Optimal CUR Matrix Decompositions [PDF]
Proceedings of the forty-sixth annual ACM symposium on Theory of computing, 2014 The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank matrix $U$ such that the matrix $C U R$ approximates the matrix $A,$ that is, $ || A - CUR ||_F^2 \le (1+ε) |
Christos Boutsidis, David P. Woodruff
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Empirical Bayes Linked Matrix Decomposition. [PDF]
Mach LearnData for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies may capture different feature sets (e.g., corresponding to rows in a matrix) and/or different sample populations ...
Lock EF.
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Singular-Value-Decomposition-Based Matrix Surgery
EntropyThis paper is motivated by the need to stabilise the impact of deep learning (DL) training for medical image analysis on the conditioning of convolution filters in relation to model overfitting and robustness.
Jehan Ghafuri, Sabah Jassim
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Interpretable, Scalable, and Transferrable Functional Projection of Large-Scale Transcriptome Data Using Constrained Matrix Decomposition. [PDF]
Front Genet, 2021 Panchy N, Watanabe K, Hong T.
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A prognostic model related to necrotizing apoptosis of breast cancer based on biorthogonal constrained depth semi-supervised nonnegative matrix decomposition and single-cell sequencing analysis. [PDF]
Am J Cancer Res, 2023 Gao Y +6 more
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Cross-domain information fusion and personalized recommendation in artificial intelligence recommendation system based on mathematical matrix decomposition. [PDF]
Sci RepMeng X.
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Mathematical Modelling and Control, 2023 This paper investigated the Kronecker product (KP) decomposition of the Boolean matrix and analyzed the topological structure of Kronecker product Boolean networks (KPBNs).
Xiaomeng Wei, Haitao Li, Guodong Zhao
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Singular Value Decomposition of Spatial Matrices
Современные информационные технологии и IT-образование, 2022 Singular value decomposition is a basic building block which is used in solution of many different problems. In cases when dimensionality of a problem exceeds two, a generalization of a singular value decomposition – tensor decompositions – are used ...
Pavel Iljin, Tatiana Samoilova
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Energy-Based Adaptive CUR Matrix Decomposition
IEEE Access, 2023 CUR decompositions are interpretable data analysis tools that express a data matrix in terms of a small number of actual columns and/or actual rows of the data matrix.
Liwen Xu, Xuejiao Zhao, Yongxia Zhang
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Prime decomposition of quadratic matrix polynomials
AIMS Mathematics, 2021 We study the prime decomposition of a quadratic monic matrix polynomial. From the prime decomposition of a quadratic matrix polynomial, we obtain a formula of the general solution to the corresponding second-order differential equation.
Yunbo Tian, Sheng Chen
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