On convergence conditions of an extended projection neural network

The output trajectory convergence of an extended projection neural network was developed under the positive definiteness condition of the Jacobian matrix of nonlinear mapping. This note offers several new convergence results. The state trajectory convergence and the output trajectory convergence of the extended projection neural network are obtained under the positive semidefiniteness condition of the Jacobian matrix. Comparison and illustrative examples demonstrate applied significance of these new results.     

On exponential convergence conditions of an extended projection neural network

Recently the extended projection neural network was proposed to solve constrained monotone variational inequality problems and a class of constrained nonmonotontic variational inequality problems. Its exponential convergence was developed under the positive definiteness condition of the Jacobian matrix of the nonlinear mapping. This note proposes new results on the exponential convergence of the output trajectory of the extended projection neural network under the weak conditions that the Jacobian matrix of the nonlinear mapping may be positive semidefinite or not. Therefore, new results further demonstrate that the extended projection neural network has a fast convergence rate when solving a class of constrained monotone variational inequality problems and nonmonotonic variational inequality problems. Illustrative examples show the significance of the obtained results.     

A Hopfield neural network with multi-compartmental activation

The Hopfield network is a form of recurrent artificial neural network. To satisfy demands of artificial neural networks and brain activity, the networks are needed to be modified in different ways. Accordingly, it is the first time that, in our paper, a Hopfield neural network with piecewise constant argument of generalized type and constant delay is considered. To insert both types of the arguments, a multi-compartmental activation function is utilized. For the analysis of the problem, we have applied the results for newly developed differential equations with piecewise constant argument of generalized type beside methods for differential equations and functional differential equations. In the paper, we obtained sufficient conditions for the existence of an equilibrium as well as its global exponential stability. The main instruments of investigation are Lyapunov functionals and linear matrix inequality method. Two examples with simulations are given to illustrate our solutions as well as global exponential stability.

     

基于阈值自适应忆阻器Hopfield神经网络的关联规则挖掘算法

针对基于Hopfield神经网络的最大频繁项集挖掘（HNNMFI）算法存在的挖掘结果不准确的问题,提出基于电流阈值自适应忆阻器（TEAM）模型的Hopfield神经网络的改进关联规则挖掘算法。首先,使用TEAM模型设计实现突触,利用阈值忆阻器的忆阻值随方波电压连续变化的能力来设定和更新突触权值,自适应关联规则挖掘算法的输入。其次,改进原算法的能量函数以对齐标准能量函数,并用忆阻值表示权值,放大权值和偏置。最后,设计由最大频繁项集生成关联规则的算法。使用10组大小在30以内的随机事务集进行1000次仿真实验,实验结果表明,与HNNMFI算法相比,所提算法在关联挖掘结果准确率上提高33.9个百分点以上,说明忆阻器能够有效提高Hopfield神经网络在关联规则挖掘中的结果准确率。     

The hysteretic Hopfield neural network

A new neuron activation function based on a property found in physical systems-hysteresis-is proposed. We incorporate this neuron activation in a fully connected dynamical system to form the hysteretic Hopfield neural network (HHNN). We then present an analog implementation of this architecture and its associated dynamical equation and energy function. We proceed to prove Lyapunov stability for this new model, and then solve a combinatorial optimization problem (i.e., the N-queen problem) using this network. We demonstrate the advantages of hysteresis by showing increased frequency of convergence to a solution, when the parameters associated with the activation function are varied.     

Stabilization of stochastic Hopfield neural network with distributed parameters

In this paper, the stability of stochastic Hopfield neural network with distributed parameters is studied. To discuss the stability of systems, the main idea is to integrate the solution to systems in the space variable. Then, the integration is considered as the solution process of corresponding neural networks described by stochastic ordinary differential equations. A Lyapunov function is constructed and Ito formula is employed to compute the derivative of the mean Lyapunov function along the systems, with respect to the space variable. It is difficult to treat stochastic systems with distributed parameters since there is no corresponding Ito formula for this kind of system. Our method can overcome this difficulty. Till now, the research of stability and stabilization of stochastic neural networks with distributed parameters has not been considered.     

基于Hopfield神经网络的数据分类

针对Hopfield神经网络的自联想特性,提出一种新的带有粒子群优化过程的Hopfield分类算法(PSO-HOP).该算法采用了Blatt-Vergin (BV)学习算法,一定程度上克服了传统Hopfield容量低的特点.与此同时,还提出了先测量后训练的方法来降低算法的复杂度,提高分类效率,并探讨了样本属性以及类标号在Hopfield神经网络的表示方法,使其能够很好地处理空缺值等噪声数据.通过采用离散型粒子群优化算法对Hopfield的拓扑结构进行优化,可以将多余的神经元分配给不同属性,使得属性在分类中的权重发生改变,从而提高分类精度,避免陷入局部最优值.从统计不同属性被分配神经元的次数中,可以反映出不同属性的重要程度.从大量实验结果可以看出,该算法具有较高的鲁棒性和分类准确度.     

Mutation Hopfield neural network and its applications

In this paper, a new operator is proposed to optimize the traditional Hopfield neural network (HNN). The key idea is to incorporate the global search capability of the Estimation of Distribution Algorithms (EDAs) into the HNN, which typically has a powerful local search capability and fast operation. On account of this property of the EDA, our proposed algorithm also exhibits a powerful global search capability. In addition, the possible infeasible solutions generated during the re-sampling period of the EDA are eliminated by the HNN. Therefore, the merits of both these methods are combined in a unified framework. The proposed model is tested on a numerical example, the max-cut problem. The new and optimized model yielded a better performance than certain traditional intelligent optimization methods, such as HNN, genetic algorithm (GA). The proposed mutation Hopfield neural network (MHNN) is also used to solve a practical problem, aircraft landing scheduling (ALS). Compared with first-come-first-served sequence, MHNN sequence reduces both total landing time and total delay.     

基于离散Hopfield神经网络的数字识别实现

介绍了离散Hopfield神经网络的基本概念;以MATLAB为工具,根据Hopfield神经网络的相关知识,设计了一个具有联想记忆功能的离散型Hopfield神经网络,并给出了设计思路、设计步骤和测试结果。实验结果表明,通过联想记忆,对于带有一定噪声的数字点阵,Hopfield网络可以正确地进行识别,且当噪声强度为0．1时的识别效果较好。     

用改进的差分式Hopfield网络实现线性二次型最优控制

为解决差分式Hopfield网络能量函数的局部极小问题,本文对之改进得到一种具有迭代学习功能的线性差分式Hopfield网络.理论分析表明,该网络具有稳定性,且稳定状态使其能量函数达到唯一极小值.基于线性差分式Hopfield网络稳定性与其能量函数收敛特性的关系,本文将该网络用于求解多变量时变系统的线性二次型最优控制问题.网络的理论设计方法表明,网络的稳态输出就是欲求的最优控制向量.数字仿真取得了与理论分析一致的实验结果.     

Chaos and hyperchaos in a Hopfield neural network

In this paper we investigate numerically the parameter-space of an autonomous system of four nonlinear first-order ordinary differential equations, which represents a Hopfield neural network with four neurons. The study considers three independent two-dimensional cross-sections of the three-dimensional parameter-space generated by this mathematical model, every constructed considering Lyapunov exponent values. We show that is possible to completely characterize the dynamics of the system based in these three plots, which are representative of the three-dimensional parameter-space as a whole.     

Classification with incomplete survey data: a Hopfield neural network approach

Survey data are often incomplete. Classification with incomplete survey data is a new subject. This study proposes a Hopfield neural network based model of classification for incomplete survey data. Using this model, an incomplete pattern is translated into fuzzy patterns. These fuzzy patterns, along with patterns without missing values, are then used as the exemplar set for teaching the Hopfield neural network. The classifier also retains information of fuzzy class membership for each exemplar pattern. When presenting a test sample, the neural network would find an exemplar that best matches the test pattern and give the classification result. Compared with other classification techniques, the proposed method can utilize more information provided by the data with missing values, and reveal the risk of the classification result on the individual observation basis.     

Hopfield神经网络在有限元求解中的应用

计算机本身固有的计算与存储之间是一对很难解决的矛盾,许多工程力学问题因计算规模大等原因还没有突破性进展,因此,需要发展新的理论与计算方法。通过对有限元求解方法和Hopfield神经网络的深入研究,在对Hopfield神经网络适当改造后,得到了有限元的神经网络计算方法,在电路实现中避免了采用高增益传递函数的假设,进而在理论上实现了有限元神经网络计算的无误差求解。     

时滞诱发的忆阻型Hopfield神经网络的复杂动力学

本文研究含时滞的忆阻型环状Hopfield神经网络的稳定性、Hopf分岔以及复杂振荡模式.根据特征方程根分布情况,获得了系统全时滞稳定条件和与时滞相关的稳定条件.通过数值计算揭示了丰富的动力学现象,如多种周期运动和混沌吸引子等,并给出了Poincaré截面上的分岔图.设计了电路实验平台,取得了与理论分析和数值计算高度吻合的实验结果.     

模糊Hopfield网络的收敛性与鲁棒性分析

收敛性与鲁棒性是模糊神经网络的两个重要性质。对带阈值的Max-T模糊Hopfield神经网络（记为Max-T-C FHNN）的收敛性及在训练模式小幅摄动情况下的鲁棒性进行了分析,从理论上给出了严格的证明。发现了采用最大权值矩阵学习算法时,Max-T-C FHNN具有良好的收敛性,同时当T模及其蕴含算子满足Lipschitz条件时,Max-T-C FHNN对训练模式摄动全局拥有好的鲁棒性,用自联想实验验证了理论的有效性。     

Hopfield神经网络在机组组合问题中的应用

提出利用多层Hopfield神经网络求解机组组合优化问题。通过构造合适的能量函数使得单层Hopfield神经网络可以解决某一时刻的机组出力问题,与之相对应的多层神经网络可以解决任意时间段的机组出力问题。多层Hopfield神经网络的层数由所需求解问题的时间段确定。给出单层及多层神经网络的能量函数及求解算法,能量函数考虑到机组升降功率和出力上下限的约束。通过对已有文献的算例进行计算比对,所得结果和遗传算法基本一致,但Hopfield神经网络通过解微分方程组来确定最优解,计算时间相对较少。     

Memristive continuous Hopfield neural network circuit for image restoration

Neural Computing and Applications - Image restoration (IR) methods based on neural network algorithms have shown great success. However, the hardware circuits that can perform real-time IR task...     

Hopfield neural network implementation of the optimal CDMAmultiuser detector

We investigate the application of Hopfield neural networks (HNN's) to the problem of multiuser detection in spread spectrum/CDMA (code division multiple access) communication systems. It is shown that the NP-complete problem of minimizing the objective function of the optimal multiuser detector (OMD) can be translated into minimizing an HNN “energy” function, thus allowing to take advantage of the ability of HNN's to perform very fast gradient descent algorithms in analog hardware and produce in real-time suboptimal solutions to hard combinatorial optimization problems. The performance of the proposed HNN receiver is evaluated via computer simulations and compared to that of other suboptimal schemes as well as to that of the OMD for both the synchronous and the asynchronous CDMA transmission cases. It is shown that the HNN detector exhibits a number of attractive properties and that it provides a powerful generalization of a well-known and extensively studied suboptimal scheme, namely the multistage detector     

Recursive neural network rule extraction for data with mixed attributes

In this paper, we present a recursive algorithm for extracting classification rules from feedforward neural networks (NNs) that have been trained on data sets having both discrete and continuous attributes. The novelty of this algorithm lies in the conditions of the extracted rules: the rule conditions involving discrete attributes are disjoint from those involving continuous attributes. The algorithm starts by first generating rules with discrete attributes only to explain the classification process of the NN. If the accuracy of a rule with only discrete attributes is not satisfactory, the algorithm refines this rule by recursively generating more rules with discrete attributes not already present in the rule condition, or by generating a hyperplane involving only the continuous attributes. We show that for three real-life credit scoring data sets, the algorithm generates rules that are not only more accurate but also more comprehensible than those generated by other NN rule extraction methods.     

一种基于遗传Hopfield神经网络求解TSP问题的算法

针对Hopfield网络求解TSP问题时出现无效解和收敛性能差的问题,对约束条件能量函数进行改进,构造了一种求解TSP问题的遗传Hopfield神经网络算法,并与经典Hopfield神经网络求解TSP方法进行对比.实验结果表明,本文算法具有更好的整体求解性能.