Adaptive Normalized Quasi-Newton Algorithms for Extraction of Generalized Eigen-Pairs and Their Convergence Analysis

Nguyen, Tuan Duong; Yamada, Isao

doi:10.1109/tsp.2012.2234744

Cited by 33 publications

(9 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We know that the neural network technology was first used to eigen-pairs problems about in the 1980's [1], which is also known as principal component analysis (PCA), and then motivated broad interests from engineering and theoretical research [2][3][4][5][6][7][8][9][10][11][12][13]. In the very recent years, some adaptive generalized eigen-pairs extraction algorithms of Hermite matrices have been developed by some authors [8].…”

Section: Introductionmentioning

confidence: 99%

A novel complex neural network model for computing the largest real part of eigenvalues and the corresponding eigenvector of a real matrix

Ye¹,

Tan²,

Liang³

et al. 2017

Proceedings of the 2nd Annual International Conference on Electronics, Electrical Engineering and Information Science (EEEIS 20

View full text Add to dashboard Cite

A novel complex neural network modelwasproposed, which can be used to compute the largestreal part of eigenvalues and the corresponding eigenvector of a general real matrixin this work. Because of the smart regulatory factorof the model, the largest real part also can be extracted in the case of all the real parts of eigenvalues less than 0. Meanwhile, the presented paper provides a rigorous mathematical proof for its convergence for a more clear understanding of network dynamic behaviors relating to the computation of the eigenvector and the eigenvalue. Numerical example showsthat the proposed model has good performance for a general real matrix.

show abstract

Section: Introductionmentioning

confidence: 99%

A novel complex neural network model for computing the largest real part of eigenvalues and the corresponding eigenvector of a real matrix

Ye¹,

Tan²,

Liang³

et al. 2017

Proceedings of the 2nd Annual International Conference on Electronics, Electrical Engineering and Information Science (EEEIS 20

View full text Add to dashboard Cite

show abstract

“…In 1995, Luo et al [2,3] presented another neural network algorithm for computing not only modulus largest eigenvalue but also modulus smallest eigenvalue and their corresponding eigenvectors of real symmetric matrices. In recent years, some adaptive generalized eigen-pairs extraction algorithms of Hermite matrices have been developed by some authors in [7,8].…”

Section: Introductionmentioning

confidence: 99%

A complex neural network algorithm for computing the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvector of a real normal matrix

Tan¹,

Wan²,

Ye³

et al. 2017

Proceedings of the 2nd Annual International Conference on Electronics, Electrical Engineering and Information Science (EEEIS 20

View full text Add to dashboard Cite

In this study, we proposed a novel complex neural network algorithm, which extends the neural networks based approaches that can asymptotically compute the largest modulus of eigenvalues and the corresponding eigenvector to the case of directly computing the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvectors of a real normal matrix. The proposed neural network algorithm is described by a group of complex differential equations. And the algorithm has parallel processing ability in an asynchronous manner and could achieve high computing capability. This paper also provides a rigorous mathematical proof for its convergence for a more clear understanding of network dynamic behaviors relating to the computation of the eigenvector and the eigenvalue. Numerical example showed that the proposed algorithm has good performance for a general real normal matrix.

show abstract

“…Using the neural network technology to extract the eigenvector corresponding to the modulus maximum eigenvalue of a real symmetric matrix was first presented about 30 years ago [1], then motivated broad interests from engineering and theoretical researches [2][3][4][5][6][7][8][9][10][11][12]. In 1995, Luo et al [5,6] proposed a very classical neural network algorithm for extracting not only modulus maximum eigenvalue but also modulus minimum eigenvalue and their corresponding eigenvectors of real symmetric matrices, but the convergence proof of this algorithm not be presented until 2004 by Zhang et al [7].…”

Section: Introductionmentioning

confidence: 99%

“…In 1995, Luo et al [5,6] proposed a very classical neural network algorithm for extracting not only modulus maximum eigenvalue but also modulus minimum eigenvalue and their corresponding eigenvectors of real symmetric matrices, but the convergence proof of this algorithm not be presented until 2004 by Zhang et al [7]. In the recently years, some adaptive generalized eigen-pairs extraction algorithms have been presented by some authors [11,12].…”

Section: Introductionmentioning

confidence: 99%

A Complex Neural Network Algorithm for Computing the Largest Real Part Eigenvalue and the corresponding Eigenvector of a Real Matrix

Tan¹,

Liang²,

Wan³

2016

Proceedings of the 2016 4th International Conference on Sensors, Mechatronics and Automation (ICSMA 2016)

View full text Add to dashboard Cite

In this study, we propose a novel complex neural network algorithm, which extends the neural network based approaches that can asymptotically compute the largest or smallest eigenvalues and the corresponding eigenvectors of real symmetric matrices, to the case of directly calculating the largest real part eigenvalue and the corresponding eigenvector of a real matrix. The proposed neural network algorithm is described by a group of complex differential equations, which is deduced from the classical neural network model. The proposed algorithm is a class of continuous time recurrent neural network (RNN), it has parallel processing ability in an asynchronous manner and could achieve high computing capability. This paper provides a rigorous mathematical proof for its convergence in the case of real matrices for a more clear understanding of network dynamic behaviors relating to the computation of eigenvector and eigenvalue. The proposed approach has obvious virtues such as fast convergence speed and non-sensitivity to initial value. Numerical examples showed that the proposed algorithm has good performance. The Proposed Complex Neural Network ModelThe classical neural network algorithm for computing the eigenvector corresponding to the modulus maximum eigenvalue or modulus minimum eigenvalue can be illustrated as follows [5,6]

show abstract

Adaptive Normalized Quasi-Newton Algorithms for Extraction of Generalized Eigen-Pairs and Their Convergence Analysis

Cited by 33 publications

References 29 publications

A novel complex neural network model for computing the largest real part of eigenvalues and the corresponding eigenvector of a real matrix

A novel complex neural network model for computing the largest real part of eigenvalues and the corresponding eigenvector of a real matrix

A complex neural network algorithm for computing the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvector of a real normal matrix

A Complex Neural Network Algorithm for Computing the Largest Real Part Eigenvalue and the corresponding Eigenvector of a Real Matrix

Contact Info

Product

Resources

About