Some Properties on the Capability of Associative Memory for Higher Order Neural Networks

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

10.4018/978-1-5225-0063-6.ch016 ◽

2016 ◽

pp. 391-419

Author(s):

Hiromi Miyajima ◽

Shuji Yatsuki ◽

Noritaka Shigei ◽

Hirofumi Miyajima

Keyword(s):

Neural Networks ◽

Associative Memory ◽

Memory Capacity ◽

Higher Order ◽

Higher Order Neural Networks ◽

Theoretical Results

Higher order neural networks (HONNs) have been proposed as new systems. In this paper, we show some theoretical results of associative capability of HONNs. As one of them, memory capacity of HONNs is much larger than one of the conventional neural networks. Further, we show some theoretical results on homogeneous higher order neural networks (HHONNs), in which each neuron has identical weights. HHONNs can realize shift-invariant associative memory, that is, HHONNs can associate not only a memorized pattern but also its shifted ones.

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Some Properties on the Capability of Associative Memory for Higher Order Neural Networks

Nature-Inspired Computing ◽

10.4018/978-1-5225-0788-8.ch004 ◽

2016 ◽

pp. 57-86

Author(s):

Hiromi Miyajima ◽

Shuji Yatsuki ◽

Noritaka Shigei ◽

Hirofumi Miyajima

Keyword(s):

Neural Networks ◽

Associative Memory ◽

Memory Capacity ◽

Higher Order ◽

Higher Order Neural Networks ◽

Theoretical Results

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Statistical dynamics of associative memory for higher order neural networks

2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353) ◽

10.1109/iscas.2000.856149 ◽

2002 ◽

Cited By ~ 4

Author(s):

S. Yatsuki ◽

H. Miyajima

Keyword(s):

Neural Networks ◽

Associative Memory ◽

Higher Order ◽

Statistical Dynamics ◽

Higher Order Neural Networks

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Dynamics in Artificial Higher Order Neural Networks with Delays

Artificial Higher Order Neural Networks for Economics and Business ◽

10.4018/978-1-59904-897-0.ch018 ◽

2009 ◽

pp. 389-429 ◽

Cited By ~ 1

Author(s):

Jinde Cao ◽

Fengli Ren ◽

Jinling Liang

Keyword(s):

Neural Networks ◽

Stability Analysis ◽

Linear Matrix Inequalities ◽

Associative Memory ◽

Periodic Oscillation ◽

Higher Order ◽

Linear Matrix ◽

Matrix Inequalities ◽

Bidirectional Associative Memory ◽

Higher Order Neural Networks

This chapter concentrates on studying the dynamics of artificial higher order neural networks (HONNs) with delays. Both stability analysis and periodic oscillation are discussed here for a class of delayed HONNs with (or without) impulses. Most of the sufficient conditions obtained in this chapter are presented in linear matrix inequalities (LMIs), and so can be easily computed and checked in practice using the Matlab LMI Toolbox. In reality, stability is a necessary feature when applying artificial neural networks. Also periodic solution plays an important role in the dynamical behavior of all solutions though other dynamics such as bifurcation and chaos do coexist. So here we mainly focus on questions of the stability and periodic solutions of artificial HONNs with (or without) impulses. Firstly, stability analysis and periodic oscillation are analyzed for higher order bidirectional associative memory (BAM) neural networks without impulses. Secondly, global exponential stability and exponential convergence are studied for a class of impulsive higher order bidirectional associative memory neural networks with time-varying delays. The main methods and tools used in this chapter are linear matrix inequalities (LMIs), Lyapunov stability theory and coincidence degree theory.

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Artificial Tactile Sensing and Robotic Surgery Using Higher Order Neural Networks

Artificial Higher Order Neural Networks for Computer Science and Engineering ◽

10.4018/978-1-61520-711-4.ch021 ◽

2010 ◽

pp. 514-544 ◽

Cited By ~ 3

Author(s):

Siamak Najarian ◽

Sayyed Mohsen Hosseini ◽

Mehdi Fallahnezhad

Keyword(s):

Neural Networks ◽

Medical Instrument ◽

Research Work ◽

Higher Order ◽

Ann Model ◽

Nonlinear Input ◽

Higher Order Neural Networks ◽

Sense Of Touch ◽

Theoretical Analyses ◽

Theoretical Results

In this chapter, a new medical instrument, namely, the Tactile Tumor Detector (TTD) able to simulate the sense of touch in clinical and surgical applications is introduced. All theoretical and experimental attempts for its construction are presented. Theoretical analyses are mostly based on finite element method (FEM), artificial neural networks (ANN), and higher order neural networks (HONN). The TTD is used for detecting abnormal masses in biological tissue, specifically for breast examinations. We also present a research work on ANN and HONN done on the theoretical results of the TTD to reduce the subjectivity of estimation in diagnosing tumor characteristics. We used HONN as a stronger open box intelligent unit than traditional black box neural networks (NN) for estimating the characteristics of tumor and tissue. The results show that by having an HONN model of our nonlinear input-output mapping, there are many advantages compared with ANN model, including faster running for new data, lesser RMS error and better fitting properties.

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