Multilayer Perceptrons to Approximate Quaternion Valued Functions

Arena, Paolo; Fortuna, Luigi; Muscato, Giovanni; Xibilia, Maria Gabriella

doi:10.1016/s0893-6080(96)00048-2

Cited by 138 publications

(64 citation statements)

References 24 publications

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“…If the linear system (9) admits an exponential dichotomy, then the pseudo almost periodic system (11) has a unique pseudo almost periodic solution ( ) as follows:…”

Section: Preliminariesmentioning

confidence: 99%

“…Quaternion neural networks have been widely used in many fields and demonstrated better performances than the real number neural networks in chaotic time series prediction [10], approximate quaternionvalued functions [11], 3D wind forecasting [12,13], image processing [14,15], color-face recognition [16], vector sensor processing [17], and so on.…”

Section: Introductionmentioning

confidence: 99%

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Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

Meng

2017

Complexity

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We propose a class of neutral type quaternion-valued neural networks with delays in the leakage term on time scales that can unify the discrete-time and the continuous-time neural networks. In order to avoid the difficulty brought by the noncommutativity of quaternion multiplication, we first decompose the quaternion-valued system into four real-valued systems. Then, by applying the exponential dichotomic theory of linear dynamic equations on time scales, Banach's fixed point theorem, the theory of calculus on time scales, and inequality techniques, we obtain some sufficient conditions on the existence and global exponential stability of pseudo almost periodic solutions for this class of neural networks. Our results are completely new even for both the case of the neural networks governed by differential equations and the case of the neural networks governed by difference equations and show that, under a simple condition, the continuous-time quaternion-valued network and its corresponding discrete-time quaternionvalued network have the same dynamical behavior for the pseudo almost periodicity. Finally, a numerical example is given to illustrate the feasibility of our results.

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“…If the linear system (9) admits an exponential dichotomy, then the pseudo almost periodic system (11) has a unique pseudo almost periodic solution ( ) as follows:…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

Meng

2017

Complexity

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show abstract

“…Before we proceed with our proposed fusion model, let us introduce some important notions used later in the paper: & Vectorial neural network (NN) is a network with multiple heterogeneous inputs, operating in R. For more details, please refer to [13]. This is effectively a multivariate model with two inputs, which may or may not be correlated.…”

Section: Data Fusion Via Vector Spacesmentioning

confidence: 99%

Sequential Data Fusion via Vector Spaces: Fusion of Heterogeneous Data in the Complex Domain

Mandic

Goh

Aihara

2006

J VLSI Sign Process Syst Sign Im

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A sequential data fusion approach via higher dimensional vector spaces is introduced. This is achieved by making use of the representation of directional signals within the field of complex numbers C. The concept of data fusion is next introduced and the place of the proposed approach within that framework is identified. The benefits of such an approach are illustrated and a range of possible applications is shown. The concept introduced is supported by a real world case study which focuses on simultaneous forecasting of wind speed and direction. The architectures and learning algorithms which support this concept are introduced and their distributed sequential fusion nature is highlighted.

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“…For instance, complex-valued, quaternion-valued, and octonion-valued neural networks are able to process two, four, and eight dimensional data, respectively. Applications of hypercomplexvalued neural networks include control [1,4], color image processing [14,17,18], and prediction [3,16,22].…”

Section: Introductionmentioning

confidence: 99%

Continuous-Valued Octonionic Hopfield Neural Network

Castro¹,

Valle²

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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In this paper, we generalize the famous Hopfield neural network to unit octonions. In the proposed model, referred to as the continuous-valued octonionic Hopfield neural network (CV-OHNN), the next state of a neuron is obtained by setting its octonionic activation potential to length one. We show that, like the traditional Hopfield network, a CV-OHNN operating in an asynchronous update mode always settles down to an equilibrium state under mild conditions on the octonionic synaptic weights.

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Multilayer Perceptrons to Approximate Quaternion Valued Functions

Cited by 138 publications

References 24 publications

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

Sequential Data Fusion via Vector Spaces: Fusion of Heterogeneous Data in the Complex Domain

Continuous-Valued Octonionic Hopfield Neural Network

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