Cancer Class Discovery Using Non-negative Matrix Factorization Based on Alternating Non-negativity-Constrained Least Squares

Many bioinformatics problems deal with chemical concentrations that should be non-negative. Non-negative matrix factorization (NMF) is an approach to take advantage of non-negativity in data. We have recently developed sparse NMF algorithms via alternating nonnegativity-constrained least squares in order to obtain sparser basis vectors or sparser mixing coefficients for each sample, which lead to easier interpretation. However, the additional sparsity constraints are not always required. In this paper, we conduct cancer class discovery using NMF based on alternating non-negativity-constrained least squares (NMF/ANLS) without any additional sparsity constraints after introducing a rigorous convergence criterion for biological data analysis.