dimensionality reduction

A from-scratch favorite that tests linear algebra fluency. The signal is centering first, using SVD instead of forming the covariance matrix, and reading variance off the singular values. Here is the implementation and the details interviewers push on.

Dimensionality questions test linear-algebra intuition and practical judgment at once. The signal is what PCA actually does (project onto max-variance directions), why high dimensions hurt, and the honest catch: it is unsupervised, so it can throw away the exact direction your label needs. Here is the answer.

These three get conflated, but they answer different questions: one is a preprocessing tool, two are eyeballing tools. The candidates who pass know exactly which structure each preserves and which it quietly throws away.

LDA is the supervised cousin of PCA, and the contrast is a favorite. The signal is knowing that LDA spends the labels to maximize class separation while PCA only chases variance, plus the C minus 1 dimension cap that catches most candidates off guard.

High-dimensional data breaks the intuitions and methods that work in two or three dimensions. The signal is naming the concrete effects (distances concentrate, data goes sparse, overfitting climbs) and the mitigations that actually move the needle.