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One of the fundamental tasks in pattern recognition is color image restoration. Every color image has three channels in the RGB color space, in contrast to grayscale images. The restoration of color images is typically far more challenging than that of grayscale images because of the internal relationships among the three channels. Given that the color image restoration can be represented as a dynamic problem with quaternion matrices, a new high order zeroing neural network (HZNN) model is developed to tackle this issue. Specifically, the time-varying quaternion matrix linear equations can be solved using the HZNN design, which is a member of the family of zeroing neural network (ZNN) models that correlate to hyperpower iterative techniques. In a realistic color image restoration application, the HZNN design outperforms the ZNN design, although both approaches work amazingly well.

In today's corporate world, acquiring and keeping clients are the most important priorities. Every business’s market is expanding quickly, which is increasing the number of subscribers. Because neglect could result in a drop in profitability from a major standpoint, it has become imperative for service providers to limit churn rates. These days, identifying which customers are most likely to leave a business requires a lot less work thanks to machine learning. Taking this into account, a novel weights and structure determination (WASD) neural network has been built to meet the aforementioned challenge of customer churn classification, as well as to handle its unique characteristics. Motivated by the observation that WASD neural networks outperform conventional back-propagation neural networks in terms of slow training speed and trapping in a local minimum, we enhance the WASD algorithm's learning process with a new activation function for best adapting to the customer churn model. Superior performance and flexibility to problems are demonstrated in an experimental investigation using a dataset from a telecommunications provider.

Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel HZNN model, called HZ-QNARE, is presented for solving the TQNARE. The model functions fairly well, as demonstrated by two simulation tests. Additionally, the results demonstrated that, while both approaches function remarkably well, the HZNN architecture works better than the ZNN architecture. [ABSTRACT FROM AUTHOR]

The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called 'ZQ-ARE' that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor's flight control system faster than the traditional differential-algebraic Riccati equation solution. [ABSTRACT FROM AUTHOR]

Undoubtedly, one of the most common machine learning challenges is multiclass classification. In light of this, a novel bio-inspired neural network (NN) has been developed to address multiclass classification-related issues. Given that weights and structure determination (WASD) NNs have been acknowledged to alleviate the disadvantages of conventional back-propagation NNs, such as slow training pace and trapping in a local minimum, we developed a bio-inspired WASD algorithm for multiclass classification problems (BWASDC) by using the metaheuristic beetle antennae search (BAS) algorithm to enhance the WASD algorithm's learning process. The BWASDC's effectiveness is then evaluated through applications in occupational classification systems. It is important to mention that systems of occupational classification serve as a fundamental indicator of occupational exposure. For this reason, they are highly significant in social science research. According to the findings of four occupational classification experiments, the BWASDC model outperformed some of the most modern classification models obtainable through MATLAB's classification learner app on all fronts. [ABSTRACT FROM AUTHOR]

Dynamic Sylvester equation (DSE) problems have drawn a lot of interest from academics due to its importance in science and engineering. Due to this, the quest for the quaternion DSE (QDSE) solution is the subject of this work. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. Keeping in mind that the original ZNN can handle QDSE successfully in a noise-free environment, but it might not work in a noisy one, and the noise-resilient ZNN (NZNN) technique is also utilized. In light of that, one new ZNN model is introduced to solve the QDSE problem and one new NZNN model is introduced to solve the QDSE problem under different types of noises. Two simulation experiments and one application to control of the sine function memristor (SFM) chaotic system show that the models function superbly. [ABSTRACT FROM AUTHOR]

Due to its significance in science and engineering, time-varying linear matrix equation (LME) problems have received a lot of attention from scholars. It is for this reason that the issue of finding the minimum-norm least-squares solution of the time-varying quaternion LME (ML-TQ-LME) is addressed in this study. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. In light of that, two new ZNN models are introduced to solve the ML-TQ-LME problem for time-varying quaternion matrices of arbitrary dimension. Two simulation experiments and two practical acoustic source tracking applications show that the models function superbly. [ABSTRACT FROM AUTHOR]

One of the most often used data science techniques in business, finance, supply chain management, production, and inventory planning is time-series forecasting. Due to the dearth of studies in the literature that propose unique weights and structure (WASD) based models for regression issues, the goal of this research is to examine the creation of such a model for time-series forecasting. Given that WASD neural networks have been shown to overcome limitations of traditional back-propagation neural networks, including slow training speed and local minima, a multi-function activatedWASD for time-series (MWASDT) model that uses numerous activation functions, a new auto cross-validation method and a new prediction mechanism are proposed. The MWASDT model was used in forecasting the gross domestic product (GDP) for numerous nations to show off its exceptional capacity for learning and predicting. Compared to previous WASD-based models for time-series forecasting and traditional machine learning models that MATLAB has to offer, the new model has produced noticeably better forecasting results, especially on unseen data. [ABSTRACT FROM AUTHOR]

In recent years, it has become essential to compute the time-varying quaternion (TVQ) matrix Moore-Penrose inverse (MP-inverse or pseudoinverse) to solve time-varying issues in a range of disciplines, including engineering, physics and computer science. This study examines the problem of computing the TVQ matrix MP-inverse using the zeroing neural network (ZNN) approach, which is nowadays considered a cutting edge technique. As a consequence, three new ZNN models are introduced for computing the TVQ matrix MP-inverse in the literature for the first time. Particularly, one model directly employs the TVQ input matrix in the quaternion domain, while the other two models, respectively, use its complex and real representations. In four numerical simulations and a real-world application involving robotic motion tracking, the models exhibit excellent performance. [ABSTRACT FROM AUTHOR]

The efficient solution of the time-varying quaternion matrix inverse (TVQ-INV) is a challenging but crucial topic due to the significance of quaternions in many disciplines, including physics, engineering, and computer science. The main goal of this research is to employ the higher-order zeroing neural network (HZNN) strategy to address the TVQ-INV problem. HZNN is a family of zeroing neural network models that correlates to the hyperpower family of iterative methods with adjustable convergence order. Particularly, three novel HZNN models are created in order to solve the TVQ-INV both directly in the quaternion domain and indirectly in the complex and real domains. The noise-handling version of these models is also presented, and the performance of these models under various types of noises is theoretically and numerically tested. The effectiveness and practicality of these models are further supported by their use in robotic motion tracking. According to the principal results, each of these six models can solve the TVQ-INV effectively, and the HZNN strategy offers a faster convergence rate than the conventional zeroing neural network strategy. [ABSTRACT FROM AUTHOR]