---
title: "Unsupervised Learning"
url: "/learn/machine-learning/unsupervised-learning"
category: "machine-learning"
---

There is no loss function handed to you here — no label to be wrong about —
which is what makes this subcategory a genuinely different kind of problem
rather than a variation on supervised learning.

K-means and hierarchical clustering answer "what groups exist" two different
ways, with different assumptions about what a cluster even is. Principal
component analysis answers a related but distinct question: which directions
in the data carry the information, and which are close enough to noise to drop.

## Posts

- Hierarchical Clustering and the Shape of Real-World Data (unpublished): Where k-means demands a number of clusters before it starts, hierarchical clustering builds a full nested structure — a dendrogram — and lets you choose where to cut it afterwards. This post derives agglomerative clustering, the linkage criteria that decide how clusters merge, and when the flexibility is worth the cost.
- K-Means Clustering: The Algorithm and Its Failure Modes (unpublished): K-means alternates between assigning points to the nearest centroid and recomputing centroids, and that simplicity hides several sharp edges — sensitivity to initialisation, the assumption of round clusters, and the need to choose the number of clusters in advance. This post derives the algorithm and each failure mode.
- Principal Component Analysis: Dimensionality Reduction as Reconstruction (unpublished): Principal component analysis has two equivalent derivations — maximising variance along a direction, and minimising reconstruction error when compressing to fewer dimensions. This post works through the reconstruction framing, connects it back to the singular value decomposition, and shows what a principal component represents.