CH05_SEC04_1_Dendrogram.ipynb

Kernel: Python 3

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
from scipy.cluster import hierarchy
from scipy.spatial.distance import pdist

rcParams.update({'font.size': 18})
plt.rcParams['figure.figsize'] = [12, 12]

# Training and testing set sizes
n1 = 100 # Train
n2 = 50  # Test

# Random ellipse 1 centered at (0,0)
x = np.random.randn(n1+n2)
y = 0.5*np.random.randn(n1+n2)

# Random ellipse 2 centered at (1,-2)
x2 = np.random.randn(n1+n2) + 1
y2 = 0.2*np.random.randn(n1+n2) - 2

# Rotate ellipse 2 by theta
theta = np.pi/4
A = np.zeros((2,2))
A[0,0] = np.cos(theta)
A[0,1] = -np.sin(theta)
A[1,0] = np.sin(theta)
A[1,1] = np.cos(theta)

x3 = A[0,0]*x2 + A[0,1]*y2
y3 = A[1,0]*x2 + A[1,1]*y2

plt.figure()
plt.plot(x[:n1],y[:n1],'ro')
plt.plot(x3[:n1],y3[:n1],'bo')
plt.show()

# Training set: first 200 of 240 points
X1 = np.column_stack((x3[:n1],y3[:n1]))
X2 = np.column_stack((x[:n1],y[:n1]))

Y = np.concatenate((X1,X2))
Z = np.column_stack((np.ones(n1),2*np.ones(n1)))

# Test set: remaining 40 points
x1test = np.column_stack((x3[n1:],y3[n1:]))
x2test = np.column_stack((x[n1:],y[n1:]))

## Dendrograms

Y3 = np.concatenate((X1[:50,:],X2[:50,:]))

Y2 = pdist(Y3,metric='euclidean')
Z = hierarchy.linkage(Y2,method='average')
thresh = 0.85*np.max(Z[:,2])

plt.figure()
dn = hierarchy.dendrogram(Z,p=100,color_threshold=thresh)
plt.axis('off')

plt.show()

plt.bar(range(100),dn['leaves'])
plt.plot(np.array([0, 100]),np.array([50, 50]),'r:',linewidth=2)
plt.plot(np.array([50.5, 50.5]),np.array([0, 100]),'r:',linewidth=2)

plt.show()

thresh = 0.25*np.max(Z[:,2])

plt.figure()
dn = hierarchy.dendrogram(Z,p=100,color_threshold=thresh)
plt.axis('off')
plt.show()