K-Means Doesn't Find Your Clusters. It Finds Its Own.

Classic Machine Learning Through the Eyes of an SRE — Part 5

Supervised learning at least tells you when it's wrong. Unsupervised learning will happily hand you a confident answer to a question your data never contained.

K-Means is where that lesson starts, because K-Means always gives you the K clusters you asked for. Ask it for 5 clusters of your client accounts and you will receive exactly 5 clusters, with centroids and an objective value. Whether your accounts actually form 5 groups — or any groups at all — is not something the algorithm can tell you.

It answers the question "what's the best way to split this into 5 compact groups?", not "are there 5 groups here?"

Those are very different questions. Only one of them was yours.