Quaternion Neural Network and Its Application

Isokawa, Teijiro; Kusakabe, T.; Matsui, Nobuyuki; Peper, Ferdinand

doi:10.1007/978-3-540-45226-3_44

Cited by 125 publications

(52 citation statements)

References 2 publications

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“…The quaternionic NN [14][15][16][17][18][19] is an extension of the classical real-valued neural network to quaternions, whose weights, threshold values, input and output signals are all quaternions where a quaternion is a four-dimensional number and was invented by W. R. Hamilton in 1843 [20].…”

Section: Construction Of 4-4-4 Real-valued Nnmentioning

confidence: 99%

Neural Networks with Comparatively Few Critical Points

Nitta¹

2013

Procedia Computer Science

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A critical point is a point on which the derivatives of an error function are all zero. It has been shown in the literatures that the critical points caused by the hierarchical structure of the real-valued neural network could be local minima or saddle points, whereas most of the critical points caused by the hierarchical structure are saddle points in the case of complexvalued neural networks. Several studies have demonstrated that that kind of singularity has a negative effect on learning dynamics in neural networks. In this paper, we will demonstrate via some examples that the decomposition of highdimensional NNs into real-valued NNs equivalent to the original NNs yields the NNs that do not have critical points based on the hierarchical structure.

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Section: Construction Of 4-4-4 Real-valued Nnmentioning

confidence: 99%

Neural Networks with Comparatively Few Critical Points

Nitta¹

2013

Procedia Computer Science

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“…They considered the learning dynamics of large number of oscillators (traffic signals) connected by roads to make cars flow better. Regarding higher-order complex numbers, we have a quaternion neural-network application, for example, in learning in three-dimensional RGB space to transform color images proposed by Isokawa et al [82]. Regarding higher-order complex numbers, we have a quaternion neural-network application, for example, in learning in three-dimensional RGB space to transform color images proposed by Isokawa et al [82].…”

Section: Applicationsmentioning

confidence: 99%

Complex-Valued Neural Networks

Hirose¹

2006

Studies in Computational Intelligence

150

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“…Due to the noncommutativity of quaternion multiplication, the study of quaternion is much more difficult than that of plurality, which is one of the reasons for the slow development of quaternion. Fortunately, over the past two decades, the quaternion theory has achieved a rapid development, especially in algebra, and found many applications in the real world, like attitude control, quantum mechanics, robotics, computer graphics, and so on [1][2][3][4][5]. For example, in the application of color image compression technology, one can apply the quaternion theory to encode and improve the color image; see [5].…”

Section: Introductionmentioning

confidence: 99%

Almost Periodic Synchronization for Quaternion‐Valued Neural Networks with Time‐Varying Delays

Meng

2018

Complexity

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This paper focuses on the global exponential almost periodic synchronization of quaternion-valued neural networks with timevarying delays. By virtue of the exponential dichotomy of linear differential equations, Banach's fixed point theorem, Lyapunov functional method, and differential inequality technique, some sufficient conditions are established for assuring the existence and global exponential synchronization of almost periodic solutions of the delayed quaternion-valued neural networks, which are completely new. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.

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Quaternion Neural Network and Its Application

Cited by 125 publications

References 2 publications

Neural Networks with Comparatively Few Critical Points

Neural Networks with Comparatively Few Critical Points

Complex-Valued Neural Networks

Almost Periodic Synchronization for Quaternion‐Valued Neural Networks with Time‐Varying Delays

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