Customer segmentation: k-means clustering step by step

Segmentation is the most common unsupervised-learning task in financial services: group policyholders or investors into a handful of segments that behave alike, then tailor pricing, marketing, service and risk appetite to each. k-means is the usual first tool. It places k centres and alternates between assigning every customer to the nearest centre and moving each centre to the mean of its customers, until nothing changes. It always returns k segments, whether or not the data contain any.

This module lets you watch that happen one iteration at a time, from k-means++ starting points, on three synthetic books: policyholders described by annual premium and claims frequency (four compact groups, the case k-means was built for), investors described by portfolio size and trading activity (three groups of very unequal size, one long and tilted), and a "No real segments" book drawn from a single population. Turn off standardisation and the lesson is immediate: with one feature in dollars and the other in counts, the dollar axis carries almost all of the raw variance and k-means simply cuts the book into premium bands.

Choosing k is a judgement call that the elbow chart (within-cluster sum of squares against k) and the average silhouette score inform but do not settle. On the policyholder book both point to the true four groups (silhouette about 0.70). On the no-segments book k-means still draws tidy, confidently labelled segments, but the silhouette never exceeds about 0.37 and the elbow has no sharp bend: the diagnostics say the groups are not there. A segment profile table translates each cluster back into original units with a plain-English label, which is the output a marketing or risk team actually uses.