Rainfall Estimation Using Neuron-Adaptive Higher Order Neural Networks

2021 ◽  
pp. 375-414
Keyword(s):  
Neural Network ◽  
High Frequency ◽  
Network Models ◽  
Higher Order ◽  
Rainfall Estimation ◽  
Neural Network Models ◽  
Real World Data ◽  
Higher Order Neural Networks ◽  
Optimum Model ◽  
Discontinuous Data

Real-world data is often nonlinear, discontinuous, and may comprise high frequency, multi-polynomial components. Not surprisingly, it is hard to find the best models for modeling such data. Classical neural network models are unable to automatically determine the optimum model and appropriate order for data approximation. In order to solve this problem, neuron-adaptive higher order neural network (NAHONN) models have been introduced. Definitions of one-dimensional, two-dimensional, and n-dimensional NAHONN models are studied. Specialized NAHONN models are also described. NAHONN models are shown to be “open box.” These models are further shown to be capable of automatically finding not only the optimum model but also the appropriate order for high frequency, multi-polynomial, discontinuous data. Rainfall estimation experimental results confirm model convergence. The authors further demonstrate that NAHONN models are capable of modeling satellite data.

Models of Artificial Multi-Polynomial Higher Order Neural Networks

2021 ◽  
pp. 97-136
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Real World ◽  
Network Models ◽  
Higher Order ◽  
Neural Network Models ◽  
Real World Data ◽  
World Data ◽  
Higher Order Neural Networks ◽  
Improved Accuracy

This chapter introduces multi-polynomial higher order neural network models (MPHONN) with higher accuracy. Using Sun workstation, C++, and Motif, a MPHONN simulator has been built. Real-world data cannot always be modeled simply and simulated with high accuracy by a single polynomial function. Thus, ordinary higher order neural networks could fail to simulate complicated real-world data. But MPHONN model can simulate multi-polynomial functions and can produce results with improved accuracy through experiments. By using MPHONN for financial modeling and simulation, experimental results show that MPHONN can always have 0.5051% to 0.8661% more accuracy than ordinary higher order neural network models.

Models of Artificial Higher Order Neural Networks

2021 ◽  
pp. 1-96
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
High Frequency ◽  
Learning Algorithm ◽  
Network Models ◽  
Higher Order ◽  
Neural Network Models ◽  
Ultra High Frequency ◽  
Higher Order Neural Networks

This chapter introduces the background of the higher order neural network (HONN) model developing history and overviews 24 applied artificial higher order neural network models. This chapter provides 24 HONN models and uses a single uniform HONN architecture for all 24 HONN models. This chapter also uses a uniform learning algorithm for all 24 HONN models and uses uniform weight update formulae for all 24 HONN models. In this chapter, polynomial HONN, Trigonometric HONN, Sigmoid HONN, SINC HONN, and Ultra High Frequency HONN structure and models are overviewed too.

Artificial Multi-Polynomial Higher Order Neural Network Models

2013 ◽  
pp. 1-29 ◽  
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
Real World ◽  
Network Models ◽  
Higher Order ◽  
Polynomial Functions ◽  
Neural Network Models ◽  
Real World Data ◽  
World Data ◽  
Higher Order Neural Networks ◽  
Improved Accuracy

This chapter introduces Multi-Polynomial Higher Order Neural Network (MPHONN) models with higher accuracy. Using Sun workstation, C++, and Motif, a MPHONN Simulator has been built. Real world data cannot always be modeled simply and simulated with high accuracy by a single polynomial function. Thus, ordinary higher order neural networks could fail to simulate complicated real world data. However, the MPHONN model can simulate multi-polynomial functions, and can produce results with improved accuracy through experiments. By using MPHONN for financial modeling and simulation, experimental results show that MPHONN can always have 0.5051% to 0.8661% more accuracy than ordinary higher order neural network models.

Group Models of Artificial Polynomial and Trigonometric Higher Order Neural Networks

2021 ◽  
pp. 137-172
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Trigonometric Polynomial ◽  
Network Models ◽  
Higher Order ◽  
Financial Data ◽  
Neural Network Models ◽  
Higher Order Neural Networks ◽  
Piecewise Continuous ◽  
Discontinuous Data

Real-world financial data is often discontinuous and non-smooth. Neural network group models can perform this function with more accuracy. Both polynomial higher order neural network group (PHONNG) and trigonometric polynomial higher order neural network group (THONNG) models are studied in this chapter. These PHONNG and THONNG models are open box, convergent models capable of approximating any kind of piecewise continuous function, to any degree of accuracy. Moreover, they are capable of handling higher frequency, higher order nonlinear, and discontinuous data. Results confirm that PHONNG and THONNG group models converge without difficulty and are considerably more accurate (0.7542% - 1.0715%) than neural network models such as using polynomial higher order neural network (PHONN) and trigonometric polynomial higher order neural network (THONN) models.

Artificial Polynomial and Trigonometric Higher Order Neural Network Group Models

2013 ◽  
pp. 78-102 ◽  
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Continuous Function ◽  
Trigonometric Polynomial ◽  
Network Models ◽  
Higher Order ◽  
Financial Data ◽  
Neural Network Models ◽  
Piecewise Continuous ◽  
Discontinuous Data

Real world financial data is often discontinuous and non-smooth. Accuracy will be a problem, if we attempt to use neural networks to simulate such functions. Neural network group models can perform this function with more accuracy. Both Polynomial Higher Order Neural Network Group (PHONNG) and Trigonometric polynomial Higher Order Neural Network Group (THONNG) models are studied in this chapter. These PHONNG and THONNG models are open box, convergent models capable of approximating any kind of piecewise continuous function to any degree of accuracy. Moreover, they are capable of handling higher frequency, higher order nonlinear, and discontinuous data. Results obtained using Polynomial Higher Order Neural Network Group and Trigonometric polynomial Higher Order Neural Network Group financial simulators are presented, which confirm that PHONNG and THONNG group models converge without difficulty, and are considerably more accurate (0.7542% - 1.0715%) than neural network models such as using Polynomial Higher Order Neural Network (PHONN) and Trigonometric polynomial Higher Order Neural Network (THONN) models.

Rainfall Estimation Using Neuron-Adaptive Higher Order Neural Networks

2010 ◽  
pp. 159-186 ◽  
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
High Frequency ◽  
Higher Order ◽  
Rainfall Estimation ◽  
Test Error ◽  
Artificial Neural ◽  
Training Error ◽  
Optimum Model ◽  
Artificial Neural Network Ann

Real world data is often nonlinear, discontinuous and may comprise high frequency, multi-polynomial components. Not surprisingly, it is hard to find the best models for modeling such data. Classical neural network models are unable to automatically determine the optimum model and appropriate order for data approximation. In order to solve this problem, Neuron-Adaptive Higher Order Neural Network (NAHONN) Models have been introduced. Definitions of one-dimensional, two-dimensional, and n-dimensional NAHONN models are studied. Specialized NAHONN models are also described. NAHONN models are shown to be “open box”. These models are further shown to be capable of automatically finding not only the optimum model but also the appropriate order for high frequency, multi-polynomial, discontinuous data. Rainfall estimation experimental results confirm model convergence. We further demonstrate that NAHONN models are capable of modeling satellite data. When the Xie and Scofield (1989) technique was used, the average error of the operator-computed IFFA rainfall estimates was 30.41%. For the Artificial Neural Network (ANN) reasoning network, the training error was 6.55% and the test error 16.91%, respectively. When the neural network group was used on these same fifteen cases, the average training error of rainfall estimation was 1.43%, and the average test error of rainfall estimation was 3.89%. When the neuron-adaptive artificial neural network group models was used on these same fifteen cases, the average training error of rainfall estimation was 1.31%, and the average test error of rainfall estimation was 3.40%. When the artificial neuron-adaptive higher order neural network model was used on these same fifteen cases, the average training error of rainfall estimation was 1.20%, and the average test error of rainfall estimation was 3.12%.

Financial Data Prediction by Artificial Sine and Cosine Trigonometric Higher Order Neural Networks

2021 ◽  
pp. 262-301
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Models ◽  
Higher Order ◽  
Financial Data ◽  
Data Simulation ◽  
Neural Network Models ◽  
Data Prediction ◽  
Higher Order Neural Networks

This chapter develops two new nonlinear artificial higher order neural network models. They are sine and sine higher order neural networks (SIN-HONN) and cosine and cosine higher order neural networks (COS-HONN). Financial data prediction using SIN-HONN and COS-HONN models are tested. Results show that SIN-HONN and COS-HONN models are good models for some sine feature only or cosine feature only financial data simulation and prediction compared with polynomial higher order neural network (PHONN) and trigonometric higher order neural network (THONN) models.

Artificial Higher Order Neural Network Models

2016 ◽  
pp. 241-311
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
High Frequency ◽  
Learning Algorithm ◽  
Network Models ◽  
Higher Order ◽  
Neural Network Models ◽  
Ultra High Frequency

This chapter introduces the background of HONN model developing history and overview 24 applied artificial higher order neural network models. This chapter provides 24 HONN models and uses a single uniform HONN architecture for ALL 24 HONN models. This chapter also uses a uniform learning algorithm for all 24 HONN models and uses a uniform weight update formulae for all 24 HONN models. In this chapter, Polynomial HONN, Trigonometric HONN, Sigmoid HONN, SINC HONN, and Ultra High Frequency HONN structure and models are overviewed too.

Artificial Sine and Cosine Trigonometric Higher Order Neural Networks for Financial Data Prediction

2016 ◽  
pp. 716-744
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Models ◽  
Higher Order ◽  
Financial Data ◽  
Neural Network Models ◽  
Data Prediction ◽  
Higher Order Neural Networks

This chapter develops two new nonlinear artificial higher order neural network models. They are Sine and Sine Higher Order Neural Networks (SIN-HONN) and Cosine and Cosine Higher Order Neural Networks (COS-HONN). Financial data prediction using SIN-HONN and COS-HONN models are tested. Results show that SIN-HONN and COS-HONN models are good models for financial data prediction compare with Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models.

Artificial Higher Order Neural Network Models

2016 ◽  
pp. 282-350
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
High Frequency ◽  
Learning Algorithm ◽  
Network Models ◽  
Higher Order ◽  
Neural Network Models ◽  
Ultra High Frequency

This chapter introduces the background of HONN model developing history and overview 24 applied artificial higher order neural network models. This chapter provides 24 HONN models and uses a single uniform HONN architecture for ALL 24 HONN models. This chapter also uses a uniform learning algorithm for all 24 HONN models and uses a uniform weight update formulae for all 24 HONN models. In this chapter, Polynomial HONN, Trigonometric HONN, Sigmoid HONN, SINC HONN, and Ultra High Frequency HONN structure and models are overviewed too.

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