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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 71; no. Suppl 1; pp. 617 - 643
Main Authors: Manoj, N., Sriraman, R., Gurusamy, R., Shang, Yilun
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2025
Springer Nature B.V
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-025-02485-1