Lecture

Dimensionality Reduction

Description

This lecture covers the concepts of Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) for dimensionality reduction. It explains how to find low-dimensional representations of high-dimensional data, with applications in visualization, noise reduction, and efficiency. The lecture also delves into the spectral theorem, SVD existence, low-rank approximation, and best rank(r)-approximation. Additionally, it explores the interpretation of SVD, covariance vs correlation matrix in PCA, Multidimensional Scaling (MDS), non-linear embedding techniques like Isomap, and concludes with a summary of lessons learned.

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