Dimensionality Reduction

Relate PCA variance objectives to covariance eigenvectors and SVD.

Use https://mlprep.iwase.dev/practice/machine-learning/dimensionality-reduction/. This is a Practice set, not a Screening result. If window.mlPrepAgent is available, read local attempt history before planning. Help me work through the set without revealing full answers first, and save each real attempt through the bridge with recorded_by agent and agent_session_id when available.

Recommended resources

Probabilistic Machine Learning: An Introduction — online draft dated 2025-04-18 — Kevin P. Murphy and MIT Press

Instructions

Center the data conceptually before applying PCA.

Ordered items

PCA direction and explained varianceDimensionality Reduction · Easy · 7 min · Original
Low-rank error and explained varianceLinear Algebra · Medium · 8 min · Original
Deriving the second principal componentDimensionality Reduction · Hard · 18 min · External

Completion

Explain both reconstruction-error and retained-variance views of PCA.

Next

Unsupervised Learning