.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/svm/plot_svm_margin.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_svm_plot_svm_margin.py>`
        to download the full example code. or to run this example in your browser via JupyterLite or Binder

.. rst-class:: sphx-glr-example-title

.. _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.

.. GENERATED FROM PYTHON SOURCE LINES 15-91



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/svm/images/sphx_glr_plot_svm_margin_001.png
         :alt: plot svm margin
         :srcset: /auto_examples/svm/images/sphx_glr_plot_svm_margin_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/svm/images/sphx_glr_plot_svm_margin_002.png
         :alt: plot svm margin
         :srcset: /auto_examples/svm/images/sphx_glr_plot_svm_margin_002.png
         :class: sphx-glr-multi-img





.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause

    import matplotlib.pyplot as plt
    import numpy as np

    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.get_cmap("RdBu"), edgecolors="k"
        )

        plt.axis("tight")
        x_min = -4.8
        x_max = 4.2
        y_min = -6
        y_max = 6

        YY, XX = np.meshgrid(yy, xx)
        xy = np.vstack([XX.ravel(), YY.ravel()]).T
        Z = clf.decision_function(xy).reshape(XX.shape)

        # Put the result into a contour plot
        plt.contourf(XX, YY, Z, cmap=plt.get_cmap("RdBu"), alpha=0.5, linestyles=["-"])

        plt.xlim(x_min, x_max)
        plt.ylim(y_min, y_max)

        plt.xticks(())
        plt.yticks(())
        fignum = fignum + 1

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.065 seconds)


.. _sphx_glr_download_auto_examples_svm_plot_svm_margin.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.6.X?urlpath=lab/tree/notebooks/auto_examples/svm/plot_svm_margin.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/index.html?path=auto_examples/svm/plot_svm_margin.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

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

    .. container:: sphx-glr-download sphx-glr-download-python

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_svm_margin.zip <plot_svm_margin.zip>`


.. include:: plot_svm_margin.recommendations


.. only:: html

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

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