.. _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
    :align: center


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

 Out::

      standard: 0.2 sec
    ltsa: 0.35 sec
    hessian: 0.48 sec
    modified: 0.39 sec
    Isomap: 0.47 sec
    MDS: 2.4 sec
    SpectralEmbedding: 0.21 sec
    t-SNE: 3.8 sec




|


.. code-block:: python


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

    print(__doc__)

    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.samples_generator.make_s_curve(n_points, random_state=0)
    n_neighbors = 10
    n_components = 2

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

    try:
        # compatibility matplotlib < 1.0
        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)
    except:
        ax = fig.add_subplot(251, projection='3d')
        plt.scatter(X[:, 0], X[:, 2], c=color, cmap=plt.cm.Spectral)

    methods = ['standard', 'ltsa', 'hessian', 'modified']
    labels = ['LLE', 'LTSA', 'Hessian LLE', 'Modified LLE']

    for i, method in enumerate(methods):
        t0 = time()
        Y = manifold.LocallyLinearEmbedding(n_neighbors, n_components,
                                            eigen_solver='auto',
                                            method=method).fit_transform(X)
        t1 = time()
        print("%s: %.2g sec" % (methods[i], t1 - t0))

        ax = fig.add_subplot(252 + i)
        plt.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
        plt.title("%s (%.2g sec)" % (labels[i], t1 - t0))
        ax.xaxis.set_major_formatter(NullFormatter())
        ax.yaxis.set_major_formatter(NullFormatter())
        plt.axis('tight')

    t0 = time()
    Y = manifold.Isomap(n_neighbors, n_components).fit_transform(X)
    t1 = time()
    print("Isomap: %.2g sec" % (t1 - t0))
    ax = fig.add_subplot(257)
    plt.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
    plt.title("Isomap (%.2g sec)" % (t1 - t0))
    ax.xaxis.set_major_formatter(NullFormatter())
    ax.yaxis.set_major_formatter(NullFormatter())
    plt.axis('tight')


    t0 = time()
    mds = manifold.MDS(n_components, max_iter=100, n_init=1)
    Y = mds.fit_transform(X)
    t1 = time()
    print("MDS: %.2g sec" % (t1 - t0))
    ax = fig.add_subplot(258)
    plt.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
    plt.title("MDS (%.2g sec)" % (t1 - t0))
    ax.xaxis.set_major_formatter(NullFormatter())
    ax.yaxis.set_major_formatter(NullFormatter())
    plt.axis('tight')


    t0 = time()
    se = manifold.SpectralEmbedding(n_components=n_components,
                                    n_neighbors=n_neighbors)
    Y = se.fit_transform(X)
    t1 = time()
    print("SpectralEmbedding: %.2g sec" % (t1 - t0))
    ax = fig.add_subplot(259)
    plt.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
    plt.title("SpectralEmbedding (%.2g sec)" % (t1 - t0))
    ax.xaxis.set_major_formatter(NullFormatter())
    ax.yaxis.set_major_formatter(NullFormatter())
    plt.axis('tight')

    t0 = time()
    tsne = manifold.TSNE(n_components=n_components, init='pca', random_state=0)
    Y = tsne.fit_transform(X)
    t1 = time()
    print("t-SNE: %.2g sec" % (t1 - t0))
    ax = fig.add_subplot(2, 5, 10)
    plt.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
    plt.title("t-SNE (%.2g sec)" % (t1 - t0))
    ax.xaxis.set_major_formatter(NullFormatter())
    ax.yaxis.set_major_formatter(NullFormatter())
    plt.axis('tight')

    plt.show()

**Total running time of the script:**
(0 minutes 9.038 seconds)



.. container:: sphx-glr-download

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


.. container:: sphx-glr-download

    **Download IPython notebook:** :download:`plot_compare_methods.ipynb <plot_compare_methods.ipynb>`