2016/05/25 by Hao Ji, Wenjian Yu, Ji, Hao +3
Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1605.08134
openalex publication_date 2016/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a Rank Revealing Randomized Singular Value\nDecomposition (R3SVD) algorithm to incrementally construct a low-rank\napproximation of a potentially large matrix while adaptively estimating the\nappropriate rank that can capture most of the actions of the matrix. Starting\nfrom a low-rank approximation with an initial guessed rank, R3SVD adopts an\northogonal Gaussian sampling approach to obtain the dominant subspace within\nthe leftover space, which is used to add up to the existing low-rank\napproximation. Orthogonal Gaussian sampling is repeated until an appropriate\nlow-rank approximation with satisfactory accuracy, measured by the overall\nenergy percentage of the original matrix, is obtained. While being a fast\nalgorithm, R3SVD is also a memory-aware algorithm where the computational\nprocess can be decomposed into a series of sampling tasks that use constant\namount of memory. Numerical examples in image compression and matrix completion\nare used to demonstrate the effectiveness of R3SVD in low-rank approximation.\n