Syllabus Map

• Study map: Syllabus Study Map

Core Idea

• SVD factorizes any matrix into orthogonal directions and singular values.
• PCA uses top-variance directions for dimensionality reduction.

Key Formulas

Practical Notes

Keep components by explained variance.

• Avoid over-compression that removes predictive information.

PCA assumes linear structure.

• Nonlinear manifolds may need methods like UMAP/t-SNE.

Why This Matters for ML

• SVD powers low-rank compression, denoising, and latent-structure extraction.
• PCA is a standard preprocessing step for high-dimensional tabular and vision features.
• Principal components can reduce overfitting and improve downstream training efficiency.
• Spectral views connect directly to embedding quality and variance-preserving representations.