.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_magnitude_shape_synthetic.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_plot_magnitude_shape_synthetic.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_plot_magnitude_shape_synthetic.py:


Magnitude-Shape Plot synthetic example
======================================

Shows the use of the MS-Plot applied to a synthetic dataset.

.. GENERATED FROM PYTHON SOURCE LINES 7-19

.. code-block:: Python


    # Author: Carlos Ramos Carreño
    # License: MIT

    # sphinx_gallery_thumbnail_number = 3

    import matplotlib.pyplot as plt
    import numpy as np

    import skfda
    from skfda.exploratory.visualization import MagnitudeShapePlot








.. GENERATED FROM PYTHON SOURCE LINES 20-21

First, we generate a synthetic dataset following [DaWe18]_

.. GENERATED FROM PYTHON SOURCE LINES 21-33

.. code-block:: Python


    random_state = np.random.RandomState(0)
    n_samples = 200

    fd = skfda.datasets.make_gaussian_process(
        n_samples=n_samples,
        n_features=100,
        cov=skfda.misc.covariances.Exponential(),
        mean=lambda t: 4 * t,
        random_state=random_state,
    )








.. GENERATED FROM PYTHON SOURCE LINES 34-35

We now add the outliers

.. GENERATED FROM PYTHON SOURCE LINES 35-94

.. code-block:: Python


    magnitude_outlier = skfda.datasets.make_gaussian_process(
        n_samples=1,
        n_features=100,
        cov=skfda.misc.covariances.Exponential(),
        mean=lambda t: 4 * t + 20,
        random_state=random_state,
    )

    shape_outlier_shift = skfda.datasets.make_gaussian_process(
        n_samples=1,
        n_features=100,
        cov=skfda.misc.covariances.Exponential(),
        mean=lambda t: 4 * t + 10 * (t > 0.4),
        random_state=random_state,
    )

    shape_outlier_peak = skfda.datasets.make_gaussian_process(
        n_samples=1,
        n_features=100,
        cov=skfda.misc.covariances.Exponential(),
        mean=lambda t: 4 * t - 10 * ((0.25 < t) & (t < 0.3)),
        random_state=random_state,
    )

    shape_outlier_sin = skfda.datasets.make_gaussian_process(
        n_samples=1,
        n_features=100,
        cov=skfda.misc.covariances.Exponential(),
        mean=lambda t: 4 * t + 2 * np.sin(18 * t),
        random_state=random_state,
    )

    shape_outlier_slope = skfda.datasets.make_gaussian_process(
        n_samples=1,
        n_features=100,
        cov=skfda.misc.covariances.Exponential(),
        mean=lambda t: 10 * t,
        random_state=random_state,
    )

    magnitude_shape_outlier = skfda.datasets.make_gaussian_process(
        n_samples=1,
        n_features=100,
        cov=skfda.misc.covariances.Exponential(),
        mean=lambda t: 4 * t + 2 * np.sin(18 * t) - 20,
        random_state=random_state,
    )


    fd = fd.concatenate(
        magnitude_outlier,
        shape_outlier_shift,
        shape_outlier_peak,
        shape_outlier_sin,
        shape_outlier_slope,
        magnitude_shape_outlier,
    )








.. GENERATED FROM PYTHON SOURCE LINES 95-96

The data is plotted to show the curves we are working with.

.. GENERATED FROM PYTHON SOURCE LINES 96-103

.. code-block:: Python

    labels = [0] * n_samples + [1] * 6

    fd.plot(
        group=labels,
        group_colors=['lightgrey', 'black'],
    )




.. image-sg:: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_001.png
   :alt: plot magnitude shape synthetic
   :srcset: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Figure size 640x480 with 1 Axes>



.. GENERATED FROM PYTHON SOURCE LINES 104-107

The MS-Plot is generated. In order to show the results, the
:func:`~skfda.exploratory.visualization.MagnitudeShapePlot.plot`
method is used.

.. GENERATED FROM PYTHON SOURCE LINES 107-112

.. code-block:: Python


    msplot = MagnitudeShapePlot(fd)

    msplot.plot()




.. image-sg:: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_002.png
   :alt: plot magnitude shape synthetic
   :srcset: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Figure size 640x480 with 1 Axes>



.. GENERATED FROM PYTHON SOURCE LINES 113-115

To show the utility of the plot, the curves are plotted showing each outlier
in a different color

.. GENERATED FROM PYTHON SOURCE LINES 115-132

.. code-block:: Python


    labels = [0] * n_samples + [1, 2, 3, 4, 5, 6]
    colors = [
        'lightgrey',
        'orange',
        'blue',
        'black',
        'green',
        'brown',
        'lightblue',
    ]

    fd.plot(
        group=labels,
        group_colors=colors,
    )




.. image-sg:: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_003.png
   :alt: plot magnitude shape synthetic
   :srcset: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_003.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Figure size 640x480 with 1 Axes>



.. GENERATED FROM PYTHON SOURCE LINES 133-134

We now show the points in the MS-plot using the same colors

.. GENERATED FROM PYTHON SOURCE LINES 134-146

.. code-block:: Python


    fig = plt.figure()
    ax = fig.add_subplot(1, 1, 1)
    ax.scatter(
        msplot.points[:, 0].ravel(),
        msplot.points[:, 1].ravel(),
        c=colors[:1] * n_samples + colors[1:],
    )
    ax.set_title("MS-Plot")
    ax.set_xlabel("magnitude outlyingness")
    ax.set_ylabel("shape outlyingness")




.. image-sg:: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_004.png
   :alt: MS-Plot
   :srcset: /auto_examples/images/sphx_glr_plot_magnitude_shape_synthetic_004.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(47.097222222222214, 0.5, 'shape outlyingness')



.. GENERATED FROM PYTHON SOURCE LINES 147-151

.. rubric:: References
.. [DaWe18] Dai, Wenlin, and Genton, Marc G. "Multivariate functional data
   visualization and outlier detection." Journal of Computational and
   Graphical Statistics 27.4 (2018): 923-934.


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

   **Total running time of the script:** (0 minutes 1.872 seconds)


.. _sphx_glr_download_auto_examples_plot_magnitude_shape_synthetic.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/GAA-UAM/scikit-fda/develop?filepath=examples/plot_magnitude_shape_synthetic.py
        :alt: Launch binder
        :width: 150 px

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

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

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

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


.. only:: html

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

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