.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/dimension_reduction/diffusion_maps/dmaps_swiss_role.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_dimension_reduction_diffusion_maps_dmaps_swiss_role.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_dimension_reduction_diffusion_maps_dmaps_swiss_role.py:


S-Curve
=====================

This example shows how to use the :class:`.DiffusionMaps` class to reveal the embedded structure of S-Curve data.

.. GENERATED FROM PYTHON SOURCE LINES 10-17

.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt
    from UQpy.utilities.kernels.GaussianKernel import GaussianKernel
    from UQpy.dimension_reduction.diffusion_maps.DiffusionMaps import DiffusionMaps
    from sklearn.datasets import make_swiss_roll, make_s_curve


.. GENERATED FROM PYTHON SOURCE LINES 18-19

Sample points randomly following a parametric curve and plot the 3D graphic.

.. GENERATED FROM PYTHON SOURCE LINES 22-29

.. code-block:: default


    n = 4000  # number of samples

    # generate point cloud
    # X, X_color = make_s_curve(n, random_state=3, noise=0)
    X, X_color = make_s_curve(n, random_state=3, noise=0)


.. GENERATED FROM PYTHON SOURCE LINES 30-31

plot the point cloud

.. GENERATED FROM PYTHON SOURCE LINES 31-40

.. code-block:: default

    fig = plt.figure(figsize=(8, 8))
    ax = fig.add_subplot(111, projection="3d")
    ax.scatter(X[:, 0], X[:, 1], X[:, 2], c=X_color, cmap=plt.cm.Spectral)
    ax.set_xlabel("x")
    ax.set_ylabel("y")
    ax.set_zlabel("z")
    ax.set_title("S-curve data")
    ax.view_init(10, 70)


.. GENERATED FROM PYTHON SOURCE LINES 41-42

Case 1: Find the optimal parameter of the Gaussian kernel scale epsilon

.. GENERATED FROM PYTHON SOURCE LINES 43-52

.. code-block:: default

    kernel = GaussianKernel(epsilon=0.65)


    dmaps_object = DiffusionMaps(data=X,
                                 alpha=1.0, n_eigenvectors=9,
                                 is_sparse=True, n_neighbors=100,
                                 kernel=kernel)



.. GENERATED FROM PYTHON SOURCE LINES 53-55

Find the parsimonious representation of the eigenvectors. Identify the two most informative
eigenvectors.

.. GENERATED FROM PYTHON SOURCE LINES 56-61

.. code-block:: default


    dmaps_object.parsimonious(dim=2)

    print('most informative eigenvectors:', dmaps_object.parsimonious_indices)


.. GENERATED FROM PYTHON SOURCE LINES 62-63

Plot the diffusion coordinates

.. GENERATED FROM PYTHON SOURCE LINES 64-68

.. code-block:: default


    DiffusionMaps._plot_eigen_pairs(dmaps_object.eigenvectors, pair_indices=dmaps_object.parsimonious_indices,
                                    color=X_color, figure_size=[12, 12])
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_dimension_reduction_diffusion_maps_dmaps_swiss_role.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/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/dimension_reduction/diffusion_maps/dmaps_swiss_role.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


.. only:: html

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

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