Results 1 to 10 of about 150,932 (264)
Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups [PDF]
SIAM Journal on Matrix Analysis and Applications, 2004 The polar decomposition of \(A\) is \(A=UH\), where \(A\) has complex elements, \(U\) is unitary, \(H\) is Hermitian positive semi-definite. The authors identify a family of globally convergent rational iterations that preserve group structure. They show how the structure preservation leads to particularly convenient convergence tests in the case of ...
Nicholas Higham +2 more
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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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Fast Polar Decomposition of an Arbitrary Matrix [PDF]
SIAM Journal on Scientific and Statistical Computing, 1990 The polar decomposition of an $m \times n$ matrix A of full rank, where $m \geqq n$, can be computed using a quadratically convergent algorithm of Higham [SIAM J. Sci. Statist. Comput., 7(1986), pp. 1160–1174]. The algorithm is based on a Newton iteration involving a matrix inverse.
Nicholas Higham
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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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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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Frontiers in Neuroscience, 2022 Multi-modal magnetic resonance imaging (MRI) is widely used for diagnosing brain disease in clinical practice. However, the high-dimensionality of MRI images is challenging when training a convolution neural network.
Liangliang Liu +5 more
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Incremental multi‐view correlated feature learning based on non‐negative matrix factorisation
IET Computer Vision, 2021 In real‐world applications, large amounts of data from multiple sources come in the form of streams. This makes multi‐view feature learning cost much time when new instances rise incrementally.
Liang Zhao +3 more
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IET Control Theory & Applications, 2023 The approximating sequence Riccati equation method is an efficient approach for solving the nonlinear optimal control problems, but its neglect of nonlinear dynamics and necessary optimality condition makes the control law difficult to satisfy the ...
Jianfeng Sun, Xuesong Chen
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Improvement of CRF-Based Saliency Detection Algorithm Using Matrix Decomposition Based Features [PDF]
مدیریت مهندسی و رایانش نرم, 2020 One of the most important processing steps in the human vision system is the detection of a scene saliency map. Since saliency map can be applied to algorithms such as segmentation, compression and image retrieval, Researchers have focused on providing ...
Mohammad Shouryabi +1 more
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