Block Coordinate Descent for Sparse NMF

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 La norm, however its optimization is NP-hard. Mixed norms, such as Ll/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 La 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