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
|
"""
=============================================================================
t-SNE: The effect of various perplexity values on the shape
=============================================================================
An illustration of t-SNE on the two concentric circles and the S-curve
datasets for different perplexity values.
We observe a tendency towards clearer shapes as the perplexity value increases.
The size, the distance and the shape of clusters may vary upon initialization,
perplexity values and does not always convey a meaning.
As shown below, t-SNE for higher perplexities finds meaningful topology of
two concentric circles, however the size and the distance of the circles varies
slightly from the original. Contrary to the two circles dataset, the shapes
visually diverge from S-curve topology on the S-curve dataset even for
larger perplexity values.
For further details, "How to Use t-SNE Effectively"
https://distill.pub/2016/misread-tsne/ provides a good discussion of the
effects of various parameters, as well as interactive plots to explore
those effects.
"""
# Author: Narine Kokhlikyan <narine@slice.com>
# License: BSD
from time import time
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.ticker import NullFormatter
from sklearn import datasets, manifold
n_samples = 150
n_components = 2
(fig, subplots) = plt.subplots(3, 5, figsize=(15, 8))
perplexities = [5, 30, 50, 100]
X, y = datasets.make_circles(
n_samples=n_samples, factor=0.5, noise=0.05, random_state=0
)
red = y == 0
green = y == 1
ax = subplots[0][0]
ax.scatter(X[red, 0], X[red, 1], c="r")
ax.scatter(X[green, 0], X[green, 1], c="g")
ax.xaxis.set_major_formatter(NullFormatter())
ax.yaxis.set_major_formatter(NullFormatter())
plt.axis("tight")
for i, perplexity in enumerate(perplexities):
ax = subplots[0][i + 1]
t0 = time()
tsne = manifold.TSNE(
n_components=n_components,
init="random",
random_state=0,
perplexity=perplexity,
n_iter=300,
)
Y = tsne.fit_transform(X)
t1 = time()
print("circles, perplexity=%d in %.2g sec" % (perplexity, t1 - t0))
ax.set_title("Perplexity=%d" % perplexity)
ax.scatter(Y[red, 0], Y[red, 1], c="r")
ax.scatter(Y[green, 0], Y[green, 1], c="g")
ax.xaxis.set_major_formatter(NullFormatter())
ax.yaxis.set_major_formatter(NullFormatter())
ax.axis("tight")
# Another example using s-curve
X, color = datasets.make_s_curve(n_samples, random_state=0)
ax = subplots[1][0]
ax.scatter(X[:, 0], X[:, 2], c=color)
ax.xaxis.set_major_formatter(NullFormatter())
ax.yaxis.set_major_formatter(NullFormatter())
for i, perplexity in enumerate(perplexities):
ax = subplots[1][i + 1]
t0 = time()
tsne = manifold.TSNE(
n_components=n_components,
init="random",
random_state=0,
perplexity=perplexity,
learning_rate="auto",
n_iter=300,
)
Y = tsne.fit_transform(X)
t1 = time()
print("S-curve, perplexity=%d in %.2g sec" % (perplexity, t1 - t0))
ax.set_title("Perplexity=%d" % perplexity)
ax.scatter(Y[:, 0], Y[:, 1], c=color)
ax.xaxis.set_major_formatter(NullFormatter())
ax.yaxis.set_major_formatter(NullFormatter())
ax.axis("tight")
# Another example using a 2D uniform grid
x = np.linspace(0, 1, int(np.sqrt(n_samples)))
xx, yy = np.meshgrid(x, x)
X = np.hstack(
[
xx.ravel().reshape(-1, 1),
yy.ravel().reshape(-1, 1),
]
)
color = xx.ravel()
ax = subplots[2][0]
ax.scatter(X[:, 0], X[:, 1], c=color)
ax.xaxis.set_major_formatter(NullFormatter())
ax.yaxis.set_major_formatter(NullFormatter())
for i, perplexity in enumerate(perplexities):
ax = subplots[2][i + 1]
t0 = time()
tsne = manifold.TSNE(
n_components=n_components,
init="random",
random_state=0,
perplexity=perplexity,
n_iter=400,
)
Y = tsne.fit_transform(X)
t1 = time()
print("uniform grid, perplexity=%d in %.2g sec" % (perplexity, t1 - t0))
ax.set_title("Perplexity=%d" % perplexity)
ax.scatter(Y[:, 0], Y[:, 1], c=color)
ax.xaxis.set_major_formatter(NullFormatter())
ax.yaxis.set_major_formatter(NullFormatter())
ax.axis("tight")
plt.show()
|
