Principal Component Analysis Deep Dive

Studied Principal Component Analysis (PCA) from first principles, covering linear algebra basics such as projections and projected variance, eigenvectors and eigenvalues, and Lagrange multipliers as the optimization tool connecting them.

Produced a short explainer video breaking down the concept in my native language, using Manim, a Python library for mathematical animation, to visualize projections and variance maximization.

• Covered linear algebra fundamentals underlying PCA: projections and projected variance.

• Studied eigenvectors and eigenvalues as the core mathematical objects PCA optimizes over.

• Used Lagrange multipliers to understand the constrained optimization behind PCA's variance-maximization objective.

• Created and published a Manim-animated explainer video on PCA in my native language.

Explainer Video