Choose k and Check the Shape

The algorithm always returns clusters

K-means will partition data even when no meaningful groups exist. The elbow method plots inertia against k and looks for diminishing returns. The silhouette score compares how close each point is to its own cluster versus others. Both are aids, not automatic truth; domain usefulness and stability matter too.

K-means assumes roughly compact, spherical, similarly sized clusters under Euclidean distance. It struggles with curved shapes, very unequal density, outliers, and categorical features. Scaling is critical because large-unit columns dominate distance and centroid movement.

k:        2    3    4    5    6
inertia: 900  510  330  290  270
possible elbow near 4; now inspect meaning and stability

Warning: Selecting k because it creates convenient marketing segments is not validation. Check whether clusters repeat across samples and support a real decision.

Tip: Inspect centroid feature values in original units after reversing scaling. A cluster becomes useful only when humans can characterize and act on it.