Linear Dimensionality Reduction: PCA and LDA

This lecture covers the concepts of Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) for dimensionality reduction in data. Starting with a toy example, the instructor explains how PCA maps data to a lower-dimensional space while incurring some information loss. The lecture then delves into the optimal linear mapping using PCA, the importance of clustering samples within the same class, and separating different classes using LDA. The Fisher Linear Discriminant Analysis (LDA) is introduced as a method to cluster and separate classes effectively. The lecture concludes with a comparison between PCA and LDA, showcasing their distinct approaches to dimensionality reduction.