Volume 4, Issue 5, October 2011, Pages 991 - 1001
A Globally Convergent MCA Algorithm by Generalized Eigen-Decomposition
- Jianbin Gao, Mao Ye, Jianping Li, Qi Xia
- Corresponding Author
- Jianbin Gao
Available Online 6 December 2011.
- https://doi.org/10.2991/ijcis.2011.4.5.22How to use a DOI?
- generalized eigen-decomposition, minor component analysis, eigenvector, eigenvalue
- 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.
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 -