121 lines
3.7 KiB
Python
121 lines
3.7 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 problems.
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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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def make_meshgrid(x, y, h=.02):
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"""Create a mesh of points to plot in
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Parameters
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----------
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x: data to base x-axis meshgrid on
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y: data to base y-axis meshgrid on
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h: stepsize for meshgrid, optional
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Returns
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-------
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xx, yy : ndarray
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"""
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x_min, x_max = x.min() - 1, x.max() + 1
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y_min, y_max = y.min() - 1, y.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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return xx, yy
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def plot_contours(ax, clf, xx, yy, **params):
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"""Plot the decision boundaries for a classifier.
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Parameters
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----------
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ax: matplotlib axes object
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clf: a classifier
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xx: meshgrid ndarray
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yy: meshgrid ndarray
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params: dictionary of params to pass to contourf, optional
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"""
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Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
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Z = Z.reshape(xx.shape)
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out = ax.contourf(xx, yy, Z, **params)
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return out
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# import some data to play with
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iris = datasets.load_iris()
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# Take the first two features. We could avoid this by using a two-dim dataset
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X = iris.data[:, :2]
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y = iris.target
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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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models = (svm.SVC(kernel='linear', C=C),
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svm.LinearSVC(C=C),
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svm.SVC(kernel='rbf', gamma=0.7, C=C),
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svm.SVC(kernel='poly', degree=3, C=C))
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models = (clf.fit(X, y) for clf in models)
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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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# Set-up 2x2 grid for plotting.
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fig, sub = plt.subplots(2, 2)
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plt.subplots_adjust(wspace=0.4, hspace=0.4)
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X0, X1 = X[:, 0], X[:, 1]
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xx, yy = make_meshgrid(X0, X1)
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for clf, title, ax in zip(models, titles, sub.flatten()):
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plot_contours(ax, clf, xx, yy,
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cmap=plt.cm.coolwarm, alpha=0.8)
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ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
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ax.set_xlim(xx.min(), xx.max())
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ax.set_ylim(yy.min(), yy.max())
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ax.set_xlabel('Sepal length')
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ax.set_ylabel('Sepal width')
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ax.set_xticks(())
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ax.set_yticks(())
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ax.set_title(title)
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plt.show()
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