Multi-valued Neural Network Research Articles

Frequency Characterization of Medium Voltage Cables for Fault Prevention Through Multi-Valued Neural Networks and Power Line Communication Technologies

Frequency Characterization of Medium Voltage Cables for Fault Prevention Through Multi-Valued Neural Networks and Power Line Communication Technologies

Correction to: Multi-valued neural networks I: a multi-valued associative memory

Here we provide a corrigendum on Theorem 2 to Article Title: Multi-Valued Neural Networks I: A Multi-Valued Associative Memory. https://doi.org/10.1007/s00521-021-05781-6.

A note on the complex and bicomplex valued neural networks

In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued neural networks (BMVNNs) and other important results in the theory of neural networks based on a bicomplex algebra.

Artificial Neural Network for Dimensionality Reduction and Its Application to Microwave Filters Inverse Modeling

The purpose of filters’ inverse modeling is to acquire the values of physical or geometrical parameters for the specified electrical response. In this article, a dimensionality reduction (DR) strategy is proposed through the artificial neural network (ANN) approach, for the first time, to simplify the filters’ inverse modeling. First, all physical/geometrical variables are divided into two parts, partial variables and other ones, through a selection mechanism, and only partial variables are to be determined in the inverse modeling solution. Then, an ANN for DR (DR-ANN) is constructed to form the relationship between partial variables and other ones for given electrical response. Third, the predicted partial variables are set as known input and then run the DR-ANN to acquire the value of remaining variables. The proposed DR-ANN framework can be easily introduced to many existing inverse modeling problems. Specifically, a multivalued neural network approach and a well-known differential evolutional (DE) optimization method are combined with DR-ANN. The improvement of the modified methods is demonstrated with some examples, including coupling matrix extraction and waveguide filter optimization. The experiment results show that the proposed solution is more robust with faster convergence in comparison with existing methods.

An Effective Antenna Array Diagnosis Method via Multivalued Neural Network Inverse Modeling Approach

Failure of element (s) in antenna arrays impair (s) symmetry and lead to unwanted distorted radiation pattern. The replacement of defective elements in aircraft antennas is a solution to the problem, but it remains a critical problem in space stations. In this paper, an antenna array diagnosis technique based on multivalued neural network (mNN) inverse modeling is proposed. Since inverse analytical input-to-output formulation is generally a challenging and important task in solving the inverse problem of array diagnosis, ANN is a compelling alternative, because it is trainable and learns from data in inverse modelling. The mNN technique proposed is an inverse modelling technique, which accommodates measurements for output model. This network takes radiation pattern samples with faults and matches it to the corresponding position or location of the faulty elements in that antenna array. In addition, we develop a new training error function, which focuses on the matching of each training sample by a value of our proposed inverse model, while the remaining values are free, and trained to match distorted radiation patterns. Thereby, mNN learns all training data by redirecting the faulty elements patterns into various values of the inverse model. Therefore, mNN is able to perform accurate array diagnosis in an automated and simpler manner.

Multi-valued neural networks I: a multi-valued associative memory

A new concept of a multi-valued associative memory is introduced, generalizing a similar one in fuzzy neural networks. We expand the results on fuzzy associative memory with thresholds, to the case of a multi-valued one: we introduce the novel concept of such a network without number representation of weights and data, investigate its properties, and give a learning algorithm in the multi-valued case. We discovered conditions under which it is possible to store given pairs of network variable patterns in such a multi-valued associative memory. In the multi-valued neural network, not all variables are numbers, but elements or subsets of a lattice, i.e., they are all only partially ordered. Lattice operations are used to build the network output by inputs. In this paper, the lattice is assumed to be Brouwer and determines the implication used, together with other lattice operations, to determine the neural network output. We give the example of the network use to classify aircraft/spacecraft trajectories.

Multi-Valued Neural Networks II: A Robot Group Control

For the new concept of a multi-valued neural network introduced earlier, an analogue of the T-norm in fuzzy mathematics is considered. In the multi-valued neural network, all variables are elements of the lattice of linguistic variables, i.e., they are all only partially-ordered. The lattice operations are used to build the network output by inputs. However, a lattice elements' multiplication may also be used to determine such operations in the case when not all of them are allowed by the lattice construction. In this paper, the lattice is assumed to be residuated, and the residual construction gives the analogue of a T-norm. The lattice elements' multiplication determines the implication which is used, together with other lattice operations, in output determining of the neural network. Though, such a construction determines a multi-valued associative memory similar to the Brouwer lattice case considered earlier, this variant is more natural to use in the Kohonen-like networks that we demonstrate with the example of a robot group management.

Multivalued Neural Network Inverse Modeling and Applications to Microwave Filters

This paper presents a new technique for artificial neural network (ANN) inverse modeling and applications to microwave filters. In inverse modeling of a microwave component, the inputs to the model are electrical parameters such as $S$ -parameters, and the outputs of the model are geometrical or physical parameters. Since the analytical formula of the inverse input–output relationship does not exist, the ANN becomes a logical choice, because it can be trained to learn from the data in inverse modeling. The main challenge of inverse modeling is the nonuniqueness problem. This problem in the ANN inverse modeling is that different training samples with the same or very similar input values have quite different (contradictory) output values (multivalued solutions). In this paper, we propose a multivalued neural network inverse modeling technique to associate a single set of electrical parameters with multiple sets of geometrical or physical parameters. One set of geometrical or physical parameters is called one value of our proposed inverse model. Our proposed multivalued neural network is structured to accommodate multiple values for the model output. We also propose a new training error function to focus on matching each training sample using only one value of our proposed inverse model, while other values are free and can be trained to match other contradictory samples. In this way, our proposed multivalued neural network can learn all the training data by automatically redirecting contradictory information into different values of the proposed inverse model. Therefore, our proposed technique can solve the nonuniqueness problem in a simpler and more automated way compared with the existing ANN inverse modeling techniques. This technique is illustrated by inverse modeling and parameter extraction of four microwave filter examples.

Introducing quaternion multi-valued neural networks with numerical examples

This paper introduces a new quaternion multi-valued neural network architecture and demonstrates its potential with numerical examples of multi-channel prediction and classification. A variety of real-valued learning structures have been introduced in prior literature; an important example is the multilayer perceptron neural network, which forms the underlying basis for modern deep learning architectures. However, in multidimensional information processing problems, real-valued learning structures perform suboptimally due to distortion of inter-channel relationships. A natural way to represent multidimensional data is using quaternions, a four-dimensional associative normed division algebra over the real numbers that allows for the multiplication and division of points in three-dimensional space. This paper introduces quaternion multi-valued neural networks, which perform nonlinear operations on the three-dimensional phase of quaternion data points. As shown with two numerical examples, the proposed quaternion multi-valued neural network outperforms existing learning structures, particularly in cases where limited training data is available.

Multi-Valued Quantization Neural Networks toward Hardware Implementation

Multi-Valued Quantization Neural Networks toward Hardware Implementation

New stability condition for discrete-time fully coupled neural networks with multivalued neurons

This paper discusses the stability condition for discrete-time multi-valued recurrent neural networks (MVNRNNs) in asynchronous update mode. In the existing research literature, an MVNRNN in asynchronous update mode has been found convergent if its weight matrix is Hermitian with nonnegative diagonal entries. However, our finding has been that the weight matrix with zero diagonal entries cannot guarantee the network stability. Furthermore, the new stability condition and proof is offered to allow diagonal entries to be complex-valued, which extends previous theoretical result. Simulation results are used to illustrate the theory.

System identification and modelling based on a double modified multi-valued neural network

A novel identification technique for the extraction of lumped circuit models of general distributed or stray devices is presented. The approach is based on two multi-valued neuron neural networks used in a joined architecture able to extract hidden parameters. The convergence allows the validation of the approximated lumped model and the extraction of the correct values. The inputs of the neural network are the geometrical parameters of a given structure, while the outputs represent the estimation of the lumped circuit parameters. The method uses a frequency response analysis approach in order to elaborate the data to present to the net.

A new multi-valued neural network for the extraction of lumped models of analog circuits

A novel identification technique for lumped models of general distributed circuits (i.e. microwave transmission lines, monolithic integrated circuits and filters) is presented. The approach is based on a hybrid multi-valued neuron neural network with a modified layer and learning process, whose convergence allows the validation of the approximated lumped model. The modified layer is generated by symbolic analysis of the model under exam. The inputs of the neural network are geometrical parameters, while the outputs represent the estimation of the lumped circuit parameters.

A New Multivalued Neural Network for Isomorphism Identification of Kinematic Chains

A lot of methods have been proposed for the kinematic chain isomorphism problem. However, the tool is still needed in building intelligent systems for product design and manufacturing. In this paper, we design a novel multivalued neural network that enables a simplified formulation of the graph isomorphism problem. In order to improve the performance of the model, an additional constraint on the degree of paired vertices is imposed. The resulting discrete neural algorithm converges rapidly under any set of initial conditions and does not need parameter tuning. Simulation results show that the proposed multivalued neural network performs better than other recently presented approaches.

A New Family of Multivalued Networks

This paper introduces a new family of multivalued neural networks. We have interpreted the Hopfield network as encoding the same/different information of elements of binary patterns in the connections and developed a scheme which encodes bigger/smaller information of multivalued patterns in the connections with the aid of signum function. The model can be constructed as an autoassociative memory (multivalued counterpart of Hopfield) or heteroassociative memory (multivalued counterpart of BAM). We have used Lyapunov stability analysis in showing the stability of networks. In simulations the energy surface topography of the model is compared to that of Hopfield. Also, asymptotic stability and basin of attraction of the stored patterns are examined. The proposed model can also be used in solving the optimization problems. Mapping a problem on to the network is relatively easy compared to the Hopfield model because of the multivalued representation. Very good results are obtained in traveling salesperson problem simulations. Copyright © 1996 Elsevier Science Ltd.