Fundamental Theory of Artificial Higher Order Neural Networks

Fundamental Theory of Artificial Higher Order Neural Networks

Madan M. Gupta (University of Saskatchewan, Canada), Noriyasu Homma (Tohoku University, Japan), Zeng-Guang Hou (The Chinese Academy of Sciences, China), Ashu M. G. Solo (Maverick Technologies America Inc., USA) and Takakuni Goto (Tohoku University, Japan)
Copyright: © 2009 |Pages: 20
DOI: 10.4018/978-1-59904-897-0.ch017
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Abstract

In this chapter, we aim to describe fundamental principles of artificial higher order neural units (AHONUs) and networks (AHONNs). An essential core of AHONNs can be found in higher order weighted combinations or correlations between the input variables. By using some typical examples, this chapter describes how and why higher order combinations or correlations can be effective.
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Introduction

The human brain has more than 10 billion neurons, which have complicated interconnections, and these neurons constitute a large-scale signal processing and memory network. Indeed, the understanding of neural mechanisms of higher functions of the brain is very complex. In the conventional neurophysiological approach, one can obtain only some fragmentary knowledge of neural processes and formulate only some mathematical models for specific applications. The mathematical study of a single neural model and its various extensions is the first step in the design of a complex neural network for solving a variety of problems in the fields of signal processing, pattern recognition, control of complex processes, neurovision systems, and other decision making processes. Neural network solutions for these problems can be directly used for business and economic applications.

A simple neural model is presented in Figure 1. In terms of information processing, an individual neuron with dendrites as multiple-input terminals and an axon as a single-output terminal may be considered a multiple-input/single-output (MISO) system. The processing functions of this MISO neural processor may be divided into the following four categories:

Figure 1.

A simple neural model as a multiinput (dendrites) and single-output (axon) processor

  • i.

    Dendrites: They consist of a highly branching tree of fibers and act as input points to the main body of the neuron. On average, there are 103 to 104 dendrites per neuron, which form receptive surfaces for input signals to the neurons.

  • ii.

    Synapse: It is a storage area of past experience (knowledge base). It provides long-term memory (LTM) to the past accumulated experience. It receives information from sensors and other neurons and provides outputs through the axons.

  • iii.

    Soma: The neural cell body is called the soma. It is the large, round central neuronal body. It receives synaptic information and performs further processing of the information. Almost all logical functions of the neuron are carried out in the soma.

  • iv.

    Axon: The neural output line is called the axon. The output appears in the form of an action potential that is transmitted to other neurons for further processing.

The electrochemical activities at the synaptic junctions of neurons exhibit a complex behavior because each neuron makes hundreds of interconnections with other neurons. Each neuron acts as a parallel processor because it receives action potentials in parallel from the neighboring neurons and then transmits pulses in parallel to other neighboring synapses. In terms of information processing, the synapse also performs a crude pulse frequency-to-voltage conversion as shown in Figure 1.

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Dedication
Table of Contents
Acknowledgment
Ming Zhang
Chapter 1
Ming Zhang
This chapter delivers general format of Higher Order Neural Networks (HONNs) for nonlinear data analysis and six different HONN models. This chapter... Sample PDF
Artificial Higher Order Neural Network Nonlinear Models: SAS NLIN or HONNs?
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Chapter 2
Adam Knowles, Abir Hussain, Wael El Deredy, Paulo G.J. Lisboa, Christian L. Dunis
Multi-Layer Perceptrons (MLP) are the most common type of neural network in use, and their ability to perform complex nonlinear mappings and... Sample PDF
Higher Order Neural Networks with Bayesian Confidence Measure for the Prediction of the EUR/USD Exchange Rate
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Chapter 3
Da Shi, Shaohua Tan, Shuzhi Sam Ge
Real-world financial systems are often nonlinear, do not follow any regular probability distribution, and comprise a large amount of financial... Sample PDF
Automatically Identifying Predictor Variables for Stock Return Prediction
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Chapter 4
John Seiffertt, Donald C. Wunsch II
As the study of agent-based computational economics and finance grows, so does the need for appropriate techniques for the modeling of complex... Sample PDF
Higher Order Neural Network Architectures for Agent-Based Computational Economics and Finance
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Chapter 5
Yuehui Chen, Peng Wu, Qiang Wu
Forecasting exchange rates is an important financial problem that is receiving increasing attention especially because of its difficulty and... Sample PDF
Foreign Exchange Rate Forecasting Using Higher Order Flexible Neural Tree
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Chapter 6
Yuehui Chen, Peng Wu, Qiang Wu
Artificial Neural Networks (ANNs) have become very important in making stock market predictions. Much research on the applications of ANNs has... Sample PDF
Higher Order Neural Networks for Stock Index Modeling
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Chapter 7
Ming Zhang
This chapter develops a new nonlinear model, Ultra high frequency Trigonometric Higher Order Neural Networks (UTHONN), for time series data... Sample PDF
Ultra High Frequency Trigonometric Higher Order Neural Networks for Time Series Data Analysis
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Chapter 8
Panos Liatsis, Abir Hussain, Efstathios Milonidis
The research described in this chapter is concerned with the development of a novel artificial higher order neural networks architecture called the... Sample PDF
Artificial Higher Order Pipeline Recurrent Neural Networks for Financial Time Series Prediction
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Chapter 9
Abir Hussain, Panos Liatsis
The research described in this chapter is concerned with the development of a novel artificial higherorder neural networks architecture called the... Sample PDF
A Novel Recurrent Polynomial Neural Network for Financial Time Series Prediction
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Chapter 10
David R. Selviah, Janti Shawash
Generalized correlation higher order neural network designs are developed. Their performance is compared with that of first order networks... Sample PDF
Generalized Correlation Higher Order Neural Networks for Financial Time Series Prediction
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Chapter 11
Godfrey C. Onwubolu
Real world problems are described by nonlinear and chaotic processes, which makes them hard to model and predict. This chapter first compares the... Sample PDF
Artificial Higher Order Neural Networks in Time Series Prediction
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Chapter 12
Rozaida Ghazali, Dhiya Al-Jumeily
This chapter discusses the use of two artificial Higher Order Neural Networks (HONNs) models; the Pi- Sigma Neural Networks and the Ridge Polynomial... Sample PDF
Application of Pi-Sigma Neural Networks and Ridge Polynomial Neural Networks to Financial Time Series Prediction
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Chapter 13
Edgar N. Sanchez, Alma Y. Alanis, Jesús Rico
In this chapter, we propose the use of Higher Order Neural Networks (HONNs) trained with an extended Kalman filter based algorithm to predict the... Sample PDF
Electric Load Demand and Electricity Prices ForecastingUsing Higher Order Neural Networks Trained by Kalman Filtering
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Chapter 14
Shuxiang Xu
Business is a diversified field with general areas of specialisation such as accounting, taxation, stock market, and other financial analysis.... Sample PDF
Adaptive Higher Order Neural Network Models and Their Applications in Business
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Chapter 15
Jean X. Zhang
This chapter proposes nonlinear models using artificial neural network models to study the relationship between chief elected official (CEO) tenure... Sample PDF
CEO Tenure and Debt: An Artificial Higher Order Neural Network Approach
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Chapter 16
Christian L. Dunis, Jason Laws, Ben Evans
This chapter investigates the soybean-oil “crush” spread, that is the profit margin gained by processing soybeans into soyoil. Soybeans form a large... Sample PDF
Modelling and Trading the Soybean-Oil Crush Spread with Recurrent and Higher Order Networks: A Comparative Analysis
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Chapter 17
Madan M. Gupta, Noriyasu Homma, Zeng-Guang Hou, Ashu M. G. Solo, Takakuni Goto
In this chapter, we aim to describe fundamental principles of artificial higher order neural units (AHONUs) and networks (AHONNs). An essential core... Sample PDF
Fundamental Theory of Artificial Higher Order Neural Networks
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Chapter 18
Jinde Cao, Fengli Ren, Jinling Liang
This chapter concentrates on studying the dynamics of artificial higher order neural networks (HONNs) with delays. Both stability analysis and... Sample PDF
Dynamics in Artificial Higher Order Neural Networks with Delays
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Chapter 19
Zhao Lu, Leang-san Shieh, Guanrong Chen
Aiming to develop a systematic approach for optimizing the structure of artificial higher order neural networks (HONN) for system modeling and... Sample PDF
A New Topology for Artificial Higher Order Neural Networks: Polynomial Kernel Networks
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Chapter 20
David R. Selviah
This chapter describes the progress in using optical technology to construct high-speed artificial higher order neural network systems. The chapter... Sample PDF
High Speed Optical Higher Order Neural Networks for Discovering Data Trends and Patterns in Very Large Databases
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Chapter 21
Zidong Wang, Yurong Liu, Xiaohui Liu
This chapter deals with the analysis problem of the global exponential stability for a general class of stochastic artificial higher order neural... Sample PDF
On Complex Artificial Higher Order Neural Networks: Dealing with Stochasticity, Jumps and Delays
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Chapter 22
Lei Zhang, Simeon J. Simoff, Jing Chun Zhang
This chapter introduces trigonometric polynomial higher order neural network models. In the area of financial data simulation and prediction, there... Sample PDF
Trigonometric Polynomial Higher Order Neural Network Group Models and Weighted Kernel Models for Financial Data Simulation and Prediction
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