Results 271 to 280 of about 9,171,861 (296)
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2019
A principal components analysis models high dimensional data points with an accurate, low dimensional, model. Now form a data matrix from the approximate points. This data matrix must have low rank (because the model is low dimensional) and it must be close to the original data matrix (because the model is accurate). This suggests modelling data with a
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A principal components analysis models high dimensional data points with an accurate, low dimensional, model. Now form a data matrix from the approximate points. This data matrix must have low rank (because the model is low dimensional) and it must be close to the original data matrix (because the model is accurate). This suggests modelling data with a
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Convex Envelopes for Low Rank Approximation
2015In this paper we consider the classical problem of finding a low rank approximation of a given matrix. In a least squares sense a closed form solution is available via factorization. However, with additional constraints, or in the presence of missing data, the problem becomes much more difficult.
Viktor Larsson, Carl Olsson
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Low rank approximation of a set of matrices
Proceedings of 2010 IEEE International Symposium on Circuits and Systems, 2010In this paper, we present dynamical systems for computing the low rank approximation of a single matrix and of a set of matrices. These dynamical systems arise from solving an optimization problem involving these matrices. The proposed methods are based on applying smooth optimization techniques on smooth manifolds.
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On the Low-Rank Approximation of Data on the Unit Sphere
SIAM Journal on Matrix Analysis and Applications, 2005Summary: In various applications, data in multidimensional space are normalized to unit length. This paper considers the problem of best fitting given points on the \(m\)-dimensional unit sphere \(S^{m-1}\) by \(k\)-dimensional great circles with \(k\) much less than \(m\).
Moody T. Chu +3 more
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A Schur Method for Low-Rank Matrix Approximation
SIAM Journal on Matrix Analysis and Applications, 1996Summary: The usual way to compute a low-rank approximant of a matrix \(H\) is to take its singular value decomposition (SVD) and truncate it by setting the small singular values equal to 0. However, the SVD is computationally expensive. This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants.
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2019
This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented.
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This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented.
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Generalized Nonconvex Low-Rank Tensor Approximation for Multi-View Subspace Clustering
IEEE Transactions on Image Processing, 2021Zhongyun Hua, Yicong Zhou, Chong Peng
exaly
The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems
SIAM Journal on Matrix Analysis and Applications, 2012Xinzhen Zhang, Chen LING, Liqun Qi
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Empirical Low-Rank Approximation for Seismic Noise Attenuation
IEEE Transactions on Geoscience and Remote Sensing, 2017Yangkang Chen, Yatong Zhou, Yatong Zhou
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