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%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

Manifold Learning



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from sklearn.datasets import make_s_curve
X, y = make_s_curve(n_samples=1000)

from mpl_toolkits.mplot3d import Axes3D
ax = plt.axes(projection='3d')

ax.scatter3D(X[:, 0], X[:, 1], X[:, 2], c=y)
ax.view_init(10, -60)



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from sklearn.decomposition import PCA
pca = PCA(n_components=2).fit(X)
X_pca = pca.transform(X)
plt.scatter(X_pca[:, 0], X_pca[:, 1], c=y)



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from sklearn.manifold import Isomap

iso = Isomap(n_neighbors=20)
iso.fit(X)
X_iso = iso.transform(X)
plt.scatter(X_iso[:, 0], X_iso[:, 1], c=y)

Not all manifold learning algorithms can generalize!



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from sklearn.manifold import TSNE

tsne = TSNE()
tsne.fit(X)



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X_tsne = tsne.transform(X)



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X_tsne = tsne.embedding_



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X_tsne = tsne.fit_transform(X)

plt.scatter(X_tsne[:, 0], X_tsne[:, 1], c=y)

TSNE on the digits dataset



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from sklearn.datasets import load_digits
digits = load_digits(n_class=5)
X, y = digits.data, digits.target



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X_tsne = TSNE().fit_transform(X)



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plt.scatter(X_tsne[:, 0], X_tsne[:, 1])



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plt.scatter(X_tsne[:, 0], X_tsne[:, 1], c=y)