.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_packages_scikit-learn_auto_examples_plot_svm_non_linear.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_packages_scikit-learn_auto_examples_plot_svm_non_linear.py:


Example of linear and non-linear models
========================================

This is an example plot from the tutorial which accompanies an explanation
of the support vector machine GUI.



.. code-block:: python


    import numpy as np
    from matplotlib import pyplot as plt

    from sklearn import svm







data that is linearly separable



.. code-block:: python


    def linear_model(rseed=42, n_samples=30):
        " Generate data according to a linear model"
        np.random.seed(rseed)

        data = np.random.normal(0, 10, (n_samples, 2))
        data[:n_samples // 2] -= 15
        data[n_samples // 2:] += 15

        labels = np.ones(n_samples)
        labels[:n_samples // 2] = -1

        return data, labels


    X, y = linear_model()
    clf = svm.SVC(kernel='linear')
    clf.fit(X, y)

    plt.figure(figsize=(6, 4))
    ax = plt.subplot(111, xticks=[], yticks=[])
    ax.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.bone)

    ax.scatter(clf.support_vectors_[:, 0],
                clf.support_vectors_[:, 1],
                s=80, edgecolors="k", facecolors="none")

    delta = 1
    y_min, y_max = -50, 50
    x_min, x_max = -50, 50
    x = np.arange(x_min, x_max + delta, delta)
    y = np.arange(y_min, y_max + delta, delta)
    X1, X2 = np.meshgrid(x, y)
    Z = clf.decision_function(np.c_[X1.ravel(), X2.ravel()])
    Z = Z.reshape(X1.shape)

    ax.contour(X1, X2, Z, [-1.0, 0.0, 1.0], colors='k',
               linestyles=['dashed', 'solid', 'dashed'])





.. image:: /packages/scikit-learn/auto_examples/images/sphx_glr_plot_svm_non_linear_001.png
    :class: sphx-glr-single-img




data with a non-linear separation



.. code-block:: python


    def nonlinear_model(rseed=42, n_samples=30):
        radius = 40 * np.random.random(n_samples)
        far_pts = radius > 20
        radius[far_pts] *= 1.2
        radius[~far_pts] *= 1.1

        theta = np.random.random(n_samples) * np.pi * 2

        data = np.empty((n_samples, 2))
        data[:, 0] = radius * np.cos(theta)
        data[:, 1] = radius * np.sin(theta)

        labels = np.ones(n_samples)
        labels[far_pts] = -1

        return data, labels


    X, y = nonlinear_model()
    clf = svm.SVC(kernel='rbf', gamma=0.001, coef0=0, degree=3)
    clf.fit(X, y)

    plt.figure(figsize=(6, 4))
    ax = plt.subplot(1, 1, 1, xticks=[], yticks=[])
    ax.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.bone, zorder=2)

    ax.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],
               s=80, edgecolors="k", facecolors="none")

    delta = 1
    y_min, y_max = -50, 50
    x_min, x_max = -50, 50
    x = np.arange(x_min, x_max + delta, delta)
    y = np.arange(y_min, y_max + delta, delta)
    X1, X2 = np.meshgrid(x, y)
    Z = clf.decision_function(np.c_[X1.ravel(), X2.ravel()])
    Z = Z.reshape(X1.shape)

    ax.contour(X1, X2, Z, [-1.0, 0.0, 1.0], colors='k',
                linestyles=['dashed', 'solid', 'dashed'], zorder=1)

    plt.show()



.. image:: /packages/scikit-learn/auto_examples/images/sphx_glr_plot_svm_non_linear_002.png
    :class: sphx-glr-single-img




**Total running time of the script:** ( 0 minutes  0.047 seconds)


.. _sphx_glr_download_packages_scikit-learn_auto_examples_plot_svm_non_linear.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_svm_non_linear.py <plot_svm_non_linear.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_svm_non_linear.ipynb <plot_svm_non_linear.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_