Define the two-cluster customer segmenter data contract

Make malformed input fail before it reaches the interesting algorithm. The accepted contract is rows shaped as (visits, basket_value), normalized before Euclidean distance. This boundary matters because feature scale domination, empty clusters, and unstable labels; allowing a bad value through makes later debugging look like an algorithm problem. Keep transformation functions separate from scoring or prediction so a test can identify which boundary changed the data.

The artifact's user-facing goal is specific: group six unlabeled customers by annual visits and average basket value without pretending the groups are permanent identities. Its accepted input is rows shaped as (visits, basket_value), normalized before Euclidean distance. Those statements are intentionally narrower than “build an AI system.” Narrow scope lets us inspect every input and expected result, and it prevents a toy result from being presented as a production claim. The example implements or probes the input boundary. Copy it into a fresh file and run it without extra packages.

Save this as lesson.py and run python3 lesson.py. It uses only the language standard library, so the example is reproducible offline.

def scale(points):
 xs=[p[0] for p in points]; ys=[p[1] for p in points]
 return [((x-min(xs))/(max(xs)-min(xs)),(y-min(ys))/(max(ys)-min(ys))) for x,y in points]
print(scale([(2,18),(15,82)]))

Expected output: [(0.0, 0.0), (1.0, 1.0)]. Exact floating-point formatting may vary slightly, but the asserted behavior must not. Read the output as evidence about this stage, not merely proof that the interpreter started.

Print the scaled coordinates, distance from every point to every center, assignment vector, and recomputed centers. If only the numeric cluster IDs swap, the partition did not change; compare pairs of points rather than label 0 versus label 1. If one center receives no points, preserve or reseed it explicitly instead of dividing by zero. Re-run with several starting centers and inspect whether the same customers remain together.

At the data contract stage, save the smallest failing fixture beside the expected result. Change one cause at a time and rerun the exact command printed above; that makes the repair reviewable and keeps this chapter's progressive artifact reproducible.

Report WCSS beside a one-cluster baseline, then compare partitions across seeds. A lower WCSS always follows from adding clusters, so it cannot select k by itself. Review whether each segment has enough members and whether a plain-language description is supported by visits and basket value. Never name a segment with a personality or sensitive identity that the features do not measure.

For this data contract page, preserve the fixture and result as evidence for the next page. Label observations separately from conclusions: a passing assertion establishes the behavior it names, while broader usefulness requires the chapter's full evaluation set and stated operating limits.