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

    Click :ref:`here <sphx_glr_download_auto_examples_manifold_plot_compare_methods.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_manifold_plot_compare_methods.py:


=========================================
Comparison of Manifold Learning methods
=========================================

An illustration of dimensionality reduction on the S-curve dataset
with various manifold learning methods.

For a discussion and comparison of these algorithms, see the
:ref:`manifold module page <manifold>`

For a similar example, where the methods are applied to a
sphere dataset, see :ref:`sphx_glr_auto_examples_manifold_plot_manifold_sphere.py`

Note that the purpose of the MDS is to find a low-dimensional
representation of the data (here 2D) in which the distances respect well
the distances in the original high-dimensional space, unlike other
manifold-learning algorithms, it does not seeks an isotropic
representation of the data in the low-dimensional space.



.. image:: /auto_examples/manifold/images/sphx_glr_plot_compare_methods_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    LLE: 0.098 sec
    LTSA: 0.13 sec
    Hessian LLE: 0.21 sec
    Modified LLE: 0.18 sec
    Isomap: 0.38 sec
    MDS: 1.4 sec
    SE: 0.069 sec
    t-SNE: 6.8 sec






|


.. code-block:: default


    # Author: Jake Vanderplas -- <vanderplas@astro.washington.edu>

    print(__doc__)

    from collections import OrderedDict
    from functools import partial
    from time import time

    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    from matplotlib.ticker import NullFormatter

    from sklearn import manifold, datasets

    # Next line to silence pyflakes. This import is needed.
    Axes3D

    n_points = 1000
    X, color = datasets.make_s_curve(n_points, random_state=0)
    n_neighbors = 10
    n_components = 2

    # Create figure
    fig = plt.figure(figsize=(15, 8))
    fig.suptitle("Manifold Learning with %i points, %i neighbors"
                 % (1000, n_neighbors), fontsize=14)

    # Add 3d scatter plot
    ax = fig.add_subplot(251, projection='3d')
    ax.scatter(X[:, 0], X[:, 1], X[:, 2], c=color, cmap=plt.cm.Spectral)
    ax.view_init(4, -72)

    # Set-up manifold methods
    LLE = partial(manifold.LocallyLinearEmbedding,
                  n_neighbors, n_components, eigen_solver='auto')

    methods = OrderedDict()
    methods['LLE'] = LLE(method='standard')
    methods['LTSA'] = LLE(method='ltsa')
    methods['Hessian LLE'] = LLE(method='hessian')
    methods['Modified LLE'] = LLE(method='modified')
    methods['Isomap'] = manifold.Isomap(n_neighbors, n_components)
    methods['MDS'] = manifold.MDS(n_components, max_iter=100, n_init=1)
    methods['SE'] = manifold.SpectralEmbedding(n_components=n_components,
                                               n_neighbors=n_neighbors)
    methods['t-SNE'] = manifold.TSNE(n_components=n_components, init='pca',
                                     random_state=0)

    # Plot results
    for i, (label, method) in enumerate(methods.items()):
        t0 = time()
        Y = method.fit_transform(X)
        t1 = time()
        print("%s: %.2g sec" % (label, t1 - t0))
        ax = fig.add_subplot(2, 5, 2 + i + (i > 3))
        ax.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
        ax.set_title("%s (%.2g sec)" % (label, t1 - t0))
        ax.xaxis.set_major_formatter(NullFormatter())
        ax.yaxis.set_major_formatter(NullFormatter())
        ax.axis('tight')

    plt.show()


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

   **Total running time of the script:** ( 0 minutes  9.983 seconds)

**Estimated memory usage:**  53 MB


.. _sphx_glr_download_auto_examples_manifold_plot_compare_methods.py:


.. only :: html

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


  .. container:: binder-badge

    .. image:: https://mybinder.org/badge_logo.svg
      :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.22.X?urlpath=lab/tree/notebooks/auto_examples/manifold/plot_compare_methods.ipynb
      :width: 150 px


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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