Dendrogram visualization in SciPy

Introduction

A dendrogram helps us see how data groups together step by step. It shows the order and distance of joining groups in a tree-like picture.

When you want to find groups or clusters in your data without labels.

To understand how similar or different items are in a dataset.

When you want to decide the number of clusters by looking at the tree.

To visualize hierarchical relationships in data like family trees or document topics.

When exploring data before applying other machine learning methods.

Syntax

SciPy

from scipy.cluster.hierarchy import dendrogram

dendrogram(Z, p=30, truncate_mode=None, color_threshold=None, get_leaves=True, orientation='top', labels=None, leaf_rotation=0, leaf_font_size=10, show_contracted=False, show_leaf_counts=True)

Z is the linkage matrix from hierarchical clustering.

You can customize the dendrogram look with options like truncate_mode to shorten the tree or orientation to change its direction.

Examples

Basic dendrogram plot from linkage matrix Z.

SciPy

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

dendrogram(Z)
plt.show()

Shows only the last 5 merged clusters to simplify the tree.

SciPy

dendrogram(Z, truncate_mode='lastp', p=5)
plt.show()

Draws dendrogram with leaves on the left and rotated labels for better readability.

SciPy

dendrogram(Z, orientation='left', leaf_rotation=90, leaf_font_size=12)
plt.show()

Sample Program

This code creates a dendrogram from 5 points. It shows how points group together by distance. Labels A to E identify each point.

SciPy

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

# Sample data: 5 points in 2D
X = np.array([[1, 2], [2, 3], [3, 2], [8, 7], [7, 8]])

# Create linkage matrix using 'ward' method
Z = linkage(X, method='ward')

# Plot dendrogram
plt.figure(figsize=(6, 4))
dendrogram(Z, labels=['A', 'B', 'C', 'D', 'E'], leaf_rotation=45)
plt.title('Dendrogram Example')
plt.xlabel('Sample')
plt.ylabel('Distance')
plt.tight_layout()
plt.show()

Important Notes

Make sure to import matplotlib.pyplot to display the dendrogram plot.

The linkage matrix Z is created from your data using methods like 'ward', 'single', or 'complete'.

Labels help identify leaves; if none are given, numeric indices are used.

Summary

Dendrograms visualize hierarchical clustering as a tree.

They help understand data grouping and distances between clusters.

Use scipy.cluster.hierarchy.dendrogram with a linkage matrix to create them.

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