Block Coordinate Descent for Sparse NMF
Abstract
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 NPhard. 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 realworld datasets that shows our new algorithm performs an order of magnitude faster compared to the current stateoftheart solvers optimizing the mixed norm and is suitable for largescale datasets.
 Publication:

arXiv eprints
 Pub Date:
 January 2013
 arXiv:
 arXiv:1301.3527
 Bibcode:
 2013arXiv1301.3527P
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Numerical Analysis