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