Dimensionality Reduction: PCA and LDA

This lecture covers the concepts of dimensionality reduction through techniques like Principal Component Analysis (PCA) and Fisher Linear Discriminant Analysis (LDA). It explains how PCA aims to retain important data signal while removing noise by maximizing variance, and how LDA focuses on clustering samples from the same class and separating different classes. The lecture also introduces Kernel PCA for nonlinear data, t-SNE for visualization, and discusses clustering methods like K-means. It delves into Gaussian Mixture Models (GMM) for density estimation, KDE for smooth distribution estimates, and Mean Shift for clustering by finding density maxima. The presentation concludes with a comparison of KDE and histograms for data representation.