scholarly journals Learning Dynamics of the Complex-Valued Neural Network in the Neighborhood of Singular Points

2014 ◽  
Vol 02 (01) ◽  
pp. 27-32 ◽  
Author(s):  
Tohru Nitta
Keyword(s):  
Neural Network ◽  
Singular Points ◽  
Learning Dynamics ◽  
Complex Valued

Learning Dynamics of a Single Polar Variable Complex-Valued Neuron

2015 ◽  
Vol 27 (5) ◽  
pp. 1120-1141 ◽  
Author(s):  
Tohru Nitta
Keyword(s):  
Computer Simulations ◽  
Gradient Descent ◽  
Phase Error ◽  
Descent Method ◽  
Singular Points ◽  
Polar Coordinates ◽  
Gradient Descent Method ◽  
Learning Dynamics ◽  
Polar Variable ◽  
Complex Valued

This letter investigates the characteristics of the complex-valued neuron model with parameters represented by polar coordinates (called polar variable complex-valued neuron). The parameters of the polar variable complex-valued neuron are unidentifiable. The plateau phenomenon can occur during learning of the polar variable complex-valued neuron. Furthermore, computer simulations suggest that a single polar variable complex-valued neuron has the following characteristics in the case of using the steepest gradient-descent method with square error: (1) unidentifiable parameters (singular points) degrade the learning speed and (2) a plateau can occur during learning. When the weight is attracted to the singular point, the learning tends to become stuck. However, computer simulations also show that the steepest gradient-descent method with amplitude-phase error and the complex-valued natural gradient method could reduce the effects of the singular points. The learning dynamics near singular points depends on the error functions and the training algorithms used.

scholarly journals An Approach for Sound Source Localization by Complex-Valued Neural Network

2013 ◽  
Vol E96.D (10) ◽  
pp. 2257-2265 ◽  
Author(s):  
Hirofumi TSUZUKI ◽  
Mauricio KUGLER ◽  
Susumu KUROYANAGI ◽  
Akira IWATA
Keyword(s):  
Neural Network ◽  
Source Localization ◽  
Sound Source ◽  
Sound Source Localization ◽  
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.

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