This course on Singular Value Decomposition aims to teach learners the fundamentals and applications of the SVD algorithm. By the end of the course, students will be able to understand the mathematical concepts behind SVD, apply SVD for matrix approximation, image compression, and dominant correlations, as well as utilize SVD for linear regression, principal component analysis, and eigenface analysis. The course covers various tools such as Matlab and Python for practical implementation. The teaching method includes theoretical explanations, hands-on coding exercises, and real-world examples. This course is intended for individuals interested in data processing, reduced-order modeling, high-dimensional statistics, and those looking to enhance their skills in machine learning, dynamical systems, and control.
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
Related Courses
Related articles
Reviews
5.0 rating, based on 2 Class Central reviews
-
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!
-
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.
