Hierarchical clustering (linkage) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function for hierarchical clustering linkage.

SciPy

from scipy.cluster.hierarchy import [1]

Drag options to blanks, or click blank then click option'

Adendrogram

Bcophenet

Cfcluster

Dlinkage

Attempts:

3 left

💡 Hint

Common Mistakes

Importing dendrogram instead of linkage

Importing fcluster which is for flat clusters

Importing cophenet which measures cluster quality

The linkage function is used to perform hierarchical clustering linkage.

2fill in blank

medium

Complete the code to perform linkage clustering on data using the 'ward' method.

SciPy

Z = linkage(data, method=[1])

Drag options to blanks, or click blank then click option'

A'ward'

B'average'

C'complete'

D'single'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'single' which links based on minimum distance

Using 'complete' which links based on maximum distance

Using 'average' which links based on average distance

The 'ward' method minimizes the variance of clusters being merged.

3fill in blank

hard

Fix the error in the code to generate a dendrogram from linkage matrix Z.

SciPy

dendrogram([1])

Drag options to blanks, or click blank then click option'

Alinkage

BZ

Cdata

Dmethod

Attempts:

3 left

💡 Hint

Common Mistakes

Passing raw data instead of linkage matrix

Passing the function name instead of its output

Passing the method name as argument

The dendrogram function requires the linkage matrix Z as input.

4fill in blank

hard

Fill both blanks to create a linkage matrix using 'complete' method and plot its dendrogram.

SciPy

Z = linkage(data, method=[1])
dendrogram([2])

Drag options to blanks, or click blank then click option'

A'complete'

B'single'

CZ

Ddata

Attempts:

3 left

💡 Hint

Common Mistakes

Passing raw data to dendrogram

Using wrong method string

Confusing linkage matrix variable with data

Use 'complete' method for linkage and pass the linkage matrix Z to dendrogram.

5fill in blank

hard

Fill all three blanks to compute linkage with 'average' method, plot dendrogram, and set color threshold to 1.5.

SciPy

Z = linkage(data, method=[1])
dendrogram(Z, color_threshold=[2], [3]=True)

Drag options to blanks, or click blank then click option'

A'average'

B1.5

Cabove_threshold_color

Dshow_leaf_counts

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong method string

Setting color_threshold to a string

Using wrong parameter name for showing leaf counts

Use 'average' method for linkage, set color threshold to 1.5, and enable leaf counts display.

Practice

1. What does the linkage function in scipy.cluster.hierarchy do in hierarchical clustering?

easy

A. It calculates distances between clusters step-by-step to form a hierarchy.

B. It assigns data points to fixed clusters before clustering.

C. It visualizes the final clusters using a scatter plot.

D. It normalizes the data before clustering.

Solution

1. Step 1: Understand hierarchical clustering process

   Hierarchical clustering builds clusters step-by-step by merging closest groups.

2. Step 2: Role of linkage function

   The linkage function calculates distances between clusters at each step to decide which to merge next.

3. Final Answer:

   It calculates distances between clusters step-by-step to form a hierarchy. -> Option A

4. Quick Check:

   Linkage = stepwise cluster distance calculation [OK]

Hint: Linkage = stepwise cluster distance calculation [OK]

Common Mistakes:

• Thinking linkage assigns fixed clusters first
• Confusing linkage with visualization functions
• Assuming linkage normalizes data

2. Which of the following is the correct way to import the linkage function from scipy.cluster.hierarchy?

easy

A. from scipy.cluster import linkage

B. import linkage from scipy.cluster.hierarchy

C. import linkage from scipy.cluster

D. from scipy.cluster.hierarchy import linkage

Solution

1. Step 1: Identify correct module path

   The linkage function is inside the hierarchy submodule of scipy.cluster.

2. Step 2: Use correct Python import syntax

   Python import syntax for functions is from module import function. So, from scipy.cluster.hierarchy import linkage is correct.

3. Final Answer:

   from scipy.cluster.hierarchy import linkage -> Option D

4. Quick Check:

   Correct import = from scipy.cluster.hierarchy import linkage [OK]

Hint: Use 'from scipy.cluster.hierarchy import linkage' [OK]

Common Mistakes:

• Using wrong module path
• Wrong import syntax like 'import linkage from ...'
• Importing from scipy.cluster directly

3. What is the output of this code snippet?

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

X = np.array([[1, 2], [3, 4], [5, 6]])
Z = linkage(X, method='single')
print(Z.shape)

medium

A. (2, 3)

B. (3, 4)

C. (2, 4)

D. (3, 3)

Solution

1. Step 1: Understand linkage output shape

   For n data points, linkage returns a matrix with n-1 rows and 4 columns.

2. Step 2: Calculate shape for 3 points

   Here, n=3, so output shape is (2, 4).

3. Final Answer:

   (2, 4) -> Option C

4. Quick Check:

   Linkage shape = (n-1, 4) = (2, 4) [OK]

Hint: Linkage output shape = (n-1, 4) for n points [OK]

Common Mistakes:

• Expecting shape (n, 4) instead of (n-1, 4)
• Confusing columns count
• Miscounting number of data points

4. Identify the error in this code snippet:

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

X = np.array([[1, 2], [3, 4], [5, 6]])
Z = linkage(X, method='fast')
print(Z)

medium

A. The method 'fast' is not a valid linkage method.

B. The input array X must be 1-dimensional.

C. The linkage function requires a distance matrix, not raw data.

D. The print statement is missing parentheses.

Solution

1. Step 1: Check valid linkage methods

   Valid methods include 'single', 'complete', 'average', 'ward', etc. 'fast' is not valid.

2. Step 2: Confirm input data and syntax

   Input can be raw data array; print statement syntax is correct in Python 3.

3. Final Answer:

   The method 'fast' is not a valid linkage method. -> Option A

4. Quick Check:

   Invalid method name causes error [OK]

Hint: Check method names carefully; 'fast' is invalid [OK]

Common Mistakes:

• Assuming 'fast' is a valid method
• Thinking input must be 1D array
• Confusing linkage input requirements

5. You have a dataset with 5 points and want to perform hierarchical clustering using the 'ward' method. After computing linkage, how many merges will be recorded in the linkage matrix, and why?

hard

A. 3 merges, because only the closest points are merged.

B. 4 merges, because each merge reduces clusters by one until one cluster remains.

C. 6 merges, because the 'ward' method adds an extra merge step.

D. 5 merges, because there are 5 points to merge individually.

Solution

1. Step 1: Understand merges in hierarchical clustering

   For n points, hierarchical clustering performs n-1 merges to combine all points into one cluster.

2. Step 2: Apply to 5 points with 'ward' method

   With 5 points, the linkage matrix records 4 merges regardless of method.

3. Final Answer:

   4 merges, because each merge reduces clusters by one until one cluster remains. -> Option B

4. Quick Check:

   Merges = n-1 = 4 for 5 points [OK]

Hint: Number of merges = number of points minus one [OK]

Common Mistakes:

• Thinking merges equal number of points
• Assuming method changes merge count
• Confusing merges with cluster count