersecting hyperplanes) while the non-linear kernel models (polynomial or Gaussian RBF) have more flexible non-linear decision boundaries with shapes that depend on the kind of kernel and its parameters.
while plotting the decision function of classifiers for toy 2D datasets can help get an intuitive understanding of their respective expressive power, be aware that those intuitions don’t always generalize to more realistic high-dimensional problems.
import matplotlib.pyplot as plt from sklearn import svm, datasets from sklearn.inspection import DecisionBoundaryDisplay # import some data to play with iris = datasets.load_iris() # Take the first two features. We could avoid this by using a two-dim dataset X = iris.data[:, :2] y = iris.target # we create an instance of SVM and fit out data. We do not scale our # data since we want to plot the support vectors C = 1.0 # SVM regularization parameter models = ( svm.SVC(kernel="linear", C=C), svm.LinearSVC(C=C, max_iter=10000), svm.SVC(kernel="rbf", gamma=0.7, C=C), svm.SVC(kernel="poly", degree=3, gamma="auto", C=C), ) models = (clf.fit(X, y) for clf in models) # title for the plots titles = ( "SVC with linear kernel", "LinearSVC (linear kernel)", "SVC with RBF kernel", "SVC with polynomial (degree 3) kernel", ) # Set-up 2x2 grid for plotting. fig, sub = plt.subplots(2, 2) plt.subplots_adjust(wspace=0.4, hspace=0.4) X0, X1 = X[:, 0], X[:, 1] for clf, title, ax in zip(models, titles, sub.flatten()): disp = DecisionBoundaryDisplay.from_estimator( clf, X, response_method="predict", cmap=plt.cm.coolwarm, alpha=0.8, ax=ax, xlabel=iris.feature_names, ylabel=iris.feature_names, ) ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors="k") ax.set_xticks(()) ax.set_yticks(()) ax.set_title(title) plt.show()
Total running time of the script: ( 0 minutes 0.227 seconds)