Article
Computer Science, Artificial Intelligence
Bingxin Zhou, Xuebin Zheng, Yu Guang Wang, Ming Li, Junbin Gao
Summary: This paper presents a new graph representation learning scheme called EGG, which preserves the similarity relationship of original graph data in the embedded space and demonstrates superior performance in clustering and classification tasks.
Article
Computer Science, Information Systems
Wentao Rong, Enhong Zhuo, Hong Peng, Jiazhou Chen, Haiyan Wang, Chu Han, Hongmin Cai
Summary: The proposed integrative multi-view subspace clustering method learns a consensus affinity by merging subspace representations of different views on a Grassmann manifold, enhancing clustering performance while preserving geometric structures. The method outperforms state-of-the-art approaches on synthetic and real-world datasets, extracting highly representative and latent common information for improved clustering performance.
INFORMATION SCIENCES
(2021)
Article
Mathematics, Applied
Tim Marrinan, P-A Absil, Nicolas Gillis
Summary: This paper discusses the problem of finding the minimax center of linear subspaces, proposing a method to find the center of a minimum enclosing ball on a Grassmann manifold. Despite the undefined problem for subspaces of differing dimensions, it can be solved through geometric mappings and an optimization problem parameterized by the rank of the minimax center is proposed. The solution is computed using subgradient algorithms, aiming to jointly recover the optimal dimension and subspace that best represents the data.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
Ahmad Y. Al-Dweik, Ryad Ghanam, Gerard Thompson, Hassan Azad
Summary: This article introduces a new method to solve the problem of finding the common invariant subspaces of a single or of a set of matrices. The method utilizes common eigenvectors for the exterior powers of the matrices and employs the Plucker relations to ensure that these eigenvectors correspond to subspaces or provide initial constraints for eigenvectors involving parameters. The article also provides a procedure for computing the divisors of a totally decomposable vector and demonstrates the use of coding in Maple for performing the calculations. The main motivation of the research lies in Lie symmetry, where explicit and comprehensive knowledge of the invariant subspaces of the adjoint representations for the Lie symmetry algebra of a differential equation is necessary to determine all the ideals of the Lie symmetry algebra.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2023)
Article
Computer Science, Information Systems
Predrag B. Petrovic
Summary: This paper presents new current mode grounded memcapacitor emulator circuits based on VDTA and two grounded capacitors. The circuits have a single active component matching constraint and can use MOS capacitors in a high frequency range. The emulator offers a variable switching mechanism and the possibility of negative memcapacitance.
Article
Mathematics, Applied
Samuel E. Otto, Alberto Padovan, Clarence W. Rowley
Summary: Reduced-order modeling techniques accurately capture dynamics, but neglect low-energy features with high dynamical significance for nonlinear systems far from equilibria. To improve accuracy, we propose optimizing reduced-order models using coarsely sampled trajectories from the original system.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Francesco Romor, Marco Tezzele, Andrea Lario, Gianluigi Rozza
Summary: Nonlinear extensions of the active subspaces method have achieved remarkable results in dimension reduction for parameter space and response surface design. The researchers further developed a kernel-based nonlinear method that considers the reduction of parameter space for multivariate objective functions. They thoroughly discussed the implementation and tested it on more challenging benchmarks than those previously reported. Additionally, they presented a complete pipeline for designing response surfaces using this new methodology in the context of parametric computational fluid dynamics.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Chemistry, Multidisciplinary
Martin Mrovec, J. A. Berger
Summary: A local optimization algorithm is proposed for solving the Kohn-Sham equations, which minimizes the energy functional under equality constraints without requiring eigendecomposition. The algorithm aims to reduce the number of matrix evaluations and compete with the standard SCF approach accelerated by DIIS. Numerical experiments show high reliability of the algorithm in cases where SCF iterations fail to converge, with most cases converging to the correct solution after randomizing the initial approximation.
JOURNAL OF COMPUTATIONAL CHEMISTRY
(2021)
Article
Computer Science, Artificial Intelligence
Danyang Wu, Zhanxuan Hu, Feiping Nie, Rong Wang, Hui Yang, Xuelong Li
Summary: This paper proposes a novel multi-view clustering method, MCIM, which learns a uniform graph and spectral embedding through an interactive mechanism, promoting each other. Experimental results demonstrate the superiority of MCIM on real image datasets compared to several SOTA methods.
Article
Engineering, Multidisciplinary
Mian Xiao, WaiChing Sun
Summary: This paper introduces a new elastoplasticity model which utilizes deep geometric learning to reconstruct the yield surface based on a set of data points in a parametric space. The use of coordinate charts and local parametrization provides advantages in terms of accuracy and feasibility.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Electrical & Electronic
Yanan Ma, Ming Li, Yang Liu, Qingqing Wu, Qian Liu
Summary: This paper investigates the design problem of dual-functional active RIS in RIS-enhanced multiuser multiple-input single-output systems, and proposes a DF-ARIS architecture that can simultaneously achieve reflection and transmission functionalities. Efficient iterative algorithms and optimization techniques are developed to address the non-convexity problem. Simulation results demonstrate the superiority of the proposed architecture and algorithms in extending signal coverage and enhancing service quality.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Zhenhai Liu, Nikolaos S. Papageorgiou
Summary: This article studies an eigenvalue problem for the Dirichlet (p, q)-Laplacian, where q is a variable with q(z) < p for all z in Ω. Using the Nehari method, a complete description of the spectrum is given in terms of the principal eigenvalue of (-∆p, W1,p0(Ω)).
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Sanpeng Zheng, Renzhong Feng
Summary: The variable projection (VP) method is a classical and effective approach for solving the separable nonlinear least squares (SNLLS) problem. While the classical VP method has been applied to one-output radial basis function neural networks (ORBFNN), this study proposes a new VP method for general radial basis function neural networks (GRBFNN) that can have multiple output neurons. The new VP method transforms the SSE minimization problem of GRBFNN into a lower-dimensional optimization problem, and theoretical analysis shows that the stationary points of the lower-dimensional problem are equivalent to those of the original objective function. Numerical experiments demonstrate that minimizing the new objective function leads to faster convergence, smaller training errors, and smaller testing errors compared to minimizing the original objective function.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Proceedings Paper
Acoustics
Roberto Pereira, Xavier Mestre, David Gregoratti
Summary: A methodology based on the alignment of column spaces is proposed for clustering multiple sets of Gaussian multivariate complex observations. This method compares subspaces identified with points in the Grass-mann manifold using a similarity measure derived from a chosen manifold distance. By normalizing the decision statistics, a new statistic exclusively built from the observations is obtained, leading to improved classification performance.
2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
(2022)
Proceedings Paper
Acoustics
Maha Mahyub, Lincon S. Souza, Bojan Batalo, Kazuhiro Fukui
Summary: In this paper, a signal latent subspace (SLS) method is proposed as an alternative sound classification approach, achieving competitive results without requiring a large amount of data by extracting sound features using pre-trained CNN models and unifying them on a product Grassmann manifold for classification.
2022 INTERNATIONAL WORKSHOP ON ACOUSTIC SIGNAL ENHANCEMENT (IWAENC 2022)
(2022)
Article
Mathematics, Applied
Jeffrey M. Hokanson, Paul G. Constantine
Summary: The Lipschitz matrix is a generalization of the scalar Lipschitz constant for functions with many inputs, providing a function-dependent metric and improving performance in computational science tasks. The Lipschitz matrix reduces worst-case cost and dimensionality curse, with the ability to define uncertainty and perform parameter reduction in complex computational models.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Jeffrey M. Hokanson
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)
Article
Mathematics, Applied
Jeffrey M. Hokanson, Caleb C. Magruder
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)