Python Programming for Students in Bordeaux

Chapter 132 – K-Means Part 2: Test and Improve

1. Pipeline Overview

Without labels, we cannot use accuracy or precision. Quality is judged by inertia (within-cluster sum of squares) and metrics like the silhouette score. Pipeline: load data → scale features → choose K (elbow) → fit → visualize → evaluate.

2. Wine Data and Scaling

Wine has 178 samples × 13 chemical features. Scales differ a lot (Alcohol ~10–20, Proline in the 1000s). Unscaled, large-magnitude features dominate Euclidean distances. StandardScaler puts features on a comparable range before clustering.

from sklearn.datasets import load_wine
from sklearn.preprocessing import StandardScaler
import pandas as pd

wine = load_wine()
df = pd.DataFrame(wine.data, columns=wine.feature_names)
X_selected = df[["alcohol", "malic_acid"]].values
X_scaled = StandardScaler().fit_transform(X_selected)

3. Elbow for K

Loop K from 1–10 with n_init=10, plot inertia. Sharp drop through K=3, then flattening — so K=3 is the elbow; higher K mainly over-splits groups.

4. Fit, Predict, Plot

from sklearn.cluster import KMeans
import matplotlib.pyplot as plt

kmeans = KMeans(n_clusters=3, n_init=10, random_state=42)
labels = kmeans.fit_predict(X_scaled)
centroids = kmeans.cluster_centers_

plt.scatter(X_scaled[labels == 0, 0], X_scaled[labels == 0, 1], c="black", label="Cluster 0")
plt.scatter(X_scaled[labels == 1, 0], X_scaled[labels == 1, 1], c="green", label="Cluster 1")
plt.scatter(X_scaled[labels == 2, 0], X_scaled[labels == 2, 1], c="yellow", label="Cluster 2")
plt.scatter(centroids[:, 0], centroids[:, 1], s=200, c="red", marker="X", label="Centroids")
plt.xlabel("Scaled Alcohol"); plt.ylabel("Scaled Malic Acid"); plt.legend(); plt.show()

5. Silhouette and Balance

Average silhouette ≈ 0.48 (between overlap and ideal separation): boundaries are close but groups remain clear. Counts were roughly balanced (e.g. 66 / 63 / 49 across clusters).

6. Pipeline Summary

Step	Tool	Outcome
Ingest	load_wine()	(178, 13) features
Scale	StandardScaler	Comparable feature ranges
Choose K	Elbow / inertia	K = 3
Fit	fit_predict	Labels + centroids
Validate	silhouette_score	~0.48; balanced counts