Principal Component Analysis

Phase: 1 | Status: ✅ Complete | Prerequisites: Linear Algebra, Probability & Statistics

Overview

Variance maximization, eigendecomposition, SVD, dimensionality reduction, reconstruction error, explained variance ratio, standardization effects.

Contents

#	File	Type	Description
1	theory.md	Theory	WHY, covariance, variance maximization, reconstruction, SVD connection, failure cases
2	first_principles.ipynb	Computation	WHY→WHAT→HOW→BUILD→VERIFY — PCA from scratch via SVD, scree plot, sklearn comparison
3	exercises.ipynb	Practice	Hand eigendecomposition, reconstruction error, standardization comparison, failure analysis, SVD connection

Connections

• Prereqs: Linear Algebra, Probability & Statistics
• Synthesis: Geometry of ML
• Next: 12 Dimensionality Reduction, 17 Autoencoder