1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
|
"""
=============================================================================
Manifold learning on handwritten digits: Locally Linear Embedding, Isomap...
=============================================================================
An illustration of various embeddings 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__
from time import time
import numpy as np
import pylab as pl
from matplotlib import offsetbox
from sklearn.utils.fixes import qr_economic
from sklearn import manifold, datasets, decomposition, lda
digits = datasets.load_digits(n_class=6)
X = digits.data
y = digits.target
n_samples, n_features = X.shape
n_neighbors = 30
#----------------------------------------------------------------------
# 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 images of the digits
N = 20
img = np.zeros((10 * N, 10 * N))
for i in range(N):
ix = 10 * i + 1
for j in range(N):
iy = 10 * j + 1
img[ix:ix + 8, iy:iy + 8] = X[i * N + j].reshape((8, 8))
pl.imshow(img, cmap=pl.cm.binary)
pl.xticks([])
pl.yticks([])
pl.title('A selection from the 64-dimensional digits dataset')
#----------------------------------------------------------------------
# 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
plot_embedding(X_projected, "Random Projection of the digits")
#----------------------------------------------------------------------
# Projection on to the first 2 principal components
print "Computing PCA projection"
t0 = time()
X_pca = decomposition.RandomizedPCA(n_components=2).fit_transform(X)
plot_embedding(X_pca,
"Principal Components projection of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# 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
t0 = time()
X_lda = lda.LDA(n_components=2).fit_transform(X2, y)
plot_embedding(X_lda,
"Linear Discriminant projection of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Isomap projection of the digits dataset
print "Computing Isomap embedding"
t0 = time()
X_iso = manifold.Isomap(n_neighbors, n_components=2).fit_transform(X)
print "Done."
plot_embedding(X_iso,
"Isomap projection of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Locally linear embedding of the digits dataset
print "Computing LLE embedding"
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='standard')
t0 = time()
X_lle = clf.fit_transform(X)
print "Done. Reconstruction error: %g" % clf.reconstruction_error_
plot_embedding(X_lle,
"Locally Linear Embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Modified Locally linear embedding of the digits dataset
print "Computing modified LLE embedding"
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='modified')
t0 = time()
X_mlle = clf.fit_transform(X)
print "Done. Reconstruction error: %g" % clf.reconstruction_error_
plot_embedding(X_mlle,
"Modified Locally Linear Embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# HLLE embedding of the digits dataset
print "Computing Hessian LLE embedding"
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='hessian')
t0 = time()
X_hlle = clf.fit_transform(X)
print "Done. Reconstruction error: %g" % clf.reconstruction_error_
plot_embedding(X_hlle,
"Hessian Locally Linear Embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# LTSA embedding of the digits dataset
print "Computing LTSA embedding"
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='ltsa')
t0 = time()
X_ltsa = clf.fit_transform(X)
print "Done. Reconstruction error: %g" % clf.reconstruction_error_
plot_embedding(X_ltsa,
"Local Tangent Space Alignment of the digits (time %.2fs)" %
(time() - t0))
pl.show()
|
