📊 K-Means Clustering

About this simulation

K-means is an unsupervised algorithm: it is handed a cloud of points with no labels and asked to sort them into K groups. Here each point lives in a 3D feature space. Colored spheres are the data; the larger glowing orbs are the centroids — the current best guess at each cluster's center.

How it works (Lloyd's algorithm)

• Assign — every data point is colored by whichever centroid is currently closest to it (Euclidean distance).
• Update — each centroid then jumps to the mean position of all points assigned to it.
• These two steps repeat. Centroids drift less and less each round, and the total inertia (sum of squared distances from points to their centroid) only ever goes down.
• When centroids stop moving meaningfully, the algorithm has converged on a local optimum — not necessarily the global best grouping.

Controls

• Clusters (K) — how many centroids the algorithm is told to find. Try setting it far from "True data blobs" to see under- or over-clustering.
• True data blobs — the actual number of hidden groups used to generate the data. K-means never sees this number.
• Data points — how many unlabeled points populate the scene.
• Auto-iterate — runs assign/update automatically; turn off and use Step once to watch each iteration individually.
• New data — regenerates random blobs and restarts centroids from scratch.

Did you know?

Because k-means always converges to a local minimum of inertia, real-world use runs it many times from different random starts (or uses smarter seeding like k-means++) and keeps the run with the lowest inertia.