.. _sphx_glr_auto_examples_svm_plot_separating_hyperplane.py: ========================================= SVM: Maximum margin separating hyperplane ========================================= Plot the maximum margin separating hyperplane within a two-class separable dataset using a Support Vector Machine classifier with linear kernel. .. image:: /auto_examples/svm/images/sphx_glr_plot_separating_hyperplane_001.png :align: center .. code-block:: python print(__doc__) 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 # fit the model clf = svm.SVC(kernel='linear') 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 b = clf.support_vectors_[0] yy_down = a * xx + (b[1] - a * b[0]) b = clf.support_vectors_[-1] yy_up = a * xx + (b[1] - a * b[0]) # plot the line, the points, and the nearest vectors to the plane 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') plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired) plt.axis('tight') plt.show() **Total running time of the script:** (0 minutes 0.061 seconds) .. container:: sphx-glr-download **Download Python source code:** :download:`plot_separating_hyperplane.py ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_separating_hyperplane.ipynb `