PCA projection without covariance inversion

Question

Implement a training-only PCA fit and projection using SVD. Return k feature directions and explain what must be reused on test data.

Short answer

Centre with the training mean and use the first k right singular vectors as feature directions. Test rows must reuse both the mean and directions. Singular-vector signs can differ without changing the represented subspace.

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Lessons behind this question

Principal Component Analysis and the SVD View
The Supervised Learning Problem and the ML Pipeline
Covariance and Correlation

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