Dimensionality Reduction

High-dimensional data has structure. You find it by looking from the right angle.

Build 1.5 hr Python

Prerequisites: Phase 1, Lessons 01 (Linear Algebra Intuition), 02 (Vectors, Matrices & Operations), 03 (Eigenvalues & Eigenvectors), 06 (Probability & Distributions)

#Learning Objectives

Implement PCA from scratch: center data, compute the covariance matrix, eigendecompose, and project
Use explained variance ratio and the elbow method to choose the number of principal components
Compare PCA, t-SNE, and UMAP for visualizing MNIST digits in 2D and explain their tradeoffs
Apply kernel PCA with an RBF kernel to separate nonlinear data structures that standard PCA cannot handle

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The text and code of this lesson are based on AI Engineering from Scratch by Rohit Ghumare, MIT licensed.