Sublinear Cost Low Rank Approximation via Subspace Sampling

• Published in: Mathematical Aspects of Computer and Information Sciences Vol. 11989; pp. 89 - 104
• Main Authors: Pan, Victor Y., Luan, Qi, Svadlenka, John, Zhao, Liang
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2020; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: 15A52; 65F30; 65Y20; 68Q25; 68W20; Low-rank approximation; Sublinear cost; Subspace sampling
• ISBN: 3030431193; 9783030431198
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-43120-4_9

Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with LRA can be performed at sublinear cost, that is, by using much fewer memory cells and arithmetic operations than an input matrix has entries. Although every sublinear cost algorithm for LRA fails to approximate the worst case inputs, we prove that our sublinear cost variations of a popular subspace sampling algorithm output accurate LRA of a large class of inputs. Namely, they do so with a high probability (whp) for a random input matrix that admits its LRA. In other papers we propose and analyze other sublinear cost algorithms for LRA and Linear Least Sqaures Regression. Our numerical tests are in good accordance with our formal results.