扩展交替投影神经网络 ——具备联想记忆功能的充分必要条件

对交替投影神经网络(APNN)的连接权矩阵进行修改,将其应用范围从实数域拓展到复数域,从而得到一种新的神经网络——扩展交替投影神经网络(Extended Alternating Projection Neural Networks).对EAPNN网络进行深入研究后,给出了网络稳态值的通用数学表达式,并从表达式中推出了网络具备联想记忆功能的充分必要条件.最后设计仿真实验对文中的理论分析结果进行了验证.

Sufficient and Necessary Condition of the Extended Alternating Projection Neural Network Configured as a Content Addressable Memory

The paper extends the original Alternating Projection Neural Network(APNN) and proposes an Extended Alternating Projection Neural Network (EAPNN) which functions in the field of complex numbers. An improved weight-learning approach, which permits linear dependence of complex patterns,has been presented. A general mathematical expression of the EAPNN steady-state solution has been obtained. From the general mathematical expression we have derived the sufficient and necessary condition of the EAPNN configured as a content addressable memory. In addition, simulation experiments have been designed to verify the theoretical analyses in the paper. Finally it is pointed out that the EAPNN has been applied to signal processing such as band-limited signal extrapolation, notch filter and weak-signal separation.