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ml-recall

#reconstruction-error

3 questions from Dimensionality Reduction, Autoencoders & VAEs

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3 questions · 3 min · score and explanations at the end

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Question 1: Short answer

hardAI-checkedDimensionality Reduction

The centered data matrix XX has singular values 5, 3, 15,\ 3,\ 1. You reconstruct it from the first principal component only, which gives the best rank-1 approximation X1X_1. What is the reconstruction error ∥X−X1∥F\lVert X - X_1 \rVert_F (Frobenius norm)?

3 decimals