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.

Practice

1. What is the main purpose of the fcluster function in scipy's hierarchical clustering?

easy

A. To cut a hierarchical cluster tree into flat clusters based on a threshold

B. To compute the distance matrix between data points

C. To perform dimensionality reduction before clustering

D. To normalize data before clustering

Solution

1. Step 1: Understand hierarchical clustering output

   Hierarchical clustering produces a tree (dendrogram) showing nested clusters.

2. Step 2: Role of fcluster

   fcluster cuts this tree at a chosen threshold to form flat, non-overlapping clusters.

3. Final Answer:

   To cut a hierarchical cluster tree into flat clusters based on a threshold -> Option A

4. Quick Check:

   Flat clustering = cutting tree with threshold [OK]

Hint: Remember: fcluster cuts dendrogram into flat groups [OK]

Common Mistakes:

• Confusing fcluster with distance calculation
• Thinking fcluster normalizes data
• Assuming fcluster reduces dimensions

2. Which of the following is the correct syntax to assign flat clusters using fcluster with a distance threshold of 1.5 from a linkage matrix Z?

easy

A. clusters = fcluster(Z, threshold=1.5, criterion='distance')

B. clusters = fcluster(Z, 1.5, method='distance')

C. clusters = fcluster(Z, 1.5, criterion='distance')

D. clusters = fcluster(Z, 1.5, criterion='maxclust')

Solution

1. Step 1: Check fcluster parameters

   The function signature is fcluster(Z, t, criterion='distance') where t is the threshold.

2. Step 2: Identify correct usage

   clusters = fcluster(Z, 1.5, criterion='distance') uses t=1.5 and criterion='distance', which is correct syntax.

3. Final Answer:

   clusters = fcluster(Z, 1.5, criterion='distance') -> Option C

4. Quick Check:

   Threshold = 1.5, criterion = 'distance' [OK]

Hint: Use t for threshold and criterion='distance' in fcluster [OK]

Common Mistakes:

• Using 'method' instead of 'criterion'
• Passing threshold as keyword 'threshold'
• Using wrong criterion like 'maxclust' for distance cut

3. Given the linkage matrix Z = [[0, 1, 0.5, 2], [2, 3, 1.5, 2], [4, 5, 2.5, 4]], what is the output of fcluster(Z, 1.0, criterion='distance')?

medium

A. [1 1 1 1]

B. [1 2 3 4]

C. [1 2 2 3]

D. [1 1 2 3]

Solution

1. Step 1: Understand linkage matrix and threshold

   The linkage matrix Z shows merges with distances: 0.5, 1.5, 2.5. Threshold is 1.0.

2. Step 2: Assign clusters by cutting at distance 1.0

   Clusters merge if distance ≤ 1.0. The first merge (0.5) joins points 0 and 1 into cluster 1. The second merge (1.5 > 1.0) does not merge points 2 and 3, so point 2 gets cluster 2 and point 3 gets cluster 3.

3. Final Answer:

   [1 1 2 3] -> Option D

4. Quick Check:

   Distance ≤ 1.0 merges points 0 and 1 only [OK]

Hint: Cut dendrogram at threshold; merges below threshold cluster together [OK]

Common Mistakes:

• Merging clusters above threshold
• Assigning all points to one cluster
• Misreading linkage matrix format

4. You run the code clusters = fcluster(Z, 2, criterion='maxclust') but get an error. What is the likely cause?

medium

A. The linkage matrix Z is not defined or invalid

B. The criterion 'maxclust' requires an integer number of clusters, but 2 is passed as a float

C. The threshold parameter must be a float when using 'maxclust'

D. The criterion 'maxclust' expects the threshold to be the maximum cluster distance

Solution

1. Step 1: Check parameter types for 'maxclust'

   When using criterion='maxclust', the threshold t must be an integer specifying the number of clusters.

2. Step 2: Identify common error

   If Z is not defined or invalid, fcluster raises an error unrelated to parameter types.

3. Step 3: Analyze options

   The criterion 'maxclust' requires an integer number of clusters, but 2 is passed as a float is incorrect because 2 as an integer or float is accepted; The threshold parameter must be a float when using 'maxclust' is wrong because threshold can be int; The criterion 'maxclust' expects the threshold to be the maximum cluster distance is false because 'maxclust' uses number of clusters, not distance.

4. Final Answer:

   The linkage matrix Z is not defined or invalid -> Option A

5. Quick Check:

   Undefined Z causes error, not threshold type [OK]

Hint: Ensure linkage matrix Z is valid before calling fcluster [OK]

Common Mistakes:

• Passing float instead of int for maxclust threshold
• Misunderstanding criterion parameter
• Ignoring linkage matrix validity

5. You have a dataset with 10 points clustered hierarchically. You want exactly 3 clusters. Which fcluster call correctly achieves this?

hard

A. fcluster(Z, 0.5, criterion='inconsistent')

B. fcluster(Z, 3, criterion='maxclust')

C. fcluster(Z, 0.5, criterion='maxclust')

D. fcluster(Z, 3, criterion='distance')

Solution

1. Step 1: Understand criteria for exact cluster count

   To get exactly 3 clusters, use criterion='maxclust' with t=3 specifying number of clusters.

2. Step 2: Analyze options

   fcluster(Z, 3, criterion='maxclust') correctly uses maxclust with 3 clusters. fcluster(Z, 3, criterion='distance') uses distance criterion which does not guarantee exact cluster count. Options A and C use incorrect thresholds or criteria.

3. Final Answer:

   fcluster(Z, 3, criterion='maxclust') -> Option B

4. Quick Check:

   maxclust + t=number of clusters = exact clusters [OK]

Hint: Use criterion='maxclust' with t = desired cluster count [OK]

Common Mistakes:

• Using distance criterion to get exact cluster count
• Passing float threshold for maxclust
• Confusing inconsistent criterion with maxclust