scholarly journals Randomized SVD Methods in Hyperspectral Imaging

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Jiani Zhang ◽  
Jennifer Erway ◽  
Xiaofei Hu ◽  
Qiang Zhang ◽  
Robert Plemmons
Keyword(s):  
Lossless Compression ◽  
Principal Component ◽  
Low Rank ◽  
Random Projections ◽  
Matrix Approximation ◽  
Numerical Tests ◽  
Rank Matrix ◽  
Approximation Errors ◽  
Value Decomposition ◽  
Low Rank Matrix

We present a randomized singular value decomposition (rSVD) method for the purposes of lossless compression, reconstruction, classification, and target detection with hyperspectral (HSI) data. Recent work in low-rank matrix approximations obtained from random projections suggests that these approximations are well suited for randomized dimensionality reduction. Approximation errors for the rSVD are evaluated on HSI, and comparisons are made to deterministic techniques and as well as to other randomized low-rank matrix approximation methods involving compressive principal component analysis. Numerical tests on real HSI data suggest that the method is promising and is particularly effective for HSI data interrogation.

scholarly journals Least upper bound of truncation error of low-rank matrix approximation algorithm using QR decomposition with pivoting

2021 ◽  
Author(s):  
Haruka Kawamura ◽  
Reiji Suda
Keyword(s):  
Upper Bound ◽  
Truncation Error ◽  
Qr Decomposition ◽  
Low Rank ◽  
Matrix Approximation ◽  
Low Rank Approximation ◽  
Rank Matrix ◽  
Rank Approximation ◽  
Value Decomposition ◽  
Low Rank Matrix

AbstractLow-rank approximation by QR decomposition with pivoting (pivoted QR) is known to be less accurate than singular value decomposition (SVD); however, the calculation amount is smaller than that of SVD. The least upper bound of the ratio of the truncation error, defined by $$\Vert A-BC\Vert _2$$ ‖ A - B C ‖ 2 , using pivoted QR to that using SVD is proved to be $$\sqrt{\frac{4^k-1}{3}(n-k)+1}$$ 4 k - 1 3 ( n - k ) + 1 for $$A\in {\mathbb {R}}^{m\times n}$$ A ∈ R m × n $$(m\ge n)$$ ( m ≥ n ) , approximated as a product of $$B\in {\mathbb {R}}^{m\times k}$$ B ∈ R m × k and $$C\in {\mathbb {R}}^{k\times n}$$ C ∈ R k × n in this study.

Adaptive Local Low-rank Matrix Approximation for Recommendation

2019 ◽  
Vol 37 (4) ◽  
pp. 1-34 ◽  
Author(s):  
Huafeng Liu ◽  
Liping Jing ◽  
Yuhua Qian ◽  
Jian Yu
Keyword(s):  
Low Rank ◽  
Matrix Approximation ◽  
Rank Matrix ◽  
Low Rank Matrix ◽  
Low Rank Matrix Approximation

scholarly journals Convergence of Gradient Descent for Low-Rank Matrix Approximation

2015 ◽  
Vol 61 (8) ◽  
pp. 4451-4457 ◽  
Author(s):  
Renaud-Alexandre Pitaval ◽  
Wei Dai ◽  
Olav Tirkkonen
Keyword(s):  
Gradient Descent ◽  
Low Rank ◽  
Matrix Approximation ◽  
Rank Matrix ◽  
Low Rank Matrix ◽  
Low Rank Matrix Approximation
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