Versatile sparse matrix factorization: Theory and applications

In the recent years, non-negative matrix factorization and sparse representation models have been successfully applied in high-throughput biological data analysis due to its interpretability and robustness to noise. In this paper, we propose a unified matrix factorization model, coined versatile sparse matrix factorization (VSMF) model, for biological data analysis. We discuss the modelling, optimization, and applications of VSMF. We show that many well-known sparse matrix factorization models are specific cases of our VSMF. Through tuning parameters, sparsity, smoothness, and non-negativity can be easily controlled in VSMF. Our computational experiments for feature extraction, feature selection, and clustering corroborate the advantages of VSMF.