Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 9 / b / i

Principal component analysis finds orthogonal directions of greatest sample variation, ordered by the variance explained. It can summarize correlated variables, reveal lower-dimensional structure, and provide a reduced representation by retaining only the first few principal components. Centering is standard; scaling may also be appropriate when the variables have incomparable units.