Cognitive Quaternion Valued Neural Network and some applications

Fast Algorithms for Deep Octonion Networks

This brief presents the results of a study of the possibilities of reducing the arithmetic complexity of computing basic operations in octonionic neural networks and also proposes new algorithmic solutions for efficiently performing these operations. Here, we primarily mean the operation of multiplying octonions, the operation of computing the dot product of two octonion-valued vectors, and the operation of multiple multiplications of an octonion by several other octonions. In order to reduce the computational complexity of these operations, it is proposed to use the fast Walsh-Hadamard transform, which is well known in digital signal processing. Using this transform reduces the number of multiplications and additions of real numbers required to perform computations. Thus, the use of the proposed algorithms will speed up computations in octonion-valued neural networks.

A T-S Fuzzy Quaternion-Value Neural Network-Based Data-Driven Generalized Predictive Control Scheme for Mecanum Mobile Robot

Four-mecanum-wheeled omnidirectional mobile robots (FMOMR) are widely used in many practical scenarios because of their high mobility and flexibility. However, the performance of trajectory tracking would be degenerated largely due to various reasons. To deal with this issue, this paper proposes a data-driven algorithm by using the T-S fuzzy quaternion-value neural network (TSFQVNN). TSFQVNN is tailored to obtain the controlled autoregressive integral moving average (CARIMA) model, and then the generalized predictive controller (GPC) is designed based on the CARIMA model. In this way, the spatial relationship between the three-dimensional pose coordinates can be preserved and training times can be reduced. Furthermore, the convergence of the proposed algorithm is verified by the Stone–Weierstrass theorem, and the convergence conditions of the algorithm are discussed. Finally, the proposed control scheme is applied to the three-dimensional (3D) trajectory tracking problem on the arc surface, and the simulation results prove the necessity and feasibility of the algorithm.

Analysing the Exponentially Varying Viscosity of Micropolar Carreau Nanofluid Flow with Variable Fluid Properties in Stretching Porous Sheet

In this study, the researchers assumed a thermal energy system with variable controlling properties, mainly like varying viscosity parameters, and power-law index, which has an impact on the overall procedure. Variable thermo-physical features of induced magnetic field on Carreau flow settled with micropolar nanofluid are explored on account of wide range of applications. The micropolar fluids theory focuses on a type of fluids that have tiny effects resulting from the fluid’s micro-motions. Evaluating an micropolar nanofluid’s electrically conducting flows in magnetohydrodynamic (MHD) by virtue of the thermal device is crucial in present metalworking and metallurgy processes. Therefore, the proposed research came with a novel method of neural network with optimization technique also to calculate the accurate result of varying parameters. The obtained differential equation with partial derivatives is transformed into differential equations with ordinary coefficients using the transformation functions. Consecutively, the differential equations with ordinary coefficients are solved using the solution methods of Adam predictor collector and Runge Kutta Fehlberg methods. The thermal extrusion system includes profiles of angular velocity, velocity, concentration, magnetic field, and temperature, in addition to the governing parameters for each. The effectiveness of values acquired by the solution approach was inadequate to continue the investigation, thus a neural network based quaternion values technique was used in solving differential equations to obtain the optimized values of the novel parameters studied in this research. The Mat Lab software is used to carry out for this research’s execution. The research focuses on the varying parameter of viscosity of the nanofluid, therefore the profiles considered was resultant as that the concentration, temperature, and angular velocity profiles decreases as the values of 0.233886, 0.220491, and 0.107346 in addition to a rise in viscosity parameter. However, the velocity rises with the value of 0.970122 as the viscosity parameter values are steadily increased. The effect of utilizing a genetic algorithm based quaternion neural network to optimise the values of the result is compared to two other optimization strategies (MLP + GA and MLP + GD), moreover to the solved numerical values. The novel optimization technique with neural networks gives a better result than the existing methods and the solved numerical values. As a result, this study examined at the MHD based micropolar Carreau nanofluid’s mass and heat transfer on a permeable stretching surface of an induced magnetic field, and it came up with accurate values optimised by a novel neural network model with a genetic algorithm, which gives less error in training and testing data.

A Parallel Algorithm for Dividing Octonions

The article presents a parallel hardware-oriented algorithm designed to speed up the division of two octonions. The advantage of the proposed algorithm is that the number of real multiplications is halved as compared to the naive method for implementing this operation. In the synthesis of the discussed algorithm, the matrix representation of this operation was used, which allows us to present the division of octonions by means of a vector–matrix product. Taking into account a specific structure of the matrix multiplicand allows for reducing the number of real multiplications necessary for the execution of the octonion division procedure.

Fast Algorithms for Quaternion-Valued Convolutional Neural Networks

In this article, we analyze algorithmic ways to reduce the arithmetic complexity of calculating quaternion-valued linear convolution and also synthesize a new algorithm for calculating this convolution. During the synthesis of the discussed algorithm, we use the fact that quaternion multiplication may be represented as a matrix-vector product. The matrix participating in the product has unique structural properties that allow performing its advantageous decomposition. Namely, this decomposition leads to reducing the multiplicative complexity of computations. In addition, we used the fact that when calculating the elements of the quaternion-valued convolution, the part of the calculations of all matrix-vector products is common. It gives an additional reduction in the number of additions of real numbers and, consequently, a decrease in the additive complexity of calculations. Thus, the use of the proposed algorithm will contribute to the acceleration of calculations in quaternion-valued convolution neural networks.

Metacognitive Octonion-Valued Neural Networks as They Relate to Time Series Analysis

In this paper, a metacognitive octonion-valued neural network (Mc-OVNN) learning algorithm and its application to diverse time series prediction are presented. The Mc-OVNN is comprised of two components: the octonion-valued neural network that represents the cognitive component and the metacognitive component that serves to self-regulate the learning algorithm. At each epoch, the metacognitive component decides if, how, and when learning occurs. The algorithm deletes unneeded samples and only stores those that will be used. This decision is determined by the octonion magnitude and the seven phases. To evaluate the Mc-OVNN algorithm's performance, it is applied to five real-world forecasting problems: the power consumption of a home in Honolulu, HI, USA, Box and Jenkins J series, Euro to Algerian Dinar (DZ) real-time conversion rates, the Mackey-Glass equation, and Europe Brent oil price prediction in a time series. When comparing the Mc-OVNN to other relevant techniques, Mc-OVNN displays its capability for efficient time series prediction. The real-time evaluation of the proposed algorithm is presented using the power consumption of a home in Boumerdès, Algeria, as a case study.