In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any m × n matrix via an extension of the polar decomposition.
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Singular Value Decomposition (SVD)
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7 items
Singular Value Decomposition (SVD): Dominant Correlations
11 min
Intermediate
Video
Theory
This lectures discusses how the SVD captures dominant correlations in a matrix of data.
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Randomized SVD: Power Iterations and Oversampling
4 min
Intermediate
Video
Theory
This video discusses the randomized SVD and how to make it more accurate with power iterations (multiple passes through the data matrix) and oversampling.
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SVD and Optimal Truncation
11 min
Intermediate
Video
Theory
This video describes how to truncate the singular value decomposition (SVD) for matrix approximation.
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Randomized Singular Value Decomposition (SVD)
13 min
Intermediate
Video
Theory
This video describes how to use recent techniques in randomized linear algebra to efficiently compute the singular value decomposition (SVD) for extremely large matrices.
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SVD and Alignment: A Cautionary Tale
7 min
Intermediate
Video
Theory
This video describes the importance of data alignment when performing the singular value decomposition (SVD). Translations and rotations both present challenges for the SVD.
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Singular Value Decomposition (SVD): Matrix Approximation
14 min
Intermediate
Video
Theory
This video describes how the singular value decomposition (SVD) can be used for matrix approximation.
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Singular Value Decomposition (SVD): Mathematical Overview
12 min
Intermediate
Video
Theory
This video presents a mathematical overview of the singular value decomposition (SVD).
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