k-Means y elección de k

k-Means is the most popular clustering algorithm: it splits your data into k groups by grouping points around central anchors. 🎯

Each cluster has a centroid, the mean position of its members. Points join the cluster whose centroid sits closest to them.

k-Means alternates two steps: assign every point to its nearest centroid, then recompute each centroid from its new members.

Those steps repeat until assignments stop changing. The algorithm has converged, and the clusters are final.

k-Means cannot invent the number of groups. You must pick k up front, and the right value is rarely obvious.

scikit-learn makes fitting easy. Set n_clusters to your chosen k and call fit on your scaled data.

After fitting, inertia reports the total squared distance from points to their centroids. Lower means tighter clusters.

Plot inertia for many k values. Where the curve bends sharply, the elbow, often marks a good number of clusters.

Past the elbow, adding clusters barely lowers inertia. That flattening signals you are just splitting groups that already fit well.

A second guide is the silhouette score: it rewards points that sit close to their own cluster and far from others.

Random starts can land badly, so scikit-learn defaults to k-means++, which spreads initial centroids out for steadier results.

Let us check how you would pick a sensible k.

k-Means groups points around centroids for a chosen k; the elbow and silhouette help you pick that k well. 🎯