Article
Mathematics, Applied
Ke Li, Gang Wu
Summary: High-dimensionality reduction techniques are crucial in machine learning and data mining, and the randomized GLRAM algorithm based on randomized singular value decomposition (RSVD) offers a more cost-effective solution with superior performance in real-world data sets. The theoretical contributions of the algorithm include discussing the decaying property of singular values, establishing the relationship between reconstruction errors, and investigating the convergence of the algorithm.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Chen Ling, Hongjin He, Liqun Qi
Summary: This paper studies some basic properties of dual quaternion matrices and proposes a method for best low-rank approximation. These results are important for applications in rigid body motion and data reduction.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2022)
Article
Engineering, Electrical & Electronic
Tuersunjiang Yimamu, Toshio Eisaka
Summary: Low-rank matrices are crucial in signal processing and large-scale data analysis. This paper proposes a new method based on generalised Tikhonov regularisation for recovering low-rank matrices from incomplete and indirect observations, effectively correcting errors and reducing outliers and random corruptions.
IET SIGNAL PROCESSING
(2023)
Article
Computer Science, Software Engineering
M. Ridwan Apriansyah, Rio Yokota
Summary: The study introduces two new algorithms for Householder QR factorization of Block Low-Rank (BLR) matrices, achieving arithmetic complexities of O(mn) and O(mn(1.5)) respectively. The algorithms are compared in terms of parallel task-based execution and performance, showing significant speedups compared to dense QR methods. The study also demonstrates robustness to ill conditioning and better orthogonal factors compared to existing methods.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2022)
Article
Optics
Hongli Lv
Summary: In this paper, a despeckling method using generalized low rank approximations of matrices (GLRAM) is proposed to effectively reduce speckle noise in optical coherence tomography (OCT) images. Nonlocal similar blocks are found using the Manhattan distance (MD)-based block matching method, and the left and right projection matrices shared by these blocks are determined using the GLRAM approach. An adaptive method based on asymptotic matrix reconstruction is used to determine the number of eigenvectors present in the projection matrices, and the despeckled OCT image is created by aggregating all the reconstructed image blocks. The proposed method also utilizes an edge-guided adaptive back-projection strategy to improve despeckling performance.
Article
Computer Science, Artificial Intelligence
Hu Zhu, Zhongyang Wang, Taiyu Yan, Yu-Feng Yu, Lizhen Deng, Bing-Kun Bao
Summary: This paper introduces an adaptive tensor completion method based on parallel multi-block ADMM algorithm to address the issue of high missing ratio in nuclear norm minimization. This method derives the model from initial estimate and computes the next estimate from current solution, greatly improving processing power and reliability.
IET IMAGE PROCESSING
(2021)
Article
Mathematics, Applied
Frank de Hoog, Markus Hegland
Summary: A new and improved bound for the Chebyshev norm of the error of a maximal volume pseudo-skeleton matrix approximation is proposed. This bound utilizes all the singular values of the approximated matrix up to the r + 1st rank. It is particularly useful for matrices with slowly decaying singular values and moderate-sized approximation ranks, providing better convergence indication compared to original bounds.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Engineering, Electrical & Electronic
Shuang Xu, Jiangshe Zhang, Chunxia Zhang
Summary: This paper proposes a new method for hyperspectral image denoising, called Hyper-Laplacian spectral-spatial total variation (HTV), and designs two low-rank models. Experimental results demonstrate the superiority of the HTV method over traditional TV regularization methods and other commonly used hyperspectral image denoising algorithms.
Article
Computer Science, Information Systems
Derek Desantis, Erik Skau, Duc P. Truong, Boian Alexandrov
Summary: This work examines the factorizations of binary matrices using standard arithmetic and logical operations, and discusses the uniqueness conditions of the factorization. The introduced method BMFk accurately determines the number of Boolean latent features and reconstructs the factors.
ACM TRANSACTIONS ON KNOWLEDGE DISCOVERY FROM DATA
(2022)
Article
Computer Science, Interdisciplinary Applications
Jun Lang, Chongyang Lin
Summary: Nuclear magnetic resonance (NMR) spectroscopy is widely used in chemistry and medicine to study matter composition and protein spatial structure. To speed up NMR signal acquisition, Non-Uniform Sampling (NUS) methods and mathematical algorithms are used to recover the original NMR signals from NUS data. This paper proposes a Fast Tri-Factorization (FTF) method that decomposes the low-rank Hankel matrix into three small-scale matrices, reducing the computational complexity of singular value decomposition (SVD) and speeding up NMR reconstruction.
JOURNAL OF COMPUTATIONAL SCIENCE
(2023)
Article
Mathematics, Applied
Ali Ruhsen Cete, Oguz Kaan Onay
Summary: The study combines a novel fast-implicit iteration scheme called the alternating cell direction implicit (ACDI) method with the approximate factorization scheme to increase the accuracy of numerical solutions for partial differential equations. By applying the ACDI method to unstructured grids, the study shows improvement in the method's capabilities. The research results validate the enhancements brought by the ACDI method and demonstrate its potential for broader applications beyond structured grids.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2022)
Article
Engineering, Electrical & Electronic
Xiang-Yu Wang, Xiao Peng Li, Hing Cheung So
Summary: Low-rank matrix completion is an important research topic with wide applications. We propose a new rank substitution method using truncated quadratic norm and solve the problem through alternating minimization. Experimental results demonstrate excellent recovery accuracy of our method.
Article
Mathematics, Applied
Patrick Amestoy, Olivier Boiteau, Alfredo Buttari, Matthieu Gerest, Fabienne Jezequel, Jean-Yves L'excellent, Theo Mary
Summary: This research introduces a novel approach that exploits mixed precision arithmetic for low-rank approximations, specifically in the context of block low-rank (BLR) matrices. An LU factorization algorithm is proposed to take advantage of the mixed precision representation of the blocks. Rounding error analysis demonstrates that the use of mixed precision arithmetic does not compromise the numerical stability, leading to significant reductions of storage and time costs.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Computer Science, Artificial Intelligence
Yang Zhou, Yiu-ming Cheung
Summary: A new robust tensor factorization method is proposed, which can automatically determine the tensor rank and infer the trade-off between low-rank and sparse components. By Bayesian treatment and a generalized sparsity-inducing prior, the method excels in preserving low-rank structures and image processing.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2021)
Article
Engineering, Electrical & Electronic
Maboud F. Kaloorazi, Jie Chen
Summary: A new algorithm called PbP-QLP is introduced in this paper for efficiently approximating low-rank matrices without using pivoting strategy, which allows it to leverage modern computer architectures better than competing randomized algorithms. The efficiency and effectiveness of PbP-QLP are demonstrated through various classes of synthetic and real-world data matrices.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)