Day 27 Outline

Tuesday, May 8, 2018

SVD

What is it?

mxn matrix A = UΣVT, where ...

What does it mean?

Any matrix just does rotate-scale-rotate

(Strictly speaking can combine axis flips with rotation.)

What does it look like?

Some examples of SVD, showing shapes of A, U, Σ, VT:

A in blue, U in yellow, sigma in red, VT in green

svd_examples.png

How to calculate it?

Look at ATA and AAT

What is it good for?

1. low-rank approximation of matrices

Approximation of matrix by sum of rank-1 matrices (data compression)

Examples

i. O'Brian 112

obrian112.jpg

ii. student gallery

More applications on Thursday