A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix”
The concept presented in this paper is based on previous dynamical methods to realize a time-varying matrix inversion. It is essentially a set of coupled ordinary differential equations (ODEs) which does indeed constitute a recurrent neural network (RNN) model. The coupled ODEs constitute a universa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/19/18/4002 |
| _version_ | 1817996577325711360 |
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| author | Vahid Tavakkoli Jean Chamberlain Chedjou Kyandoghere Kyamakya |
| author_facet | Vahid Tavakkoli Jean Chamberlain Chedjou Kyandoghere Kyamakya |
| author_sort | Vahid Tavakkoli |
| collection | DOAJ |
| description | The concept presented in this paper is based on previous dynamical methods to realize a time-varying matrix inversion. It is essentially a set of coupled ordinary differential equations (ODEs) which does indeed constitute a recurrent neural network (RNN) model. The coupled ODEs constitute a universal modeling framework for realizing a matrix inversion provided the matrix is invertible. The proposed model does converge to the inverted matrix if the matrix is invertible, otherwise it converges to an approximated inverse. Although various methods exist to solve a matrix inversion in various areas of science and engineering, most of them do assume that either the time-varying matrix inversion is free of noise or they involve a denoising module before starting the matrix inversion computation. However, in the practice, the noise presence issue is a very serious problem. Also, the denoising process is computationally expensive and can lead to a violation of the real-time property of the system. Hence, the search for a new ‘matrix inversion’ solving method inherently integrating noise-cancelling is highly demanded. In this paper, a new combined/extended method for time-varying matrix inversion is proposed and investigated. The proposed method is extending both the gradient neural network (GNN) and the Zhang neural network (ZNN) concepts. Our new model has proven that it has exponential stability according to Lyapunov theory. Furthermore, when compared to the other previous related methods (namely GNN, ZNN, Chen neural network, and integration-enhanced Zhang neural network or IEZNN) it has a much better theoretical convergence speed. To finish, all named models (the new one versus the old ones) are compared through practical examples and both their respective convergence and error rates are measured. It is shown/observed that the novel/proposed method has a better practical convergence rate when compared to the other models. Regarding the amount of noise, it is proven that there is a very good approximation of the matrix inverse even in the presence of noise. |
| first_indexed | 2024-04-14T02:24:33Z |
| format | Article |
| id | doaj.art-6fd6b19e604f498ba3c0333a59409ba9 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-04-14T02:24:33Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-6fd6b19e604f498ba3c0333a59409ba92022-12-22T02:17:56ZengMDPI AGSensors1424-82202019-09-011918400210.3390/s19184002s19184002A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix”Vahid Tavakkoli0Jean Chamberlain Chedjou1Kyandoghere Kyamakya2Institute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, AustriaInstitute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, AustriaInstitute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, AustriaThe concept presented in this paper is based on previous dynamical methods to realize a time-varying matrix inversion. It is essentially a set of coupled ordinary differential equations (ODEs) which does indeed constitute a recurrent neural network (RNN) model. The coupled ODEs constitute a universal modeling framework for realizing a matrix inversion provided the matrix is invertible. The proposed model does converge to the inverted matrix if the matrix is invertible, otherwise it converges to an approximated inverse. Although various methods exist to solve a matrix inversion in various areas of science and engineering, most of them do assume that either the time-varying matrix inversion is free of noise or they involve a denoising module before starting the matrix inversion computation. However, in the practice, the noise presence issue is a very serious problem. Also, the denoising process is computationally expensive and can lead to a violation of the real-time property of the system. Hence, the search for a new ‘matrix inversion’ solving method inherently integrating noise-cancelling is highly demanded. In this paper, a new combined/extended method for time-varying matrix inversion is proposed and investigated. The proposed method is extending both the gradient neural network (GNN) and the Zhang neural network (ZNN) concepts. Our new model has proven that it has exponential stability according to Lyapunov theory. Furthermore, when compared to the other previous related methods (namely GNN, ZNN, Chen neural network, and integration-enhanced Zhang neural network or IEZNN) it has a much better theoretical convergence speed. To finish, all named models (the new one versus the old ones) are compared through practical examples and both their respective convergence and error rates are measured. It is shown/observed that the novel/proposed method has a better practical convergence rate when compared to the other models. Regarding the amount of noise, it is proven that there is a very good approximation of the matrix inverse even in the presence of noise.https://www.mdpi.com/1424-8220/19/18/4002matrix inversiontime-varying matrixnoise problem in time-varying matrix inversionrecurrent neural network (RNN)RNN-based solverreal-time fast computing |
| spellingShingle | Vahid Tavakkoli Jean Chamberlain Chedjou Kyandoghere Kyamakya A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix” Sensors matrix inversion time-varying matrix noise problem in time-varying matrix inversion recurrent neural network (RNN) RNN-based solver real-time fast computing |
| title | A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix” |
| title_full | A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix” |
| title_fullStr | A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix” |
| title_full_unstemmed | A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix” |
| title_short | A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix” |
| title_sort | novel recurrent neural network based ultra fast robust and scalable solver for inverting a time varying matrix |
| topic | matrix inversion time-varying matrix noise problem in time-varying matrix inversion recurrent neural network (RNN) RNN-based solver real-time fast computing |
| url | https://www.mdpi.com/1424-8220/19/18/4002 |
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