Karhunen-Loeve decomposition in the presence of symmetry. I

Author

Lahme, Brigitte ; Miranda, Rick

Author_Institution

Dept. of Math., Arizona Univ., Tucson, AZ, USA

Volume

Issue

fYear

1999

fDate

9/1/1999 12:00:00 AM

Firstpage

1183

Lastpage

1190

Abstract

The Karhunen-Loeve (KL) decomposition is widely used for data which very often exhibit some symmetry, afforded by a group action. For a finite group, we derive an algorithm using group representation theory to reduce the cost of determining the KL basis. We demonstrate the technique on a Lorenz-type ODE system. For a compact group such as tori or SO(3,R) the method also applies, and we extend results to these cases. As a short example, we consider the circle group S¹

Keywords

Karhunen-Loeve transforms; Lie groups; SO(3) groups; computational complexity; data compression; KL basis; Karhunen-Loeve decomposition; Lorenz-type ODE system; SO(3,R); circle group S¹; compact group; finite group; group action; group representation theory; symmetry; tori; Biological system modeling; Costs; Data analysis; Data compression; Finite wordlength effects; Functional analysis; Helium; Image analysis; Mathematics; Vectors;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.784431

Filename

784431

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1546091