Karhunen-Loeve decomposition in the presence of symmetry - Part I

被引：7

作者：

Lahme, B ^{[1
]}

Miranda, R

机构：

[1] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

[2] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA

来源：

IEEE TRANSACTIONS ON IMAGE PROCESSING | 1999年 / 8卷 / 09期

基金：

美国国家科学基金会;

关键词：

data compression; dimension reduction; finite groups; Karhunen-Loeve decomposition; Lie groups; representation theory; symmetry;

D O I：

10.1109/83.784431

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The Karhunen-Loeve (KL) decomposition is widely used to 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, IR) the method also applies, and we extend results to these cases. As a short example, we consider the circle group S-1.

引用

页码：1183 / 1190

页数：8

共 19 条

[1] Ash RB., 1975, Topics in Stochastic Processes
[2] ATALLAH MJ, 1985, IEEE T COMPUT, V34, P663, DOI 10.1109/TC.1985.1676605
[3] CIARLET PG, 1982, INTRO NUMERICAL LINE
[4] Curtis C. W., 1962, Wiley Class. Libr.
[5] Fulton W., 2004, REPRESENT THEOR, V129
[6] HARGITTAI I, 1990, QUASICRYSTALS NETWOR
[7] Similarity and symmetry measures for convex shapes using Minkowski addition
Heijmans, HJAM
Tuzikov, AV
[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1998, 20 (09) : 980 - 993
[8] APPLICATION OF THE KARHUNEN-LOEVE PROCEDURE FOR THE CHARACTERIZATION OF HUMAN FACES
KIRBY, M
SIROVICH, L
[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1990, 12 (01) : 103 - 108
[9] Detecting symmetry in grey level images: The global optimization approach
Kiryati, N
Gofman, Y
[J]. INTERNATIONAL JOURNAL OF COMPUTER VISION, 1998, 29 (01) : 29 - 45
[10] Loeb A. L., 1971, COLOR SYMMETRY

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