Dendrogram visualization in SciPy - Step-by-Step Execution

Concept Flow - Dendrogram visualization

Start with data points

↓

Calculate distances

↓

Perform hierarchical clustering

↓

Create linkage matrix

↓

Plot dendrogram

↓

Visualize cluster merges

↓

End

This flow shows how data points are clustered step-by-step and visualized as a dendrogram.

Execution Sample

SciPy

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

X = [[1, 2], [3, 4], [5, 6], [7, 8]]
Z = linkage(X, 'single')
dendrogram(Z)
plt.show()

This code clusters 4 points and plots their dendrogram showing merges.

Execution Table

Step	Action	Data/Variables	Result/Output
1	Input data points	X = [[1,2],[3,4],[5,6],[7,8]]	Data ready for clustering
2	Calculate linkage matrix	linkage(X, 'single')	Z = [[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]
3	Plot dendrogram	dendrogram(Z)	Dendrogram plot shows cluster merges
4	Show plot	plt.show()	Visual dendrogram displayed
5	End		Process complete

💡 All data points clustered and dendrogram displayed

Variable Tracker

Variable	Start	After Step 2	After Step 3	Final
X	[[1,2],[3,4],[5,6],[7,8]]	[[1,2],[3,4],[5,6],[7,8]]	[[1,2],[3,4],[5,6],[7,8]]	[[1,2],[3,4],[5,6],[7,8]]
Z	None	[[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]	[[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]	[[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]

Key Moments - 3 Insights

Why does the linkage matrix Z have 3 rows for 4 data points?

Because hierarchical clustering merges points step-by-step, for n points there are n-1 merges, so Z has n-1 rows (3 rows for 4 points). See execution_table step 2.

What does each row in the linkage matrix represent?

Each row shows a merge: the two clusters merged, the distance between them, and the number of original points in the new cluster. This is shown in execution_table step 2.

Why do we use 'single' linkage in linkage()?

'Single' linkage means clusters are merged based on the smallest distance between points in clusters. This affects the shape of the dendrogram, as seen in execution_table step 2.

Visual Quiz - 3 Questions

Look at the execution_table step 2, what does the number 2.828 represent in the linkage matrix?

A The index of a data point

B The number of clusters

C The distance between two clusters merged

D The height of the dendrogram

💡 Hint

Check the 'Result/Output' column in step 2 of execution_table where linkage matrix is shown.

At which step is the dendrogram plot created according to the execution_table?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look at the 'Action' column for plotting dendrogram in execution_table.

If we add more data points, how will the linkage matrix Z change?

A It will have fewer rows

B It will have more rows

C It will stay the same size

D It will become empty

💡 Hint

Recall from key_moments that linkage matrix has n-1 rows for n points.

Concept Snapshot

Dendrogram visualization:
- Use scipy.cluster.hierarchy linkage() to cluster data
- linkage() returns a matrix showing cluster merges
- dendrogram() plots this matrix as a tree
- Each merge shows which clusters joined and distance
- Visualizes hierarchical clustering step-by-step

Full Transcript

We start with data points and calculate distances between them. Then we perform hierarchical clustering using linkage() which returns a matrix showing how clusters merge step-by-step. This matrix is passed to dendrogram() to create a tree plot. The dendrogram visually shows the order and distance of merges. The process ends when all points are clustered. This helps us understand cluster relationships visually.

Practice

1. What is the main purpose of a dendrogram in data science?

easy

A. To visualize hierarchical clustering as a tree

B. To perform linear regression analysis

C. To calculate the mean of a dataset

D. To create a scatter plot of two variables

Solution

1. Step 1: Understand dendrogram function

   A dendrogram is used to show hierarchical clustering results visually as a tree structure.

2. Step 2: Compare with other options

   The other options describe different data analysis or visualization methods unrelated to dendrograms.

3. Final Answer:

   To visualize hierarchical clustering as a tree -> Option A

4. Quick Check:

   Dendrogram = hierarchical clustering tree [OK]

Hint: Dendrograms always show clusters as tree diagrams [OK]

Common Mistakes:

• Confusing dendrogram with scatter plot
• Thinking dendrogram calculates statistics
• Mixing dendrogram with regression plots

2. Which of the following is the correct way to import the dendrogram function from scipy?

easy

A. from scipy.visualization import dendrogram

B. import scipy.dendrogram

C. import dendrogram from scipy.cluster

D. from scipy.cluster.hierarchy import dendrogram

Solution

1. Step 1: Recall correct import syntax

   The dendrogram function is located in scipy.cluster.hierarchy, so the correct import is from scipy.cluster.hierarchy import dendrogram.

2. Step 2: Check other options for syntax errors

   The other options use incorrect module paths or invalid import syntax.

3. Final Answer:

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

4. Quick Check:

   Correct import path = from scipy.cluster.hierarchy import dendrogram [OK]

Hint: Remember dendrogram is in scipy.cluster.hierarchy [OK]

Common Mistakes:

• Using wrong module path
• Incorrect import syntax
• Assuming dendrogram is in scipy.visualization

3. Given the following code, what will be the output type of dn?

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

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

medium

A. A NumPy array of cluster labels

B. A dictionary containing dendrogram data

C. A matplotlib figure object

D. A list of linkage distances

Solution

1. Step 1: Understand dendrogram return value

   The dendrogram function returns a dictionary with keys like 'icoord', 'dcoord', 'leaves', and 'color_list' describing the dendrogram structure.

2. Step 2: Check other options

   A NumPy array of cluster labels is incorrect because cluster labels are not returned by dendrogram. A matplotlib figure object is wrong because dendrogram does not return a figure object. A list of linkage distances is incorrect as linkage distances are part of the linkage matrix, not dendrogram output.

3. Final Answer:

   A dictionary containing dendrogram data -> Option B

4. Quick Check:

   dendrogram() returns dict = A dictionary containing dendrogram data [OK]

Hint: dendrogram() returns a dict with plotting info [OK]

Common Mistakes:

• Expecting dendrogram to return a plot object
• Confusing dendrogram output with linkage matrix
• Thinking dendrogram returns cluster labels

4. Identify the error in this code snippet for plotting a dendrogram:

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

X = [[1, 2], [3, 4], [5, 6]]
Z = linkage(X, 'ward')
dendrogram(Z)
plt.show()

medium

A. Linkage method 'ward' is invalid

B. Missing import for numpy

C. No error; code runs and plots dendrogram correctly

D. X should be a NumPy array, not a list

Solution

1. Step 1: Check data input type

   Linkage accepts array-like input, so a Python list of lists is valid for X.

2. Step 2: Verify linkage method and plotting

   'ward' is a valid linkage method. The code imports matplotlib.pyplot as plt and calls plt.show(), so the dendrogram will plot correctly.

3. Final Answer:

   No error; code runs and plots dendrogram correctly -> Option C

4. Quick Check:

   List input and 'ward' method are valid [OK]

Hint: Linkage accepts lists; 'ward' is valid method [OK]

Common Mistakes:

• Assuming input must be NumPy array
• Thinking 'ward' is invalid linkage method
• Forgetting plt.show() to display plot

5. You want to visualize clusters with different colors in a dendrogram using scipy.cluster.hierarchy.dendrogram. Which parameter should you set to control the color threshold for cluster coloring?

hard

A. color_threshold

B. linkage_method

C. leaf_rotation

D. distance_metric

Solution

1. Step 1: Identify parameter for cluster color control

   The parameter color_threshold in dendrogram controls the threshold distance to color clusters differently.

2. Step 2: Eliminate unrelated parameters

   linkage_method and distance_metric relate to clustering, not coloring. leaf_rotation controls label rotation, not colors.

3. Final Answer:

   color_threshold -> Option A

4. Quick Check:

   Cluster colors controlled by color_threshold [OK]

Hint: Use color_threshold to set cluster color boundaries [OK]

Common Mistakes:

• Confusing color_threshold with linkage method
• Using leaf_rotation to change colors
• Assuming distance_metric affects dendrogram colors