Unsupervised Learning and PCA

This lecture shifts from supervised to unsupervised learning — methods that find structure without a target variable. We cover principal component analysis (PCA) for dimensionality reduction: how components are constructed, what explained-variance ratios tell you, and why scaling matters.

Optional: technical supplement

For students who want the linear algebra: solving the variance-maximisation problem with a Lagrange multiplier (the answer is an eigenvector, and the variance along it is the eigenvalue), explained-variance ratios as eigenvalue shares, the SVD that scikit-learn actually computes, and the bridge that connects PCA to ridge regression through the eigenvalues of X^⊤X.

Open the supplementary slides ↗ — optional and self-contained; nothing in it is required for the project.