Unified stabilization approach to principal and minor components extraction algorithms

被引：65

作者：

Chen, TP ^{[1
]}

Amari, S

机构：

[1] Fudan Univ, Dept Math, Shanghai 200433, Peoples R China

[2] RIKEN, Brain Sci Inst, Wako, Saitama 3510198, Japan

来源：

NEURAL NETWORKS | 2001年 / 14卷 / 10期

关键词：

principal component extraction; minor component extraction; singular value decomposition; stability of dynamical system; natural gradient;

D O I：

10.1016/S0893-6080(01)00116-2

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Principal component and minor component extractions provide powerful techniques in many information processing fields. There have been proposed a number of algorithms for principal and minor component (or subspace) extraction, which have different dynamical behaviors. In this paper, we give rigorous stability analysis of these algorithms, obtaining a unified insight view on the dynamical behaviors of various algorithms. (C) 2001 Elsevier Science Ltd. All rights reserved.

引用

页码：1377 / 1387

页数：11

共 20 条

[1] Adaptive method of realizing natural gradient learning for multilayer perceptrons [J].

Amari, S ;

Park, H ;

Fukumizu, K .

NEURAL COMPUTATION, 2000, 12 (06) :1399-1409

[2] Stability analysis of learning algorithms for blind source separation [J].

Amari, S ;

Chen, TP ;

Cichocki, A .

NEURAL NETWORKS, 1997, 10 (08) :1345-1351

[3] Natural gradient works efficiently in learning [J].

Amari, S .

NEURAL COMPUTATION, 1998, 10 (02) :251-276

[4]

Amari S., 1985, SPRINGER LECT NOTES, V28

[5]

Amari S.I., 1997, Contemp. Math., V203, P81, DOI DOI 10.1090/C0NM/203/02554

[6] NEURAL THEORY OF ASSOCIATION AND CONCEPT-FORMATION [J].

AMARI, SI .

BIOLOGICAL CYBERNETICS, 1977, 26 (03) :175-185

[7] DYNAMIC-SYSTEMS THAT SORT LISTS, DIAGONALIZE MATRICES, AND SOLVE LINEAR-PROGRAMMING PROBLEMS [J].

BROCKETT, RW .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 146 :79-91

[8] LEAST-SQUARES MATCHING PROBLEMS [J].

BROCKETT, RW .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 122 :761-777

[9] A unified algorithm for principal and minor components extraction [J].

Chen, TP ;

Amari, SI ;

Lin, Q .

NEURAL NETWORKS, 1998, 11 (03) :385-390

[10]

Chen TP, 1997, NEURAL PROCESS LETT, V5, P105

← 1 2 →