  Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data
analysis. An important variant is the sparse NMF problem which arises when we
explicitly require the learnt features to be sparse. A natural measure of
sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms,
such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based
on intuitive attributes that such measures need to satisfy. This is in contrast
to computationally cheaper alternatives such as the plain L$_1$ norm. However,
present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow
and other formulations for sparse NMF have been proposed such as those based on
L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm
sparsity constraints while not sacrificing computation time. We present
experimental evidence on real-world datasets that shows our new algorithm
performs an order of magnitude faster compared to the current state-of-the-art
solvers optimizing the mixed norm and is suitable for large-scale datasets.
