Randomized nonnegative matrix factorization - Erichson, N. Benjamin; Mendible, Ariana; Wihlborn, Sophie; Kutz, J. Nathan (Pattern recognition letters, 2018)
•A novel randomized hierarchical alternating least squares algorithm for NMF.•The randomized algorithm scales up to big data.•The algorithm outperforms previous compressed NMF algorithms in speed and accuracy.•Both synthetic and real-world data are used for evaluation.•A Python implementation is provided on GitHub. 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, i.e., the algorithm scales with the target rank of the data rather than the ambient dimension of measurement space. The proposed algorithm is evaluated using synthetic and real world data and shows substantial speedups compared to deterministic HALS.