Clustering

Finding groups nobody labelled

Clustering is the task of grouping data points by similarity with no label telling the algorithm which group anything actually belongs to — the unsupervised counterpart to the classification lessons earlier in this roadmap. Customer segments nobody predefined, or genuinely distinct types of behaviour hiding inside a single undifferentiated dataset, are the kind of structure clustering is built to surface.

K-means: assign, then recompute, repeat

K-means starts by choosing a number of clusters, k, and placing that many initial centroids — points representing the centre of each cluster — usually at random. Every data point is then assigned to whichever centroid is closest to it, using ordinary distance (see Euclidean norm for the underlying formula). Once every point has an assignment, each centroid moves to the average position of all the points now assigned to it. These two steps, assign and recompute, repeat until the assignments stop changing between iterations, at which point the algorithm has converged on a final set of clusters.

Choosing k is not something the algorithm does on its own — it is a decision made before the algorithm runs at all. The elbow method is the standard approach: run k-means across a range of values for k, and plot how much the total within-cluster distance improves as k increases. That improvement is steep at first and then flattens out, and the point where it bends — the “elbow” — is a reasonable choice, since adding more clusters beyond that point buys only a diminishing improvement.

What to watch for

The video covers exactly this mechanism — centroids, iterative reassignment, and choosing k via the elbow method — at a clear beginner pace from the channel most reliably trusted for this kind of explanation.

Hierarchical clustering: no k required up front

Rather than choosing a fixed number of clusters in advance, hierarchical clustering builds a complete tree of nested groupings. The agglomerative version, the more common approach, starts with every point as its own cluster and repeatedly merges the two closest clusters into one, continuing until everything has merged into a single cluster containing the whole dataset. The result is a dendrogram — a tree diagram showing the full merge history — which can be cut at any height to produce however many clusters are wanted after the fact, rather than requiring that choice before the algorithm ever runs. This flexibility is the main practical advantage hierarchical clustering has over k-means, at the cost of being considerably more expensive to compute on a large dataset.

Judging a clustering with no ground truth

Supervised learning is checked against labels nobody disputes. Clustering has no such anchor — there is no file somewhere recording the “correct” grouping to compare against, because if there were, the problem would already be solved. Quality instead has to be judged by internal properties of the result itself: are points within a cluster genuinely close together, and are different clusters well separated from one another? Metrics exist to quantify exactly this, but they are checking internal consistency, not agreement with a ground truth, which is a meaningfully different and in some ways less certain kind of evaluation than anything covered in the evaluating models group later in this roadmap.