Work

Energy-Based Sequential Sampling for Low-Rank PSD-Matrix Approximation

Year: 2024

Type: article

Abstract: . We introduce a pseudoconvex differentiable relaxation of the column-sampling problem for the Nyström approximation of positive-semidefinite (PSD) matrices. The relaxation is based on the interpretation of PSD matrices as integral operators and relies on the supports of measures to characterize samples of columns. We describe a class of gradient-based sequential sampling strategies which leverages the properties of the considered framework, and we demonstrate its ability to produce accurate Nyström approximations. The time-complexity of the stochastic variants of the discussed strategies is linear in the order of the considered matrices, and the underlying computations can be easily parallelized.

Source: SIAM Journal on Mathematics of Data Science

DOI: 10.1137/23m162449x

Authors: Matthew Hutchings, Bertrand Gauthier

Institution: Cardiff University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Engineering and Physical Sciences Research Council

Awards: DTP 2020-2021 Cardiff University, G8962097125