Hierarchical clustering (linkage) in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is hierarchical clustering?

Hierarchical clustering is a method to group similar data points into clusters by building a tree of clusters. It does not require a fixed number of clusters beforehand.

beginner

What does the 'linkage' function in scipy do?

The 'linkage' function in scipy calculates distances between clusters and merges them step-by-step to form a hierarchy, producing a linkage matrix that shows how clusters combine.

intermediate

Name three common linkage methods used in hierarchical clustering.

Three common linkage methods are: 1) Single linkage - distance between closest points, 2) Complete linkage - distance between farthest points, 3) Average linkage - average distance between all points in clusters.

beginner

What is the output of the scipy linkage function?

The output is a linkage matrix, a 2D array where each row shows which clusters were merged, the distance between them, and the number of original points in the new cluster.

intermediate

Why is hierarchical clustering useful compared to k-means?

Hierarchical clustering does not need you to choose the number of clusters in advance and shows the full cluster tree, which helps understand data structure better.

What does the 'linkage' function in scipy.cluster.hierarchy return?

A A linkage matrix showing cluster merges

B A list of cluster labels for each data point

C A distance matrix between all points

D A dendrogram plot

The linkage function returns a linkage matrix that records how clusters are merged step-by-step.

Which linkage method uses the shortest distance between points in clusters?

A Complete linkage

B Ward linkage

C Single linkage

D Average linkage

Single linkage uses the shortest distance between points in two clusters.

In hierarchical clustering, what does the dendrogram represent?

A A plot showing cluster centers

B A tree showing cluster merges and distances

C A heatmap of data values

D A scatter plot of data points

A dendrogram is a tree diagram that shows how clusters merge at different distances.

Which of these is NOT a valid linkage method in scipy?

A Single

B Complete

C Median

D K-means

K-means is a different clustering algorithm, not a linkage method.

What is the main advantage of hierarchical clustering over k-means?

A It does not require specifying the number of clusters

B It is faster for large datasets

C It always produces spherical clusters

D It uses random initialization

Hierarchical clustering builds a cluster tree without needing the number of clusters upfront.

Explain how the linkage matrix represents cluster merges in hierarchical clustering.

Think about what information you need to know how clusters combine step-by-step.

Describe the difference between single, complete, and average linkage methods.

Focus on how distance between clusters is measured.

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