Unit 7 Summary

Linear Algebra for Machine Learning · Axiom Academy

Unit 7: PCA & Dimensionality Reduction What is Dimensionality Reduction? Dimensionality reduction transforms high-dimensional data to lower dimensions while preserving important structure. It's essential for: Visualization (2D/3D plots of high-D data) Computational efficiency (fewer features = faster algorithms) Denoising (keeping important structure, discarding noise) Feature engineering (better input for downstream models) 1. Covariance Matrix (Modules 7.2-7.3) 2. Principal Component Analysis (Modules 7.1-7.10) 3. How Many Components? (Modules 7.7-7.9) 4. Preprocessing is Critical (Module 7.10) 5. SVD Alternative (Module 7.6) 6. Nonlinear Extensions (Modules 7.11-7.14) 7. Real Applications (Modules 7.15-7.16) You now understand the mathematical foundations of dimensionality reduction. Next units might explore: Clustering algorithms (using PCA-reduced data) Feature selection methods (alternative to dimensionality reduction) Deep learning approaches to feature learning (autoencoders) Applications in computer vision, NLP, and biology

This is the written version of the interactive lesson above. See the full Linear Algebra for Machine Learning course.