# Subspace-Orbit Randomized Decomposition for Low-rank Matrix Approximation

arXiv: https://arxiv.org/abs/1804.00462 · HTML: https://mlsanity.com/paper/1804.00462/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2018.

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## Abstract (arXiv)

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed Subspace-Orbit Randomized singular value decomposition (SOR-SVD), which makes use of random sampling techniques to give an approximation to a low-rank matrix. Given a large and dense data matrix of size m× n with numerical rank k, where k ll min m,n, the algorithm requires a few passes through data, and can be computed in O(mnk) floating-point operations. Moreover, the SOR-SVD algorithm can utilize advanced computer architectures, and, as a result, it can be optimized for maximum efficiency. The SOR-SVD algorithm is simple, accurate, and provably correct, and outperforms previously reported techniques in terms of accuracy and efficiency. Our numerical experiments support these claims.