Randomized Nonnegative Matrix Factorization

TL;DR

This paper introduces a randomized hierarchical alternating least squares algorithm for nonnegative matrix factorization, enabling efficient computation on large datasets with significant speed improvements over traditional methods.

Contribution

It proposes a novel randomized HALS algorithm that scales NMF to big data by deriving smaller matrices for faster computation.

Findings

Achieves substantial speedups over deterministic HALS

Maintains near-optimal factorization quality

Effective on both synthetic and real-world data

Abstract

Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper presents a randomized hierarchical alternating least squares (HALS) algorithm to compute the NMF. By deriving a smaller matrix from the nonnegative input data, a more efficient nonnegative decomposition can be computed. Our algorithm scales to big data applications while attaining a near-optimal factorization. The proposed algorithm is evaluated using synthetic and real world data and shows substantial speedups compared to deterministic HALS.