93 lines
3.2 KiB
Python
93 lines
3.2 KiB
Python
"""
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===============================================
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Handwritten digits and Locally Linear Embedding
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===============================================
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An illustration of locally linear embedding on the digits dataset.
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"""
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# Authors: Fabian Pedregosa <fabian.pedregosa@inria.fr>
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# Olivier Grisel <olivier.grisel@ensta.org>
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# Mathieu Blondel <mathieu@mblondel.org>
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# License: BSD, (C) INRIA 2011
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print __doc__
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import numpy as np
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import pylab as pl
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from matplotlib import offsetbox
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from scikits.learn.utils.fixes import qr_economic
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from scikits.learn import manifold, datasets, decomposition, lda
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digits = datasets.load_digits(n_class=6)
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X = digits.data
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y = digits.target
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n_samples, n_features = X.shape
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#----------------------------------------------------------------------
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# Random 2D projection using a random unitary matrix
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print "Computing random projection"
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rng = np.random.RandomState(42)
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Q, _ = qr_economic(rng.normal(size=(n_features, 2)))
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X_projected = np.dot(Q.T, X.T).T
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#----------------------------------------------------------------------
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# Projection on to the first 2 principal components
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print "Computing PCA projection"
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X_pca = decomposition.RandomizedPCA(n_components=2).fit_transform(X)
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#----------------------------------------------------------------------
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# Projection on to the first 2 linear discriminant components
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print "Computing LDA projection"
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X2 = X.copy()
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X2.flat[::X.shape[1] + 1] += 0.01 # Make X invertible
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X_lda = lda.LDA(n_components=2).fit_transform(X2, y)
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#----------------------------------------------------------------------
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# Locally linear embedding of the digits dataset
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print "Computing LLE embedding"
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X_lle, err = manifold.locally_linear_embedding(X, 30, 2, reg=1e-2)
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print "Done. Reconstruction error: %g" % err
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#----------------------------------------------------------------------
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# Scale and visualize the embedding vectors
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def plot_embedding(X, title=None):
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x_min, x_max = np.min(X, 0), np.max(X, 0)
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X = (X - x_min) / (x_max - x_min)
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pl.figure()
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ax = pl.subplot(111)
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for i in range(digits.data.shape[0]):
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pl.text(X[i, 0], X[i, 1], str(digits.target[i]),
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color=pl.cm.Set1(digits.target[i] / 10.),
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fontdict={'weight': 'bold', 'size': 9})
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if hasattr(offsetbox, 'AnnotationBbox'):
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# only print thumbnails with matplotlib > 1.0
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shown_images = np.array([[1., 1.]]) # just something big
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for i in range(digits.data.shape[0]):
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dist = np.sum((X[i] - shown_images) ** 2, 1)
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if np.min(dist) < 4e-3:
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# don't show points that are too close
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continue
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shown_images = np.r_[shown_images, [X[i]]]
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imagebox = offsetbox.AnnotationBbox(
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offsetbox.OffsetImage(digits.images[i], cmap=pl.cm.gray_r),
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X[i])
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ax.add_artist(imagebox)
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pl.xticks([]), pl.yticks([])
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if title is not None:
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pl.title(title)
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plot_embedding(X_projected, "Random Projection of the digits")
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plot_embedding(X_pca, "Principal Components projection of the digits")
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plot_embedding(X_lda, "Linear Discriminant projection of the digits")
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plot_embedding(X_lle, "Locally Linear Embedding of the digits")
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pl.show()
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