Design and Analysis of Quaternion-Valued Neural Networks for Associative Memories
研究了基于四元数值神经网络设计联想记忆的方法，通过四元数矩阵分解将给定状态设为平衡点，并用李雅普诺夫方法证明其渐近稳定性，数值实验显示能有效存储和检索模糊灰度及真彩色图像。
This paper addresses the problem of designing associative memories based on quaternion-valued neural networks (QVNNs). A system designing procedure for QVNNs is developed by employing quaternion matrix decomposition, and a given set of states can be assigned as the equilibrium points of the designed QVNNs. Moreover, some sufficient conditions for the asymptotic stability of the equilibrium points are obtained via Lyapunov's direct method. Numerical simulations manifest that the constructed QVNNs work efficiently on storing and retrieving blurred gray-scale and true color images.