Sequential Sparse NMF

Nonnegative Matrix Factorization (NMF) is a standard tool for data analysis. An important variant is the Sparse NMF problem. A natural measure of sparsity is the L₀ norm, however its optimization is NP-hard. Here, we consider a sparsity measure linear in the ratio of the L₁ and L₂ norms, and propose an efficient algorithm to handle the norm constraints which arise when optimizing this measure. Although algorithms for solving these are available, they are typically inefficient. We present experimental evidence that our new algorithm performs an order of magnitude faster compared to the previous state-of-the-art