Module 5: Dimensionality Reduction

High-dimensional data is hard to visualize, slow to train on, and prone to overfitting. This module covers compressing data onto lower-dimensional subspaces while keeping the structure that matters.

What You’ll Learn¶

• Principal component analysis (PCA) for unsupervised compression

• Linear discriminant analysis (LDA) for supervised, class-separating projections

• Nonlinear dimensionality reduction and manifold learning (t-SNE)

• How to choose the number of components and interpret explained variance

Lecture Materials¶

• 📝 Lecture Notes (PDF)

• 🧮 Math Notes (PDF)

• 📓 Chapter notebook: Compressing Data via Dimensionality Reduction, plus an additional worked example notebook

Lecture Videos¶

Part 1: Introduction and Principal Component Analysis | CAP 6606 — Module 5, Part 1¶

Part 2: PCA Examples in Jupyter | CAP 6606 — Module 5, Part 2¶

Part 3: The Main Steps Behind PCA, Step by Step | CAP 6606 — Module 5, Part 3¶

Part 4: Supervised Compression with Linear Discriminant Analysis | CAP 6606 — Module 5, Part 4¶

Part 5: The Inner Workings of LDA | CAP 6606 — Module 5, Part 5¶

Part 6: Nonlinear Dimensionality Reduction and t-SNE | CAP 6606 — Module 5, Part 6¶

Prerequisites¶

• Module 4

• Eigenvalues/eigenvectors (reviewed in the math notes)

Reference¶

Raschka & Mirjalili, Machine Learning with PyTorch and Scikit-Learn, Chapter 5.