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

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

.. _sphx_glr_packages_scikit-learn_auto_examples_plot_separator.py:


Simple picture of the formal problem of machine learning
=========================================================

This example generates simple synthetic data ploints and shows a
separating hyperplane on them.




.. image:: /packages/scikit-learn/auto_examples/images/sphx_glr_plot_separator_001.png
    :class: sphx-glr-single-img





.. code-block:: python


    import numpy as np
    import matplotlib.pyplot as plt
    from sklearn.linear_model import SGDClassifier
    from sklearn.datasets.samples_generator import make_blobs

    # we create 50 separable synthetic points
    X, Y = make_blobs(n_samples=50, centers=2,
                      random_state=0, cluster_std=0.60)

    # fit the model
    clf = SGDClassifier(loss="hinge", alpha=0.01,
                        fit_intercept=True)
    clf.fit(X, Y)

    # plot the line, the points, and the nearest vectors to the plane
    xx = np.linspace(-1, 5, 10)
    yy = np.linspace(-1, 5, 10)

    X1, X2 = np.meshgrid(xx, yy)
    Z = np.empty(X1.shape)
    for (i, j), val in np.ndenumerate(X1):
        x1 = val
        x2 = X2[i, j]
        p = clf.decision_function([[x1, x2]])
        Z[i, j] = p[0]

    plt.figure(figsize=(4, 3))
    ax = plt.axes()
    ax.contour(X1, X2, Z, [-1.0, 0.0, 1.0], colors='k',
               linestyles=['dashed', 'solid', 'dashed'])
    ax.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)

    ax.axis('tight')


    plt.show()

**Total running time of the script:** ( 0 minutes  0.026 seconds)


.. _sphx_glr_download_packages_scikit-learn_auto_examples_plot_separator.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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