Golden
Singular value decomposition (SVD)

Singular value decomposition (SVD)

A popular method of matrix decomposition that reduces a complex matrix into its constituent parts so that subsequent matrix calculations are simpler.

Singular value decomposition (SVD) is a popular method of matrix decomposition that reduces a complex matrix into its constituent parts so that subsequent matrix calculations are simpler.



The general equation for SVD for real-valued matrices is:



A = U * Σ * V^T



Where A represents the real m x n matrix that is being decomposed, U is a m x m matrix, Σ is an m x n diagonal matrix, and V^T (i.e. V transposed) is the transpose of an n x n matrix.



The columns of the U matrix are called the left-singular vectors of matrix A, while the columns of the V matrix are called the right-singular vectors of A. The diagonal values of the Σ matrix are the singular values of matrix A.

Singular Value Decomposition in Machine Learning

SVD is a commonly used method for data reduction in machine learning, particularly in unsupervised learning algorithms. It's one of the core elements of the recommender systems of international companies like Google, Facebook, Netflix and Youtube, helping them determine the order that pages appear in search results, what content and ads you see, and what shows / movies / videos you might enjoy.





Timeline

People

Name
Role
LinkedIn







Further reading

Title
Author
Link
Type
Date

A Gentle Introduction to Singular-Value Decomposition for Machine Learning

Jason Brownlee

Web



Foundations of Machine Learning : Singular Value Decomposition (SVD)

Patrick Luboobi

Web



Documentaries, videos and podcasts

Title
Date
Link

Singular Value Decomposition (SVD) - MIT OpenCourseWare

May 6th, 2016

Companies

Company
CEO
Location
Products/Services









References