Clustering with k-means

Why cluster?

Often there is no label to predict. A supermarket chain has purchase data for 20 lakh loyalty-card holders and wants to understand its customers. Clustering finds natural groups, such as "weekly family shoppers", "late-night snack buyers" and "festival-only shoppers", so each group can get the right offers. This is unsupervised learning: the algorithm finds structure on its own.

The k-means loop

1. Choose k, the number of clusters, and pick k starting centroids.
2. Assign step: put each point in the cluster of its nearest centroid (Euclidean distance).
3. Update step: move each centroid to the mean of the points assigned to it.
4. Repeat the assign and update steps until the assignments stop changing.

points = [(1, 1), (1, 2), (2, 1), (8, 8), (9, 8), (8, 9)]
centroids = [(0, 0), (10, 10)]
# assign: the first three are nearer (0, 0), the last three nearer (10, 10)
# update: new centroids are the means of each group
group_a = points[:3]
print(tuple(round(sum(c) / 3, 2) for c in zip(*group_a)))

Choosing k

k-means always gives exactly k clusters, even if the data has no real groups. To choose k, try several values. Inertia is the total squared distance of points to their centroid; it always falls as k grows. The elbow method plots inertia against k and picks the point where the curve bends and extra clusters stop helping much. The silhouette score (from −1 to 1) measures how much closer points are to their own cluster than to the next one; higher is better. Business sense matters too: five segments a marketing team can act on beat twelve nobody understands.

from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

for k in range(2, 7):
    km = KMeans(n_clusters=k, n_init=10, random_state=0).fit(X_scaled)
    print(k, round(km.inertia_), round(silhouette_score(X_scaled, km.labels_), 3))

Things k-means assumes

• Clusters are roughly round blobs of similar size. Long or curved shapes confuse it.
• Features are on similar scales; scale them first (topic 4).
• Every point belongs to some cluster, so outliers drag centroids around.
• The result depends on the starting centroids, which is why several restarts are used.

Common mistakes

• Not scaling, so "annual spend in rupees" decides everything and "visits per month" is ignored.
• Treating clusters as truth. They are a useful summary; describe each with plain statistics and check they make sense.
• Using k-means on categories directly. Distances between encoded categories are not meaningful; use other methods (for example k-modes) or careful encoding.