Complex-Valued Neural Networks

Hirose, Akira

doi:10.1007/978-3-540-33457-6

Cited by 154 publications

(2 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, applications of high‐dimensional neural networks have become widespread . Especially, high‐dimensional neural networks by Clifford algebra, such as complex and hyperbolic numbers, have been studied as promising models .…”

Section: Introductionmentioning

confidence: 99%

Rotational invariance of quaternionic hopfield neural networks

Kobayashi

2016

IEEJ Transactions Elec Engng

View full text Add to dashboard Cite

High-dimensional neural networks have been studied by many researchers for their flexible representation. Quaternionic Hopfield neural networks (QHNNs) are one of them. Quaternions have the inherent property of non-commutative multiplication. Connection weights act differently from left and right in QHNNs, and we can have left QHNNs (LQHNNs) and right QHNNs (RQHNNs). Hybrid QHNNs (HQHNNs), which are the compound models of LQHNNs and RQHNNs, have been proposed, and their excellent noise tolerance has been shown through computer simulations. It has been pointed out that the improvement in their noise tolerance is related to the avoidance of rotational invariance. Thus, it is very important to study rotational invariance. In this paper, we investigate the rotational invariance of QHNNs. Rotational invariance in LQHNNs and RQHNNs is different. We define the left and right-rotated vectors, which are fixed in RQHNNs and LQHNNs, respectively. From the standpoint of HQHNNs, the common rotated vectors are important. We also study the common rotated vectors and provide a couple of exceptional examples.

show abstract

Section: Introductionmentioning

confidence: 99%

Rotational invariance of quaternionic hopfield neural networks

Kobayashi

2016

IEEJ Transactions Elec Engng

View full text Add to dashboard Cite

show abstract

“…These days, high‐dimensional neural networks and their applications are being studied by many researchers . Especially, two‐dimensional multistate neurons are available for representing multilevel data.…”

Section: Introductionmentioning

confidence: 99%

Pseudomemories of two‐dimensional multistate hopfield neural networks

Kobayashi

2016

IEEJ Transactions Elec Engng

View full text Add to dashboard Cite

Complex-valued Hopfield neural networks (CVHNNs) are available for storage of multilevel data, such as gray-scale images. Such networks have low noise tolerance. This is a severe problem for their applications. To improve the noise tolerance, we have to study pseudomemories. In the case of one training pattern, CVHNNs have only rotated patterns as pseudomemories. There are many rotated patterns. This is considered the reason why CVHNNs have low noise tolerance. In the present paper, we investigate the pseudomemories of two-dimensional multistate Hopfield neural networks, including the complex-valued ones, with multiple training patterns. Computer simulations show that there are many pseudomemories other than the rotated patterns.

show abstract

Application Fields and Fundamental Merits of Complex‐Valued Neural Networks

Hirose

2013

Complex‐Valued Neural Networks

View full text Add to dashboard Cite

Complex-Valued Neural Networks

Cited by 154 publications

References 53 publications

Rotational invariance of quaternionic hopfield neural networks

Rotational invariance of quaternionic hopfield neural networks

Pseudomemories of two‐dimensional multistate hopfield neural networks

Application Fields and Fundamental Merits of Complex‐Valued Neural Networks

Contact Info

Product

Resources

About