Stability analysis of dynamical systems for minor and principal component analysis

被引：0

作者：

Hasan, Mohammed A. ^{[1
]}

机构：

[1] Univ Minnesota, Dept Elect & Comp Engn, Duluth, MN 55812 USA

来源：

2006 AMERICAN CONTROL CONFERENCE, VOLS 1-12 | 2006年 / 1-12卷

关键词：

dynamical flow; gradient flow; asymptotic stability; global stability; optimization over Stiefel manifold; PCA; MCA; PSA; MSA; Oja's Rule; analytic solutions; exact solutions;

D O I：

10.1109/ACC.2006.1657277

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Algorithms that extract the principal or minor components of a signal are widely used in signal processing and control applications. This paper explores new frameworks for generating learning rules for iteratively computing the principal and minor components (or subspaces) of a given matrix. Stability analysis using Liapunov theory and La Salle invariance principle is provided to determine regions of attraction of these learning rules. Among many derivations, it is specifically shown that Oja's rule and many variations of it are asymptotically globally stable. Liapunov stability theory is also applied to weighted learning rules. Some of the essential features for the proposed MCA/PCA learning rules are that they are self normalized and can be applied to non-symmetric matrices. Exact solutions for some nonlinear dynamical systems are also provided.

引用

页码：3600 / 3605

页数：6

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