Sketching for low-rank nonnegative matrix approximation: Numerical study

TL;DR

This paper introduces randomized sketching methods for low-rank nonnegative matrix approximation, demonstrating faster computation with comparable convergence to existing deterministic approaches through numerical experiments.

Contribution

It presents novel randomized sketching algorithms for low-rank nonnegative matrix approximation and analyzes their computational complexity and performance.

Findings

Randomized methods are faster than deterministic ones.

The proposed algorithms have similar convergence properties.

Numerical experiments confirm efficiency and effectiveness.

Abstract

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose factors can be arbitrary. We calculate the computational complexities of the proposed methods and evaluate their performance in numerical experiments. The comparison with the known deterministic alternating projection methods shows that the randomized approaches are faster and exhibit similar convergence properties.