  Nonnegative matrix factorization (NMF) is a powerful technique for dimension
reduction, extracting latent factors and learning part-based representation.
For large datasets, NMF performance depends on some major issues: fast
algorithms, fully parallel distributed feasibility and limited internal memory.
This research aims to design a fast fully parallel and distributed algorithm
using limited internal memory to reach high NMF performance for large datasets.
In particular, we propose a flexible accelerated algorithm for NMF with all its
$L_1$ $L_2$ regularized variants based on full decomposition, which is a
combination of an anti-lopsided algorithm and a fast block coordinate descent
algorithm. The proposed algorithm takes advantages of both these algorithms to
achieve a linear convergence rate of $\mathcal{O}(1-\frac{1}{||Q||_2})^k$ in
optimizing each factor matrix when fixing the other factor one in the sub-space
of passive variables, where $r$ is the number of latent components; where
$\sqrt{r} \leq ||Q||_2 \leq r$. In addition, the algorithm can exploit the data
sparseness to run on large datasets with limited internal memory of machines.
Furthermore, our experimental results are highly competitive with 7
state-of-the-art methods about three significant aspects of convergence,
optimality and average of the iteration number. Therefore, the proposed
algorithm is superior to fast block coordinate descent methods and accelerated
methods.
