92 lines
2.5 KiB
Python
92 lines
2.5 KiB
Python
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"""
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=========================================================
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SVM Margins Example
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=========================================================
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The plots below illustrate the effect the parameter `C` has
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on the separation line. A large value of `C` basically tells
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our model that we do not have that much faith in our data's
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distribution, and will only consider points close to line
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of separation.
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A small value of `C` includes more/all the observations, allowing
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the margins to be calculated using all the data in the area.
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"""
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# Code source: Gaël Varoquaux
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# Modified for documentation by Jaques Grobler
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# License: BSD 3 clause
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn import svm
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# we create 40 separable points
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np.random.seed(0)
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X = np.r_[np.random.randn(20, 2) - [2, 2], np.random.randn(20, 2) + [2, 2]]
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Y = [0] * 20 + [1] * 20
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# figure number
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fignum = 1
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# fit the model
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for name, penalty in (("unreg", 1), ("reg", 0.05)):
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clf = svm.SVC(kernel="linear", C=penalty)
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clf.fit(X, Y)
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# get the separating hyperplane
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w = clf.coef_[0]
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a = -w[0] / w[1]
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xx = np.linspace(-5, 5)
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yy = a * xx - (clf.intercept_[0]) / w[1]
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# plot the parallels to the separating hyperplane that pass through the
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# support vectors (margin away from hyperplane in direction
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# perpendicular to hyperplane). This is sqrt(1+a^2) away vertically in
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# 2-d.
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margin = 1 / np.sqrt(np.sum(clf.coef_**2))
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yy_down = yy - np.sqrt(1 + a**2) * margin
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yy_up = yy + np.sqrt(1 + a**2) * margin
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# plot the line, the points, and the nearest vectors to the plane
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plt.figure(fignum, figsize=(4, 3))
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plt.clf()
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plt.plot(xx, yy, "k-")
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plt.plot(xx, yy_down, "k--")
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plt.plot(xx, yy_up, "k--")
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plt.scatter(
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clf.support_vectors_[:, 0],
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clf.support_vectors_[:, 1],
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s=80,
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facecolors="none",
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zorder=10,
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edgecolors="k",
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)
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plt.scatter(
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X[:, 0], X[:, 1], c=Y, zorder=10, cmap=plt.get_cmap("RdBu"), edgecolors="k"
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)
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plt.axis("tight")
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x_min = -4.8
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x_max = 4.2
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y_min = -6
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y_max = 6
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YY, XX = np.meshgrid(yy, xx)
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xy = np.vstack([XX.ravel(), YY.ravel()]).T
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Z = clf.decision_function(xy).reshape(XX.shape)
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# Put the result into a contour plot
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plt.contourf(XX, YY, Z, cmap=plt.get_cmap("RdBu"), alpha=0.5, linestyles=["-"])
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plt.xlim(x_min, x_max)
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plt.ylim(y_min, y_max)
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plt.xticks(())
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plt.yticks(())
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fignum = fignum + 1
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plt.show()
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