An Input Weights Dependent Complex-Valued Learning Algorithm Based on Wirtinger Calculus

2021 ◽  
pp. 1-13
Author(s):  
Yi-Fei Pu ◽  
Xuetao Xie ◽  
Jinde Cao ◽  
Hua Chen ◽  
Kai Zhang ◽  
...  
Keyword(s):  
Learning Algorithm ◽  
Wirtinger Calculus ◽  
Complex Valued

scholarly journals A MLMVN with Arbitrary Complex-Valued Inputs and a Hybrid Testability Approach for the Extraction of Lumped Models Using FRA

2019 ◽  
Vol 9 (1) ◽  
pp. 5-19 ◽  
Author(s):  
Igor Aizenberg ◽  
Antonio Luchetta ◽  
Stefano Manetti ◽  
Maria Cristina Piccirilli
Keyword(s):  
Neural Network ◽  
Frequency Response ◽  
Learning Algorithm ◽  
Repeated Measurements ◽  
Distributed Parameter ◽  
Response Analysis ◽  
Frequency Response Analysis ◽  
Arbitrary Complex ◽  
Lumped Models ◽  
Complex Valued

Abstract A procedure for the identification of lumped models of distributed parameter electromagnetic systems is presented in this paper. A Frequency Response Analysis (FRA) of the device to be modeled is performed, executing repeated measurements or intensive simulations. The method can be used to extract the values of the components. The fundamental brick of this architecture is a multi-valued neuron (MVN), used in a multilayer neural network (MLMVN); the neuron is modified in order to use arbitrary complex-valued inputs, which represent the frequency response of the device. It is shown that this modification requires just a slight change in the MLMVN learning algorithm. The method is tested over three completely different examples to clearly explain its generality.

A new learning algorithm with logarithmic performance index for complex-valued neural networks

2009 ◽  
Vol 72 (16-18) ◽  
pp. 3771-3781 ◽  
Author(s):  
R. Savitha ◽  
S. Suresh ◽  
N. Sundararajan ◽  
P. Saratchandran
Keyword(s):  
Neural Networks ◽  
Performance Index ◽  
Learning Algorithm ◽  
New Learning ◽  
Complex Valued

Recurrent Neural Adaptive Control of Nonlinear Oscillatory Systems Using a Complex-valued Levenberg-Marquardt Learning Algorithm

2015 ◽  
Vol 13 (1-2) ◽  
pp. 10-24
Author(s):  
Ieroham Baruch ◽  
Edmundo P. Reynaud
Keyword(s):  
Adaptive Control ◽  
Learning Algorithm ◽  
Back Propagation ◽  
Neural Adaptive Control ◽  
Oscillatory Systems ◽  
Control Schemes ◽  
Levenberg Marquardt ◽  
Gradient Based ◽  
Adaptive Neural Controller ◽  
Complex Valued

Abstract In this work, a Recursive Levenberg-Marquardt learning algorithm in the complex domain is developed and applied in the training of two adaptive control schemes composed by Complex-Valued Recurrent Neural Networks. Furthermore, we apply the identification and both control schemes for a particular case of nonlinear, oscillatory mechanical plant to validate the performance of the adaptive neural controller and the learning algorithm. The comparative simulation results show the better performance of the newly proposed Complex-Valued Recursive Levenberg-Marquardt learning algorithm over the gradient-based recursive Back-propagation one.

COMPLEX-VALUED MINIMAL RESOURCE ALLOCATION NETWORK FOR NONLINEAR SIGNAL PROCESSING

2000 ◽  
Vol 10 (02) ◽  
pp. 95-106 ◽  
Author(s):  
JIANPING DENG ◽  
N. SUNDARARAJAN ◽  
P. SARATCHANDRAN
Keyword(s):  
Resource Allocation ◽  
Signal Processing ◽  
Communication Systems ◽  
Learning Algorithm ◽  
Nonlinear Signal Processing ◽  
Hidden Neurons ◽  
Nonlinear Signal ◽  
Complex Valued ◽  
Complex Channel ◽  
Minimal Resource

This paper presents a sequential learning algorithm and evaluates its performance on complex valued signal processing problems. The algorithm is referred to as Complex Minimal Resource Allocation Network (CMRAN) algorithm and it is an extension of the MRAN algorithm originally developed for online learning in real valued RBF networks. CMRAN has the ability to grow and prune the (complex) RBF network's hidden neurons to ensure a parsimonious network structure. The performance of the learning algorithm is illustrated using two applications from signal processing of communication systems. The first application considers identification of a nonlinear complex channel. The second application considers the use of CMRAN to QAM digital channel equalization problems. Simulation results presented clearly show that CMRAN is very effective in modeling and equalization with performance achieved often being superior to that of some of the well known methods.

A FULLY COMPLEX-VALUED RADIAL BASIS FUNCTION NETWORK AND ITS LEARNING ALGORITHM

2009 ◽  
Vol 19 (04) ◽  
pp. 253-267 ◽  
Author(s):  
R. SAVITHA ◽  
S. SURESH ◽  
N. SUNDARARAJAN
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Radial Basis Function Network ◽  
Activation Function ◽  
Rbf Network ◽  
Practical Applications ◽  
Xor Problem ◽  
Radial Basis ◽  
Complex Valued

In this paper, a fully complex-valued radial basis function (FC-RBF) network with a fully complex-valued activation function has been proposed, and its complex-valued gradient descent learning algorithm has been developed. The fully complex activation function, sech(.) of the proposed network, satisfies all the properties needed for a complex-valued activation function and has Gaussian-like characteristics. It maps Cn → C, unlike the existing activation functions of complex-valued RBF network that maps Cn → R. Since the performance of the complex-RBF network depends on the number of neurons and initialization of network parameters, we propose a K-means clustering based neuron selection and center initialization scheme. First, we present a study on convergence using complex XOR problem. Next, we present a synthetic function approximation problem and the two-spiral classification problem. Finally, we present the results for two practical applications, viz., a non-minimum phase equalization and an adaptive beam-forming problem. The performance of the network was compared with other well-known complex-valued RBF networks available in literature, viz., split-complex CRBF, CMRAN and the CELM. The results indicate that the proposed fully complex-valued network has better convergence, approximation and classification ability.

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