一对多联想记忆中的细胞神经网络建模及参数获取方法研究

项目名称： 一对多联想记忆中的细胞神经网络建模及参数获取方法研究

项目编号： No.61503050

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 其他

项目作者： 韩琦

作者单位： 重庆科技学院

项目金额： 20万元

中文摘要： 以前的研究成果集中研究了细胞神经网络联想记忆中一个输入模式对应一个标准模式的问题，而对一个输入模式对应多个标准模式的联想记忆几乎没有进行过研究。并且之前对细胞神经网络联想记忆的研究存在细胞间权值相关性较大的问题，而且没有解决像素点较多的图像之间的联想记忆，并对联想记忆性能评价没有基本标准，从而导致研究成果间的比较较为困难。本项目将针对以上问题系统深入地研究基于细胞神经网络的一对多联想记忆问题。首先，建立多层细胞神经网络模型，并给出数学描述，同时考虑使用空间可变模板降低细胞间权值的相关性；其次，研究多层细胞神经网络的稳定性，获得全局和局部稳定条件；再将所得稳定条件转换为适合联想记忆的条件，然后设计实现联想记忆的算法，并且要实现多幅图像间的联想记忆，特别是像素点较多的图像；接下来对联想记忆性能进行评价，给出评价联想记忆性能的基本标准；最后通过数值仿真来展现所提理论和方法的正确性和有效性。

中文关键词： 稳定性；联想记忆；收敛性；细胞神经网络

英文摘要： Previous research achievements were mainly concentrated on a question about one-to-one association based on cellular neural networks (CNNs), while less attention has been paid to other forms of associative memory, such as one-to-many associations based on CNNs. And the correlation between weights of cells in CNNs is enhanced in previous research about associative memories. It has not been solved about realizing associative memories based on CNNs for some pictures with a lot of pixels. There is also not a set of basic standards for performance of associative memories, which leads to difficulty about comparison of research results. For these problems, one-to-many association based on CNNs is investigated deeply in the project. First, multi-layer CNNs are used to solve the questions about one-to-many association, and mathematical model will be obtained about multi-layer CNNs. Value-varying templates will be used to reduce the correlation between weights of cells. Next, the stability of CNNs will be researched, and the conditions of global stability and local stability will be obtained. Then, these conditions of stability will be transformed as appropriate conditions of associative memories. A design procedure of associative memories is given by our theories and methods. Associative memories of multiple images will be considered, especially the images with a lot of pixels. Next, the performance of associative memories will be analyzed, and a set of basic standards will be given. Finally, numerical simulations are used to verify our theories and methods.

英文关键词： Stability;Associative memory;Convergence;Cellular neural networks