Stability properties of labeling recursive auto-associative memory

Labeling recursive auto-associative memory (LRAAM) is an extension of the RAAM model by Pollack (1990) to obtain distributed reduced representations of labeled directed graphs. In this paper some mathematical properties of LRAAM are discussed. Specifically, sufficient conditions on the asymptotical stability of the decoding process along a cycle of the encoded structure are given. LRAAM can be transformed into an analog Hopfield network with hidden units and an asymmetric connections matrix by connecting the output units with the input units. In this architecture encoded data can be accessed by content and different access procedures can be defined depending on the access key. Each access procedure corresponds to a particular constrained version of the recurrent network. The authors give sufficient conditions under which the property of asymptotical stability of a fixed point in one particular constrained version of the recurrent network can be extended to related fixed points in different constrained versions of the network. An example of encoding of a labeled directed graph on which the theoretical results are applied is given and discussed.     

A shortest path routing algorithm using Hopfield neural network with an improved energy function

A shortest path routing algorithm using the Hopfield neural network with a modified Lyapunov function is proposed. The modified version of the Lyapunov energy function for an optimal routing problem is proposed for determining routing order for a source and multiple destinations. The proposed energy function mainly prevents the solution path from having loops and partitions. Experiments are performed on 3000 networks of up to 50 nodes with randomly selected link costs. The performance of the proposed algorithm is compared with several conventional algorithms including Ali and Kamoun's, Park and Choi's, and Ahn and Ramakrishna's algorithms in terms of the route optimality and convergence rate. The results show that the proposed algorithm outperforms conventional methods in all cases of experiments. The proposed algorithm particularly shows significant improvements on the route optimality and convergence rate over conventional algorithms when the size of the network approaches 50 nodes.     

一种改进型离散Hopfield学习算法

针对离散Hopfield 神经网络(DHNN) 的权值设计问题, 提出一种改进型学习算法, 并在DHNN动力学分析的基础上设计该学习算法. 利用矩阵分解的方法(MD) 得到正交矩阵, 并采用得到的正交矩阵直接计算DHNN的权值矩阵. 通过该学习算法得到的权值矩阵, 可以很好地存储训练样本的信息, 使测试样本收敛到稳定点. 该学习算法不需要进行分块计算, 减少了计算步骤和计算量, 降低了网络的迭代次数, 从而提高了网络运行速度. 最后, 将该学习算法应用于水质评价, 验证了其有效性和可行性.     

A new design method for the complex-valued multistate Hopfield associative memory

A method to store each element of an integral memory set M subset {1,2,...,K}/sup n/ as a fixed point into a complex-valued multistate Hopfield network is introduced. The method employs a set of inequalities to render each memory pattern as a strict local minimum of a quadratic energy landscape. Based on the solution of this system, it gives a recurrent network of n multistate neurons with complex and symmetric synaptic weights, which operates on the finite state space {1,2,...,K}/sup n/ to minimize this quadratic functional. Maximum number of integral vectors that can be embedded into the energy landscape of the network by this method is investigated by computer experiments. This paper also enlightens the performance of the proposed method in reconstructing noisy gray-scale images.     

A modified Hopfield neural networks model for graphs-based kinematic structure design

Graph theory can be used efficiently for both kinematic and dynamics analysis of mechanical structures. One of the most important and difficult issues in graphs theory-based structures design is graphs isomorphism discernment. The problem is vital for graph theory-based kinematic structures enumeration, which is known to be nondeterministic polynomial-complete problem. To solve the problem, a Hopfield neural networks (HNN) model is presented and some operators are improved to prevent premature convergence. By comparing with genetic algorithm, the computation times of the HNN model shows less affection when the number of nodes were enhanced. It is concluded that the algorithm presented in this paper is efficient for large-scale graphs isomorphism problem.     

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.     

Characteristics of the Hopfield associative memory utilizingisomorphism relations

Isomorphism relations are utilized to analyze the Hopfield associative memory. When the number of fundamental memories m=/<3, it is proved that two Hopfield associative memories are isomorphic if they have the same mutual distances between the fundamental memories. The number of stable states and the synchronous convergence time of a Hopfield associative memory are shown to be less than or equal to 2 to the power 2(m-1) and 4 to the power 2(m-1), respectively, where m>/=1.     

Adaptive reversible watermarking with improved embedding capacity

Embedding capacity is one of the most important issues of the reversible watermarking. However, the theoretical maximum embedding capacity of most reversible watermarking algorithms is only 1.0 bits per pixel (bpp). To achieve a higher capacity, we have to modify the least significant bit (LSB) multiple times which definitely lowers the quality of the embedded image. To this end, this paper proposes a novel reversible watermarking algorithm by employing histogram shifting and adaptive embedding. Specifically, the amount of the embedded watermark is adaptively determined in terms of the context of each pixel. For pixels with small prediction error, we modify the second, third and even the fourth LSBs as well to embed more than one watermark bit. Consequently, the proposed method achieves the embedding capacity larger than 1.0 bpp in single-pass embedding as well as bringing relatively low embedding distortion. The superiority of the proposed method is experimental verified by comparing with other existing schemes.     

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.

     

Effects of noise in training patterns on the memory capacity of thefully connected binary Hopfield neural network: mean-field theory andsimulations

We show that the memory capacity of the fully connected binary Hopfield network is significantly reduced by a small amount of noise in training patterns. Our analytical results obtained with the mean field method are supported by extensive computer simulations.     

Synaptic compensation on Hopfield network: implications for memory rehabilitation

The discrete-time neural network proposed by Hopfield can be used for storing and recognizing binary patterns. Here, we investigate how the performance of this network on pattern recognition task is altered when neurons are removed and the weights of the synapses corresponding to these deleted neurons are divided among the remaining synapses. Five distinct ways of distributing such weights are evaluated. We speculate how this numerical work about synaptic compensation may help to guide experimental studies on memory rehabilitation interventions.     

基于改进型Hopfield神经网络的盲多用户检测算法

基于Hopfield神经网络没有学习规则,不需要训练,也不会自学习,靠Lyapunov函数的设计过程来调节权值的特点,将广义罚函数与Hopfield神经网络的能量函数结合,基于最小平均输出能量准则,构造出更合适的新目标函数,分析讨论了一种实现DS/CDMA盲多用户检测的改进型Hopfield神经网络方法。仿真结果表明,该算法在误码率、抗远近效应方面都有明显的改善。     

On fuzzy associative memory with multiple-rule storage capacity

Kosko's fuzzy associative memory (FAM) is the very first neural network model for implementing fuzzy systems. Despite its success in various applications, the model suffers from very low storage capacity, i.e., one rule per FAM matrix. A lot of hardware and computations are usually required to implement the model and, hence, it is limited to applications with small fuzzy rule-base. In this paper, the inherent property for storing multiple rules in a FAM matrix is identified. A theorem for perfect recalls of all the stored rules is established and based upon which the hardware and computation requirements of the FAM model can be reduced significantly. Furthermore, we have shown that when the FAM model is generalized to the one with max-bounded-product composition, single matrix implementation is possible if the rule-base is a set of semi-overlapped fuzzy rules. Rule modification schemes are also developed and the inference performance of the established high capacity models is reported through a numerical example     

基于改进Hopfield神经网络的图像特征点匹配算法

针对图像特征点匹配算法的运行时间呈指数增长的问题,提出了一种新的匹配算法NHop.该算法通过加入新的网络输入输出函数、点对间差异的度量和启发式选择目标点的方式,对传统的Hopfield神经网络进行了改进.新算法不仅解决了传统Hopfield神经网络运行时间长、能量函数易陷入局部极小点的问题,而且也有效地实现了图像特征点的匹配.实验结果表明,与传统的Hopfield神经网络相比,NHop算法的匹配速度更快、准确率更高,对于图像特征点的匹配效果更好.     

Memory capacity and information capacity of sparsely encoded associative memory with replacement units

We introduce sparse encoding into the autoassociative memory model with replacement units. Utilizing computer simulation, we search the optimal number of replacement units in two terms: the memory capacity and the information capacity of the network. We show that the optimal number of replacement units to maximize the memory capacity and the information capacity decreases as the firing ratio decreases, and that the difference in the memory capacity between sparse encoding and non-sparse encoding becomes small as the number of replacement units increases.     

A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems

This paper presents a novel constrained optimization algorithm named MAL-IGWO, which integrates the benefit of the improved grey wolf optimization (IGWO) capability for discovering the global optimum with the modified augmented Lagrangian (MAL) multiplier method to handle constraints. In the proposed MAL-IGWO algorithm, the MAL method effectively converts a constrained problem into an unconstrained problem and the IGWO algorithm is applied to deal with the unconstrained problem. This algorithm is tested on 24 well-known benchmark problems and 3 engineering applications, and compared with other state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm shows better performance in comparison to other approaches.

     

Agriculture satellite image segmentation using a modified artificial Hopfield neural network

Beekeeping plays an important role in increasing and diversifying the incomes of many rural communities in Kingdom of Saudi Arabia. However, despite the region’s relatively good rainfall, which results in better forage conditions, bees and beekeepers are greatly affected by seasonal shortages of bee forage. Because of these shortages, beekeepers must continually move their colonies in search of better forage. The aim of this paper is to determine the actual bee forage areas with specific characteristics like population density, ecological distribution, flowering phenology based on color satellite image segmentation. Satellite images are currently used as an efficient tool for agricultural management and monitoring. It is also one of the most difficult image segmentation problems due to factors like environmental conditions, poor resolution and poor illumination. Pixel clustering is a popular way of determining the homogeneous image regions, corresponding to the different land cover types, based on their spectral properties. In this paper Hopfield neural network (HNN) is introduced as Pixel clustering based segmentation method for agriculture satellite images.     

一种Hopfield神经网络能量函数改进下的作业车间调度*

由于作业车间调度问题的目标函数目前还无法用换位矩阵的元素以数学公式的形式表示,因此无法保证求出全局最优解。文中首先对换位矩阵表示方法进行了改进,给出新的带有目标函数的能量函数表达式,然后提出改进的Hopfield神经网络作业车间调度方法,并将模拟退火应用于Hopfield神经网络求解,避免了陷入局部极值。仿真结果表明,该方法具有全局搜索能力,并能够保证神经网络的稳态输出为全局最优或近似全局最优。