Emerging Capabilities and Applications of Artificial Higher Order Neural Networks

Emerging Capabilities and Applications of Artificial Higher Order Neural Networks
Table of Contents
Detailed Table of Contents
Preface
REFERENCES
Acknowledgment
Section 1: Models of Artificial Higher Order Neural Networks
1 Models of Artificial Higher Order Neural Networks
INTRODUCTION
BACKGROUND
HIGHER ORDER NEURAL NETWORK ARCHITECTURE AND MODELS
PHONN Model
XSHONN Model
XCHONN Model
SIN-HONN Model
COS-HONN Model
THONN Model
SINCHONN Model
SSINCHONN Model
CSINCHONN Model
YSINCHONN Model
SPHONN Model
SS-HONN Model
PS-HONN Model
CS-HONN Model
NS-HONN Model
UCSHONN Model
UCCHONN Model
USSHONN Mosdel
UPS-HONN Model
UPC-HONN Model
UGS-HONN Model
UGC-HONN Model
UNS-HONN Model
UNC-HONN Model
GENERAL LEARNING ALGORITHM AND WEIGHT UPDATE FORMULAE
Output Neurons in HONN Model (Model 0, 1, and 2)
Second-Hidden Layer Neurons in HONN Model (Model 2)
First Hidden Layer x Neurons in HONN (Model 1 and Model 2)
First Hidden Layer y Neurons in HONN (Model 1 and Model 2)
24 HONN MODELS LEARNING ALGORITHM AND WEIGHT UPDATE FORMULAE
PHONN Model First Layer Neuron Weights Learning Formula
XSHONN Model First Layer Neuron Weights Learning Formula
XCHONN Model First Layer Neuron Weights Learning Formula
SIN-HONN Model First Layer Neuron Weights Learning Formula
COS-HONN Model First Layer Neuron Weights Learning Formula
THONN Model First Layer Neuron Weights Learning Formula
SINCHONN Model First Layer Neuron Weights Learning Formula
SSINCHONN Model First Layer Neuron Weights Learning Formula
CSINCHONN Model First Layer Neuron Weights Learning Formula
YSINCHONN Model First Layer Neuron Weights Learning Formula
SPHONN Model First Layer Neuron Weights Learning Formula
SS-HONN Model First Layer Neuron Weights Learning Formula
PS-HONN Model First Layer Neuron Weights Learning Formula
CS-HONN Model First Layer Neuron Weights Learning Formula
NS-HONN Model First Layer Neuron Weights Learning Formula
UCSHONN Model First Layer Neuron Weights Learning Formula
UCCHONN Model First Layer Neuron Weights Learning Formula
USSHONN Model First Layer Neuron Weights Learning Formula
UPS-HONN Model First Layer Neuron Weights Learning Formula
UPC-HONN Model First Layer Neuron Weights Learning Formula
UGS-HONN Model First Layer Neuron Weights Learning Formula
UGC-HONN Model First Layer Neuron Weights Learning Formula
UNS-HONN Model First Layer Neuron Weights Learning Formula
UNC-HONN Model First Layer Neuron Weights Learning Formula
FUTURE RESEARCH DIRECTIONS
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
2 Models of Artificial Multi-Polynomial Higher Order Neural Networks
INTRODUCTION
HONN Applications
Motivation
Contributions
BACKGROUND
HONN Modeling
HONN Models
HONN Theories
HIGHER ORDER NEURAL NETWORKS
MULTI-POLYNOMIAL HIGHER ORDER NEURAL NETWORK MODEL (MPHONN)
MPHONN STRUCTURE
LEARNING ALGORITHM FOR MPHONN MODEL
Output Layer Neurons in MPHONN Model (Model 0, 1, and 2)
Second-Hidden Layer Neurons in MPHONN Model (Model 2)
First Hidden Layer x Neurons in MPHONN (Model 1 and Model 2)
First Hidden Layer y Neurons in HONN (Model 1 and Model 2)
APPLICATIONS OF MPHONN
FUTURE RESEARCH DIRECTIONS
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
3 Group Models of Artificial Polynomial and Trigonometric Higher Order Neural Networks
INTRODUCTION
HONN Models for Simulation
The Motivations of Use of Artificial Higher Order Neural Network Group Theory
BACKGROUND
Dynamic HONN Models for Simulation
HONN for Prediction
HONN for Time Series Data Predication
Adaptive HONN Adaptive, Group and Other Models
Artificial Neural Network Group
PHONNG GROUP
PHONNG Definition
Additive Generalized Artificial Higher Order Neural Network Sets
Product Generalized Artificial Higher Order Neural Network Sets
Inference of Higher Order Neural Network Piecewise Function Groups
HONN Models
PHONN Models
PHONG Model
TRIGINIMETRIC POLYNOMIAL HIGHER ORDER NEURAL NETWORK GROUPS
THONNG Definition
Additive Generalized Artificial Higher Order Neural Network Sets
Product Generalized Artificial Higher Order Neural Network Sets
Trigonometric Polynomial Higher Order Neural Network (Thonn) Model
Trigonometric Polynomial Higher Order Neural Network Group (THONG) Model
HIGHER ORDER NEURAL NETWORK GROUP FINANCIAL SIMULATION SYSTEM
PRELIMINARY TESTING OF PHONNG AND THONNG SIMULATOR
FUTURE RESEARCH DIRECTIONS
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
Section 2: Artificial Higher Order Neural Networks for Economics and Business
4 SAS Nonlinear Models or Artificial Higher Order Neural Network Nonlinear Models?
INTRODUCTION
Applications of HONNs in Economics, Finance, and Accounting
SAS
Motivations, Contributions, and Outline of this Chapter
HONN STRUCTURE AND NONLINEAR MODLES
CONVERGENCE THEORIES OF HONN
LEARNING ALGORITHM OF HONN MODEL
HONN Learning Algorithm and Update Formulae
HONN NONLINEAR MODELS and Learning Update Formulae
PHONN Model
THONN Model
SINCHONN
SSINCHONN Model
SPHONN
UCSHONN Model
COMPARISONS OF SAS NONLINEAR MODELS AND HONN NONLINEAR MODELS
Comparison Using Quadratic With Plateau Data (45.1)
Comparison Using US Population Growth Data
Comparison Using Japanese vs. US Dollar Exchange Data
Comparison Using US Consumer Price Index 1992-2004 Data
FININDING MODEL, ORDER, & COEFFICIENT BY HONN NONLINEAR MODELS
HONN Can Choose the Best Model in a Pool of HONN Nonlinear Models for Different Data
HONN Can Select the Best Order for the Data Simulation
HONN Can Find the Coefficients for Data Simulation
CONCLUSION
FUTHER RESEARCH DIRECTIONS
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
5 Time Series Data Analysis by Ultra-High Frequency Trigonometric Higher Order Neural Networks
INTRODUCTION
UTHONN MODELS
UCSHONN Model
UCCHONN Model
USSHONN Model
LEARNING ALGORITHM OF UTHONN MODELS
Learning Formulae of Output Neurons in UTHONN Model (model 0, 1, and 2)
Learning Formulae of Second-Hidden Layer Neurons in UTHONN Model (Model 2)
General Learning Formulae of First Hidden Layer x Neurons in UTHONN (Model 1 and Model 2)
General Learning Formulae of First Hidden Layer y Neurons in UTHONN (Model 1 and Model 2)
Learning Formulae of UCSHONN Model for the First Hidden Layer
Learning Formulae of UCCHONN Model for the First Hidden Layer
Learning Formulae of USSHONN Model for the First Hidden Layer
UTHONN TESTING
COMPARISON OF THONN WITH OTHER HIGHER ORDER NEURAL NETWORKS
COMPARISONS WITH UTHONN AND EQUILIBRIUM REAL EXCHANGE RATES
Chile Exchange Rate Estimation
Ghana Exchange Rate
India Exchange Rate
APPLICATIONS
Exchange Rate Predication Simulation
US Consumer Price Index Analysis
Japan Consumer Price Index Prediction Simulation
CONCLUSION
FUTHER RESEARCH DIRECTIONS
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
6 Financial Data Prediction by Artificial Sine and Cosine Trigonometric Higher Order Neural Networks
INTRODUCTION
BACKGROUND
Background of Higher-Order Neural Networks (HONNs)
SIN-HONN AND COS-HONN MODELS
SIN-HONN Model
COS-HONN Model
LEARNING ALGORITHM OF SIN-HONN Model and COS-HONN MODEL
Learning Formulae of Output Neurons in SIN-HONN Model and COS-HONN Model (Model 0, 1, and 2)
Learning Formulae of Second-Hidden Layer Neurons in SIN-HONN Model and COS-HONN Model (Model 2)
General Learning Formulae of First Hidden Layer x Neurons in SIN-HONN Model and COS-HONN Model (Model 1 and Model 2)
General Learning Formulae of First Hidden Layer y Neurons in SIN-HONN Model and COS-HONN Model (Model 1 and Model 2)
Learning formulae of SIN-HONN Model for the First Hidden Layer
Learning Formulae of COS-HONN Model for the First Hidden Layer
FINANCIAL DATA PREDICTION USING HONN MODELS
Time Series Data Prediction Simulation Test Using SIN-HONN
COS-HONN Model Prediction for All Banks Deposits Repayable in Australia
COS-HONN Model Prediction for All Banks Credit Card Lending in Australia
FUTURE RESEARCH DIRECTIONS
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
Section 3: Artificial Higher Order Neural Networks for Modeling and Simulation
7 Data Classification Using Ultra-High Frequency SINC and Trigonometric Higher Order Neural Networks
INTRODUCTION
BACKGROUND
ULTRA-HIGH FREQUENCY SINC AND TRIGONOMETRIC HIGHER ORDER NEURAL NETWORKS (UNT-HONN)
UNS-HONN Model
UNC-HONN Model
LEARNING ALGORITHM OF UNS-HONN Model and UNC-HONN MODEL
Learning Formulae of Output Neurons in UNS-HONN Model and UNC-HONN Model (model 0, 1, and 2)
Learning Formulae of Second-Hidden Layer Neurons in UNS-HONN Model and UNC-HONN Model (Model 2)
General Learning Formulae of First Hidden Layer x Neurons in UNS-HONN Model and UNC-HONN Model (Model 1 and Model 2)
General Learning Formulae of First Hidden Layer y Neurons in UNS-HONN Model and UNC-HONN Model (Model 1 and Model 2)
Learning formulae of UNS-HONN Model for the First Hidden Layer
Learning Formulae of UNC-HONN Model for the First Hidden Layer
UNS-HONN AND UNC-HONN MODEL TESTING
FUTURE RESEARCH DIRECTIONS
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
8 Data Simulations Using Cosine and Sigmoid Higher Order Neural Networks
INTRODUCTION
BACKGROUND
MODELS OF CS-HONN
CS-HONN TIME SERIES ANALYSIS SYSTEM
LEARNING ALGORITHM OF CS-HONN
Learning Formulae of Output Neurons in CS-HONN Models (model 0, 1, and 2)
Learning Formulae of Second-Hidden Layer Neurons in CS-HONN Models (Model 2)
General Learning Formulae of First Hidden Layer x Neurons in CS-HONN Models (Model 1 and Model 2)
General Learning Formulae of First Hidden Layer y Neurons in CS-HONN Models (Model 1 and Model 2)
Learning Formulae of CS-HONN Model for the First Hidden Layer
TIME SERIES DATA TEST USING CS-HONN
FUTURE RESEARCH DIRECTIONS
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
9 Rainfall Estimation Using Neuron-Adaptive Higher Order Neural Networks
INTRODUCTION
NEURON-ADAPTIVE HIGHER ORDER NEURAL NETWORK (NAHONN)
Multi m Dimensional NAHONN Definition
m Dimensional NAHONN Definition
Two-Dimensional NAHONN Definition
One-Dimensional NAHONN Definition
Learning Algorithm and Universal Approximation Capability of NAHONN
HEAVY RAINFALL ESTIMATION USING NAHONN MODELS
ANSER Architecture
The Structures of NAHONNs for ANSER System
Results of NAHONN for Rainfall Estimate Factor
NAHONN Reasoning Network Structure
Rainfall Estimation Results Using NAHONN Model
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
Section 4: Artificial Higher Order Neural Networks for Control and Recognition
10 Control Signal Generator Based on Ultra-High Frequency Polynomial and Trigonometric Higher Order Neural Networks
INTRODUCTION
BACKGROUND
Neural Networks for Control Signals and Control Systems
Higher Order Neural Networks for Control Signals and Control Systems
Detail Examples of Artificial Higher Order Neural Networks for Control
UPT-HONN MODELS
UPS-HONN Model and UPC-HONN Model
UPC-HONN Model
LEARNING ALGORITHM OF UPT-HONN MODELS
Learning Formulae of Output Neurons in UPS-HONN Model and UPC-HONN Model (model 0, 1, and 2)
Learning Formulae of Second-Hidden Layer Neurons in UPS-HONN Model and UPC-HONN Model (Model 2)
General Learning Formulae of First Hidden Layer x Neurons in UPS-HONN Model and UPC-HONN Model (Model 1 and Model 2)
General Learning Formulae of First Hidden Layer y Neurons in UPS-HONN Model and UPC-HONN Model (Model 1 and Model 2)
Learning Formulae of UPS-HONN Model for the First Hidden Layer
Learning Formulae of UPC-HONN Model for the First Hidden Layer
UPT-HONN TESTING
FUTHER RESEARCH DIRECTIONS
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
11 Data Pattern Recognition Based on Ultra-High Frequency Sigmoid and Trigonometric Higher Order Neural Networks
INTRODUCTION
BACKGROUND
UGT-HONN MODELS
UGS-HONN Model
UGC-HONN Model
LEARNING ALGORITHM OF UGT-HONN MODELS
Learning Formulae of Output Neurons in UGS-HONN Model and UGC-HONN Model (model 0, 1, and 2)
Learning Formulae of Second-Hidden Layer Neurons in UGS-HONN Model and UGC-HONN Model (Model 2)
General Learning Formulae of First Hidden Layer x Neurons in UGS-HONN Model and UGC-HONN Model (Model 1 and Model 2)
General Learning Formulae of First Hidden Layer y Neurons in UGS-HONN Model and UGC-HONN Model (Model 1 and Model 2)
Learning Formulae of UGS-HONN Model for the First Hidden Layer
Learning Formulae of UGC-HONN Model for the First Hidden Layer
UGT-HONN TESTING
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
12 Face Recognition Based on Higher Order Neural Network Group-Based Adaptive Tolerance Trees
INTRODUCTION
ARTIFICIAL HIGHER ORDER NEURAL NETWORK SETS
HIGHER ORDER NEURAL NETWORK GROUP
Additive Notation of Higher Order Neural Network Groups
Product Notation of Higher Order Neural Network Groups
Higher Order Neural Network Algebra Sum Groups
Higher Order Neural Network Piecewise Function Groups
Inference of Higher Order Neural Network Piecewise Function Groups
HIGHER ORDER NEURAL NETWORK GROUP MODELS
Trigonometric Polynomial Higher Order Neural Network (THONN) Model
Polynomial Higher Order Neural Network (PHONN) Model
Sigmoid polynomial Higher Order Neural Network (SPHONN) Model
Polynomial Higher Order Neural Network Group (PHONNG) Model
Trigonometric Polynomial Higher Order Neural Network Group (THONNG) Model
Sigmoid Polynomial Higher Order Neural Network Group (SPHONNG) Model
HIGHER ORDER NEURAL NETWORK GROUP NODE OF TREE
HONNGAT TREE MODEL
FACE RECOGNITION USING HONNGAT TREE MODELS
Face Recognition System
Face Perception Recognition Using HONNGAT Trees
Recognition of Glasses and/or Beards Using HONNGAT Tree
Front Face Recognition Using HONNGAT Tree
CONCLUSION
REFERENCES
ADDITIONAL READING
KEY TERMS AND DEFINITIONS
APPENDIX
A. Generalised Artificial Higher Order Neural Network Sets
B. Proof of the Inference
C. HONNGAT Tree Definitions
About the Author
Index