K-Means Clustering — Assign → Update → Repeat

Use K-Means to partition $n$ unlabelled points into exactly $K$ clusters by minimising the within-cluster sum of squares (WCSS). It's the default choice for Customer Segmentation and other Unsupervised Learning grouping tasks.

1. Initialise — randomly place $K$ centroids in feature space.
2. Assign — assign each point to the nearest centroid (by Euclidean Distance).
3. Update — move each centroid to the mean of its assigned points.
4. Repeat steps 2–3 until assignments stop changing (convergence).

Common pitfalls

• You must choose $K$ in advance — use the Elbow Method and Silhouette Score to pick it.
• Local optima: K-Means always converges but may land on a local, not global, optimum — run with n_init=10 (the sklearn default) so it tries 10 random starts and keeps the best.
• Assumes spherical, equal-size clusters and is sensitive to outliers (means get pulled), so scale features first.

Worked example

From DS Lecture 5 (the StyleNation segmentation, which lands on $K = 4$):

from sklearn.cluster import KMeans

kmeans = KMeans(n_clusters=4, n_init=10, random_state=42)
kmeans.fit(X_scaled)

df["cluster"] = kmeans.labels_
print(df["cluster"].value_counts())

See Lecture 5 - Clustering and Dimensionality Reduction for the full walkthrough.