Sequentially-fit alternating least squares algorithms in nonnegative matrix factorization

Abstract

Nonnegative matrix factorization (NMF) and nonnegative least squares regression (NNLS regression) are widely used in the physical sciences; this thesis explores the often-overlooked origins of NMF in the psychometrics literature. Another method originating in psychometrics is sequentially-fit factor analysis (SEFIT). SEFIT was used to provide faster solutions to NMF, using both alternating least squares (ALS) with zero-substitution of negative values and NNLS. In a simulation using SEFIT for NMF, differences in fit between the ALS-based solution and the NNLS-based solution were minimal; both solutions were substantially faster than standard whole matrix based approaches to NMF.