How To Cut A Dendrogram In Python

In hierarchical clustering, a dendrogram is a tree-like diagram that shows the process of merging clusters, with each cluster being represented by a node. It can help you visualize the relationships between clusters and decide the appropriate number of clusters for your data. In this tutorial, we will learn how to cut a dendrogram in Python using the SciPy library.

Step 1: Install the required libraries

First, you need to install numpy, scipy, and matplotlib if you haven’t already. You can do this using pip:

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pip install numpy scipy matplotlib

Step 2: Import the necessary libraries

Next, you need to import the required libraries:

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

Step 3: Generate some sample data

For this tutorial, we will generate some random data points:

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np.random.seed(42)
data = np.random.rand(10, 3)

Step 4: Perform Hierarchical Clustering

Now, we need to perform hierarchical clustering on the data using the linkage function from scipy:

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Z = linkage(data, 'ward')

Here, we have used the Ward’s method as the linkage method for clustering.

Step 5: Plot the dendrogram

Before cutting the dendrogram, let’s plot it first to visualize the hierarchical clustering:

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fig = plt.figure(figsize=(10, 5))
dn = dendrogram(Z)
plt.title("Dendrogram")
plt.xlabel("Data points")
plt.ylabel("Euclidean distances")
plt.show()

This code will generate the dendrogram for the given data.

Step 6: Cutting the dendrogram

You can cut the dendrogram at a specific distance or at a specific number of clusters. In this example, we will cut the dendrogram at a maximum distance of 1.5.

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max_distance = 1.5
clusters = fcluster(Z, max_distance, criterion='distance')

Here, fcluster function takes the linkage matrix Z, the maximum distance, and the cutting criterion as input arguments.

Step 7: Visualize the clustered data

After cutting the dendrogram, we can visualize the clustered data:

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plt.scatter(data[:, 0], data[:, 1], c=clusters, cmap='viridis')
plt.title("Clustered Data")
plt.xlabel("X-axis")
plt.ylabel("Y-axis")
plt.show()

This will show the data points with different colors representing different clusters.

Full code

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import numpy as np
from scipy.cluster.hierarchy import dendrogram, linkage, fcluster
import matplotlib.pyplot as plt
 
np.random.seed(42)
data = np.random.rand(10, 3)
 
Z = linkage(data, 'ward')
 
fig = plt.figure(figsize=(10, 5))
dn = dendrogram(Z)
plt.title("Dendrogram")
plt.xlabel("Data points")
plt.ylabel("Euclidean distances")
plt.show()
 
max_distance = 1.5
clusters = fcluster(Z, max_distance, criterion='distance')
 
plt.scatter(data[:, 0], data[:, 1], c=clusters, cmap='viridis')
plt.title("Clustered Data")
plt.xlabel("X-axis")
plt.ylabel("Y-axis")
plt.show()

Output

Conclusion

In this tutorial, we have learned how to cut a dendrogram in Python using the SciPy library. Cutting a dendrogram helps in deciding the number of clusters in hierarchical clustering. By following these steps, you can visualize and analyze the hierarchical clustering of your data more effectively.