Medical image segmentation using a contextual-constraint-based Hopfield neural cube

Neural-network-based image techniques such as the Hopfield neural networks have been proposed as an alternative approach for image segmentation and have demonstrated benefits over traditional algorithms. However, due to its architecture limitation, image segmentation using traditional Hopfield neural networks results in the same function as thresholding of image histograms. With this technique high-level contextual information cannot be incorporated into the segmentation procedure. As a result, although the traditional Hopfield neural network was capable of segmenting noiseless images, it lacks the capability of noise robustness. In this paper, an innovative Hopfield neural network, called contextual-constraint-based Hopfield neural cube (CCBHNC) is proposed for image segmentation. The CCBHNC uses a three-dimensional architecture with pixel classification implemented on its third dimension. With the three-dimensional architecture, the network is capable of taking into account each pixel's feature and its surrounding contextual information. Besides the network architecture, the CCBHNC also differs from the original Hopfield neural network in that a competitive winner-take-all mechanism is imposed in the evolution of the network. The winner-take-all mechanism adeptly precludes the necessity of determining the values for the weighting factors for the hard constraints in the energy function in maintaining feasible results. The proposed CCBHNC approach for image segmentation has been compared with two existing methods. The simulation results indicate that CCBHNC can produce more continuous, and smoother images in comparison with the other methods.     

Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays

This paper investigates delay-dependent robust asymptotic state estimation of fuzzy neural networks with mixed interval time-varying delay. In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the robust state estimation of Hopfield neural networks with mixed interval time-varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error is globally asymptotically stable. Based on the Lyapunov-Krasovskii functional which contains a triple-integral term, delay-dependent robust state estimation for such T-S fuzzy Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Stability analysis for fractional-order neural networks with time-varying delay

This paper focuses on the stability analysis for fractional-order neural networks with time-varying delay. A novel Lyapunov's asymptotic stability determination theorem is proved, which can be used for fractional-order systems directly. Different from the classical Lyapunov stability theorem, constraint condition on the derivative of Lyapunov function is revised as an uniformly continuous class-K function in the fractional-order case. Based on this novel Lyapunov stability theorem and free weight matrix method, a new sufficient condition on Lyapunov asymptotic stability of fractional-order Hopfield neural networks is derived by constructing a suitable Lyapunov function. Moreover, two numerical examples are provided to illustrate the effectiveness of these criteria.     

Chaos and rigorous verification of horseshoes in a class of Hopfield neural networks

In this paper, chaos in a new class of three-dimensional continuous time Hopfield neural networks is investigated. Numerical experiments show that this class of Hopfield neural networks can have chaotic attractors and limit cycles for different parameter configurations. By virtue of horseshoes theory in dynamic systems, rigorous computer-assisted verifications are done for their chaotic behavior. In terms of topological entropy, quantitative interpretations of these neural networks’ complexity are given. A brief analysis is also presented about their robustness.     

基于局部进化的Hopfield神经网络的优化计算方法

提出一种基于局部进化的Hopfield神经网络优化计算方法，该方法将遗传算法和Hopfield神经网络结合在一起，克服了Hopfield神经网络易收敛到局部最优值的缺点，以及遗传算法收敛速度慢的缺点。该方法首先由Hopfield神经网络进行状态方程的迭代计算降低网络能量，收敛后的Hopfield神经网络在局部范围内进行遗传算法寻优，以跳出可能的局部最优值陷阱，再由Hopfield神经网络进一步迭代优化。这种局部进化的Hopfield神经网络优化计算方法尤其适合于大规模的优化问题，对图像分割问题和规模较大的200城市旅行商问题的优化计算结果表明，其全局收敛率和收敛速度明显提高。     

Model updating of multistory shear buildings for simultaneous identification of mass,stiffness and damping matrices using two different soft-computing methods

In this research, two novel methods for simultaneous identification of mass–damping–stiffness of shear buildings are proposed. The first method presents a procedure to estimate the natural frequencies, modal damping ratios, and modal shapes of shear buildings from their forced vibration responses. To estimate the coefficient matrices of a state-space model, an auto-regressive exogenous excitation (ARX) model cooperating with a neural network concept is employed. The modal parameters of the structure are then evaluated from the eigenparameters of the coefficient matrix of the model. Finally, modal parameters are used to identify the physical/structural (i.e., mass, damping, and stiffness) matrices of the structure. In the second method, a direct strategy of physical/structural identification is developed from the dynamic responses of the structure without any eigenvalue analysis or optimization processes that are usually necessary in inverse problems. This method modifies the governing equations of motion based on relative responses of consecutive stories such that the new set of equations can be implemented in a cluster of artificial neural networks. The number of neural networks is equal to the number of degree-of-freedom of the structure. It is shown the noise effects may partially be eliminated by using high-order finite impulse response (FIR) filters in both methods. Finally, the feasibility and accuracy of the presented model updating methods are examined through numerical studies on multistory shear buildings using the simulated records with various noise levels. The excellent agreement of the obtained results with those of the finite element models shows the feasibility of the proposed methods.     

Asymptotic stability of impulsive high-order Hopfield type neural networks

In this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Solving optimization problems with variable-constraint by anextended Cohen-Grossberg model

A variety of real-world problems can be formulated as continuous optimization problems with variable constraint. It is well-known, however, that it is difficult to develop a unified method for obtaining their feasible solutions. We have recognized that the recent work of solving the traveling salesman problem (TSP) by the Hopfield model explores an innovative approach to them as well as combinatorial optimization problems. The Hopfield model is generalized into the Cohen-Grossberg model (CGM) to which a specific Lyapunov function has been found. This paper thus extends the Hopfield method onto the CGM in order to develop a unified solving-method of continuous optimization problems with variable-constraint. Specifically, we consider a certain class of continuous optimization problems with a constraint equation including the Hopfield version of the TSP as a particular member. Then we theoretically develop a method that, from any given problem of that class, derives a network of an extended CGM to provide feasible solutions to it. The main idea for constructing that extended CGM lies in adding to it a synapse dynamical system concurrently operating with its current unit dynamical system so that the constraint equation can be enforced to satisfaction at final states. This construction is also motivated by previous neuron models in biophysics and learning algorithms in neural networks     

Max-Product型模糊Hopfield网络稳定性及其聚类方法研究

本文将模糊逻辑和神经网络相结合,提出了Ｍａｘ－Ｐｒｏｄｕｃｔ型Ｈｏｐｆｉｅｌｄ人工神经网络,给出了它的网络结构和形式化描述,证明了ＦｕｚｚｙＨＮ的稳定性,最后通过理论和数值实验对基于Ｍａｘ－Ｐｒｏｄｕｃｔ型Ｈｏｐｆｉｅｌｄ网络的动态聚类过程和有关性质进行了研究。     

Global exponential stability of impulsive high-order Hopfield type neural networks with delays

In this paper, we investigate the global exponential stability of impulsive high-order Hopfield type neural networks with delays. By establishing the impulsive delay differential inequalities and using the Lyapunov method, two sufficient conditions that guarantee global exponential stability of these networks are given, and the exponential convergence rate is also obtained. A numerical example is given to demonstrate the validity of the results.     

基于Hopfield神经网络的作业车间生产调度方法

该文提出了基于Hopfield神经网络的作业车间生产调度的新方法.文中给出了作业车 间生产调度问题(JSP)的约束条件及其换位矩阵表示,提出了新的包括所有约束条件的计算能 量函数表达式,得到相应的作业车间调度问题的Hopfield神经网络结构与权值解析表达式,并 提出相应的Hopfield神经网络作业车间调度方法.为了避免Hopfield神经网络容易收敛到局部 极小,从而产生非法调度解的缺点,将模拟退火算法应用于Hopfield神经网络求解,使Hopfield 神经网络收敛到计算能量函数的最小值0,从而保证神经网络输出是一个可行调度方案.该文 改进了已有文献中提出的作业调度问题的Hopfield神经网络方法,与已有算法相比,能够保证 神经网络稳态输出为可行的作业车间调度方案.     

Fuzzy Clustering Using A Compensated Fuzzy Hopfield Network

Hopfield neural networks are well known for cluster analysis with an unsupervised learning scheme. This class of networks is a set of heuristic procedures that suffers from several problems such as not guaranteed convergence and output depending on the sequence of input data. In this paper, a Compensated Fuzzy Hopfield Neural Network (CFHNN) is proposed which integrates a Compensated Fuzzy C-Means (CFCM) model into the learning scheme and updating strategies of the Hopfield neural network. The CFCM, modified from Penalized Fuzzy C-Means algorithm (PFCM), is embedded into a Hopfield net to avoid the NP-hard problem and to speed up the convergence rate for the clustering procedure. The proposed network also avoids determining values for the weighting factors in the energy function. In addition, its training scheme enables the network to learn more rapidly and more effectively than FCM and PFCM. In experimental results, the CFHNN method shows promising results in comparison with FCM and PFCM methods.     

二阶神经网络的全局指数稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间,二阶神经网络较一般神经网络具有更快的收敛速度,对于二阶连续型Hopfield神经网络,用Lyapunov方法讨论平衡点的全局指数稳定性,给出了平衡点全局指数稳定的几个判别准则,作为特例,获得了连续型Hopfield神经网络全局指数稳定的新判据。     

Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay

In this paper, we propose a new passive weight learning law for switched Hopfield neural networks with time-delay under parametric uncertainty. Based on the proposed passive learning law, some new stability results, such as asymptotical stability, input-to-state stability (ISS), and bounded input-bounded output (BIBO) stability, are presented. An existence condition for the passive weight learning law of switched Hopfield neural networks is expressed in terms of strict linear matrix inequality (LMI). Finally, numerical examples are provided to illustrate our results.     

一类具有时滞的广义Hopf ield 神经网络的全局稳定性

通过引入能量泛函，分析了一类具有时滞的广义Hopfield神经网络的全局稳定性．从理论上给出了该类网络为全局稳定的充分条件，证明了当时滞满足一个可计算的边界条件时，具有时滞的该类神经网络与相应的无时滞网络具有同样的全局稳定特性．仿真结果进一步证明了结论的有效性。     

Hopfield Neural Networks for Parametric Identification of Dynamical Systems

In this work, a novel method, based upon Hopfield neural networks, is proposed for parameter estimation, in the context of system identification. The equation of the neural estimator stems from the applicability of Hopfield networks to optimization problems, but the weights and the biases of the resulting network are time-varying, since the target function also varies with time. Hence the stability of the method cannot be taken for granted. In order to compare the novel technique and the classical gradient method, simulations have been carried out for a linearly parameterized system, and results show that the Hopfield network is more efficient than the gradient estimator, obtaining lower error and less oscillations. Thus the neural method is validated as an on-line estimator of the time-varying parameters appearing in the model of a nonlinear physical system.     

运输问题的神经网络解法

给出了利用Hopfield连续模型求解运输问题的数值算法,是对运筹学知识的补充和完善,是借助人工神经网络计算机原理解决组合优化问题的一个成功范例。     

基于离散Hopfield网络的自相关过程控制方法

对于自相关过程的统计控制,传统统计学方法虚发警报的概率较大,而BP人工神经网络方法权值训练困难,灵敏度不高。提出一种基于联想学习与离散Hopfield网络的自相关过程控制方法。不需任何训练样本,通过正交化编码将过程状态以吸引子的形式存储到Hopfield网络中,并利用网络的联想功能来检测自相关过程的阶跃型突变。算例研究表明,与Elman网络和EWMA方法相比,过程正常时,所提方法的平均链长（ARL）分别提高了27.9%和55.0%;过程异常时,所提方法的ARL分别降低了74.1%与81.8%以上。说明了方法的有效性与优越性。     

连续时间 Hopfield网络模型数值实现分析

讨论使用Euler方法和梯形方法在数值求解连续时间的Hopfield网络模型时,离散时间步长的选择和迭代停止条件问题.利用凸函数的定义研究了能量函数下降的条件,根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件.分析连续时间Hopfield网络模型的收敛性证明,提出了一个广义的连续时间Hopfield网络模型.对于常用的Euler方法和梯形方法数值求数值实现连续时间Hopfield网络,讨论了离散时间步长的选择.由于梯形方法为隐式方法,分析了它的迭代求算法的停止条件.根据连续时间Hopfield网络的特点,提出改进的迭代算法,并对其进行了分析.数值实验的结果表明,较大的离散时间步长不仅加速了数值实现,而且有利于提高优化性能.