Flat clustering (fcluster) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of fcluster with distance threshold

What is the output array of cluster labels when using fcluster with t=1.5 on the given linkage matrix?

SciPy

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

X = np.array([[1, 2], [2, 2], [5, 5], [6, 5]])
Z = linkage(X, method='single')
clusters = fcluster(Z, t=1.5, criterion='distance')
print(clusters)

A [2 2 1 1]

B [1 2 3 4]

C [1 1 1 1]

D [1 1 2 2]

💡 Hint

Clusters are formed by cutting the dendrogram at the given distance threshold.

The linkage groups the first two points together and the last two points together because their distances are less than 1.5. So, fcluster assigns labels [1,1,2,2].

❓ data_output

intermediate

Number of clusters formed by fcluster

Using the linkage matrix Z from the code below, how many clusters are formed when using fcluster with t=3 and criterion='distance'?

SciPy

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

X = np.array([[1, 1], [2, 1], [4, 4], [5, 5], [10, 10]])
Z = linkage(X, method='complete')
clusters = fcluster(Z, t=3, criterion='distance')
num_clusters = len(set(clusters))
print(num_clusters)

A 3

B 2

C 4

D 1

💡 Hint

Count unique cluster labels after applying fcluster.

The distance threshold 3 splits the data into three clusters: two close points near (1,1), two near (4,4), and one far point at (10,10).

🔧 Debug

advanced

Identify the error in fcluster usage

What error will this code raise when running fcluster with criterion='maxclust' but without specifying t properly?

SciPy

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

X = np.array([[0, 0], [1, 1], [5, 5]])
Z = linkage(X, method='ward')
clusters = fcluster(Z, criterion='maxclust')
print(clusters)

A No error, prints cluster labels

B ValueError: Invalid criterion value

C TypeError: fcluster() missing 1 required positional argument: 't'

D NameError: name 'clusters' is not defined

💡 Hint

Check the required arguments for fcluster function.

The function fcluster requires the threshold parameter 't' even when using 'maxclust' criterion. Omitting it causes a TypeError.

🧠 Conceptual

advanced

Understanding fcluster criterion 'inconsistent'

Which statement best describes how fcluster forms clusters when using criterion='inconsistent'?

A Clusters are formed by cutting the dendrogram at a fixed distance threshold.

B Clusters are formed by comparing inconsistency coefficients of links to a threshold.

C Clusters are formed by specifying the maximum number of clusters desired.

D Clusters are formed by grouping points with the same feature values.

💡 Hint

Inconsistency measures how different a link is compared to links below it.

The 'inconsistent' criterion uses inconsistency statistics to decide where to cut the dendrogram, grouping links with inconsistency below the threshold.

🚀 Application

expert

Predict cluster labels for a custom dataset

Given the dataset and linkage below, which option shows the correct cluster labels when using fcluster with t=2 and criterion='distance'?

SciPy

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

X = np.array([[0, 0], [0, 1], [1, 0], [5, 5], [6, 5], [5, 6]])
Z = linkage(X, method='average')
clusters = fcluster(Z, t=2, criterion='distance')
print(clusters)

A [1 1 1 2 2 2]

B [1 1 2 3 3 3]

C [1 2 3 4 5 6]

D [1 1 1 1 1 1]

💡 Hint

Points close together form clusters within the distance threshold.

The first three points are close and form cluster 1; the last three points are close and form cluster 2 when cut at distance 2.