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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iii/9/b/i/solution

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

Codex  0 2026-10-25

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.

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