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Singular Value Decomposition

Steve Brunton via YouTube

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Overview

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This lecture series develops singular value decomposition for matrix approximation, data processing, reduced-order modeling, and high-dimensional statistics. It includes applications such as image compression, matrix completion, least-squares and linear regression, PCA, eigenfaces, optimal truncation, and randomized SVD with MATLAB and Python examples.

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

Reviews

5.0 rating, based on 2 Class Central reviews

Start your review of Singular Value Decomposition

  • Profile image for Agrover112
    Agrover112 @agrover112
    2
    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!
  • Profile image for Krishna Reddy
    Krishna Reddy
    course 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.
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