International Journal of Computational Intelligence Systems

Volume 4, Issue 5, October 2011, Pages 991 - 1001

A Globally Convergent MCA Algorithm by Generalized Eigen-Decomposition

Authors
Jianbin Gao, Mao Ye, Jianping Li, Qi Xia
Corresponding Author
Jianbin Gao
Available Online 6 December 2011.
DOI
https://doi.org/10.2991/ijcis.2011.4.5.22How to use a DOI?
Keywords
generalized eigen-decomposition, minor component analysis, eigenvector, eigenvalue
Abstract
Minor component analysis (MCA) are used in many applications such as curve and surface fitting, robust beam forming, and blind signal separation. Based on the generalized eigen-decomposition, we present a completely different approach that leads to derive a novel MCA algorithm. First, in the sense of generalized eigen-decomposition, by using gradient ascent approach, we derive an algorithm for extracting the first minor eigenvector. Then, the algorithm used to extract multiple minor eigenvectors is proposed by using the orthogonality property. The proofs and rigorous theoretical analysis show that our proposed algorithm is convergent to their corresponding minor eigenvectors. We identify three important characteristics of these algorithms. The first is that the algorithm for extracting minor eigenvectors can be extended to generalized minor eigenvectors easily. The second is that the corresponding eigenvalues can be computed simultaneously as a byproduct of this algorithm. The third is that the algorithm is globally convergent. The simulations have been conducted for illustration of the efficiency and effectiveness of our algorithm.
Open Access
This is an open access article distributed under the CC BY-NC license.

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
4 - 5
Pages
991 - 1001
Publication Date
2011/12
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
https://doi.org/10.2991/ijcis.2011.4.5.22How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Jianbin Gao
AU  - Mao Ye
AU  - Jianping Li
AU  - Qi Xia
PY  - 2011
DA  - 2011/12
TI  - A Globally Convergent MCA Algorithm by Generalized Eigen-Decomposition
JO  - International Journal of Computational Intelligence Systems
SP  - 991
EP  - 1001
VL  - 4
IS  - 5
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.2011.4.5.22
DO  - https://doi.org/10.2991/ijcis.2011.4.5.22
ID  - Gao2011
ER  -