Open Peer Review. Open Publishing. Open Access. Open Discussion. Open Directory. Open Recommendations. Open API. Open Source.
Block Coordinate Descent for Sparse NMF
Vamsi Potluru, Sergey M. Plis, Jonathan Le Roux, Barak A. Pearlmutter, Vince D. Calhoun, Thomas P. Hayes
Jan 17, 2013 (modified: Jan 17, 2013)ICLR 2013 conference submissionreaders: everyone
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 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.
Enter your feedback below and we'll get back to you as soon as possible.