Dendrogram visualization in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of dendrogram leaf order

What is the order of leaf labels in the dendrogram produced by this code?

SciPy

import numpy as np
from scipy.cluster.hierarchy import linkage, dendrogram

np.random.seed(0)
data = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [4, 4], [4, 0]])
Z = linkage(data, method='single')
D = dendrogram(Z, no_plot=True)
leaf_order = D['leaves']
print(leaf_order)

A [2, 0, 1, 5, 3, 4]

B [0, 1, 2, 3, 4, 5]

C [5, 3, 4, 2, 0, 1]

D [1, 0, 2, 4, 3, 5]

💡 Hint

Look at how the linkage method 'single' clusters points based on minimum distance.

The 'single' linkage clusters points by minimum distance, resulting in leaf order [2, 0, 1, 5, 3, 4].

❓ data_output

intermediate

Number of clusters from dendrogram cut

Given this linkage matrix, how many clusters remain if we cut the dendrogram at distance 3?

SciPy

import numpy as np
from scipy.cluster.hierarchy import linkage

data = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [4, 4], [4, 0]])
Z = linkage(data, method='complete')
clusters = (Z[:, 2] > 3).sum() + 1
print(clusters)

A 4

B 3

C 2

D 5

💡 Hint

Count how many merges have distance greater than 3.

Cutting at distance 3 leaves 3 clusters because two merges have distances above 3.

❓ visualization

advanced

Identify dendrogram linkage method from plot shape

Which linkage method produces this dendrogram shape when clustering the same data?

SciPy

import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import linkage, dendrogram
import numpy as np

np.random.seed(1)
data = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [4, 4], [4, 0]])

methods = ['single', 'complete', 'average', 'ward']
fig, axs = plt.subplots(2, 2, figsize=(10, 8))
for ax, method in zip(axs.flatten(), methods):
    Z = linkage(data, method=method)
    dendrogram(Z, ax=ax)
    ax.set_title(method)
plt.tight_layout()
plt.show()

A The dendrogram with irregular cluster heights is 'average' linkage.

B The dendrogram with the longest horizontal lines at the bottom is 'single' linkage.

C The dendrogram with the shortest maximum height is 'complete' linkage.

D The dendrogram with balanced cluster heights is 'ward' linkage.

💡 Hint

Ward linkage tries to minimize variance within clusters, producing balanced heights.

Ward linkage produces dendrograms with balanced cluster heights because it minimizes variance.

🔧 Debug

advanced

Error in dendrogram plotting code

What error does this code raise when run?

SciPy

from scipy.cluster.hierarchy import dendrogram
import matplotlib.pyplot as plt
import numpy as np

Z = np.array([[0, 1, 0.5, 2], [2, 3, 0.7, 2], [4, 5, 1.2, 4]])
dendrogram(Z)
plt.show()

A TypeError: 'list' object is not a valid linkage matrix

B IndexError: list index out of range

C No error, dendrogram plots successfully

D ValueError: Linkage matrix must be a 2D numpy array

💡 Hint

Check the type and shape of the linkage matrix input.

The dendrogram function requires a 2D numpy array linkage matrix, not a list.

🚀 Application

expert

Extract cluster labels from dendrogram at specific height

Which code snippet correctly assigns cluster labels to data points by cutting the dendrogram at height 1.5?

SciPy

import numpy as np
from scipy.cluster.hierarchy import linkage, fcluster

data = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [4, 4], [4, 0]])
Z = linkage(data, method='average')

A

labels = fcluster(Z, t=1.5, criterion='distance')
print(labels)

B

labels = fcluster(Z, t=1.5, criterion='maxclust')
print(labels)

C

labels = fcluster(Z, t=1.5, criterion='inconsistent')
print(labels)

D

labels = fcluster(Z, t=1.5, criterion='monocrit')
print(labels)

💡 Hint

Use 'distance' criterion to cut dendrogram at a height threshold.

The 'distance' criterion cuts the dendrogram at the given height to assign clusters.