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, 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));
