84 lines
2.8 KiB
Python
84 lines
2.8 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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print(__doc__)
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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("Manifold Learning with %i points, %i neighbors"
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% (1000, n_neighbors), fontsize=14)
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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(manifold.LocallyLinearEmbedding,
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n_neighbors, n_components, eigen_solver='auto')
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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_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(n_components=n_components,
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n_neighbors=n_neighbors)
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methods['t-SNE'] = manifold.TSNE(n_components=n_components, init='pca',
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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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