.. _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 <plot_separating_hyperplane.py>`


.. container:: sphx-glr-download

    **Download IPython notebook:** :download:`plot_separating_hyperplane.ipynb <plot_separating_hyperplane.ipynb>`