.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/manifold/plot_manifold_sphere.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` 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_manifold_plot_manifold_sphere.py: ============================================= Manifold Learning methods on a severed sphere ============================================= An application of the different :ref:`manifold` techniques on a spherical data-set. Here one can see the use of dimensionality reduction in order to gain some intuition regarding the manifold learning methods. Regarding the dataset, the poles are cut from the sphere, as well as a thin slice down its side. This enables the manifold learning techniques to 'spread it open' whilst projecting it onto two dimensions. For a similar example, where the methods are applied to the S-curve dataset, see :ref:`sphx_glr_auto_examples_manifold_plot_compare_methods.py` Note that the purpose of the :ref:`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. Here the manifold problem matches fairly that of representing a flat map of the Earth, as with `map projection `_ .. GENERATED FROM PYTHON SOURCE LINES 27-158 .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_manifold_sphere_001.png :alt: Manifold Learning with 1000 points, 10 neighbors, LLE (0.059 sec), LTSA (0.1 sec), Hessian LLE (0.17 sec), Modified LLE (0.12 sec), Isomap (0.2 sec), MDS (0.84 sec), Spectral Embedding (0.048 sec), t-SNE (3.9 sec) :srcset: /auto_examples/manifold/images/sphx_glr_plot_manifold_sphere_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none standard: 0.059 sec ltsa: 0.1 sec hessian: 0.17 sec modified: 0.12 sec ISO: 0.2 sec MDS: 0.84 sec Spectral Embedding: 0.048 sec t-SNE: 3.9 sec | .. code-block:: Python # Author: Jaques Grobler # License: BSD 3 clause from time import time import matplotlib.pyplot as plt # Unused but required import for doing 3d projections with matplotlib < 3.2 import mpl_toolkits.mplot3d # noqa: F401 import numpy as np from matplotlib.ticker import NullFormatter from sklearn import manifold from sklearn.utils import check_random_state # Variables for manifold learning. n_neighbors = 10 n_samples = 1000 # Create our sphere. random_state = check_random_state(0) p = random_state.rand(n_samples) * (2 * np.pi - 0.55) t = random_state.rand(n_samples) * np.pi # Sever the poles from the sphere. indices = (t < (np.pi - (np.pi / 8))) & (t > ((np.pi / 8))) colors = p[indices] x, y, z = ( np.sin(t[indices]) * np.cos(p[indices]), np.sin(t[indices]) * np.sin(p[indices]), np.cos(t[indices]), ) # Plot our dataset. fig = plt.figure(figsize=(15, 8)) plt.suptitle( "Manifold Learning with %i points, %i neighbors" % (1000, n_neighbors), fontsize=14 ) ax = fig.add_subplot(251, projection="3d") ax.scatter(x, y, z, c=p[indices], cmap=plt.cm.rainbow) ax.view_init(40, -10) sphere_data = np.array([x, y, z]).T # Perform Locally Linear Embedding Manifold learning methods = ["standard", "ltsa", "hessian", "modified"] labels = ["LLE", "LTSA", "Hessian LLE", "Modified LLE"] for i, method in enumerate(methods): t0 = time() trans_data = ( manifold.LocallyLinearEmbedding( n_neighbors=n_neighbors, n_components=2, method=method, random_state=42 ) .fit_transform(sphere_data) .T ) t1 = time() print("%s: %.2g sec" % (methods[i], t1 - t0)) ax = fig.add_subplot(252 + i) plt.scatter(trans_data[0], trans_data[1], c=colors, cmap=plt.cm.rainbow) plt.title("%s (%.2g sec)" % (labels[i], t1 - t0)) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) plt.axis("tight") # Perform Isomap Manifold learning. t0 = time() trans_data = ( manifold.Isomap(n_neighbors=n_neighbors, n_components=2) .fit_transform(sphere_data) .T ) t1 = time() print("%s: %.2g sec" % ("ISO", t1 - t0)) ax = fig.add_subplot(257) plt.scatter(trans_data[0], trans_data[1], c=colors, cmap=plt.cm.rainbow) plt.title("%s (%.2g sec)" % ("Isomap", t1 - t0)) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) plt.axis("tight") # Perform Multi-dimensional scaling. t0 = time() mds = manifold.MDS(2, max_iter=100, n_init=1, random_state=42) trans_data = mds.fit_transform(sphere_data).T t1 = time() print("MDS: %.2g sec" % (t1 - t0)) ax = fig.add_subplot(258) plt.scatter(trans_data[0], trans_data[1], c=colors, cmap=plt.cm.rainbow) plt.title("MDS (%.2g sec)" % (t1 - t0)) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) plt.axis("tight") # Perform Spectral Embedding. t0 = time() se = manifold.SpectralEmbedding( n_components=2, n_neighbors=n_neighbors, random_state=42 ) trans_data = se.fit_transform(sphere_data).T t1 = time() print("Spectral Embedding: %.2g sec" % (t1 - t0)) ax = fig.add_subplot(259) plt.scatter(trans_data[0], trans_data[1], c=colors, cmap=plt.cm.rainbow) plt.title("Spectral Embedding (%.2g sec)" % (t1 - t0)) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) plt.axis("tight") # Perform t-distributed stochastic neighbor embedding. t0 = time() tsne = manifold.TSNE(n_components=2, random_state=0) trans_data = tsne.fit_transform(sphere_data).T t1 = time() print("t-SNE: %.2g sec" % (t1 - t0)) ax = fig.add_subplot(2, 5, 10) plt.scatter(trans_data[0], trans_data[1], c=colors, cmap=plt.cm.rainbow) 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() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 5.956 seconds) .. _sphx_glr_download_auto_examples_manifold_plot_manifold_sphere.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/main?urlpath=lab/tree/notebooks/auto_examples/manifold/plot_manifold_sphere.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/manifold/plot_manifold_sphere.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_manifold_sphere.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_manifold_sphere.py ` .. include:: plot_manifold_sphere.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_