The nonnegative representation-based classification only imposes an overall nonnegative constraint on the representation coefficients but fails to apply differentiated penalties on the coefficients of different classes, which inevitably limits its effectiveness. In response, this article proposes a dual flexible competitive nonnegative representation method, which introduces two competitive mechanisms: mean competition and inter-class competition. Mean competition relies on the class-wise mean of training samples as the competitive target, encouraging the representation coefficients to accurately capture the unique features of each class and enhancing the discriminability between the representation coefficients. Inter-class competition fully considers the intrinsic relationship between the overall representation and the class representations, strengthening the competitive representation between the true class and all remaining classes, thereby improving classification performance. Meanwhile, flexible factors are ingeniously incorporated into both competitive terms to effectively reduce interference from incorrect classes in the classification decision. The alternating direction method of multipliers is employed to solve the dual flexible competitive nonnegative representation problem, with a comprehensive explanation of the iterative procedure provided. Experimental findings indicate that the dual flexible competitive nonnegative representation method demonstrates significant advantages in face recognition tasks. The source code will be made available upon the acceptance of this article at https://github.com/li-zi-qi/DFCNR .

In this study, we aim to comprehensively explore the application of principal component analysis (PCA) and independent component analysis (ICA), considering their practical utility. We compare these two methods theoretically and practically, using both real data and simulated data. PCA and ICA algorithms are often treated as black boxes, therefore they are often seen as complex algorithms. In this research, we’ll break down some of the theory behind ICA. Subsequently, we compare principal component regression (PCR) and independent component regression (ICR) in both real and simulated datasets. Our objectives include data analysis and explanation of the superiority of each method (ICA and PCA) across different datasets. We will propose solutions to improve the performance of ICR and PCR regressions for datasets with structures suited to ICA and PCA.

Effective proportional–integral–derivative controller tuning is critical for attaining high-performance operation in direct current motor systems, especially when traditional approaches fail under nonlinear or uncertain dynamics. This study conducted a statistically robust comparative analysis of seven evolutionary algorithms for proportional–integral–derivative gain tuning: genetic algorithm, particle swarm optimisation, shuffled frog leaping algorithm, firefly algorithm, artificial bee colony, simulated annealing and invasive weed optimisation algorithm. Simulations were performed in MATLAB/Simulink using two different tuning scenarios: Case 1 (conservative bounds) and Case 2 (aggressive bounds), with the integral time absolute error serving as the primary performance metric. Analysis of variance, Tukey's honestly significant difference and Cohen's d were employed to ensure statistical validity. The results revealed distinct trade-offs among the algorithms. Particle swarm optimisation achieved the best overall performance, with a minimal integral time absolute error mean of 190.54 in Case 2, low volatility and a moderate execution time of 1200.19 s. The invasive weed optimisation algorithm was the fastest algorithm, with execution times of 285.76 and 371.43 s in Cases 1 and 2, respectively, but it exhibited higher integral time absolute error variability. Simulated annealing and the firefly algorithm yielded the lowest integral time absolute error means (158.74 and 160.22, respectively) in Case 1, but they required the highest computational time (up to 20,567.84 s for simulated annealing). In contrast, the artificial bee colony performed the worst, with a Case 2 integral time absolute error mean of 422.38 and significant gain inconsistency. Statistical analysis with analysis of variance, Tukey's honestly significant difference and Cohen's d revealed the significance of the differences. This work provides evidence-based guidance for selecting evolutionary algorithms in proportional–integral–derivative tuning based on system priorities. A hybrid invasive weed optimisation algorithm–particle swarm optimisation framework is proposed as a promising future direction, combining the rapid global search of invasive weed optimisation algorithm with the reliable convergence of particle swarm optimisation for real-time, high-precision control.

The nonnegative representation-based classification (NRC) method has attracted increasing attention in the field of face recognition. Building upon collaborative representation (CR), NRC incorporates a nonnegative constraint on the representation coefficients, thereby reducing the contribution of irrelevant training samples and enhancing overall classification performance. Despite these improvements, NRC inherits the same decision-making mechanism as the CR method, resulting in a decoupling of the representation and classification stages. This separation limits the method’s classification effectiveness. Furthermore, the presence of multicollinearity in the nonnegative representation may introduce inaccuracies in classification estimates, further undermining performance. To address these limitations, this paper proposes the competitive-collaborative nonnegative representation (CCNR) model. CCNR integrates two regularization terms: A competitive constraint and a collaborative constraint. The competitive constraint adopts a residual-based strategy during the classification stage, thereby strengthening the connection between representation and classification. This approach enables training samples from different classes to compete in representing the query sample, significantly improving classification performance. In parallel, the collaborative constraint applies an ℓ 2 -norm regularization to the representation coefficients, enhancing the stability of the model’s solution. Moreover, the CCNR model has been effectively deployed in smart campus environments. Extensive comparative experiments conducted on publicly available face datasets validate the effectiveness of the proposed model, consistently demonstrating its competitive performance. Habitually, the source code will be made available on the author’s profile page at https://github.com/li-zi-qi/CCNR .

Accurate time-series classification (TSC) remains a fundamental challenge in deep learning due to the complexity and variability of temporal patterns. While recurrent neural networks (RNNs) such as LSTM and GRU have shown promise in modeling sequential dependencies, they often suffer from limitations like vanishing gradients and high computational cost when handling long sequences. To overcome these issues, convolutional neural networks (CNNs), particularly the Inception architecture, have emerged as powerful alternatives due to their ability to capture multiscale local patterns efficiently. In this study, we propose InceptionResNet, a hybrid deep learning framework that integrates the residual learning mechanism of ResNet into the InceptionTime architecture. By replacing the fully convolutional network (FCN) shortcut module in InceptionFCN with ResNet-50, the model gains deeper representational capacity and improved gradient flow during training. We conduct extensive experiments on the UCR-85 benchmark dataset, comparing our model against state-of-the-art approaches, including InceptionTime, InceptionFCN, ResNet, FCN, and MLP. The results show that InceptionResNet achieves superior accuracy on 49 of 85 datasets, demonstrating its robustness and effectiveness in handling diverse and complex time series data. This work highlights the potential of integrating multiscale feature extraction and deep residual learning to advance the performance of TSC models in practical applications.

Using topological summary tools such as persistence landscapes have greatly enhanced the practical usage of topological data analysis to analyze large-scale, noisy, and complex datasets. A central element of persistence landscape usage involves computing the top- k landscapes. This article presents a novel output-sensitive plane sweep algorithm for computing the top- k persistence landscapes in optimal time and space: significantly outperforming previous algorithms. Our algorithm can determine in optimal O ( n * log ( n ) ) if a given birth-death pair appears in the top- k landscapes. The runtime performance of the approach on a botnet dataset and several synthetically generated point cloud topologies, showing that the algorithm can achieve significant speedups for these datasets due to its better algorithmic design. The speedups seen range from slightly worse (in some extreme examples) to equal compared to previous works while returning exactly the same output and is significantly faster when filtering is used (15x for birth-death pairs when removing 75% of birth-death pairs). Filtering is shown to maintain machine learning performance on both synthetically generated and real world datasets while providing orders of magnitude speedup depending on how intensive of filtering is done. Due to the introduced algorithm’s algorithmic design, the speedup seen is greater when filtering using the introduced birth-death filtering algorithm. The software is freely provided in Rust with Python bindings online.

This study adopts the quantile regression method to analyze the influencing factors of low-income, middle-income, and high-income groups at the national, urban, and rural levels in China, respectively, at the quantiles of 0.05, 0.20, 0.50, 0.80, and 0.95. Subsequently, the GM(1, 1) model within the gray-system theory is utilized to predict the proportion of the middle-income group in China in the future. By comparing the prediction results from 2010 to 2017 with the data of the proportion of the middle-income group at the national, urban, and rural levels obtained through kernel density estimation, it is found that the gray-system prediction exhibits high accuracy and satisfactory results. The implications of this study for future social development may lie in providing a certain degree of data reference for social governors.

This article proposes a novel approach for trajectory tracking of a six degrees-of-freedom (6-DOF) collaborative robot manipulator using an adaptive fuzzy proportional derivative (PD) controller. Based on the dynamic modeling of the robot manipulator, the PD control law is designed, and the improved dung beetle optimization (DBO) algorithm is introduced using the good point set (GPS) method for population initialization and the sine strategy for convergence factor adjustment. Furthermore, a fuzzy adaptive strategy is developed to adjust the PD controller gain based on real-time errors. This article uses discrete Lyapunov iterative stability to analyze the global asymptotic stability of the robot closed-loop system. The experimental results verify that the DBO-fuzzy-PD controller is superior to the original PD controller. The ISE value is reduced from 3.4140 to 0.0384, and the IAE value is reduced from 1.9876 to 0.1843. The DBO-fuzzy-PD controller has better tracking accuracy and response speed than traditional PD. Experimental results show that the proposed DBO-fuzzy-PD controller significantly enhances the trajectory tracking performance of the 6-DOF collaborative robot manipulator.

In manufacturing, especially in oil flow filtration, combustion systems, cooling turbines, and other areas, heat transfer performance through hybrid nanofluids (HNFs) is a key factor in achieving dominance of the final product. The present study deals with the movement of the fluid containing tri-hybrid nanoparticles on an excessively large stagnation point area on a smooth plate in a permeable medium. Additionally, the leading partial differential equations of the proposed model are converted to ordinary differential equations (ODEs) by incorporating similarity variables, and the fourth-order Runge–Kutta method is then used to solve these. To find the missing initial conditions of first-order ODEs, a shooting technique is also used. Furthermore, the consequences of heat transmission rate in the form of graphs and tables are explored. It is noticed that by enhancing the strength of the solid volume fraction the skin friction along the x-axis ( f ″ ( 0 ) or C F X ) increases as γ ∈ ( − 2 , 10 ] and decreases for the values of γ ∈ [ − 10 , 2 ) . But the converse of this behavior is true for g ″ ( 0 ) = C F Y . Moreover, the ternary fluid has taken the most significant effect on the Nusselt number, that is, 17.12978%, 8.43809%, and 19.20192% increment for Go, Ag and Cu type mono-nanofluid and 12.67309%, 18.13489%, and 13.65317% enhancement for HNF (Go-Ag, Go-Cu, Ag-Cu, respectively).

In this paper, we introduce a new approximation of the cumulative distribution function of the standard normal distribution based on Tocher's approximation. Also, we assess the quality of the new approximation using two criteria namely the maximum absolute error and the mean absolute error. The approximation is expressed in closed form and it produces a maximum absolute error of 4.43 × 10 − 10 , while the mean absolute error is 9.62 × 10 − 11 . In addition, we propose an approximation of the inverse cumulative function of the standard normal distribution based on Polya approximation and compare the accuracy of our findings with some of the existing approximations. The results show that our approximations surpass other the existing ones based on the aforementioned accuracy measures.