Modified Hopfield Neural Network Research Articles

Geometric Regularized Hopfield Neural Network for Medical Image Enhancement.

One of the major shortcomings of Hopfield neural network (HNN) is that the network may not always converge to a fixed point. HNN, predominantly, is limited to local optimization during training to achieve network stability. In this paper, the convergence problem is addressed using two approaches: (a) by sequencing the activation of a continuous modified HNN (MHNN) based on the geometric correlation of features within various image hyperplanes via pixel gradient vectors and (b) by regulating geometric pixel gradient vectors. These are achieved by regularizing proposed MHNNs under cohomology, which enables them to act as an unconventional filter for pixel spectral sequences. It shifts the focus to both local and global optimizations in order to strengthen feature correlations within each image subspace. As a result, it enhances edges, information content, contrast, and resolution. The proposed algorithm was tested on fifteen different medical images, where evaluations were made based on entropy, visual information fidelity (VIF), weighted peak signal-to-noise ratio (WPSNR), contrast, and homogeneity. Our results confirmed superiority as compared to four existing benchmark enhancement methods.

A Context-Based Image Contrast Enhancement Using Energy Equalization With Clipping Limit.

In this paper, a new context-based image contrast enhancement process using energy curve equalization (ECE) with a clipping limit has been proposed. In a fundamental anomaly to the existing contrast enhancement practice using histogram equalization, the projected method uses the energy curve. The computation of the energy curve utilizes a modified Hopfield neural network architecture. This process embraces the image's spatial adjacency information to the energy curve. For each intensity level, the energy value is calculated and the overall energy curve appears to be smoother than the histogram. A clipping limit applies to evade the over enhancement and is chosen as the average of the mean and median value. The clipped energy curve is subdivided into three regions based on the standard deviation value. Each part of the subdivided energy curve is equalized individually, and the final enhanced image is produced by combining transfer functions computed by the equalization process. The projected scheme's qualitative and quantitative efficiency is assessed by comparing it with the conventional histogram equalization techniques with and without the clipping limit.

Application Of Improved Hopfield Neural Network In Path Planning

A modified Hopfield neural network algorithm is proposed and applied to the path planning to solve some problems in the traditional Hopfield neural network. Firstly, the traditional A* algorithm is used to select the nodes in the search area that meet the criteria. Then, the nodes conforming to the standard are converted into neurons in the Hopfield neural network, and the stability of the network is used to iteratively select an optimal path. Experiments show that the improved Hopfield neural network algorithm can reduce the search time of path planning and improve efficiency.

A novel RK4-Hopfield Neural Network for Power Flow Analysis of power system

This paper presents a novel Runge–Kutta (RK4) based modified hopfield neural network (MHNN) for solving a set of non-linear transcendental power flow equations of power system. The proffered method is a Lyapunov based energy function approach to minimize real and reactive power mismatches of the system. A set of non-linear differential equations derived from energy function, describing the dynamical behavior of HNN is framed for solving Power Flow equations. These dynamic equations of the network are solved by RK4 method to deduce the unknown variables of the system. The feasibility of proposed method is tested on 5-bus, IEEE 14-bus, 39-bus and 57-bus test system. The analytical equation describing the behavior of MHNN is coded in MATLAB software. The results obtained reveal that the suggested method gives accurate solution and reduces the computational complexity than conventional Newton Raphson (NR) method. The sensitivity analysis is also tested for change in R/X ratio of the system, initial conditions and loading of the system. The proposed method is robust for above specified changes and involves less computational effort. To prove the applicability and consistency of projected method, IEEE 118-bus system has been tested. The power flow solutions found through proffered method are compared with solutions obtained from numerical approaches in order to validate the proposed approach. Moreover, the stability of the system is studied in Lyapunov sense of notion which assures converged solution of proposed method.

Exposure-Based Energy Curve Equalization for Enhancement of Contrast Distorted Images

This paper presents a novel image contrast enhancement technique that uses exposure-based energy curve equalization (ECE) with a plateau limit. In a primary deviation from the current histogram equalization process for contrast enhancement, the proposed approach uses an energy curve for the same. The energy curve is computed based on the modified Hopfield neural network architecture, which contains spatial context information. The calculated energy curve is clipped with a plateau limit computed as the average of the energy curve. The exposure threshold is computed and used to divide the clipped energy curve. The two resulting energy curves are equalized independently, and the final enhanced image is generated by integrating the images achieved by transforming the equalized energy curves. The performance of the proposed method is evaluated on a variety of low contrast images. The subjective and objective evaluations of the proposed method are compared with the various histogram equalization (HE) based methods and other state-of-the-art methods to exemplify the effectiveness.

Diabetic Retinopathy Diagnosis from Retinal Images Using Modified Hopfield Neural Network.

Disease diagnosis from medical images has become increasingly important in medical science. Abnormality identification in retinal images has become a challenging task in medical science. Effective machine learning and soft computing methods should be used to facilitate Diabetic Retinopathy Diagnosis from Retinal Images. Artificial Neural Networks are widely preferred for Diabetic Retinopathy Diagnosis from Retinal Images. It was observed that the conventional neural networks especially the Hopfield Neural Network (HNN) may be inaccurate due to the weight values are not adjusted in the training process. This paper presents a new Modified Hopfield Neural Network (MHNN) for abnormality classification from human retinal images. It relies on the idea that both weight values and output values can be adjusted simultaneously. The novelty of the proposed method lies in the training algorithm. In conventional method, the weights remain fixed but the weights are changing in the proposed method. Experimental performed on the Lotus Eye Care Hospital containing 540 images collected showed that the proposed MHNN yields an average sensitivity and specificity of 0.99 and accuracy of 99.25%. The proposed MHNN is better than HNN and other neural network approaches for Diabetic Retinopathy Diagnosis from Retinal Images.

Switching Optimization By Neural Networks

The priority switching problem is a combinatorial optimization problem searching for the best solution for frame forwarding in a switch. To solve this problem, the modified Hopfield neural network, what is able to solve the priority switching problem is introduced.

A Modified Hopfield Neural Network Algorithm (MHNNA) Using ALOS Image for Water Quality Mapping

Decreasing water pollution is a big problem in coastal waters. Coastal health of ecosystems can be affected by high concentrations of suspended sediment. In this work, a Modified Hopfield Neural Network Algorithm (MHNNA) was used with remote sensing imagery to classify the total suspended solids (TSS) concentrations in the waters of coastal Langkawi Island, Malaysia. The adopted remote sensing image is the Advanced Land Observation Satellite (ALOS) image acquired on 18 January 2010. Our modification allows the Hopfield neural network to convert and classify color satellite images. The samples were collected from the study area simultaneously with the acquiring of satellite imagery. The sample locations were determined using a handheld global positioning system (GPS). The TSS concentration measurements were conducted in a lab and used for validation (real data), classification, and accuracy assessments. Mapping was achieved by using the MHNNA to classify the concentrations according to their reflectance values in band 1, band 2, and band 3. The TSS map was color-coded for visual interpretation. The efficiency of the proposed algorithm was investigated by dividing the validation data into two groups. The first group was used as source samples for supervisor classification via the MHNNA. The second group was used to test the MHNNA efficiency. After mapping, the locations of the second group in the produced classes were detected. Next, the correlation coefficient (R) and root mean square error (RMSE) were calculated between the two groups, according to their corresponding locations in the classes. The MHNNA exhibited a higher R (0.977) and lower RMSE (2.887). In addition, we test the MHNNA with noise, where it proves its accuracy with noisy images over a range of noise levels. All results have been compared with a minimum distance classifier (Min-Dis). Therefore, TSS mapping of polluted water in the coastal Langkawi Island, Malaysia can be performed using the adopted MHNNA with remote sensing techniques (as based on ALOS images).

Fault diagnosis using partial syndromes: a modified Hopfield neural network approach

This paper presents a modified Hopfield neural network (HNN) for solving the system-level fault diagnosis problem which aims at identifying the set of faulty nodes. This problem has been extensively studied in the last three decades. Nevertheless, identifying the set of all faulty nodes using only partial syndromes, i.e. when some of the testing or comparison outcomes are missing prior to initiating the diagnosis phase, remains an outstanding research issue. The new HNN-based diagnosis algorithm does not require any prior learning or knowledge about the system, nor about any faulty situation, hence providing a better generalisation performance. Results from a thorough simulation study demonstrate the effectiveness of the HNN-based fault diagnosis algorithm in terms of diagnosis correctness, diagnosis latency and diagnosis scalability, for randomly generated diagnosable systems of different sizes and under various fault scenarios. We have also conducted extensive simulations using partial syndromes. Simulations showed that the HNN-based diagnosis performed efficiently, i.e. diagnosis correctness was around 99% when at most half of the test or comparison outcomes are missing, making it a viable alternative to existing diagnosis algorithms.

Computing Method and Circuit Realization of Neural Network on Finite Element Analysis

The finite element analysis in theory of elasticity is corresponded to the quadratic programming with equality constraint, which can be further transformed into the unconstrained optimization. In the paper, the question is solved by modified Hopfield neural network based on the energy function of the neural network equals to the objective function of the finite element method and the minimum point, which is the stable equilibrium point of the network system, is the solution. In addition the authors present the computer simulation and analogue circuit experiment to verify this method. The results are revealed that: 1) The results of improved Hopfield neural network are reliable and accuracy; 2) The improved Hopfield neural network model has an advantage on circuit realization and the computing time, which is unrelated with complexity of the structure, is constant. It is practical significance for the research and calculation.

A Hopfield Neural Network for Channel Assignment Problem in Cellular Radio Networks

In wireless mobile communication system, radio spectrum is limited resource. However, efficient use of available channels has been shown to improve the system capacity. The role of a channel assignment scheme is to allocate channels to calls or mobiles in such a way as to minimize call blocking or call dropping probabilities, and also to maximize the quality of service. Channel assignment is known to be an NP-hard optimization problem. In this paper, a new channel-assignment algorithm using a modified Hopfield neural network is proposed. The channel-assignment problem is formulated as an energy-minimization problem that is implemented by a modified discrete Hopfield network. In this algorithm, an energy function is derived, and the appropriate interconnection weights between the neurons are specified. The interconnection weights between the neurons are designed in such a way that each neuron receives inhibitory support if the constraint conditions are violated and receives excitatory support if the constraint conditions are satisfied. The algorithm will be tested by solving seven benchmark problems, where the total number of frequencies varied from 73 to 533. This new algorithm, together with the proposed regular interval initialization and new interconnection weights, has better performance results than the existing algorithms in all of the seven problems.

Appling a Novel Cost Function to Hopfield Neural Network for Defects Boundaries Detection of Wood Image

A modified Hopfield neural network with a novel cost function was presented for detecting wood defects boundary in the image. Different from traditional methods, the boundary detection problem in this paper was formulated as an optimization process that sought the boundary points to minimize a cost function. An initial boundary was estimated by Canny algorithm first. The pixel gray value was described as a neuron state of Hopfield neural network. The state updated till the cost function touches the minimum value. The designed cost function ensured that few neurons were activated except the neurons corresponding to actual boundary points and ensured that the activated neurons are positioned in the points which had greatest change in gray value. The tools of Matlab were used to implement the experiment. The results show that the noises of the image are effectively removed, and our method obtains more noiseless and vivid boundary than those of the traditional methods.

A modified Hopfield neural network for perfect calculation of magnetic resonance spectroscopy

In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called modified sequential extension of section (MSES) that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the Hopfield neural networks.

Ordinal preference and inter-rater pattern recognition: Hopfield neural network vs. measures of association

In decision analysis, if the criterion is an ordinal rather than a cardinal one, a preferential solution depends on the inter-rater agreement. The Kendall coefficient of concordance W, the Friedman ranks statistic F r , and the Page L statistic are often used to determine the association among M sets of rankings. However, they may get some anomalies because they all use the cardinal variable "variance" to judge the association. In order to correct the anomalies, we use the modified Hopfield neural network instead to determine the association among M sets of rankings. The results are not only to reduce the unidentified cases but also to solve the anomalies.

Application of a modified hopfield neural network to noisy magnetotelluric data

A new approach is presented for processing noisy magnetotelluric time series, based on a neural network algorithm. This approach structures data and removes noise and distortions from them for the subsequent correct estimation of magnetotelluric response functions. The method was tested on real data contaminated by anthropogenic noise.

A Context-Sensitive Technique for Unsupervised Change Detection Based on Hopfield-Type Neural Networks

In this paper, we propose a context-sensitive technique for unsupervised change detection in multitemporal remote sensing images. This technique is based on a modified Hopfield neural network architecture designed to model spatial correlation between neighboring pixels of the difference image produced by comparing images acquired on the same area at different times. Each spatial position in the considered scene is represented by a neuron in the Hopfield network that is connected only to its neighboring units. These connections model the spatial correlation between neighboring pixels and are associated with a context-sensitive energy function that represents the overall status of the network. Change detection maps are obtained by iteratively updating the output status of the neurons until a minimum of the energy function is reached and the network assumes a stable state. A simple heuristic thresholding procedure is presented and adopted for initializing the network. The proposed change detection technique is unsupervised and distribution free. Experimental results carried out on two multispectral and multitemporal remote sensing images confirm the effectiveness of the proposed technique

Variational PDE based image restoration using neural network

Two variational partial differential equations as regularisation terms are proposed for the image restoration model based on the modified Hopfield neural network. One is based on a harmonic model and the other is based on a total variation model. The performance of these regularisation terms is analysed from the viewpoint of nonlinear diffusion. It can be shown that the two proposed restoration models have edge-preserving performance superior to that of the traditional restoration model. Two algorithms have been proposed on the basis of the harmonic restoration model and the total variation model. Experimental results show that the proposed algorithms are more effective than the traditional algorithm.

Channel Assignment for Cellular Networks Based on a Local Modified Hopfield Neural Network

In this paper, we propose a modified discrete Hopfield neural networks algorithm for the channel assignment problem. In opposition to previous work, we tried to apply the optimization locally on a per cell basis in order to reduce the CPU processing time and decrease the designed system complexity while obtaining a near-optimum solution. In addition, the research is extended to study the algorithm performance in a more realistic cellular system where the number of requested channels is continuously changing with time. In this paper, the channel assignment problem is formulated as an energy function which is at its minimum when all the defined compatibility constraints are satisfied and the assigned channel number (ACN) is equal to the requested channel number (RCN) in each cell.

Image restoration using variational PDE-based neural network

In this paper we present two novel image restoration algorithms based on a modified Hopfield neural network and variational partial differential equations (PDE). The first algorithm is based on a harmonic model and the other is based on a total variation model. Both algorithms can restore the degraded images and preserve the edges. The experimental results show that our algorithms are better than other known neural network-based restoration algorithms, especially when images mainly consist of edges, such as letters.

A Particle Swarm Optimization for Economic Dispatch With Nonsmooth Cost Functions

This work presents a new approach to economic dispatch (ED) problems with nonsmooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. A modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. A constraint treatment mechanism is devised in such a way that the dynamic process inherent in the conventional PSO is preserved. Moreover, a dynamic search-space reduction strategy is devised to accelerate the optimization process. To show its efficiency and effectiveness, the proposed MPSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost functions considering valve-point effects and multi-fuel problems. The results of the MPSO are compared with the results of conventional numerical methods, Tabu search method, evolutionary programming approaches, genetic algorithm, and modified Hopfield neural network approaches.