94 lines
3.2 KiB
Python
94 lines
3.2 KiB
Python
"""
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==================================================
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Plot different SVM classifiers in the iris dataset
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==================================================
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Comparison of different linear SVM classifiers on a 2D projection of the iris
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dataset. We only consider the first 2 features of this dataset:
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- Sepal length
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- Sepal width
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This example shows how to plot the decision surface for four SVM classifiers
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with different kernels.
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The linear models ``LinearSVC()`` and ``SVC(kernel='linear')`` yield slightly
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different decision boundaries. This can be a consequence of the following
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differences:
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- ``LinearSVC`` minimizes the squared hinge loss while ``SVC`` minimizes the
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regular hinge loss.
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- ``LinearSVC`` uses the One-vs-All (also known as One-vs-Rest) multiclass
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reduction while ``SVC`` uses the One-vs-One multiclass reduction.
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Both linear models have linear decision boundaries (intersecting hyperplanes)
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while the non-linear kernel models (polynomial or Gaussian RBF) have more
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flexible non-linear decision boundaries with shapes that depend on the kind of
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kernel and its parameters.
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.. NOTE:: while plotting the decision function of classifiers for toy 2D
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datasets can help get an intuitive understanding of their respective
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expressive power, be aware that those intuitions don't always generalize to
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more realistic high-dimensional problem.
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"""
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print(__doc__)
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn import svm, datasets
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# import some data to play with
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iris = datasets.load_iris()
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X = iris.data[:, :2] # we only take the first two features. We could
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# avoid this ugly slicing by using a two-dim dataset
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y = iris.target
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h = .02 # step size in the mesh
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# we create an instance of SVM and fit out data. We do not scale our
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# data since we want to plot the support vectors
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C = 1.0 # SVM regularization parameter
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svc = svm.SVC(kernel='linear', C=C).fit(X, y)
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rbf_svc = svm.SVC(kernel='rbf', gamma=0.7, C=C).fit(X, y)
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poly_svc = svm.SVC(kernel='poly', degree=3, C=C).fit(X, y)
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lin_svc = svm.LinearSVC(C=C).fit(X, y)
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# create a mesh to plot in
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x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
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y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
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xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
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np.arange(y_min, y_max, h))
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# title for the plots
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titles = ['SVC with linear kernel',
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'LinearSVC (linear kernel)',
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'SVC with RBF kernel',
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'SVC with polynomial (degree 3) kernel']
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for i, clf in enumerate((svc, lin_svc, rbf_svc, poly_svc)):
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# Plot the decision boundary. For that, we will assign a color to each
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# point in the mesh [x_min, m_max]x[y_min, y_max].
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plt.subplot(2, 2, i + 1)
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plt.subplots_adjust(wspace=0.4, hspace=0.4)
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Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
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# Put the result into a color plot
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Z = Z.reshape(xx.shape)
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plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)
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# Plot also the training points
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plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Paired)
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plt.xlabel('Sepal length')
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plt.ylabel('Sepal width')
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plt.xlim(xx.min(), xx.max())
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plt.ylim(yy.min(), yy.max())
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plt.xticks(())
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plt.yticks(())
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plt.title(titles[i])
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plt.show()
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