Clustering with K-Means

K-means alternates assignment and updates

K-means starts with k centroids. Each observation is assigned to its nearest centroid, then each centroid moves to the mean of its assigned observations. The two steps repeat until assignments or centroid movement stabilize. The objective is to minimize within-cluster sum of squared distances. K-means is sensitive to scale, initialization and outliers, and tends to work best when clusters are reasonably compact under Euclidean distance.

from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler

X_scaled = StandardScaler().fit_transform(X_numeric)
clusterer = KMeans(n_clusters=4, n_init=20, random_state=42)
labels = clusterer.fit_predict(X_scaled)

Cluster quality is not prediction accuracy

Inertia decreases as more clusters are added, so the elbow method is a heuristic rather than proof of the correct k. A silhouette score compares how close a sample is to its own cluster relative to other clusters, but it also has assumptions and limitations. Because there are no target labels, external classification metrics are not automatically appropriate. Inspect cluster sizes, feature summaries, stability and whether a downstream decision can use the groups. A cluster is a pattern in this representation, not a discovered natural truth.