Python Coding Classes for Children in Thessaloniki

Chapter 137 – Hierarchical Clustering Part 2: Dendrograms, PCA & Evaluation

1. Pipeline Overview

End-to-end flow on the Wine dataset (178 × 13): scale features → Ward linkage dendrogram → AgglomerativeClustering (k=3) → PCA to 2D → check cluster counts. Labels are unsupervised IDs only.

2. Why StandardScaler Is Required

Features span very different ranges (e.g. Proline > 1000 vs Malic Acid ~1). Unscaled Euclidean distances would be dominated by large-magnitude columns. StandardScaler sets mean 0 and std 1 so every feature contributes fairly.

3. Dendrogram (SciPy)

from scipy.cluster.hierarchy import linkage, dendrogram
Z = linkage(X_scaled, method="ward")
plt.figure(figsize=(10, 6))
dendrogram(Z)
plt.ylabel("Merge distance")
plt.show()

Y-axis runs ~0 (leaves) to ~35 (root). Top branches support a natural cut at k = 3.

4. Fit Agglomerative Model

hc = AgglomerativeClustering(n_clusters=3, linkage="ward")
labels = hc.fit_predict(X_scaled)

Outputs integer IDs 0 / 1 / 2 for each of the 178 samples.

5. PCA Visualization

pca = PCA(n_components=2)
X_2D = pca.fit_transform(X_scaled)
plt.scatter(X_2D[:, 0], X_2D[:, 1], c=labels, cmap="Set1", edgecolors="k")
plt.xlabel("PC1"); plt.ylabel("PC2")
plt.show()

Cores of the three groups separate clearly; a few boundary points mix, which is normal for real data.

6. Cluster Balance

• Cluster 2: 64
• Cluster 0: 58
• Cluster 1: 56

Max gap is only 8 samples → balanced partition, not degenerate tiny clusters.

7. Full Script Skeleton

wine = load_wine()
X = wine.data
X_scaled = StandardScaler().fit_transform(X)
Z = linkage(X_scaled, method="ward")
# dendrogram(Z) ...
hc = AgglomerativeClustering(n_clusters=3, linkage="ward")
labels = hc.fit_predict(X_scaled)
X_2D = PCA(n_components=2).fit_transform(X_scaled)
# scatter + value_counts ...