Clustering#

Stage 4 · 🧩 Sampling, Partitioning & Segmentation · Lesson 27 of 56 · intermediate

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Important

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Algorithms for groups#

Turning the idea of clustering into practice means choosing an algorithm — a procedure that actually finds the groups. Many exist, differing in how they define a cluster and how they search. The most widely used, and the natural starting point, is k-means.

k-means#

k-means partitions the data into a pre-chosen number \(k\) of clusters, each summarised by its centroid (the mean of its members). It seeks to minimise the within-cluster sum of squares — the total squared distance from points to their centroids — through a simple, repeating two-step loop:

Assign each observation to the nearest centroid;
Update each centroid to the mean of the points now assigned to it.

Repeat until assignments stop changing. In scikit-learn this is KMeans(n_clusters=k). It is fast and intuitive, though it assumes roughly round, similarly-sized clusters and needs \(k\) chosen in advance.

Choosing k#

Since \(k\) is an input, how many clusters should there be? Two common guides: the elbow method plots the within-cluster sum of squares against \(k\) and looks for the “elbow” where adding clusters stops helping much; the silhouette score measures how well each point sits in its cluster versus the nearest other one, rewarding tight, well-separated groups. Neither is automatic — the “right” \(k\) often depends on what is useful for the business.

Other approaches#

k-means is not the only option. Hierarchical clustering builds a tree (dendrogram) of nested groups, needing no \(k\) up front and revealing structure at every scale. Density-based methods like DBSCAN grow clusters from dense regions, handling odd shapes and marking outliers as noise. Each embodies a different notion of what a cluster is — but all serve the same goal: similar together, different apart.

Hint