In this paper, we propose a new scheme which uses blind detection algorithm for recovering the conventional user signal in a system which the sporadic machine-to-machine (M2M) communication share the same spectrum with the conventional user. Compressive sensing techniques are used to estimate the M2M devices signals. Based on the Hopfield neural network (HNN), the blind detection algorithm is used to recover the conventional user signal. The simulation results show that the conventional user signal can be effectively restored under an unknown channel. Compared with the existing methods, such as using the training sequence to estimate the channel in advance, the blind detection algorithm used in this paper with no need for identifying the channel, and can directly detect the transmitted signal blindly.

Quaternionic neural networks are extensions of neural networks using quaternion algebra. 3-D and 4-D quaternionic MLPs have been studied. 3-D quaternionic neural networks are useful for handling 3-D objects, such as Euclidean transformation. As for Hopfield neural networks, only 4-D quaternionic Hopfield neural networks (QHNNs) have been studied. In this work, we propose the 3-D QHNNs. Moreover, we define the energy, and prove that it converges.

In recent years, applications of neural networks with Clifford algebra have become widespread. Hyperbolic numbers are useful Clifford algebra to deal with hyperbolic geometry. It is difficult when Hopfield neural network is extended to hyperbolic versions, though several models have been proposed. Multistate or continuous hyperbolic Hopfield neural networks are promising models. However, the connection weights and domain of activation function are limited to the right quadrant of hyperbolic plane, and the learning algorithms are restricted. In this work, the connection weights and activation function are extended to the entire hyperbolic plane. In addition, the energy is defined and it is proven that the energy does not increase.

In recent years, applications of complex-valued neural networks have become wide spread. Quaternions are an extension of complex numbers, and neural networks with quaternions have been proposed. Because quaternion algebra is non-commutative algebra, we can consider two orders of multiplication to calculate weighted input. However, both orders provide almost the same performance. We propose hybrid quaternionic Hopfield neural networks, which have both orders of multiplication. Using computer simulations, we show that these networks outperformed conventional quaternionic Hopfield neural networks in noise tolerance. We discuss why hybrid quaternionic Hopfield neural networks improve noise tolerance from the standpoint of rotational invariance.

In this letter, a neural network (NN) for peak power reduction of an orthogonal frequency-division multiplexing (OFDM) signal is improved in order to suppress its computational complexity. Numerical experiments show that the amount of IFFTs in the proposed NN can be reduced to half, and its computational time can be reduced by 21.5% compared with a conventional NN. In comparison with the SLM, the proposed NN is effective to achieve high PAPR reduction and it has an advantage over the SLM under the equal computational condition.

This paper is intended to provide an alternative approach for the design of FIR filters by using a Hopfield Neural Network (HNN). The proposed approach establishes the error function between the amplitude response of the desired FIR filter and the designed one as a Lyapunov energy function to find the HNN parameters. Using the framework of HNN, the optimal filter coefficients can be obtained from the output state of the network. With the advantages of local connectivity, regularity and modularity, the architecture of the proposed approach can be applied to the design of differentiators and Hilbert transformer with significantly reduction of computational complexity and hardware cost. As the simulation results illustrate, the proposed neural-based method is capable of achieving an excellent performance for filter design.

In this paper, we present a hill-shift learning method of the Hopfield neural network for bipartite subgraph problem. The method uses the Hopfield neural network to get a near-maximum bipartite subgraph, and shifts the local minimum of energy function by adjusts the balance between two terms in the energy function to help the network escape from the state of the near-maximum bipartite subgraph to the state of the maximum bipartite subgraph or better one. A large number of instances are simulated to verify the proposed method with the simulation results showing that the solution quality is superior to that of best existing parallel algorithm.

Both the Hopfield network and the genetic algorithm are powerful tools for object recognition tasks, e.g., subgraph matching problems. Unfortunately, they both have serious drawbacks. The Hopfield network is very sensitive to its initial state, and it stops at a local minimum if the initial state is not properly given. The genetic algorithm, on the other hand, usually only finds a near-global solution, and it is time-consuming for large-scale problems. In this paper, we propose an integrated scheme of these two methods, while eliminating their drawbacks and keeping their advantages, to solve object recognition problems under affine transformations. Some arrangements and programming strategies are required. First, we use some specialized 2-D genetic algorithm operators to accelerate the convergence. Second, we extract the "seeds" of the solution of the genetic algorithm to serve as the initial state of the Hopfield network. This procedure further improves the efficiency of the system. In addition, we also include several pertinent post matching algorithms for refining the accuracy and robustness. In the examples, the proposed scheme is used to solve some subgraph matching problems with occlusions under affine transformations. As shown by the results, this integrated scheme does outperform many counterpart algorithms in accuracy, efficiency, and stability.

We present a learning algorithm of the Hopfield neural network for minimizing edge crossings in linear drawings of nonplanar graphs. The proposed algorithm uses the Hopfield neural network to get a local optimal number of edge crossings, and adjusts the balance between terms of the energy function to make the network escape from the local optimal number of edge crossings. The proposed algorithm is tested on a variety of graphs including some "real word" instances of interconnection networks. The proposed learning algorithm is compared with some existing algorithms. The experimental results indicate that the proposed algorithm yields optimal or near-optimal solutions and outperforms the compared algorithms.

In this paper color image compression using a fuzzy Hopfield-model net based on rough-set reasoning is created to generate optimal codebook based on Vector Quantization (VQ) in Discrete Wavelet Transform (DWT). The main purpose is to embed rough-set learning scheme into the fuzzy Hopfield network to construct a compression system named Rough Fuzzy Hopfield Net (RFHN). First a color image is decomposed into 3-D pyramid structure with various frequency bands. Then the RFHN is used to create different codebooks for various bands. The energy function of RFHN is defined as the upper- and lower-bound fuzzy membership grades between training samples and codevectors. Finally, near global-minimum codebooks in frequency domain can be obtained when the energy function converges to a stable state. Therefore, only 32/N pixels are selected as the training samples if a 3N-dimensional color image was used. In the simulation results, the proposed network not only reduces the consuming time but also preserves the compression performance.

A near-optimum parallel algorithm for bipartite subgraph problem using gradient ascent learning algorithm of the Hopfield neural networks is presented. This parallel algorithm, uses the Hopfield neural network updating to get a near-maximum bipartite subgraph and then performs gradient ascent learning on the Hopfield network to help the network escape from the state of the near-maximum bipartite subgraph until the state of the maximum bipartite subgraph or better one is obtained. A large number of instances have been simulated to verify the proposed algorithm, with the simulation result showing that our algorithm finds the solution quality is superior to that of best existing parallel algorithm. We also test the proposed algorithm on maximum cut problem. The simulation results also show the effectiveness of this algorithm.

In this paper, a discrete-time convergence theorem for continuous-state Hopfield networks with self-interaction neurons is proposed. This theorem differs from the previous work by Wang in that the original updating rule is maintained while the network is still guaranteed to monotonically decrease to a stable state. The relationship between the parameters in a typical class of energy functions is also investigated, and consequently a "guided trial-and-error" technique is proposed to determine the parameter values. The third problem discussed in this paper is the post-processing of outputs, which turns out to be rather important even though it never attracts enough attention. The effectiveness of all the theorems and post-processing methods proposed in this paper is demonstrated by a large number of computer simulations on the assignment problem and the N-queen problem of different sizes.

In this paper we show that the neuron filter is effective for relaxing the coefficient sensitiveness of the Hopfield neural network for combinatorial optimization problems. Since the parameters in motion equation have a significant influence on the performance of the neural network, many studies have been carried out to support determining the value of the parameters. However, not a few researchers have determined the value of the parameters experimentally yet. We show that the use of the neuron filter is effective for the parameter tuning, particularly for determining their values experimentally through simulations.

A gradient ascent learning algorithm of the Hopfield neural networks for graph planarization is presented. This learning algorithm uses the Hopfield neural network to get a near-maximal planar subgraph, and increases the energy by modifying parameters in a gradient ascent direction to help the network escape from the state of the near-maximal planar subgraph to the state of the maximal planar subgraph or better one. The proposed algorithm is applied to several graphs up to 150 vertices and 1064 edges. The performance of our algorithm is compared with that of Takefuji/Lee's method. Simulation results show that the proposed algorithm is much better than Takefuji/Lee's method in terms of the solution quality for every tested graph.

Most scheduling applications have been classified into NP-complete problems. This fact implies that an optimal solution for a large scheduling problem is extremely time-consuming. A number of schemes are introduced to solve NP-complete scheduling applications, such as linear programming, neural network, and fuzzy logic. In this paper, we demonstrate a new approach, fuzzy Hopfield neural network, to solve the scheduling problems. This fuzzy Hopfield neural network approach integrates fuzzy c-means clustering strategies into a Hopfield neural network. In this investigation, we utilizes this new approach to demonstrate the feasibility of resolving a multiprocessor scheduling problem with no process migration, limited resources and constrained times (execution time and deadline). In the approach, the process and processor of the scheduling problem can be regarded as a data sample and a cluster, respectively. Then, an appropriate Lyapunov energy function is derived correspondingly. The scheduling results can be obtained using a fuzzy Hopfield neural network clustering technique by iteratively updating fuzzy state until the energy function gets minimized. To validate our approach, three scheduling cases for different initial neuron states as well as fuzzification parameters are taken as testbed. Simulation results reveal that imposing the fuzzy Hopfield neural network on the proposed energy function provides a sound approach in solving this class of scheduling problems.

This paper describes the application of an unsupervised parallel approach called the Annealed Hopfield Neural Network (AHNN) using a modified cost function with moment and entropy preservation for magnetic resonance image (MRI) classification. In the AHNN, the neural network architecture is same as the original 2-D Hopfield net. And a new cooling schedule is embedded in order to make the modified energy function to converge to an equilibrium state. The idea is to formulate a clustering problem where the criterion for the optimum classification is chosen as the minimization of the Euclidean distance between training vectors and cluster-center vectors. In this article, the intensity of a pixel in an original image, the first moment combined with its neighbors, and their gray-level entropy are used to construct a 3-component training vector to map a neuron into a two-dimensional annealed Hopfield net. Although the simulated annealing method can yield the global minimum, it is very time-consuming with asymptotic iterations. In addition, to resolve the optimal problem using Hopfield or simulated annealing neural networks, the weighting factors to combine the penalty terms must be determined. The quality of final result is very sensitive to these weighting factors, and feasible values for them are difficult to find. Using the AHNN for magnetic resonance image classification, the need of finding weighting factors in the energy function can be eliminated and the rate of convergence is much faster than that of simulated annealing. The experimental results show that better and more valid solutions can be obtained using the AHNN than the previous approach in classification of the computer generated images. Promising solutions of MRI segmentation can be obtained using the proposed method. In addition, the convergence rates with different cooling schedules in the test phantom will be discussed.

A method to recognize planar objects undergoing affine transformation is proposed in this paper. The method is based upon wavelet multiscale features and Hopfield neural networks. The feature vector consists of the multiscale wavelet transformed extremal evolution. The evolution contains the information of the contour primitives in a multiscale manner, which can be used to discriminate dominant points, hence a good initial state of the Hopfield network can be obtained. Such good initiation enables the network to converge more efficiently. A wavelet normalization scheme was applied to make our method scale invariant and to reduce the distortion resulting from normalizing the object contours. The Hopfield neural network was employed as a global processing mechanism for feature matching and made our method suitable to recognize planar objects whose shape distortion arising from an affine transformation. The Hopfield network was improved to guarantee unique and more stable matching results. A new matching evaluation scheme, which is computationally efficient, was proposed to evaluate the goodness of matching. Two sets of images, noiseless and noisy industrial tools, undergoing affine transformation were used to test the performance of the proposed method. Experimental results showed that our method is not only effective and robust under affine transformation but also can limit the effect of noises.

In our current work, we attempt to make an automatic diagnostic system of lung cancer based on the analysis of the sputum color images. In order to form general diagnostic rules, we have collected a database with thousands of sputum color images from normal and abnormal subjects. As a first step, in this paper, we present a segmentation method of sputum color images prepared by the Papanicalaou standard staining method. The segmentation is performed based on an energy function minimization using an unsupervised Hopfield neural network (HNN). This HNN have been used for the segmentation of magnetic resonance images (MRI). The results have been acceptable, however the method have some limitations due to the stuck of the network in an early local minimum because the energy landscape in general has more than one local minimum due to the nonconvex nature of the energy surface. To overcome this problem, we have suggested in our previous work some contributions. Similarly to the MRI images, the color images can be considered as multidimensional data as each pixel is represented by its three components in the RGB image planes. To the input of HNN we have applied the RGB components of several sputum images. However, the extreme variations in the gray-levels of the images and the relative contrast among nuclei due to unavoidable staining variations among individual cells, the cytoplasm folds and the debris cells, make the segmentation less accurate and impossible its automatization as the number of regions is difficult to be estimated in advance. On the other hand, the most important objective in processing cell clusters is the detection and accurate segmentation of the nuclei, because most quantitative procedures are based on measurements of nuclear features. For this reason, based on our collected database of sputum color images, we found an algorithm for NonSputum cell masking. Once these masked images are determined, they are given, with some of the RGB components of the raw image, to the input of HNN to make a crisp segmentation by assigning each pixel to label such as Background, Cytoplasm, and Nucleus. The proposed technique has yielded correct segmentation of complex scene of sputum prepared by ordinary manual staining method in most of the tested images selected from our database containing thousands of sputum color images.

A novel method is presented for designing discrete coeffcient FIR linear phase filters using Hopfield neural networks. The proposed method is based on the minimization of the energy function of Hopfield neural networks. In the proposed method, the optimal solution for each filter gain factor is first searched for, then the optimal filter gain factor is selected. Therefore, a good solution in the specified criterion can be obtained. The feature of the proposed method is that it can be used to design FIR linear phase filters with different criterions simultaneously. A design example is presented to demonstrate The effectiveness of the proposed method.

In case of object recognition using 3-D configuration data, the scale and poses of the object are important factors. If they are not known, we can not compare the object with the models in the database. Hence we propose a strategy for object recognition independently of its scale and poses, which is based on Hopfield neural network. And we also propose a strategy for estimation of the camera motion to reconstruct 3-D configuration of the object. In this strategy, the camera motion is estimated only with the sequential images taken by a moving camera. Consequently, the 3-D configuration of the object is reconstructed only with the sequential images. And we adopt the multiple regression analysis for estimation of the camera motion parameters so as to reduce the errors of them.