Improved Gradient Neural Networks for Solving Moore–Penrose Inverse of Full-Rank Matrix

Lv, Xudong; Xiao, Lin; Tan, Zheng; Yang, Zhi; Yuan, Junying

doi:10.1007/s11063-019-09983-x

Cited by 26 publications

(7 citation statements)

References 32 publications

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“…As a result, the following conclusions follow: Remark 2. The particular HGZNN(A T A, I, A T ) and GGNN(A T A, I, A T ) designs define the corresponding modifications of the improved GNN design proposed in [26] if A T A is invertible. In the dual case, HGZNN(I, CC T , C T ) and GGNN(I, CC T , C T ) define the corresponding modifications of the improved GNN design proposed in [26] if CC T is invertible.…”

Section: Gznn(a I B) By the Termmentioning

confidence: 99%

“…A comparison with the corresponding GNN design was considered. Two improved nonlinear GNN dynamical systems for approximating the Moore-Penrose inverse of full-row or full-column rank matrices were proposed and considered in [26]. GNN-type models for solving matrix equations and computing related generalized inverses were developed in [1,3,13,16,18,20,[27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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Application of Gradient Optimization Methods in Defining Neural Dynamics

Stanimirović,

Tešić,

Gerontitis

et al. 2024

Axioms

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Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation AXB=D which changes over time is studied using the novel GNN model, termed as GGNN(A,B,D). The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN(A,B,D) design converges asymptotically to the solution of the matrix equation AXB=D, for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.

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Section: Gznn(a I B) By the Termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Gradient Optimization Methods in Defining Neural Dynamics

Stanimirović,

Tešić,

Gerontitis

et al. 2024

Axioms

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“…Recently, various nonlinear and linear recurrent neural network (RNN) models have been developed for computing the pseudoinverse of any rectangular matrices (for more details, see [8][9][10][11]). The gradient-based neural network (GNN), whose derivation is based on the gradient of an nonnegative energy function, is an alternative for calculating the Moore-Penrose generalized inverses [12][13][14][15]. These methods for solving the inner inverses and for other generalized inverses of a matrix frequently use the matrix-matrix product operation, and consume a lot of computing time.…”

Section: Introductionmentioning

confidence: 99%

Randomized Block Kaczmarz Methods for Inner Inverses of a Matrix

Xing,

Bao,

et al. 2024

Mathematics

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“…Thus, the SLFN structure is selected in this paper for simplicity but with the limitation that it is inapplicable to the Moor–Penrose inverse computation of time‐varying matrices. Unfortunately, the gradient‐descent (GD) method is often adopted as the learning algorithm for the neural networks to solve the constant matrix inversion problems, which suffers from slow convergence and sensitivity to parameters [27]. In addition, the Moore–Penrose inverse computation of the full‐rank matrix and the rank‐deficient matrix are always studied separately in almost all the existing publications [28].…”

Section: Introductionmentioning

confidence: 99%

An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices

2022

IET Signal Processing

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The computation of the Moore-Penrose inverse is widely encountered in science and engineering. Due to the parallel-processing nature and strong-learning ability, the neural network has become a promising approach to solving the Moore-Penrose inverse recently. However, almost all the existing neural networks for matrix inversion are based on the gradient-descent (GD) method, whose main drawbacks are slow convergence and sensitivity to learning parameters. Moreover, there is no unified neural network to compute the Moore-Penrose inverse for both the full-rank matrix and rank-deficient matrix. In this paper, an efficient second-order neural network model with the improved Newton's method is proposed to obtain the accurate Moore-Penrose inverse of an arbitrary matrix by one epoch without any learning parameter. Compared with the GD-based neural networks for Moore-Penrose inverse computation, the proposed model converges faster and has lower complexity. Furthermore, through in-depth derivation, the neural network for computing the Moore-Penrose inverse is well interpretable. Numerical studies and application to the random matrix inversion in multiple-input multiple-output detection are provided to validate the efficiency of the proposed model for solving the Moore-Penrose inverse.

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Improved Gradient Neural Networks for Solving Moore–Penrose Inverse of Full-Rank Matrix

Cited by 26 publications

References 32 publications

Application of Gradient Optimization Methods in Defining Neural Dynamics

Application of Gradient Optimization Methods in Defining Neural Dynamics

Randomized Block Kaczmarz Methods for Inner Inverses of a Matrix

An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices

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