Online Nonnegative Matrix Factorization With Robust Stochastic Approximation


Nonnegative matrix factorization (NMF) has become a common dimension-reduction methodology and has been widely applied to Image Processing and pattern recognition issues. However, typical NMF learning methods require the whole dataset to reside in the memory and so cannot be applied to large-scale or streaming datasets. During this paper, we propose an efficient online RSA-NMF algorithm (OR-NMF) that learns NMF in an incremental fashion and thus solves this downside. In particular, OR-NMF receives one sample or a bit of samples per step and updates the bases via sturdy stochastic approximation. Benefitting from the well chosen learning rate and averaging technique, OR-NMF converges at the speed of $O(1/sqrtk)$ in each update of the bases. Furthermore, we have a tendency to prove that OR-NMF virtually surely converges to a local optimal answer by using the quasi-martingale. By using a buffering strategy, we keep both the time and area complexities of one step of the OR-NMF constant and make OR-NMF suitable for massive-scale or streaming datasets. Preliminary experimental results on real-world datasets show that OR-NMF outperforms the existing online NMF (ONMF) algorithms in terms of potency. Experimental results of face recognition and image annotation on public datasets ensure the effectiveness of OR-NMF compared with the prevailing ONMF algorithms.

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