Cognitive Quaternion Valued Neural Network and some applications

Saoud, Lyes Saad; Ghorbani, Reza; Rahmoune, F.

doi:10.1016/j.neucom.2016.09.060

Cited by 41 publications

(7 citation statements)

References 42 publications

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“…and have a standardized form (9) that reduces the number of multiplications. Thus, we can write:B 1 shows a data flow diagram describing the new algorithm for the computation of the product of Kaluza numbers (17). In this paper, the data flow diagram is oriented from left to right.…”

Section: Synthesis Of a Rationalized Algorithm For Computing Kaluza Numbers Productmentioning

confidence: 99%

“…However, their use in brain-inspired computation and neural networks has been largely limited due to the lack of comprehensive and all-inclusive information processing and deep learning techniques. Although there has been a number of research articles addressing the use of quaternions and octonions, higher-dimensional numbers remain a largely open problem [11][12][13][14][15][16][17][18][19][20][21][22]. Recently, new articles appeared in open access that presented a sedenion-based neural network [23,24].…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm for Fast Multiplication of Kaluza Numbers

2021

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This paper presents a new algorithm for multiplying two Kaluza numbers. Performing this operation directly requires 1024 real multiplications and 992 real additions. We presented in a previous paper an effective algorithm that can compute the same result with only 512 real multiplications and 576 real additions. More effective solutions have not yet been proposed. Nevertheless, it turned out that an even more interesting solution could be found that would further reduce the computational complexity of this operation. In this article, we propose a new algorithm that allows one to calculate the product of two Kaluza numbers using only 192 multiplications and 384 additions of real numbers.

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Section: Synthesis Of a Rationalized Algorithm For Computing Kaluza Numbers Productmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Algorithm for Fast Multiplication of Kaluza Numbers

2021

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“…Content may change prior to final publication. The stochastic gradient of the QVNN is computed using the following equations (see [34,[38][39][40] for further details).…”

Section: Im Jmentioning

confidence: 99%

“…QVNNs have achieved improvements in several tasks in image, speech, and signal processing [33]. They were recently used for time-series forecasting [34], where they achieved performance levels surpassing real-valued neural networks.…”

Section: Introductionmentioning

confidence: 99%

Wind Speed Forecasting Using the Stationary Wavelet Transform and Quaternion Adaptive-Gradient Methods

2021

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Accurate wind speed forecasting is a fundamental requirement for advanced and economically viable large-scale wind power integration. The hybridization of the quaternion-valued neural networks and stationary wavelet transform has not been proposed before. In this paper, we propose a novel wind-speed forecasting model that combines the stationary wavelet transform with quaternion-valued neural networks. The proposed forecasting model represents wavelet subbands in quaternion vectors, which avoid separating the naturally correlated subbands. The forecasting model consists of three main steps. In the first step, the wind speed signal is decomposed using the stationary wavelet transform into sublevels. In the second step, a quaternion-valued neural network is used to forecast wind speed components in the stationary wavelet domain. Finally, the inverse stationary wavelet transform is applied to estimate the predicted wind speed. In addition, a softplus quaternion variant of the RMSProp learning algorithm is developed and used to improve the performance and convergence speed of the proposed model. The proposed model is tested on wind speed data collected from different sites in China and the United States, and the results demonstrate that it consistently outperforms similar models based on real-valued neural networks, complex-valued neural networks, or LSTM units. In the meteorological terminal aviation routine (METAR) dataset experiment, the proposed wind speed forecasting model reduces the mean absolute error, and root mean squared error of predicted wind speed values by 26.5% and 33%, respectively, in comparison to a number of existing approaches INDEX TERMS Wind Speed Forecasting, Stationary Wavelet Transform, Quaternion Valued Neural Network, RMSProp learning algorithm.

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“…In this respect, the quaternion-valued neural network is a fast growing field of research in both theoretical and application points of view (see [5][6][7][8][9]). 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%

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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Cognitive Quaternion Valued Neural Network and some applications

Cited by 41 publications

References 42 publications

An Algorithm for Fast Multiplication of Kaluza Numbers

An Algorithm for Fast Multiplication of Kaluza Numbers

Wind Speed Forecasting Using the Stationary Wavelet Transform and Quaternion Adaptive-Gradient Methods

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

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