Fast CUR Approximation of Average Matrix and Extensions
Year: 2016
Type: preprint
Abstract: CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra and have applications to a variety of other highly important areas of modern computing as well -- they range from machine learning theory and neural networks to data mining and analysis. We first dramatically accelerate computation of such approximations for the average input matrix, then show some narrow classes of hard inputs for our algorithms, and finally narrowing such classes further by means of preprocessing with sparse and structured multipliers. Our extensive numerical tests with a variety of real world inputs from a Singular Matrix Database have consistently produced reasonably close CUR approximations at a low computational cost, and we conclude with novel extensions of our acceleration of CUR and low-rank approximation to the Fast Multipole Method and Conjugate Gradient Algorithms. The techniques of our algorithm design and analysis and some auxiliary results, e.g., on convergence of the probability distribution of the products of randomized bidiagonal matrices to Gaussian distribution, can be of independent interest.
Source: arXiv (Cornell University)
Authors: Victor Y. Pan, John Svadlenka, Liang Zhao
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2554005738