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Nonnegative matrix factorization (NMF) has become a ubiquitous tool for dataanalysis. An important variant is the sparse NMF problem which arises when weexplicitly require the learnt features to be sparse. A natural measure ofsparsity 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, basedon intuitive attributes that such measures need to satisfy. This is in contrastto computationally cheaper alternatives such as the plain L$_1$ norm. However,present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slowand other formulations for sparse NMF have been proposed such as those based onL$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed normsparsity constraints while not sacrificing computation time. We presentexperimental evidence on real-world datasets that shows our new algorithmperforms an order of magnitude faster compared to the current state-of-the-artsolvers optimizing the mixed norm and is suitable for large-scale datasets.

Block Coordinate Descent for Sparse NMF