Hopfield神经网络动力学分析与应用
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摘要
本文重点分析了连续时间和离散时间Hopfield网络的动力学行为,提出了设计各种神经记忆存储器的方法,并研究了神经记忆存储器在信息恢复、模式识别和系统评价等方面的应用.主要内容如下:
本文的第二章研究了不对称连续时间Hopfield网络的动力学行为,给出了网络全局和局部稳定性的充分条件.进一步的,利用矩阵分解和单层前向神经网络的方法,提出了用于不对称Hopfield网络设计的新方法.另外通过仿真讨论了连续时间Hopfield网络在信息恢复和模式识别方面的应用.
本文的第三章分析了不稳定的且具有不对称连接权值的Hopfield网络的动力学行为.研究发现网络的状态是有界的,而且网络是一个耗散系统.仿真发现一些Hopfield网络具有两个独立且关于原点对称的极限环或者混沌吸引子.基于此结果,本文提出了一个新的分段线性激活函数的混沌Hopfield网络.
本文的第四章基于矩阵分解和连接权值删除策略,提出了一个简单且有效的设计稀疏对称离散时间Hopfield网络的方法.仿真表明,虽然大约80%的连接权值被删除了,但是所设计的稀疏网络仍然可以精确地恢复所存储的模式.
本文的第五章分析了不对称离散时间Hopfield网络的动力学行为,给出了赋予网络记忆恢复能力的充分条件.另外基于权值删除策略和矩阵分解,提出了用于全连接和稀疏连接的不对称离散时间Hopfield网络设计的方法.仿真结果表明所设计的不对称离散时间Hopfield网络可以作为高效的记忆存储器来工作.
本文的第六章基于一种退化的Cohen-Grossberg网络和连续时间Hopfield网络,研究了神经记忆存储器在彩色图像恢复中的应用.仿真发现所设计的神经记忆存储器可以有效地对灰度和真彩色图像进行记忆恢复.
本文的第七章以顾客满意度测评及企业信用风险评测为例,探索了神经记忆存储器在系统评价等领域的应用.
In this dissertation, the dynamics of continuous-time and discrete-time Hopfieldneural networks (HNNs) are studied, and system designing procedures for construct-ing different neural associative memories are proposed. Furthermore, the applicationsof neural associative memories in information retrieval, pattern recognition and systemassessment are also discussed.
In chapter 2, the dynamics of the asymmetric continuous-time Hopfield networksare discussed, and the sufficient conditions for the global and local stability of thenetwork are proposed. Furthermore, two system designing methods for endowing thenetwork with retrieval properties are proposed based on the matrix decomposition andsingle-layer feed forward method, respectively. And the applications of the networkin pattern recognitions and information retrieval are also studied by numerical simula-tions.
In chapter 3, the dynamic of unstable continuous-time Hopfield networks is stud-ied. It is found that the solution of the HNN is bounded and the HNN is a dissipativesystem. In addition, some HNNs exhibit two independent limit cycles or chaotic at-tractors which are symmetric to each other with respect to the origin. Furthermore,based on these results, a new chaotic Hopfield network with piecewise linear activa-tion function is presented.
In chapter 4, An efficient system designing method for endowing the diluted sym-metric discrete-time Hopfield networks with retrieval properties is proposed based onthe matrix decomposition and connection elimination method. Numerical simulationsshow that the blurred patterns can correctly retrieved, and about 80% wiring cost canbe reduced.
In chapter 5, the dynamics of the asymmetric discrete-time Hopfield networks arestudied, and the sufficient conditions for endowing the network with retrieval proper-ties are proposed. In addition, a method for designing efficient diluted networks isproposed based on the matrix decomposition and connection elimination strategy. Nu-merical simulations show that the designed diluted network can act as efficient neural associative memories.
In chapter 6, the applications of neural associative memories in color image re-trieval are studied based on a class of reduced Cohen-Grossberg neural networks andcontinuous-time Hopfield network. Numerical simulations show that the designed net-works can perform as efficient noise-reducing systems.
In chapter 7, by taking customer satisfaction degree assessment and credit riskevaluation for example, some pioneer works about the applications of neural associa-tive memories in system assessment are presented.
本文的第二章研究了不对称连续时间Hopfield网络的动力学行为,给出了网络全局和局部稳定性的充分条件.进一步的,利用矩阵分解和单层前向神经网络的方法,提出了用于不对称Hopfield网络设计的新方法.另外通过仿真讨论了连续时间Hopfield网络在信息恢复和模式识别方面的应用.
本文的第三章分析了不稳定的且具有不对称连接权值的Hopfield网络的动力学行为.研究发现网络的状态是有界的,而且网络是一个耗散系统.仿真发现一些Hopfield网络具有两个独立且关于原点对称的极限环或者混沌吸引子.基于此结果,本文提出了一个新的分段线性激活函数的混沌Hopfield网络.
本文的第四章基于矩阵分解和连接权值删除策略,提出了一个简单且有效的设计稀疏对称离散时间Hopfield网络的方法.仿真表明,虽然大约80%的连接权值被删除了,但是所设计的稀疏网络仍然可以精确地恢复所存储的模式.
本文的第五章分析了不对称离散时间Hopfield网络的动力学行为,给出了赋予网络记忆恢复能力的充分条件.另外基于权值删除策略和矩阵分解,提出了用于全连接和稀疏连接的不对称离散时间Hopfield网络设计的方法.仿真结果表明所设计的不对称离散时间Hopfield网络可以作为高效的记忆存储器来工作.
本文的第六章基于一种退化的Cohen-Grossberg网络和连续时间Hopfield网络,研究了神经记忆存储器在彩色图像恢复中的应用.仿真发现所设计的神经记忆存储器可以有效地对灰度和真彩色图像进行记忆恢复.
本文的第七章以顾客满意度测评及企业信用风险评测为例,探索了神经记忆存储器在系统评价等领域的应用.
In this dissertation, the dynamics of continuous-time and discrete-time Hopfieldneural networks (HNNs) are studied, and system designing procedures for construct-ing different neural associative memories are proposed. Furthermore, the applicationsof neural associative memories in information retrieval, pattern recognition and systemassessment are also discussed.
In chapter 2, the dynamics of the asymmetric continuous-time Hopfield networksare discussed, and the sufficient conditions for the global and local stability of thenetwork are proposed. Furthermore, two system designing methods for endowing thenetwork with retrieval properties are proposed based on the matrix decomposition andsingle-layer feed forward method, respectively. And the applications of the networkin pattern recognitions and information retrieval are also studied by numerical simula-tions.
In chapter 3, the dynamic of unstable continuous-time Hopfield networks is stud-ied. It is found that the solution of the HNN is bounded and the HNN is a dissipativesystem. In addition, some HNNs exhibit two independent limit cycles or chaotic at-tractors which are symmetric to each other with respect to the origin. Furthermore,based on these results, a new chaotic Hopfield network with piecewise linear activa-tion function is presented.
In chapter 4, An efficient system designing method for endowing the diluted sym-metric discrete-time Hopfield networks with retrieval properties is proposed based onthe matrix decomposition and connection elimination method. Numerical simulationsshow that the blurred patterns can correctly retrieved, and about 80% wiring cost canbe reduced.
In chapter 5, the dynamics of the asymmetric discrete-time Hopfield networks arestudied, and the sufficient conditions for endowing the network with retrieval proper-ties are proposed. In addition, a method for designing efficient diluted networks isproposed based on the matrix decomposition and connection elimination strategy. Nu-merical simulations show that the designed diluted network can act as efficient neural associative memories.
In chapter 6, the applications of neural associative memories in color image re-trieval are studied based on a class of reduced Cohen-Grossberg neural networks andcontinuous-time Hopfield network. Numerical simulations show that the designed net-works can perform as efficient noise-reducing systems.
In chapter 7, by taking customer satisfaction degree assessment and credit riskevaluation for example, some pioneer works about the applications of neural associa-tive memories in system assessment are presented.
引文
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