Lecture Notes 23

Lecture Notes 23 - Lecture23 1 Outline 1 Quick Review 2 Application 1 Total Least Squares A recipe Interpretation 3 Application 2 Pattern

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture23 1 December 03, 2007 Outline: 1) Quick Review 2) Application 1: Total Least Squares A recipe Interpretation 3) Application 2: Pattern Recognition and Empirical Orthogonal Functions (EOF's/PCA etc.) Examples: Image reconstruction and compression Classification of 1-D Topography (EOF analysis) Lecture 23: Applications of the SVD SVD of a general mxn matrix A with rank r Quick Review = A V T U Σ Matlab: [U,S,V]=svd(A) SVD of a general mxn matrix A with rank r SVD: the economy sized version = A V T U Σ Matlab: [U,S,V]=svd(A,0) Least squares problems using the SVD if A is mxn overdetermined then the solution x that minimizes ||e ||=||b-Ax || is x =x + =A + b where A + =V Σ + U T is the pseudo-inverse Comments: 1) if A is invertible A + =______ and ||e ||=_______ 2) if A is full column rank x + is the unique solution to _____________________ 3) in general p =AA + b is the projection of b onto _______ ^ ^ ^ Lecture23 2 December 03, 2007 Least squares problems using the SVD Total Least squares problems using the SVD Total Least squares problems using the SVD A recipe (in matlab): Total Least squares problems using the SVD Lecture23 3 December 03, 2007...
View Full Document

This note was uploaded on 06/02/2010 for the course APMA APMA E3101 taught by Professor Spiegelman during the Fall '07 term at Columbia.

Page1 / 8

Lecture Notes 23 - Lecture23 1 Outline 1 Quick Review 2 Application 1 Total Least Squares A recipe Interpretation 3 Application 2 Pattern

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online