K-Means Clustering
K-means finds k groups in unlabeled data by repeating two simple steps: assign every point to its nearest center, then move each center to the average of its points. The loop always converges — but only to a local minimum of inertia — so careful seeding (k-means++) and restarts are what make it trustworthy.
01.The Problem: A Pile of Points, No Labels
Imagine you run an online grocery store.
You plot every customer as a dot, using two numbers: monthly spend, and orders per month.
Ten thousand dots. No colors. No names. Nobody ever labeled these people into groups.
But the dots do not look random.
There seem to be tight clumps of dots, and the clumps look different from each other. Can I find them automatically?
That is clustering — a family of unsupervised learning algorithms. Unsupervised, in one plain sentence: the data arrives without answers, and the algorithm must propose structure on its own.
Here is the chicken-and-egg catch:
To assign a point to "its group," you need groups. To form groups, you need to know which points belong together.
K-means — the most famous clustering algorithm — breaks the loop with a deceptively simple trick: guess the groups first, then polish them.
Its whole recipe is two steps, repeated:
Step 1: every point joins its nearest group-center. Step 2: every group-center moves to the average of its joined points.
That is it. Repeat until nothing moves.
The rest of this topic is about why those two steps work, what they quietly minimize, where they fail, and how practitioners make the results trustworthy.
K-Means: The Assign–Update Loop 🔄
K-Means: The Assign–Update Loop 🔄
Both steps strictly decrease total inertia, so the algorithm always converges — to a local minimum, hence multiple restarts.
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