Lecture 22 – Principal Components Analysis
Presented by Anthony D. Joseph
Content by Josh Hug, John DeNero, Sam Lau, and Suraj Rampure
The Quick Check for this lecture is due Monday, November 23rd at 11:59PM. A random one of the following Google Forms will give you an alphanumeric code once you submit; you should take this code and enter it into the “Lecture 22” question in the “Quick Check Codes” assignment on Gradescope to get credit for submitting this Quick Check.
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.