88 lines
2.7 KiB
Python
88 lines
2.7 KiB
Python
"""
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=========================================
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Comparison of Manifold Learning methods
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=========================================
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An illustration of dimensionality reduction on the S-curve dataset
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with various manifold learning methods.
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For a discussion and comparison of these algorithms, see the
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:ref:`manifold module page <manifold>`
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For a similar example, where the methods are applied to a
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sphere dataset, see :ref:`sphx_glr_auto_examples_manifold_plot_manifold_sphere.py`
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Note that the purpose of the MDS is to find a low-dimensional
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representation of the data (here 2D) in which the distances respect well
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the distances in the original high-dimensional space, unlike other
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manifold-learning algorithms, it does not seeks an isotropic
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representation of the data in the low-dimensional space.
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"""
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# Author: Jake Vanderplas -- <vanderplas@astro.washington.edu>
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from collections import OrderedDict
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from functools import partial
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from time import time
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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from matplotlib.ticker import NullFormatter
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from sklearn import manifold, datasets
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# Next line to silence pyflakes. This import is needed.
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Axes3D
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n_points = 1000
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X, color = datasets.make_s_curve(n_points, random_state=0)
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n_neighbors = 10
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n_components = 2
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# Create figure
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fig = plt.figure(figsize=(15, 8))
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fig.suptitle(
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"Manifold Learning with %i points, %i neighbors" % (1000, n_neighbors), fontsize=14
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)
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# Add 3d scatter plot
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ax = fig.add_subplot(251, projection="3d")
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ax.scatter(X[:, 0], X[:, 1], X[:, 2], c=color, cmap=plt.cm.Spectral)
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ax.view_init(4, -72)
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# Set-up manifold methods
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LLE = partial(
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manifold.LocallyLinearEmbedding,
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n_neighbors=n_neighbors,
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n_components=n_components,
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eigen_solver="auto",
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)
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methods = OrderedDict()
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methods["LLE"] = LLE(method="standard")
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methods["LTSA"] = LLE(method="ltsa")
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methods["Hessian LLE"] = LLE(method="hessian")
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methods["Modified LLE"] = LLE(method="modified")
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methods["Isomap"] = manifold.Isomap(n_neighbors=n_neighbors, n_components=n_components)
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methods["MDS"] = manifold.MDS(n_components, max_iter=100, n_init=1)
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methods["SE"] = manifold.SpectralEmbedding(
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n_components=n_components, n_neighbors=n_neighbors
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)
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methods["t-SNE"] = manifold.TSNE(n_components=n_components, init="pca", random_state=0)
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# Plot results
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for i, (label, method) in enumerate(methods.items()):
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t0 = time()
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Y = method.fit_transform(X)
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t1 = time()
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print("%s: %.2g sec" % (label, t1 - t0))
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ax = fig.add_subplot(2, 5, 2 + i + (i > 3))
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ax.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
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ax.set_title("%s (%.2g sec)" % (label, t1 - t0))
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ax.xaxis.set_major_formatter(NullFormatter())
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ax.yaxis.set_major_formatter(NullFormatter())
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ax.axis("tight")
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plt.show()
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