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.
Overview
Syllabus
Singular Value Decomposition (SVD): Overview.
Singular Value Decomposition (SVD): Mathematical Overview.
Singular Value Decomposition (SVD): Matrix Approximation.
Singular Value Decomposition (SVD): Dominant Correlations.
SVD: Image Compression [Matlab].
SVD: Image Compression [Python].
The Frobenius Norm for Matrices.
SVD Method of Snapshots.
Matrix Completion and the Netflix Prize.
Unitary Transformations.
Unitary Transformations and the SVD [Matlab].
Unitary Transformations and the SVD [Python].
Linear Systems of Equations, Least Squares Regression, Pseudoinverse.
Least Squares Regression and the SVD.
Linear Systems of Equations.
Linear Regression.
Linear Regression 1 [Matlab].
Linear Regression 2 [Matlab].
Linear Regression 1 [Python].
Linear Regression 2 [Python].
Linear Regression 3 [Python].
Principal Component Analysis (PCA).
Principal Component Analysis (PCA) [Matlab].
Principal Component Analysis (PCA) 1 [Python].
Principal Component Analysis (PCA) 2 [Python].
SVD: Eigenfaces 1 [Matlab].
SVD: Eigenfaces 2 [Matlab].
SVD: Eigenfaces 3 [Matlab].
SVD: Eigenfaces 4 [Matlab].
SVD: Eigen Action Heros [Matlab].
SVD: Eigenfaces 1 [Python].
SVD: Eigenfaces 2 [Python].
SVD: Eigenfaces 3 [Python].
SVD and Optimal Truncation.
SVD: Optimal Truncation [Matlab].
SVD: Optimal Truncation [Python].
SVD and Alignment: A Cautionary Tale.
SVD: Importance of Alignment [Python].
SVD: Importance of Alignment [Matlab].
Randomized Singular Value Decomposition (SVD).
Randomized SVD: Power Iterations and Oversampling.
Randomized SVD Code [Matlab].
Randomized SVD Code [Python].
Taught by
Steve Brunton
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Reviews
5.0 rating, based on 2 Class Central reviews
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I have tried understanding the beauty behind Linear Algebra for a long-time.
If you are like me and are sick of not having an intuitive understanding behind Linear Algebraic algorithms especially those behind Dimensionality Reduction then this is the Holy Grail.
Understanding SVD will open up a wide understanding into PCA,EigenVectors, Eigen-Decomposition, Eigen-Faces, Data Compression/Reconstruction, Least Squares Regression and a huge step into understanding Linear Algebra.
The course not only provide Python and MATLAB scripts for playing around but also goes into intutive mathmetical derviations/proofs behind SVD!
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Krishna Reddycourse provided lot of insights to the beginner. it provided the insights why we need to neural network to solve alignment and invariance problem that doesn't handled by the SVD alogrithm.
