svd

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.