SAS Nonlinear Models or Artificial Higher Order Neural Network Nonlinear Models?

This chapter delivers general format of Higher Order Neural Networks (HONNs) for nonlinear data analysis and six different HONN models. This chapter mathematically proves that HONN models could converge and have mean squared errors close to zero. This chapter illustrates the learning algorithm with update formulas. HONN models are compared with SAS Nonlinear (NLIN) models and results show that HONN models are 3 to 12% better than SAS Nonlinear models. Moreover, this chapter shows how to use HONN models to find the best model, order and coefficients, without writing the regression expression, declaring parameter names, and supplying initial parameter values.

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Ultra High Frequency SINC and Trigonometric Higher Order Neural Networks for Data Classification

Advances in Computational Intelligence and Robotics - Applied Artificial Higher Order Neural Networks for Control and Recognition ◽

10.4018/978-1-5225-0063-6.ch005 ◽

2016 ◽

pp. 113-153 ◽

Cited By ~ 1

Author(s):

Ming Zhang

Keyword(s):

Neural Network ◽

Neural Networks ◽

Nonlinear Model ◽

High Frequency ◽

Data Classification ◽

Higher Order ◽

Ultra High Frequency ◽

Higher Order Neural Networks ◽

Better Than

This chapter develops a new nonlinear model, Ultra high frequency SINC and Trigonometric Higher Order Neural Networks (UNT-HONN), for Data Classification. UNT-HONN includes Ultra high frequency siNc and Sine Higher Order Neural Networks (UNS-HONN) and Ultra high frequency siNc and Cosine Higher Order Neural Networks (UNC-HONN). Data classification using UNS-HONN and UNC-HONN models are tested. Results show that UNS-HONN and UNC-HONN models are better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models, since UNS-HONN and UNC-HONN models can classify the data with error approaching 0.0000%.

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Models of Artificial Higher Order Neural Networks

Emerging Capabilities and Applications of Artificial Higher Order Neural Networks - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-7998-3563-9.ch001 ◽

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.

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Ultra High Frequency SINC and Trigonometric Higher Order Neural Networks for Data Classification

Nature-Inspired Computing ◽

10.4018/978-1-5225-0788-8.ch031 ◽

2016 ◽

pp. 789-829

Author(s):

Ming Zhang

Keyword(s):

Neural Network ◽

Neural Networks ◽

Nonlinear Model ◽

High Frequency ◽

Data Classification ◽

Higher Order ◽

Ultra High Frequency ◽

Higher Order Neural Networks ◽

Better Than

This chapter develops a new nonlinear model, Ultra high frequency SINC and Trigonometric Higher Order Neural Networks (UNT-HONN), for Data Classification. UNT-HONN includes Ultra high frequency siNc and Sine Higher Order Neural Networks (UNS-HONN) and Ultra high frequency siNc and Cosine Higher Order Neural Networks (UNC-HONN). Data classification using UNS-HONN and UNC-HONN models are tested. Results show that UNS-HONN and UNC-HONN models are better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models, since UNS-HONN and UNC-HONN models can classify the data with error approaching 0.0000%.

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Ultra High Frequency Trigonometric Higher Order Neural Networks for Time Series Data Analysis

Artificial Higher Order Neural Networks for Economics and Business ◽

10.4018/978-1-59904-897-0.ch007 ◽

2009 ◽

pp. 133-163 ◽

Cited By ~ 10

Author(s):

Ming Zhang

Keyword(s):

Neural Network ◽

Neural Networks ◽

Time Series ◽

Data Analysis ◽

Exchange Rates ◽

Time Series Data ◽

Higher Order ◽

Series Data ◽

Higher Order Neural Networks ◽

Time Series Data Analysis

This chapter develops a new nonlinear model, Ultra high frequency Trigonometric Higher Order Neural Networks (UTHONN), for time series data analysis. Results show that UTHONN models are 3 to 12% better than Equilibrium Real Exchange Rates (ERER) model, and 4 – 9% better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models. This study also uses UTHONN models to simulate foreign exchange rates and consumer price index with error approaching 0.0000%.

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Fundamentals of Higher Order Neural Networks for Modeling and Simulation

Artificial Higher Order Neural Networks for Modeling and Simulation ◽

10.4018/978-1-4666-2175-6.ch006 ◽

2013 ◽

pp. 103-133 ◽

Cited By ~ 13

Author(s):

Madan M. Gupta ◽

Ivo Bukovsky ◽

Noriyasu Homma ◽

Ashu M. G. Solo ◽

Zeng-Guang Hou

Keyword(s):

Neural Networks ◽

Modeling And Simulation ◽

Learning Algorithm ◽

Nonlinear Approximation ◽

Higher Order ◽

Higher Order Neural Networks ◽

High Dynamic ◽

Input Variables ◽

Continuous Dynamic

In this chapter, the authors provide fundamental principles of Higher Order Neural Units (HONUs) and Higher Order Neural Networks (HONNs) for modeling and simulation. An essential core of HONNs can be found in higher order weighted combinations or correlations between the input variables and HONU. Except for the high quality of nonlinear approximation of static HONUs, the capability of dynamic HONUs for the modeling of dynamic systems is shown and compared to conventional recurrent neural networks when a practical learning algorithm is used. In addition, the potential of continuous dynamic HONUs to approximate high dynamic order systems is discussed, as adaptable time delays can be implemented. By using some typical examples, this chapter describes how and why higher order combinations or correlations can be effective for modeling of systems.

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

Emerging Capabilities and Applications of Artificial Higher Order Neural Networks - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-7998-3563-9.ch006 ◽

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.

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Ultra High Frequency Sigmoid and Trigonometric Higher Order Neural Networks for Data Pattern Recognition

Advances in Computational Intelligence and Robotics - Applied Artificial Higher Order Neural Networks for Control and Recognition ◽

10.4018/978-1-5225-0063-6.ch004 ◽

2016 ◽

pp. 80-112 ◽

Cited By ~ 1

Author(s):

Ming Zhang

Keyword(s):

Neural Network ◽

Neural Networks ◽

Pattern Recognition ◽

Nonlinear Model ◽

High Frequency ◽

Higher Order ◽

Sine Function ◽

Ultra High Frequency ◽

Higher Order Neural Networks ◽

Cosine Functions

This chapter develops a new nonlinear model, Ultra high frequency siGmoid and Trigonometric Higher Order Neural Networks (UGT-HONN), for data pattern recognition. UGT-HONN includes Ultra high frequency siGmoid and Sine function Higher Order Neural Networks (UGS-HONN) and Ultra high frequency siGmoid and Cosine functions Higher Order Neural Networks (UGC-HONN). UGS-HONN and UGC-HONN models are used to recognition data patterns. Results show that UGS-HONN and UGC-HONN models are better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models, since UGS-HONN and UGC-HONN models to recognize data pattern with error approaching 0.0000%.

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Ultra High Frequency Sigmoid and Trigonometric Higher Order Neural Networks for Data Pattern Recognition

Nature-Inspired Computing ◽

10.4018/978-1-5225-0788-8.ch027 ◽

2016 ◽

pp. 682-715

Author(s):

Ming Zhang

Keyword(s):

Neural Network ◽

Neural Networks ◽

Pattern Recognition ◽

Nonlinear Model ◽

High Frequency ◽

Higher Order ◽

Sine Function ◽

Ultra High Frequency ◽

Higher Order Neural Networks ◽

Cosine Functions

This chapter develops a new nonlinear model, Ultra high frequency siGmoid and Trigonometric Higher Order Neural Networks (UGT-HONN), for data pattern recognition. UGT-HONN includes Ultra high frequency siGmoid and Sine function Higher Order Neural Networks (UGS-HONN) and Ultra high frequency siGmoid and Cosine functions Higher Order Neural Networks (UGC-HONN). UGS-HONN and UGC-HONN models are used to recognition data patterns. Results show that UGS-HONN and UGC-HONN models are better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models, since UGS-HONN and UGC-HONN models to recognize data pattern with error approaching 0.0000%.

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Data Pattern Recognition Based on Ultra-High Frequency Sigmoid and Trigonometric Higher Order Neural Networks

Emerging Capabilities and Applications of Artificial Higher Order Neural Networks - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-7998-3563-9.ch011 ◽

2021 ◽

pp. 455-497

Keyword(s):

Neural Network ◽

Neural Networks ◽

Pattern Recognition ◽

Nonlinear Model ◽

High Frequency ◽

Higher Order ◽

Sine Function ◽

Ultra High Frequency ◽

Higher Order Neural Networks ◽

Cosine Functions

This chapter develops a new nonlinear model, ultra high frequency sigmoid and trigonometric higher order neural networks (UGT-HONN), for data pattern recognition. UGT-HONN includes ultra high frequency sigmoid and sine function higher order neural networks (UGS-HONN) and ultra high frequency sigmoid and cosine functions higher order neural networks (UGC-HONN). UGS-HONN and UGC-HONN models are used to recognition data patterns. Results show that UGS-HONN and UGC-HONN models are better than other polynomial higher order neural network (PHONN) and trigonometric higher order neural network (THONN) models, since UGS-HONN and UGC-HONN models can recognize data pattern with error approaching 10-6.

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