Phase 3: Advanced Math for AI · ~90 minutes · Python
Dimensionality Reduction
High-dimensional data has structure. You find it by looking from the right angle.
What you will learn
- 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
Introduction
- Type: Build
- Language: Python
- Prerequisites: Linear Algebra Intuition
- Time: ~90 minutes
Objective
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
Unlock the full lesson
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