Clustering discovers natural groupings in unlabelled data. Run k-means step by step, build a dendrogram by merging, weigh the trade-offs and spot outliers — then test yourself with 10 questions.
Clustering puts similar objects in the same group and dissimilar ones apart — with no labels to learn from. Good clusters have high intra-cluster similarity and low inter-cluster similarity. It's unsupervised: the structure is discovered, not taught.
k-means repeats two steps until nothing moves: assign each point to its nearest centroid, then update each centroid to the mean of its points. Press Step to watch one round, Run to animate to convergence, and change k or resample the data.
Start with every point as its own cluster, then repeatedly merge the two closest clusters until one remains. The merge order draws a dendrogram; cut it at a height to get any number of clusters.
Linkage = how cluster distance is measured: single (nearest pair), complete (farthest pair), average, or Ward (variance).
The opposite: start with all points in one cluster and recursively split. It's more expensive but can capture large structure first. Both produce a hierarchy — no need to pre-choose k.
A tree showing the merge/split order and the distance at each join.
Single linkage can "chain"; complete linkage makes compact clusters.
No need to fix k in advance; produces a full hierarchy and interpretable tree.
Costly (O(n²) or worse) and merges/splits are irreversible — a bad early step stays.
Use the elbow method (within-cluster sum of squares) or silhouette score to pick a sensible k for k-means.
Simple, fast and scalable — great for large, roughly spherical clusters.
Needs k up front, sensitive to initial centroids and outliers, and assumes convex, similar-sized clusters.
Points far from any cluster centre (or in very low-density regions) are flagged as outliers — useful for fraud and fault detection.
Uses actual data points as centres, making it more robust to outliers than k-means.
Euclidean, Manhattan or cosine — the choice of similarity shapes the clusters found.
Two clear explainers from StatQuest with Josh Starmer on the two clustering families in this unit.
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