Principal Component Analysis: Geometric Interpretation and Dimension Reduction

This lecture covers Principal Component Analysis (PCA), a method to reduce the dimensionality of data by maximizing variance along new dimensions. It explains how PCA represents data in a new orthonormal basis, the importance of centering and standardization, and the calculation of principal components. The lecture also discusses the geometric interpretation of PCA, the choice of the number of principal components, and the latent representation of data. Additionally, it touches on model selection and validation in the context of dimension reduction.