Stochastic variance reduced multiplicative update for nonnegative matrix factorization
This work addresses a specific bottleneck in NMF for researchers and practitioners, offering incremental improvements to a popular method.
The paper tackled the slow convergence of the multiplicative update rule in nonnegative matrix factorization by introducing a stochastic variance-reduced technique, resulting in algorithms that robustly outperform state-of-the-art methods on various datasets.
Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which has slow convergence property. This present paper introduces on the stochastic MU rule a variance-reduced technique of stochastic gradient. Numerical comparisons suggest that our proposed algorithms robustly outperform state-of-the-art algorithms across different synthetic and real-world datasets.