-
Notifications
You must be signed in to change notification settings - Fork 0
/
figures.py
233 lines (176 loc) · 8.44 KB
/
figures.py
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
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
import numpy as np
import matplotlib.pyplot as plt
import warnings
def plot_venn_diagram():
fig, ax = plt.subplots(subplot_kw=dict(frameon=False, xticks=[], yticks=[]))
ax.add_patch(plt.Circle((0.3, 0.3), 0.3, fc='red', alpha=0.5))
ax.add_patch(plt.Circle((0.6, 0.3), 0.3, fc='blue', alpha=0.5))
ax.add_patch(plt.Rectangle((-0.1, -0.1), 1.1, 0.8, fc='none', ec='black'))
ax.text(0.2, 0.3, '$x$', size=30, ha='center', va='center')
ax.text(0.7, 0.3, '$y$', size=30, ha='center', va='center')
ax.text(0.0, 0.6, '$I$', size=30)
ax.axis('equal')
def plot_example_decision_tree():
fig = plt.figure(figsize=(10, 4))
ax = fig.add_axes([0, 0, 0.8, 1], frameon=False, xticks=[], yticks=[])
ax.set_title('Example Decision Tree: Animal Classification', size=24)
def text(ax, x, y, t, size=20, **kwargs):
ax.text(x, y, t,
ha='center', va='center', size=size,
bbox=dict(boxstyle='round', ec='k', fc='w'), **kwargs)
text(ax, 0.5, 0.9, "How big is\nthe animal?", 20)
text(ax, 0.3, 0.6, "Does the animal\nhave horns?", 18)
text(ax, 0.7, 0.6, "Does the animal\nhave two legs?", 18)
text(ax, 0.12, 0.3, "Are the horns\nlonger than 10cm?", 14)
text(ax, 0.38, 0.3, "Is the animal\nwearing a collar?", 14)
text(ax, 0.62, 0.3, "Does the animal\nhave wings?", 14)
text(ax, 0.88, 0.3, "Does the animal\nhave a tail?", 14)
text(ax, 0.4, 0.75, "> 1m", 12, alpha=0.4)
text(ax, 0.6, 0.75, "< 1m", 12, alpha=0.4)
text(ax, 0.21, 0.45, "yes", 12, alpha=0.4)
text(ax, 0.34, 0.45, "no", 12, alpha=0.4)
text(ax, 0.66, 0.45, "yes", 12, alpha=0.4)
text(ax, 0.79, 0.45, "no", 12, alpha=0.4)
ax.plot([0.3, 0.5, 0.7], [0.6, 0.9, 0.6], '-k')
ax.plot([0.12, 0.3, 0.38], [0.3, 0.6, 0.3], '-k')
ax.plot([0.62, 0.7, 0.88], [0.3, 0.6, 0.3], '-k')
ax.plot([0.0, 0.12, 0.20], [0.0, 0.3, 0.0], '--k')
ax.plot([0.28, 0.38, 0.48], [0.0, 0.3, 0.0], '--k')
ax.plot([0.52, 0.62, 0.72], [0.0, 0.3, 0.0], '--k')
ax.plot([0.8, 0.88, 1.0], [0.0, 0.3, 0.0], '--k')
ax.axis([0, 1, 0, 1])
def visualize_tree(estimator, X, y, boundaries=True,
xlim=None, ylim=None):
estimator.fit(X, y)
if xlim is None:
xlim = (X[:, 0].min() - 0.1, X[:, 0].max() + 0.1)
if ylim is None:
ylim = (X[:, 1].min() - 0.1, X[:, 1].max() + 0.1)
x_min, x_max = xlim
y_min, y_max = ylim
xx, yy = np.meshgrid(np.linspace(x_min, x_max, 100),
np.linspace(y_min, y_max, 100))
Z = estimator.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, alpha=0.2, cmap='rainbow')
plt.clim(y.min(), y.max())
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='rainbow')
plt.axis('off')
plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
plt.clim(y.min(), y.max())
# Plot the decision boundaries
def plot_boundaries(i, xlim, ylim):
if i < 0:
return
tree = estimator.tree_
if tree.feature[i] == 0:
plt.plot([tree.threshold[i], tree.threshold[i]], ylim, '-k')
plot_boundaries(tree.children_left[i],
[xlim[0], tree.threshold[i]], ylim)
plot_boundaries(tree.children_right[i],
[tree.threshold[i], xlim[1]], ylim)
elif tree.feature[i] == 1:
plt.plot(xlim, [tree.threshold[i], tree.threshold[i]], '-k')
plot_boundaries(tree.children_left[i], xlim,
[ylim[0], tree.threshold[i]])
plot_boundaries(tree.children_right[i], xlim,
[tree.threshold[i], ylim[1]])
if boundaries:
plot_boundaries(0, plt.xlim(), plt.ylim())
def plot_tree_interactive(X, y):
from sklearn.tree import DecisionTreeClassifier
def interactive_tree(depth=1):
clf = DecisionTreeClassifier(max_depth=depth, random_state=0)
visualize_tree(clf, X, y)
from IPython.html.widgets import interact
return interact(interactive_tree, depth=[1, 2, 3, 4, 5])
def plot_kmeans_interactive(min_clusters=1, max_clusters=6):
from IPython.html.widgets import interact
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.datasets.samples_generator import make_blobs
with warnings.catch_warnings():
warnings.filterwarnings('ignore')
X, y = make_blobs(n_samples=300, centers=4,
random_state=0, cluster_std=0.60)
def _kmeans_step(frame=0, n_clusters=4):
rng = np.random.RandomState(2)
labels = np.zeros(X.shape[0])
centers = rng.randn(n_clusters, 2)
nsteps = frame // 3
for i in range(nsteps + 1):
old_centers = centers
if i < nsteps or frame % 3 > 0:
dist = euclidean_distances(X, centers)
labels = dist.argmin(1)
if i < nsteps or frame % 3 > 1:
centers = np.array([X[labels == j].mean(0)
for j in range(n_clusters)])
nans = np.isnan(centers)
centers[nans] = old_centers[nans]
# plot the data and cluster centers
plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='rainbow',
vmin=0, vmax=n_clusters - 1);
plt.scatter(old_centers[:, 0], old_centers[:, 1], marker='o',
c=np.arange(n_clusters),
s=200, cmap='rainbow')
plt.scatter(old_centers[:, 0], old_centers[:, 1], marker='o',
c='black', s=50)
# plot new centers if third frame
if frame % 3 == 2:
for i in range(n_clusters):
plt.annotate('', centers[i], old_centers[i],
arrowprops=dict(arrowstyle='->', linewidth=1))
plt.scatter(centers[:, 0], centers[:, 1], marker='o',
c=np.arange(n_clusters),
s=200, cmap='rainbow')
plt.scatter(centers[:, 0], centers[:, 1], marker='o',
c='black', s=50)
plt.xlim(-4, 4)
plt.ylim(-2, 10)
if frame % 3 == 1:
plt.text(3.8, 9.5, "1. Reassign points to nearest centroid",
ha='right', va='top', size=14)
elif frame % 3 == 2:
plt.text(3.8, 9.5, "2. Update centroids to cluster means",
ha='right', va='top', size=14)
return interact(_kmeans_step, frame=[0, 50],
n_clusters=[min_clusters, max_clusters])
def plot_image_components(x, coefficients=None, mean=0, components=None,
imshape=(8, 8), n_components=6, fontsize=12):
if coefficients is None:
coefficients = x
if components is None:
components = np.eye(len(coefficients), len(x))
mean = np.zeros_like(x) + mean
fig = plt.figure(figsize=(1.2 * (5 + n_components), 1.2 * 2))
g = plt.GridSpec(2, 5 + n_components, hspace=0.3)
def show(i, j, x, title=None):
ax = fig.add_subplot(g[i, j], xticks=[], yticks=[])
ax.imshow(x.reshape(imshape), interpolation='nearest')
if title:
ax.set_title(title, fontsize=fontsize)
show(slice(2), slice(2), x, "True")
approx = mean.copy()
show(0, 2, np.zeros_like(x) + mean, r'$\mu$')
show(1, 2, approx, r'$1 \cdot \mu$')
for i in range(0, n_components):
approx = approx + coefficients[i] * components[i]
show(0, i + 3, components[i], r'$c_{0}$'.format(i + 1))
show(1, i + 3, approx,
r"${0:.2f} \cdot c_{1}$".format(coefficients[i], i + 1))
plt.gca().text(0, 1.05, '$+$', ha='right', va='bottom',
transform=plt.gca().transAxes, fontsize=fontsize)
show(slice(2), slice(-2, None), approx, "Approx")
def plot_pca_interactive(data, n_components=6):
from sklearn.decomposition import PCA
from IPython.html.widgets import interact
pca = PCA(n_components=n_components)
Xproj = pca.fit_transform(data)
def show_decomp(i=0):
plot_image_components(data[i], Xproj[i],
pca.mean_, pca.components_)
interact(show_decomp, i=(0, data.shape[0] - 1));