1 / 6

Understanding Singular Value Decomposition (SVD) in Mathematics

Learn about SVD, M = U.S.VT, the concept of Orthogonal, Rotate, Stretch, and how to interpret matrices into scaled outer products. Explore the separate operations in each dimension. Discover the key insights behind SVD.

larrya
Download Presentation

Understanding Singular Value Decomposition (SVD) in Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math Tools

  2. Remember these?

  3. Singular Value Decomposition (SVD) M = U S VT Orthogonal Orthogonal (“Rotate”) (“Rotate”) Diagonal (“Stretch”)

  4. SVD S U VT Output Scaling Input

  5. A simple case V= U S VT u2 O S I x Outer Product! v2 u1 v1

  6. SVD can be interpreted as • A sum of outer products! • Decomposing the matrix into a sum of scaled outer products. • Key insight: The operations on respective dimensions stay separate from each other, all the way – through v, s and u. • They are grouped, each operating on another piece of the input.

More Related