147 lines
4.2 KiB
Python
147 lines
4.2 KiB
Python
"""
|
|
=============================================================================
|
|
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,
|
|
max_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",
|
|
max_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,
|
|
max_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()
|