基于Hopfield神经网络的多用户信号检测器

用连续Ｈｏｐｆｉｅｌｄ神经网络实现ＣＤＭＡ通信系统中多用户信号检测的设想，并针对同步ＣＤＭＡ系统构造了基于连续Ｈｏｐｆｉｅｌｄ神经网络的用户信号检测器。计算机仿真结果表明：这种检测器的性能远远优于传统检测器的性能，它的性能可与最佳多用户信号检测相比拟。     

Optic flow estimation by a Hopfield neural network using geometrical constraints

Sparse optic flow maps are general enough to obtain useful information about camera motion. Usually, correspondences among features over an image sequence are estimated by radiometric similarity. When the camera moves under known conditions, global geometrical constraints can be introduced in order to obtain a more robust estimation of the optic flow. In this paper, a method is proposed for the computation of a robust sparse optic flow (OF) which integrates the geometrical constraints induced by camera motion to verify the correspondences obtained by radiometric-similarity-based techniques. A raw OF map is estimated by matching features by correlation. The verification of the resulting correspondences is formulated as an optimization problem that is implemented on a Hopfield neural network (HNN). Additional constraints imposed in the energy function permit us to achieve a subpixel accuracy in the image locations of matched features. Convergence of the HNN is reached in a small enough number of iterations to make the proposed method suitable for real-time processing. It is shown that the proposed method is also suitable for identifying independently moving objects in front of a moving vehicle. Received: 26 December 1995 / Accepted: 20 February 1997     

建立Hopfield网络的一般方法

讨论了用离散的带反馈的Hopfield网络的极限环来表达概念,以及在给定不动点、极限 环或迭代序列等限制下,用线性规划和遗传算法通过求解不等式组一般性地建立Hopfield网 络的方法,从而也解决了网络联结的稀释问题.最后给出了几个实例,     

Cascade synthesis of 2-D dissipative reactance networks

In this paper, a new result, new formulas of transfer function and input impedance, for 2-D dissipative reactance network cascade synthesis is given in terms of simplified formulas to realize doubly terminated resistively 1-D dissipative reactance networks. The new result includes the more general cases, e.g. the both can be dissipative or one is dissipative and the another is a lossless reactance subnetwork and so on. Two calculation examples are given in the paper to illustrate the above realizations. Besides, considering some problems of the direct connection between two subnetworks, we also introduce one-way lines to discuss the cascade synthesis of nonreciprocal 2-D dissipative reactance networks.     

神经网络A／D转换器电路的两种改进方法

本文对Ｈｏｐｆｉｅｌｄ神经网络Ａ／Ｄ转换器电路进行了分析。对照转换条件及电路的稳态方程，讨论了输出状态与参考输入必须满足的条件。在此基础上提出了两种改进Ａ／Ｄ转换电路的途径：（１）对原电路选择适宜的参考输入；（２）根据Ｈｏｐｆｉｅｌｄ线性规划网络提出的一种新电路。文中还给出了ＰＳＰＩＣＥ模拟计算，所得结果与理论分析吻合。     

Convergence of higher-order two-state neural networks with modified updating

The Hopfield network is a standard tool for maximizing aquadratic objective function over the discrete set {− 1,1} ⁿ . It is well-known that if a Hopfield network is operated in anasynchronous mode, then the state vector of the network converges to a local maximum of the objective function; if the network is operated in asynchronous mode, then the state vector either converges to a local maximum, or else goes into a limit cycle of length two. In this paper, we examine the behaviour ofhigher-order neural networks, that is, networks used for maximizing objective functions that are not necessarily quadratic. It is shown that one can assume, without loss of generality, that the objective function to be maximized ismultilinear. Three methods are given for updating the state vector of the neural network, called the asynchronous, the best neighbour and the gradient rules, respectively. For Hopfield networks with a quadratic objective function, the asynchronous rule proposed here reduces to the standard asynchronous updating, while the gradient rule reduces to synchronous updating; the best neighbour rule does not appear to have been considered previously. It is shown that both the asynchronous updating rule and the best neighbour rule converge to a local maximum of the objective function within a finite number of time steps. Moreover, under certain conditions, under the best neighbour rule, each global maximum has a nonzero radius of direct attraction; in general, this may not be true of the asynchronous rule. However, the behaviour of the gradient updating rule is not well-understood. For this purpose, amodified gradient updating rule is presented, that incorporates bothtemporal as well as spatial correlations among the neurons. For the modified updating rule, it is shown that, after a finite number of time steps, the network state vector goes into a limit cycle of lengthm, wherem is the degree of the objective function. Ifm = 2, i.e., for quadratic objective functions, the modified updating rule reduces to the synchronous updating rule for Hopfield networks. Hence the results presented here are “true” generalizations of previously known results.     

用于求解TSP的HOPFIELD／TANK网络模型的特性及参数的理论分析＊

本文对于Hopfield/Tank网络模型在求解TSP的特性进行了理论分析。建立了参数之间的关系准则。     

基于Hopfield的脱机手写数字识别理论及算法

脱机手写数字识别在很多领域具有广泛的应用前景,国内外学者对此做了大量的研究工作,提出了很多预处理和模式识别的算法,大大提高了手写数字的识别精度。为了提高手写数字识别的精度,文章将Hopfield神经网络应用于脱机手写数字识别分析中,Hopfield神经网络的“能量函数”的能量在网络运行过程中,具有不断地减少最后趋于稳定的平衡状态的特性,而且网络一旦建立即可自动运行,无需要训练。     

基于连续型Hopfield网络的最优控制方法

为克服应用离散型Hopfield网络解决动态最优控制问题时,计算量随着系统维数和控制时域的增加而指数增大的不足,提出了一种基于连续型Hopfield网络解决线性离散系统二次型最优控制问题的方法.该方法将线性二次型性能指标转化为连续型Hopfield网络的能量函数,控制序列转化为连续型Hopfield网络神经元的输出向量,从而将线性二次型动态优化问题的求解过程转化为相应的连续型Hopfield网络从初态向终态的运行过程,网络稳态输出反映了最优控制序列.该方法计算量小,实时性好,便于在线优化控制.