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 L0​ norm, however its optimization is NP-hard. Mixed norms,
such as L1​/L2​ 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 L1​ norm. However,
present algorithms designed for optimizing the mixed norm L1​/L2​ are slow
and other formulations for sparse NMF have been proposed such as those based on
L1​ and L0​ 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