Nonnegative matrix factorization (NMF), a dimensionality reduction and factoranalysis method, is a special case in which factor matrices have low-ranknonnegative constraints. Considering the stochastic learning in NMF, wespecifically address the multiplicative update (MU) rule, which is the mostpopular, but which has slow convergence property. This present paper introduceson the stochastic MU rule a variance-reduced technique of stochastic gradient.Numerical comparisons suggest that our proposed algorithms robustly outperformstate-of-the-art algorithms across different synthetic and real-world datasets.
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