Hybrid Quaternionic Hopfield Neural Network

Masaki KOBAYASHI

doi:10.1587/transfun.E98.A.1512

Hybrid Quaternionic Hopfield Neural Network

Masaki KOBAYASHI

Full Text Views

0

Share
Cite this

Summary :

In recent years, applications of complex-valued neural networks have become wide spread. Quaternions are an extension of complex numbers, and neural networks with quaternions have been proposed. Because quaternion algebra is non-commutative algebra, we can consider two orders of multiplication to calculate weighted input. However, both orders provide almost the same performance. We propose hybrid quaternionic Hopfield neural networks, which have both orders of multiplication. Using computer simulations, we show that these networks outperformed conventional quaternionic Hopfield neural networks in noise tolerance. We discuss why hybrid quaternionic Hopfield neural networks improve noise tolerance from the standpoint of rotational invariance.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.7 pp.1512-1518

Publication Date: 2015/07/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E98.A.1512

Type of Manuscript: PAPER

Category: Nonlinear Problems

Authors

Masaki KOBAYASHI
University of Yamanashi

Keyword

Hopfield neural networks, complex-valued associative memory, quaternion, rotational invariance

Cite this

Copy

Masaki KOBAYASHI, "Hybrid Quaternionic Hopfield Neural Network" in IEICE TRANSACTIONS on Fundamentals, vol. E98-A, no. 7, pp. 1512-1518, July 2015, doi: 10.1587/transfun.E98.A.1512.
Abstract: In recent years, applications of complex-valued neural networks have become wide spread. Quaternions are an extension of complex numbers, and neural networks with quaternions have been proposed. Because quaternion algebra is non-commutative algebra, we can consider two orders of multiplication to calculate weighted input. However, both orders provide almost the same performance. We propose hybrid quaternionic Hopfield neural networks, which have both orders of multiplication. Using computer simulations, we show that these networks outperformed conventional quaternionic Hopfield neural networks in noise tolerance. We discuss why hybrid quaternionic Hopfield neural networks improve noise tolerance from the standpoint of rotational invariance.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.1512/_p

Copy

@ARTICLE{e98-a_7_1512,
author={Masaki KOBAYASHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Hybrid Quaternionic Hopfield Neural Network},
year={2015},
volume={E98-A},
number={7},
pages={1512-1518},
abstract={In recent years, applications of complex-valued neural networks have become wide spread. Quaternions are an extension of complex numbers, and neural networks with quaternions have been proposed. Because quaternion algebra is non-commutative algebra, we can consider two orders of multiplication to calculate weighted input. However, both orders provide almost the same performance. We propose hybrid quaternionic Hopfield neural networks, which have both orders of multiplication. Using computer simulations, we show that these networks outperformed conventional quaternionic Hopfield neural networks in noise tolerance. We discuss why hybrid quaternionic Hopfield neural networks improve noise tolerance from the standpoint of rotational invariance.},
keywords={},
doi={10.1587/transfun.E98.A.1512},
ISSN={1745-1337},
month={July},}

Copy

TY - JOUR
TI - Hybrid Quaternionic Hopfield Neural Network
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1512
EP - 1518
AU - Masaki KOBAYASHI
PY - 2015
DO - 10.1587/transfun.E98.A.1512
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2015
AB - In recent years, applications of complex-valued neural networks have become wide spread. Quaternions are an extension of complex numbers, and neural networks with quaternions have been proposed. Because quaternion algebra is non-commutative algebra, we can consider two orders of multiplication to calculate weighted input. However, both orders provide almost the same performance. We propose hybrid quaternionic Hopfield neural networks, which have both orders of multiplication. Using computer simulations, we show that these networks outperformed conventional quaternionic Hopfield neural networks in noise tolerance. We discuss why hybrid quaternionic Hopfield neural networks improve noise tolerance from the standpoint of rotational invariance.
ER -