.. _sphx_glr_auto_examples_svm_plot_svm_margin.py: ========================================================= SVM Margins Example ========================================================= The plots below illustrate the effect the parameter `C` has on the separation line. A large value of `C` basically tells our model that we do not have that much faith in our data's distribution, and will only consider points close to line of separation. A small value of `C` includes more/all the observations, allowing the margins to be calculated using all the data in the area. .. rst-class:: sphx-glr-horizontal * .. image:: /auto_examples/svm/images/sphx_glr_plot_svm_margin_001.png :scale: 47 * .. image:: /auto_examples/svm/images/sphx_glr_plot_svm_margin_002.png :scale: 47 .. code-block:: python print(__doc__) # Code source: Gaƫl Varoquaux # Modified for documentation by Jaques Grobler # License: BSD 3 clause import numpy as np import matplotlib.pyplot as plt from sklearn import svm # we create 40 separable points np.random.seed(0) X = np.r_[np.random.randn(20, 2) - [2, 2], np.random.randn(20, 2) + [2, 2]] Y = [0] * 20 + [1] * 20 # figure number fignum = 1 # fit the model for name, penalty in (('unreg', 1), ('reg', 0.05)): clf = svm.SVC(kernel='linear', C=penalty) clf.fit(X, Y) # get the separating hyperplane w = clf.coef_[0] a = -w[0] / w[1] xx = np.linspace(-5, 5) yy = a * xx - (clf.intercept_[0]) / w[1] # plot the parallels to the separating hyperplane that pass through the # support vectors (margin away from hyperplane in direction # perpendicular to hyperplane). This is sqrt(1+a^2) away vertically in # 2-d. margin = 1 / np.sqrt(np.sum(clf.coef_ ** 2)) yy_down = yy - np.sqrt(1 + a ** 2) * margin yy_up = yy + np.sqrt(1 + a ** 2) * margin # plot the line, the points, and the nearest vectors to the plane plt.figure(fignum, figsize=(4, 3)) plt.clf() plt.plot(xx, yy, 'k-') plt.plot(xx, yy_down, 'k--') plt.plot(xx, yy_up, 'k--') plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], s=80, facecolors='none', zorder=10, edgecolors='k') plt.scatter(X[:, 0], X[:, 1], c=Y, zorder=10, cmap=plt.cm.Paired, edgecolors='k') plt.axis('tight') x_min = -4.8 x_max = 4.2 y_min = -6 y_max = 6 XX, YY = np.mgrid[x_min:x_max:200j, y_min:y_max:200j] Z = clf.predict(np.c_[XX.ravel(), YY.ravel()]) # Put the result into a color plot Z = Z.reshape(XX.shape) plt.figure(fignum, figsize=(4, 3)) plt.pcolormesh(XX, YY, Z, cmap=plt.cm.Paired) plt.xlim(x_min, x_max) plt.ylim(y_min, y_max) plt.xticks(()) plt.yticks(()) fignum = fignum + 1 plt.show() **Total running time of the script:** ( 0 minutes 0.093 seconds) .. container:: sphx-glr-footer .. container:: sphx-glr-download :download:`Download Python source code: plot_svm_margin.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_svm_margin.ipynb ` .. rst-class:: sphx-glr-signature `Generated by Sphinx-Gallery `_