Design and analysis of quaternion-valued neural networks for storing and retrieving color images

In this paper, we address the global exponential stability (GES) issue for the quaternion-valued neural networks (QVNNs) with non-differentiable distributed delays using the matrix measure method (MMM). Given the complex nature of quaternion algebra, the QVNNs are first transformed into similar four...

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Vydáno v:Journal of applied mathematics & computing Ročník 71; číslo Suppl 1; s. 617 - 643
Hlavní autoři: Manoj, N., Sriraman, R., Gurusamy, R., Shang, Yilun
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2025
Springer Nature B.V
Témata:
Artificial intelligence
Color imagery
Computational Mathematics and Numerical Analysis
Inequality
Liapunov functions
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Multiplication
Neural networks
Original Research
Quaternions
Stability
Theory of Computation
Matrix measure method
93D23
Global exponential stability
Lyapunov functions
Quaternion-valued neural networks
93D05
Distributed delays
92B20
ISSN:1598-5865, 1865-2085
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Shrnutí:In this paper, we address the global exponential stability (GES) issue for the quaternion-valued neural networks (QVNNs) with non-differentiable distributed delays using the matrix measure method (MMM). Given the complex nature of quaternion algebra, the QVNNs are first transformed into similar four-dimensional real-valued neural networks (RVNNs) to overcome the complexities of quaternion multiplication. Through the construction of applicable Lyapunov functions and the application of MMM, rigorous stability conditions are established. Furthermore, the study presents novel and easily verifiable results, offering new perspectives into the GES of QVNNs. The proposed conditions are also applicable when QVNNs are reformulated as complex-valued neural networks (CVNNs) or RVNNs. To validate the obtained findings, some numerical examples with graphical analysis are presented, along with their application to storing and retrieving color image patterns.
Bibliografie:ObjectType-Article-1
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-025-02485-1