Lecture 21 – Principal Components Analysis
Presented by Anthony D. Joseph
Content by Josh Hug, John DeNero, Sam Lau, and Suraj Rampure
A reminder – the right column of the table below contains Quick Checks. These are not required but suggested to help you check your understanding.
Dimensionality. Visualizing high-dimensional data.
More visualizations of high-dimensional data.
Matrix decomposition, redundancy, and rank. Introduction to the singular value decomposition (SVD).
The theory behind the singular value decomposition. Orthogonality and orthonormality.
Definition and computation of principal components. Geometric interpretation of principal components and low rank approximations. Data centering.
Interpretation of singular values. The relationship between singular values and variance. Analyzing scree plots.
Introduction to principal Component analysis (PCA). PCA for exploratory data analysis.