Singular Value Decomposition
Dive deep into the Singular Value Decomposition (SVD) algorithm through this comprehensive 7-hour lecture series based on Chapter 1 of "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz. Explore SVD's mathematical foundations, matrix approximation techniques, and applications in image compression, matrix completion, and the Netflix Prize. Learn about unitary transformations, linear systems of equations, least squares regression, and the pseudoinverse. Discover Principal Component Analysis (PCA) and its implementation in MATLAB and Python. Investigate eigenfaces, optimal truncation, and the importance of alignment in SVD. Conclude with an examination of randomized SVD techniques, including power iterations and oversampling, with practical code examples in both MATLAB and Python.