Interpreting dendrograms using hierarchical clustering in Python

Dendrograms are tree-like diagrams that visualize the hierarchical relationships between data points in hierarchical clustering. Interpreting dendrograms can provide valuable insights into the underlying structure of your data.

Understanding Dendrograms

A dendrogram consists of nodes and branches. Each node represents a cluster, and the branches represent the merging of clusters. The height of a branch indicates the distance between the two clusters that were merged.

Interpreting Dendrogram Heights

The height of a branch in a dendrogram corresponds to the distance between the two clusters that were merged. This distance can be interpreted in different ways depending on the linkage criterion used:

• Single-linkage: The height represents the minimum distance between any two data points in the two clusters.
• Complete-linkage: The height represents the maximum distance between any two data points in the two clusters.
• Average-linkage: The height represents the average distance between all pairs of data points in the two clusters.
• Centroid-linkage: The height represents the distance between the centroids of the two clusters.

Identifying Clusters

To identify clusters in a dendrogram, you can look for natural breaks or gaps in the branches. These breaks often indicate the optimal number of clusters. One common approach is to select a cutoff level based on the dendrogram height. By cutting the dendrogram at this level, you can identify the clusters.

Using Python Libraries

Several Python libraries can be used to create and interpret dendrograms. The scipy.cluster.hierarchy module provides functions for performing hierarchical clustering and visualizing the results.

Python

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

# Assuming you have a distance matrix
distance_matrix = ...

Z = linkage(distance_matrix, method='ward')  # Use ward linkage for example
dendrogram(Z)

Tips for Interpreting Dendrograms

• Consider the linkage criterion: The choice of linkage criterion can affect the shape of the dendrogram and the interpretation of the results.
• Look for natural breaks: Identify gaps in the dendrogram that indicate natural divisions between clusters.
• Experiment with different cutoff levels: Try different cutoff levels to see how they affect the number and composition of the clusters.
• Use domain knowledge: If you have domain knowledge about the data, you can use it to interpret the dendrogram and identify meaningful clusters.

By understanding how to interpret dendrograms, you can gain valuable insights into the hierarchical structure of your data and identify meaningful clusters.