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We study the classic matrix cross approximation based on the maximal volume submatrices.
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Ivan Oseledets and Eugene Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra and its Applications, 432 (2010) 70–88
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N. Mitrovic, M. T. Asif, U. Rasheed, J. Dauwels, and P. Jaillet. “CUR decomposition for compression and compressed sensing of large-scale traffic data.” In 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013), pp. 1475-1480. IEEE, 2013
2013
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H. Cai, K. Hamm, L. Huang, J. Li, and T. Wang. ”Rapid robust principal component analysis: CUR accelerated inexact low rank estimation.” IEEE Signal Processing Letters 28 (2020): 116-120
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K. Hamm and L. Huang. Perspectives on CUR decompositions. Applied and Computational Harmonic Analysis 48, no. 3 (2020): 1088-1099
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K. Hamm, L. Huang, Stability of Sampling for CUR Decomposition, Foundations of Data Science, Vol. 2, No. 2 (2020), 83-99
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L. Schork and J. Gondzio, Rank revealing Gaussian elimination by the maximum volume concept. Linear Algebra and its Applications, 2020
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K. Allen, A Geometric Approach to Low-Rank Matrix and Tensor Completion, Dissertation, University of Georgia, 2021
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C. Boutsidis and D. P. Woodruff. Optimal CUR matrix decompositions. In Proceedings of the forty-sixth annual ACM symposium on Theory of computing, pp. 353-362. 2014
2014
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Z. Wang, M.-J. Lai, Z. Lu, W. Fan, H. Davulcu, and J. Ye. Orthogonal rank-one matrix pursuit for low rank matrix completion. SIAM Journal on Scientific Computing 37, no. 1 (2015): A488-A514
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Z. Drmac and S. Gugercin. A new selection operator for the discrete empirical interpolation method—improved a priori error bound and extensions. SIAM Journal on Scientific Computing 38, no. 2 (2016): A631-A648
2016
Cited alongside, same era.
D. C. Sorensen and M. Embree. A DEIM Induced CUR Factorization. SIAM Journal on Scientific Computing 38, no. 3 (2016): A1454-A1482
2016
Cited alongside, same era.
Anderson, David, and Ming Gu. ”An efficient, sparsity-preserving, online algorithm for low-rank approximation.” In International Conference on Machine Learning, pp. 156-165. PMLR, 2017
2017
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I. Georgieva and C. Hofreithery, On the Best Uniform Approximation by Low-Rank Matrices, Linear Algebra and its Applications, vol.518(2017), Pages 159–176
2017
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N. Kishore Kumar and J. Schneider, Literature survey on low rank approximation of matrices, Journal on Linear and Multilinear Algebra, vol. 65 (2017), 2212–2244
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A. Mikhaleva and I. V. Oseledets, Rectangular maximum-volume submatrices and their applications, Linear Algebra and its Applications, Vol. 538, 2018, Pages 187–211
2018
Cited alongside, same era.
H, Cai, K. Hamm, L. Huang, D. Needell. Mode-wise tensor decompositions: Multi-dimensional generalizations of CUR decompositions. The Journal of Machine Learning Research 22, no. 1 (2021): 8321-8356
2021
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2021
Later among the works it cites.
M.-J. Lai and Y. Wang. Sparse Solutions of Underdetermined Linear Systems and Their Applications, Society for Industrial and Applied Mathematics, 2021
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H. Cai, L. Huang, P. Li, D. Needell. Matrix completion with cross-concentrated sampling: Bridging uniform sampling and CUR sampling. IEEE Transactions on Pattern Analysis and Machine Intelligence (2023)
2023
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De Pascuale, Sebastian, Kenneth Allen, David L. Green, and Jeremy D. Lore. ”Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition.” Journal of Computational Physics 484 (2023): 112089
2023
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de Hoog, Frank, and Markus Hegland. ”A note on error bounds for pseudo skeleton approximations of matrices.” Linear Algebra and its Applications 669 (2023): 102-117
2023
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2024
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Shen, Zhaiming. “Sparse Solution Technique in Semi-supervised Local Clustering and High Dimensional Function Approximation.” Ph.D. dissertation, University of Georgia, May 2024
2024
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