Randomized QLP decomposition

Wu, Nian-Ci; Xiang, Hua

doi:10.1016/j.laa.2020.03.041

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…The authors made use of Flip-Flop SRQR for robust principal component analysis [29] and tensor decomposition applications. The work in [47] presented randomized QLP decomposition algorithm; the authors have replaced the SVD in R-SVD [24] by p-QLP [18] and presented error bounds (in expected value) for the approximate leading singular values of the matrix.…”

Section: Outputmentioning

confidence: 99%

Projection-based QLP Algorithm for Efficiently Computing Low-Rank Approximation of Matrices

Kaloorazi,

Chen

2021

Preprint

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Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is computationally prohibitive for large matrices. In this paper, we introduce a new algorithm termed Projection-based Partial QLP (PbP-QLP) that efficiently approximates the p-QLP with high accuracy. Fundamental in our work is the exploitation of randomization and in contrast to the p-QLP, PbP-QLP does not use the pivoting strategy. As such, PbP-QLP can harness modern computer architectures, even better than competing randomized algorithms. The efficiency and effectiveness of our proposed PbP-QLP algorithm are investigated through various classes of synthetic and real-world data matrices.

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Section: Outputmentioning

confidence: 99%

Projection-based QLP Algorithm for Efficiently Computing Low-Rank Approximation of Matrices

Kaloorazi,

Chen

2021

Preprint

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“…The MATLAB pseudo-code of rank-k randomized QLP decomposition algorithm is described as in Algorithm 2 [23].…”

Section: Randomized Qlp Decompositionmentioning

confidence: 99%

“…Algorithm 2 Randomized QLP decomposition(RQLP) [23] Input: A ∈ R m×n , target rank: k ≥ 2, oversampling parameter: p ≥ 2, and number of columns sampled: l = k + p. Output: Matrices Q, L, P such that A ≈ QLP T , where Q is a column orthogonal matrix, P is a orthogonal matrix and L is a lower triangular matrix.…”

Section: Randomized Qlp Decompositionmentioning

confidence: 99%

“…In this section, we give some numerical examples to illustrate the effectiveness of Algorithms 3-4. We also compare our algorithms with Algorithm 1 from [12] and Algorithm 2 from [23]. All experiment are performed by using MATLAB 2019b on a personal laptop with an Intel(R) CPU i5-10210U of 1.6 GHz and 8 GB of RAM.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In order to reduce the cost of data communication, some single-pass algorithms have been proposed [17][18][19][20][21][22]. In this paper, based on the idea of single-pass, we extend the work of Wu and Xiang [23] to the single-pass randomized QLP decomposition for computing low-rank approximation, where two randomized algorithms are provided. We also give the bounds of matrix approximation error and singular value approximation error for the proposed randomized algorithms, which hold with high probability.…”

Section: Introductionmentioning

confidence: 99%

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Single-pass randomized QLP decomposition for low-rank approximation

Ren¹,

Bai²

2020

Preprint

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The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the lowrank matrix approximation. Compared with the deterministic QLP decomposition, the complexity of the proposed algorithms does not increase significantly and the system matrix needs to be accessed only once. Therefore, our algorithms are very suitable for a large matrix stored outside of memory or generated by stream data. In the error analysis, we give the bounds of matrix approximation error and singular value approximation error. Numerical experiments also reported to verify our results.

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