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Journal of Advances in Mathematics and Computer Science, ISSN: 2456-9968, ISSN: 2231-0851 (Past),Vol.: 23, Issue.: 6

Original-research-article

Eigenvalue Problem with the Basis Exchange Algorithm

 

Leon Bobrowski1,2*

1Faculty of Computer Science, BiaƂystok University of Technology, Poland.

2Institute of Biocybernetics and Biomedical Engineering, PAS, Warsaw, Poland.

Article Information
Editor(s):
(1) Dariusz Jacek Jakóbczak, Chair of Computer Science and Management in this department, Technical University of Koszalin, Poland.
Reviewers:
(1) S. Graham Kelly, The University of Akron, USA.
(2) Anthony Aidoo, Eastern Connecticut State University, USA.
(3) Zhonggen wang, Anhui University, China.
(4) Okan Ozer, University of Gaziantep,Turkiye.
(5) Shenyang Tan, Taizhou institute of Sci.&Tec., National University of Sciences and Technology, Pakistan.
Complete Peer review History: http://www.sciencedomain.org/review-history/20424

Abstracts

The eigenvalue problem plays an important role in contemporary methods of exploratory data analysis. As an example, the principal component analysis (PCA) widely used in data exploration, is based on finding the eigenvalues and eigenvectors of the covariance matrix. 

The paper presents a new method of the eigenvalue problem solution which uses the basis exchange algorithms. The basis exchange algorithms, similarly to the linear programming techniques are based on the Gauss-Jordan transformation of the inverted matrices. The proposed approach to the eigenvalue problem may also be connected to the regularization of feature vectors which constitute squared matrices by single unit vectors. The proposed approach is based on inducing a linear dependence among regularized vectors.

Keywords :

Eigenvalue problem; data exploration; principal component analysis; basis exchange algorithms; linear dependency.

Full Article - PDF    Page 1-12

DOI : 10.9734/JAMCS/2017/33436

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