AI Courses for Kids in Patras

Chapter 135 – Clustering Dendrograms Explained

1. What Is a Dendrogram?

A dendrogram is the tree diagram of hierarchical clustering. It shows how points merge (or split) from individual leaves up to a single root.

• Leaf nodes (height ≈ 0): individual samples
• Branch height (Y-axis): distance / dissimilarity at each merge
• Low merge height: high similarity
• High merge height: high dissimilarity
• Root: one cluster containing everything

2. Choosing Clusters with a Horizontal Cut

A continuous hierarchy becomes discrete clusters by drawing a horizontal cut at some height y.

• Large vertical gap rule: look for the longest stretches with no merges; cut across that gap to isolate natural groups
• Validation: inconsistency coefficient or silhouette score can confirm the choice

3. Python Pipeline (SciPy + Matplotlib)

from scipy.cluster.hierarchy import linkage, dendrogram, fcluster
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt

X, _ = make_blobs(n_samples=50, centers=3, cluster_std=1.0, random_state=42)
Z = linkage(X, method="ward")

plt.figure(figsize=(12, 6))
dendrogram(Z)
plt.title("Hierarchical Clustering Dendrogram")
plt.xlabel("Sample index / count")
plt.ylabel("Distance (merge height)")
plt.axhline(y=10, color="r", linestyle="--", label="Cut at y=10")
plt.legend()
plt.grid(True, linestyle=":", alpha=0.6)
plt.show()

k = 3
labels = fcluster(Z, t=k, criterion="maxclust")
print(labels)

4. What the Run Shows

• Heights run from 0 at the leaves up to roughly 70 at the root
• A cut near y = 10 typically crosses three vertical branches → three clusters
• fcluster(..., criterion="maxclust") returns an integer label per sample

5. Quick Reference

Term / Function	Role
Dendrogram	Tree of merges/splits
Branch height	Dissimilarity of the merge
Large vertical gap	Heuristic for cut height
linkage(X, method="ward")	Build hierarchy (Ward variance)
fcluster(Z, t=k, criterion="maxclust")	Flat labels for k clusters