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Expert Systems with Applications 2025年 286卷

作者： Li, Xiangli Wei, Jiafeng Xie, Tengchi School of Mathematics and Computing Science Guilin University of Electronic Technology Guangxi 541004 China Center for Applied Mathematics of Guangxi Guangxi 541004 China Guangxi Colleges and University Key Laboratory of Data Analysis and Computation Guangxi 541004 China

In order to effectively utilize the consensus and complementary information in multi-view data to achieve better clustering performance, a large number of multi-view clustering algorithms have been proposed. A common multi-view subspace clustering method for mining consensus information is to learn a uniform consensus representation matrix for multiple views. But there are currently studies questioning the rationality of this method. To address this issue, the research in this paper establishes a link between view-specific representation matrices and consensus representation matrices, making the learning of consensus representation matrices more reasonable. Specifically, this paper considers the vectors formed by the representation coefficients of the samples as embeddings of the sample features in the Rm linear space, after which a mapping relationship will be established between the view-specific representation matrices and the consensus representation matrices to learn reasonable consensus representation matrices. Extensive experiments on eight benchmark datasets show that the proposed algorithm is effective and competitive. © 2025 Elsevier Ltd

关键词： Clustering algorithms

A SPECTRAL LEVENBERG-MARQUARDT-DEFLATION METHOD FOR MULTIPLE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEMS

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arXiv 2025年

作者： Li, Lin Zhou, Yuheng Xie, Pengcheng Li, Huiyuan School of Mathematics and Physics University of South China Hengyang China Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory 1 Cyclotron Road BerkeleyCA94720 United States State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China

Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve some applications. Developing an efficient numerical method for finding multiple solutions is very necessary due to the nonlinearity and multiple solutions of these equations. Moreover, providing an efficient iteration plays an important role in successfully obtaining multiple solutions with fast and stable convergence. In the current paper, an efficient algorithm for finding multiple solutions of semilinear elliptic systems is proposed, where the trust region Levenberg-Marquardt method is firstly used to iterate the resulted nonlinear algebraic system. When the nonlinear term in these equations has only the first derivative, our algorithm can efficiently find multiple solutions as well. Several numerical experiments are tested to show the efficiency of our algorithm, and some solutions which have not been shown in the literature are also found and *** Codes 65N35, 65N22, 65F05, 65L10 Copyright © 2025, The Authors. All rights reserved.

关键词： Nonlinear equations

A New Dual-Population Evolutionary Algorithm Leveraging Objective-Constraint Relationships for Constrained Multi-Objective Optimization

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SSRN

SSRN 2025年

作者： Ye, Jialu Tan, Chaogui Xia, Yizhang Hou, Zhanglu Liu, Yuan Zou, Juan Hunan Engineering Research Center of intelligent System Optimization and Security Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan National Applied Mathematics Center China Xiangtan University China

Population co-evolution strategies are widely used to handle constrained multi-objective optimization problems (CMOPs). However, existing coevolutionary algorithms oversimplify population collaboration and are rigid in evolving the auxiliary population, ignoring the importance of maintaining population diversity, especially for CMOPs with irregular feasible regions. To tackle this issue, we propose a new dual-population evolutionary algorithm, denoted as AACMO, which attempts to mine the relational features between the unconstrained Pareto front (UPF) and the constrained Pareto front (CPF) to better adapt to CMOPs with various constraints. Specifically, the method is categorized into two phases: a learning phase and an evolving phase. First, the main population (MP) aims to quickly learn the relationships between the UPF and the CPF by leveraging the advantages of different operators, namely, genetic algorithm operators and differential evolution operators, during the learning phase. Secondly, two auxiliary strategies are designed to collaborate with the MP during the evolving phase. These strategies are capable of employing a more effective co-evolution method to assist the MP in maintaining diversity, based on the degree of alignment between the learned UPF and CPF at the end of the learning phase. The effectiveness of AACMO is confirmed through comparative analysis with eight state-of-the-art algorithms across four CMOP benchmark suites. © 2025, The Authors. All rights reserved.

关键词： Optimization algorithms

Comparing Constraint Evaluation Methods for Shape-Constrained Regression 19thth

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Comparing Constraint Evaluation Methods for Shape-Constrain...

19th International Conference on Computer Aided Systems Theory, EUROCAST 2024

作者： Haider, Christian Bachinger, Florian Holzinger, Florian de França, Fabrício Olivetti Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Hagenberg Austria Johannes Kepler University Linz Austria Center for Mathematics Computing and Cognition Federal University of ABC Santo André Brazil

ISBN: (纸本)9783031829512

Shape-constrained regression is an important desideratum of data-based modeling when you want to enforce your model to possess an expected behavior despite the intrinsic noise of the collected data. Conventional data-based modeling approaches are solely reliant on empirical data, and thus, often fail to incorporate the essential physical constraints inherent to the underlying systems. This leads to a lack of trust in the model and a reduction of explanatory power. Recognizing these limitations of traditional data-based methodologies, the integration of shape constraints, derived from domain expertise or fundamental physical principles, emerges as a promising extension to enhance the quality of models. In this paper, we distinguish between single-objective and multi-objective approaches, as well as soft and hard constraint methods to evaluate the constraint violations of models. In the context of this research, the primary focus is on single-objective approaches that incorporate an expanded scope of features and dynamics for constraint handling. Instead of strictly enforcing hard constraints and discarding solutions solely based on constraint violation, the paper presents a dynamic method for calculating constraint violation and prediction error. The presented approach involves an incremental increase in the weighting of constraint violation during the modeling process, achieving an initial, wide-ranging exploration of the solution space followed by a comprehensive investigation of potential models through an in-depth search. Furthermore, we want to explore the critical issue of premature stagnation, a phenomenon wherein the search for a conformant model, plateaus before reaching an acceptable local optima solution. This paper tries to address this challenge through different strategies to maintain a certain diversity of solutions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Regression analysis

On the -differential spectra of two classes of power functions over finite fields

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Applicable Algebra in Engineering, Communication and computing 2025年 1-30页

作者： Liu, Qian Huang, Zhiwei Chen, Zhixiong Jiang, Rong Zhang, Liupiao Key Laboratory of Information Security of Network Systems College of Computer and Data Science Fuzhou University Fuzhou China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan China Yunnan Key Laboratory of Service Computing Yunnan University of Finance and Economics Kunming China Fujian Key Laboratory of Financial Information Processing Putian University Putian China School of Computer Science and Technology Dongguan University of Technology Dongguan China

Recently, a new concept called multiplicative differential was introduced by Ellingsen et al. [7]. As an extension of the differential uniformity, it is theoretically appealing to determine the properties of c-differential uniformity and the corresponding c-differential spectrum. In this paper, based on certain quadratic character sums and two special elliptic curves over $$\mathbb {F}_p$$ , the $$(-1)$$ -differential spectra of the following two classes of power functions over $$\mathbb {F}_{p^n}$$ is completely determined: (1) $$f_1(x)=x^{\frac{p^n+3}{2}}$$ , where $$p>3$$ and $$p\equiv 3\pmod 4$$ ; (2) $$f_2(x)=x^{p^n-3}$$ , where $$p>3$$ . The obtained result shows that the $$(-1)$$ -differential spectra of $$f_1(x)$$ and $$f_2(x)$$ can be expressed explicitly in terms of n. Moreover, an upper bound of the c-differential uniformity of $$f_2(x)$$ is given.

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Background subtraction based on tensor Robust principal component analysis with side information

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Signal, Image and Video Processing 2025年第8期19卷 1-11页

作者： Xu, Xin Chen, Lixia Wang, Xuewen School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin People’s Republic of China Center for Applied Mathematics of Guangxi (GUET) Guilin People’s Republic of China School of Computer Science and Information Security Guilin University of Electronic Technology Guilin China

In the field of video image processing, moving target detection remains a hot topic. To address the limitations of existing methods in complex environments, This paper proposes a novel TRPCA model based on Tensor Singular Value Decomposition (T-SVD), incorporating the advantages of side information. Firstly, by imposing $$\gamma $$ -norm constraints, the method incorporates feature side information into the background component processing, addresses the over-penalization issue caused by the nuclear norm in traditional RPCA. Secondly, for the foreground part, $$L_{1,1,2}$$ norm and tensor total variation (TTV) regularization constraints are applied to enhance the model’s sensitivity to tubal sparsity and spatiotemporal continuity, effectively reducing the interference of dynamic backgrounds on foreground extraction. To solve this model, we employ the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on the datasets CDnet2014 and LASIESTA demonstrate that the proposed method achieves optimal or near-optimal performance in terms of F-measure for the majority of cases, highlighting its superiority in foreground detection precision.

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Learning with Noisy Labels: the Exploration of Error Bounds in Classification

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arXiv 2025年

作者： Liu, Haixia Li, Boxiao Yang, Can Wang, Yang School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan China Department of Mathematics The Hong Kong University of Science and Technology Clear Water Bay China

Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the presence of noisy labels is of considerable practical significance. In this paper, we focus on the error bounds of excess risks for classification problems with noisy labels within deep learning frameworks. We begin by exploring loss functions with noise-tolerant properties, ensuring that the empirical minimizer on noisy data aligns with that on the true data. Next, we estimate the error bounds of the excess risks, expressed as a sum of statistical error and approximation error. We estimate the statistical error on a dependent (mixing) sequence, bounding it with the help of the associated independent block sequence. For the approximation error, we first express the classifiers as the composition of the softmax function and a continuous function from [0, 1]d to RK. The main task is then to estimate the approximation error for the continuous function from [0, 1]d to RK. Finally, we focus on the curse of dimensionality based on the low-dimensional manifold assumption. Copyright © 2025, The Authors. All rights reserved.

关键词： Risk assessment

A diffuse-interface lattice Boltzmann method for the dissolution through nonlinear heterogeneous reaction

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Physics of Fluids 2025年第5期37卷

作者： Yang, Xiaofeng Zhan, Chengjie Liu, Xi Chai, Zhenhua School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China The State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China

In this work, a diffuse-interface lattice Boltzmann method (DI-LBM) is proposed for the dissolution through nonlinear heterogeneous reaction. In this method, the sharp boundary between the fluid and solid phases is replaced by a diffuse interface with a nonzero thickness. To describe the changes of physical variables from the fluid region to the solid region, a smooth function is introduced, and simultaneously, the nonlinear Robin boundary condition imposed on the fluid-solid interface is reformulated as a source term into the modified convection-diffusion equation. We then test the DI-LBM through several benchmark problems, and find that the numerical results are in agreement with the analytical solutions and available data. Finally, the present DI-LBM is adopted to study the dissolution in a two-dimensional porous medium, and the results show that with the decrease in reaction order, the reactant in the central region with a large fluid velocity reacts faster and forms a conical pathway. © 2025 Author(s).

关键词： Kinetic theory of gases

EHands: Quantum Protocol for Polynomial Computation on Real-Valued Encoded States

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arXiv 2025年

作者： Balewski, Jan Amankwah, Mercy G. Bethel, E. Wes Perciano, Talita Van Beeumen, Roel National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University ClevelandOH44106 United States Computer Science Department San Francisco State University San FranciscoCA94132 United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

The novel constructive EHands protocol defines a universal set of quantum operations for multivariable polynomial transformations on quantum processors by introducing four basic subcircuits—multiplication, addition, negation, and parity flip—and by using expectation-value encoding (EVEN) to represent real numbers in quantum states. These elementary arithmetic operations can be systematically composed to compute degree-d polynomials, Pd(x), on a QPU. The resulting quantum circuit structure closely mirrors the stepwise evaluation of polynomials on a classical calculator, providing an intuitive and efficient approach to polynomial computation on quantum hardware. By enabling direct, predictable polynomial and nonlinear data transformations on a QPU, our method reduces dependence on classical post-processing in hybrid quantum-classical algorithms, enabling advancements in many quantum algorithms. The EHands quantum circuits are compact enough to deliver meaningful and accurate results on today’s noisy quantum processors. We present a detailed implementation of P4(x) and report experimental results for polynomial approximations of common functions, obtained using IBM’s Heron-class quantum processors and an ideal Qiskit simulator. Copyright © 2025, The Authors. All rights reserved.

关键词： Polynomial approximation

GBFRS: Robust Fuzzy Rough Sets via Granular-ball computing

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arXiv 2025年

作者： Xia, Shuyin Lian, Xiaoyu Sang, Binbin Wang, Guoyin Gao, Xinbo Chongqing Key Laboratory of Computational Intelligence Key Laboratory of Big Data Intelligent Computing Key Laboratory of Cyberspace Big Data Intelligent Security Ministry of Education Chongqing University of Posts and Telecommunications Chongqing400065 China College of Computer and Information Science the National Center for Applied Mathematics in Chongqing Chongqing Normal University Chongqing401331 China

Fuzzy rough set theory is effective for processing datasets with complex attributes, supported by a solid mathematical foundation and closely linked to kernel methods in machine learning. Attribute reduction algorithms and classifiers based on fuzzy rough set theory exhibit promising performance in the analysis of high-dimensional multivariate complex data. However, most existing models operate at the finest granularity, rendering them inefficient and sensitive to noise, especially for high-dimensional big data. Thus, enhancing the robustness of fuzzy rough set models is crucial for effective feature selection. Muiti-garanularty granular-ball computing, a recent development, uses granular-balls of different sizes to adaptively represent and cover the sample space, performing learning based on these granular-balls. This paper proposes integrating multi-granularity granular-ball computing into fuzzy rough set theory, using granular-balls to replace sample points. The coarse-grained characteristics of granular-balls make the model more robust. Additionally, we propose a new method for generating granular-balls, scalable to the entire supervised method based on granular-ball computing. A forward search algorithm is used to select feature sequences by defining the correlation between features and categories through dependence functions. Experiments demonstrate the proposed model’s effectiveness and superiority over baseline methods. The source codes and datasets are both available on the public link: https://***/lianxiaoyu724/GBFRS Copyright © 2025, The Authors. All rights reserved.

关键词： Granular computing